Quadrant Model of Reality: Quadrant Model of Reality Book 1 Philosophy

CHAPTER XXVI: The Pattern of Four in Philosophy

Philosophy is said to have started with the Greeks. Philosophy means love of knowledge. In Greek philosophy are the pre-Socratics. They are the first square--sensation and perception. They looked at the physical world in an attempt to understand it. Some dealt exclusively with the nature of Being. Many proposed that everything was comprised of one thing, which they called the arche. Others said that everything derives from either air, water, earth, or fire. From these theories arose the four element theory of Aristotle proposing that everything was comprised of these four elements. This fits the quadrant model pattern.

Mathematics is one attempt to look at and understand the physical world. Euclid, a famous Greek mathematician, is called the "Father of Geometry". His book, “The Elements” is one of the most popular books in the world, behind only the Bible. It is the foundation for all geometry and it fits the quadrant model pattern. The book contains the five postulates underlying all geometry. Placing them within the quadrant model pattern reveals the underlying Form of Existence.

*Square one: “A straight line can be drawn from one point to another.” This is directly connected with the next square.

*Square two: “A straight line can be extended continuously.” The first two squares are a duality; they are related to each other in that both are related to lines. The first two squares are not yet solid. The third square is the solid square.

*Square three: “A circle can be created with an equal radius from a center point.” The third square is always the solid square. The first two squares are about lines; the third square is about a circle, which is an enclosed shape, therefore it is the solid square.

*Square four: “All right angles are equal to each other.” What is interesting is that a right angle is the angle found in the four quadrants. The fourth square is related to the divine, and is transcendent. The fourth is always different from the previous three. The fourth is related to the quadrant itself.

*Square five: The fifth square is the parallel postulate. The idea behind this postulate is that if two straight lines are intersected, and the line that intersects them intersects at right angles, then the two lines are parallel and will never meet. The fifth is always questionable. It turns out that the fifth postulate is false. It is good that Euclid never really needs to use this postulate. Again, the fifth is always questionable. The fourth often seems not to belong, but the fifth does not belong at all. Also the fourth points to the fifth. The fourth is about right angles, and the fifth is about parallel lines that are produced when a line intersects them to form right angles.

Euclid’s Postulates

A straight line can be drawn from one point to another	A circle can be created with an equal radius from a center point
A straight line can be extended continuously	All right angles are equal to each other

parallel postulate

For thousands of years it was thought that the fifth postulate was correct. But around the time of Einstein this postulate was questioned. Two people came up with the same conclusion independently. Some question why Euclid made a fifth postulate if he did not really need it. Some have said that Euclid intentionally did this so people would later try to prove it wrong, and in so doing discover new geometries. Others say that Euclid’s fifth postulate is not wrong, but is wrong only if other spatial planes are added. They say on a Euclidean plane the fifth postulate is correct, so it is incorrect to say the fifth postulate is wrong. But the point is the fifth is always questionable. That is the nature of the quadrant model. The fourth is transcendent, and fifth is ultra-transcendent.

Euclid's elements are also founded upon five axioms that fulfill the quadrant model pattern. They are as follows:

*Square one: “Things that are equal to the same thing are equal to one another” (Transitive property of equality).

*Square two: “If equals are added to equals, then the wholes are equal” (Addition property of equality). The first two squares are a duality, and are also conservative. They are about maintaining and building.

*Square three: “If equals are subtracted from equals, then the remainders are equal” (Subtraction property of equality). The third square is about destruction--it is about subtracting.

*Square four: “Things that coincide with one another are equal to one another” (Reflexive Property). The fourth square seems different and seems like nothing is there.

*Square five: “The whole is greater than the part.” The fifth square is always questionable. In fractal mathematics it has been discovered that the whole is not greater than the part; the whole can be in the part. Also in quantum mechanics it has been discovered that particles can decay and create wholes that are greater than the parts. Again the fifth is questionable. But using the five postulates that fit the quadrant model pattern and the five axioms, Euclid derived all of geometry.

Euclid’s axioms

Transitive Property of Equality	Subtraction Property of Equality
Additive Property of Equality	Reflexive Property

The whole is greater than the part

Euclid's book itself fits the quadrant model pattern; it is organized in terms of the quadrant model pattern.

Quadrant 1: The first four books of Euclid's Elements fit the qualities of the first four squares of the quadrant model.

*Square one: Book 1--discusses the five postulates and five axioms.

*Square two: Book 2--talks about geometric algebra and finding the square of a number.

*Square three: Book 3--talks about circles. The third square is when things start getting solid--the first two squares are not solid, but in the third square things are a little more solid. Circles are enclosed.

*Square four: Book 4--incircles and semicircles, along with regular polygons, are described. The figures are flat, more solid and complex. The fourth square is more abstract. Each square builds upon the last.

Quadrant 2: The second four books of Euclid's book fit the qualities of the next four squares of the quadrant model. These squares are:

*Square one: Book 5--discusses proportions and magnitudes. The second quadrant, about relationships, is the cultural quadrant, and deals with relationships. Proportions and magnitudes are about relationships between things. The second quadrant is about relationships.

*Square two: Book 6--applies proportions to geometry. Square 6 is the second square of the second quadrant. The second square is about structure and relationships. Here proportions are discussed, which are about relationships;

proportions are discussed in relationship to geometry, which is about shape and form. The second square is related to form, and its shape and structure.

*Square three: Book 7--deals with elementary number theory. It is more related to doing, but number theory is still about relationships between numbers. The second quadrant deals with relationships.

Square four: Book 8--deals with proportions in number theory and geometric sequences. The second quadrant again is about proportions, which is about relationships. But these proportions are related to number theory, and number theory is more related to doing.

Quadrant 3: Book 9, the third of four books of Euclid's Elements fits the qualities of the next four squares of the quadrant model.

*Square one: Book 9--talks about the infinitude of prime numbers, the sum of a geometric series, and the construction of even perfect numbers. The third quadrant is more wild. The first square of the third quadrant is thinking. Thinking is wild; it is also doing. Now Euclid is performing serious mathematics.

*Square two: Book 10--an attempt to classify irrational magnitudes by using the method of exhaustion. This is the second square of the third quadrant. The tenth square is the emotion square. The third quadrant is wild. The third quadrant is also doing. But we are not yet at the third square of the third quadrant. The third square of the third quadrant must be the most solid, because the third is the most solid and is the most related to doing. The third square of the third quadrant is doing.

*Square three: Book 11--finds the volume of parallelepipeds. Volume is the amount of area within a solid structure. Physical objects occupy space; the nature of the third square is the most solid.

*Square four: Book 12--studies the volume of square one: cones, square two: pyramids, square three: cylinders and square four: spheres. Book 12 is the fourth square of the third quadrant. It is therefore still solid, but it is even more abstract than the third square of the third quadrant, because the fourth square is always more abstract and complex.

Finally Quadrant 4: Book 13- is the first square of the fourth quadrant. Quadrant 4 is the contemplation square. Here Euclid discusses the Platonic solids. Euclid sees these as divine, as did Plato. These are the five platonic solids that fit the quadrant model pattern. The fourth quadrant is divine and transcends the previous three.

Aristotle is known as one of the founders of logic; he invented the logic square. Logic squares fit the form of the quadrant model of reality. In logic squares there are four proposition forms. They are:

*Square one: the A proposition, called the universal affirmative, and goes “Every S is P”. For instance every collie is a dog.

*Square two: The E proposition--called the universal negative. It is translated “No S are P.” For instance, no humans are dogs.

*Square three: The I proposition--called the particular affirmative. It is translated “Some S are P.” For instance, some four legged animals are dogs.

*Square four: O is the particular negative--translated, “Some S are not P.” For instance, some four legged animals are not dogs.

In his Categories, Aristotle identifies ten possible kinds of things that may be the subject or the predicate of a proposition. For Aristotle there are four different ontological dimensions:[citation needed]

according to the various categories or ways of addressing a being as such

according to its truth or falsity (e.g. fake gold, counterfeit money)

whether it exists in and of itself or simply 'comes along' by accident

according to its potency, movement (energy) or finished presence (Metaphysics Book Theta).

The tetralemma is a figure that is prominent in the classical logic of India. It states that with reference to any a logical proposition X, there are four possibilities:

Square 1: X(affirmation)

Square 2: \neg X (negation)

Square 3: X \land \neg X (both) equiv.

Square 4: \neg (X \lor \neg X) (neither)

The tetralemmic model which has been developed in oriental logic stipulates the existence of four lemmas: (a) affirmation (b) negation (c) non-affirmation and non-negation (d) affirmation and negation (49, p. 21)

Here (a) and (b) both belong to formal logic, whereas (c) and (d) are unacceptable to it, although they are acceptable in theoretical physics. "Only an acceptance of the third and fourth lemmas can allow a full representation of the contemporary world problematique in its totality since contemporary world reality is full of cases where a mere affirmation or negation does not make sense.

The semiotic square, derived from Aristotle's logical square of opposition, which I already mentioned in the book, was developed by Algirdas J. Greimas. It is a tool used in structural analysis of the relationships between semiotic signs through the opposition of concepts, such as feminine-masculine or beautiful-ugly, mean-nice and of extending the relevant ontology.

Square 1: The Semiotic Square is formed by an initial binary relationship between two contrary signs. S1 is considered to be the assertion/positive element and S2 is the negation/negative element in the binary pair:

Square 2: The second binary relationship is now created on the ~S axis. ~S1 is considered to be the complex term, and ~S2 is the neutral term. This is where the principle of difference is brought into play: every element in a system is defined by its differences from the other elements.

Square 3: In most modes of interpretation, the S-axis is a hyponym of the ~S-axis. The ~S1 element combines aspects of S1 and S2 and is also contradictory to S1 . The ~S2 element contains aspects of neither S1 nor S2 .

Square 4: Finally, the ~S2 element can be identified. Considered to be "always the most critical position and the one that remains open or empty the longest time, for its identification completes the process and in that sense constitutes the most creative act of the construction."

Kinhide Mushakoji (Scientific revolution and interparadigmatic dialogue, 1978; Global Issues and Interparadigmatic Dialogue, 1988) distinguishes from Eastern traditions four modalities through which the human mind grasps reality:

Affirmation: Leading to affirmative action in the form of support, commitment, initiative, proposition, cooperation, consensus formation, empowering, "opening".

Negation: Leading to negative action in the form of sanction, withdrawal (of support), denial, disassociation, delimitation, criticism, opposition, promotion of dissent, disempowering, "closing".

Affirmation and negation: Leading to ambiguous action, non-violent resistance, "dumb insolence", "giving with one hand and taking with the other", "double dealing", "stick and carrot tactics", the "yes but no" response of the frustrated cross-examinee.

Non-affirmation and Non-negation: Leading to action in the form of indifference, indecision, non-action (in the oriental sense), "neither confirm nor deny", "opening and closing".

The first two correspond to the kataphatic and apophatic modes. It is the sense in which individuals may dance between all four modes -- in response to different circumstances -- that is a challenge to further reflection. Although seemingly abstract, the familiarity of many with all four modes is evident in the challenge of interpersonal relations, especially those associated with the mysteries, dynamics and uncertainties of being in love.

In mathematics, the Fibonacci numbers or Fibonacci sequence are the numbers in the following integer sequence:[1][2]

1,\;1,\;2,\;3,\;5,\;8,\;13,\;21,\;34,\;55,\;89,\;144,\; \ldots\;

or (often, in modern usage):

0,\;1,\;1,\;2,\;3,\;5,\;8,\;13,\;21,\;34,\;55,\;89,\;144,\; \ldots\;

What it involves is the quadrature of of the length of the longest side of each square in a Fibonacci Diagram. The Fibonacci spiral is made by making QUArter circles in each square (the circle of the unit square quadrant)

The fibonnaci diagram is made of squares which arguable look like quadrants.

Aristotle’s proposition forms

A Proposition- Universal Affirmative	I Proposition- Particular Affirmative
E Proposition Universal Negative	O Proposition- Particular negative

Aristotle postulates that there are four logical relationships among the propositions. These fit the quadrant model pattern. They are:

*Square one: Contraries. Universal statements are contraries. Contrary statements cannot both be true at the same time. For instance, it cannot be said that every collie is a dog and no collies are dogs. A contradictory is true when its opposite is false. For instance, if no collies are dogs is false, then collies are dogs must be true.

*Square two: Subcontraries. Particular statements are subcontraries. Subcontraries can both be true, but they cannot both be false. Contraries and subcontraries are a duality. The first two squares are always a duality. For instance it cannot be that “some ghosts are real is false” and “some ghosts are not real is false”. If one is false then the other must be true.

*Square three: Sublanterns--when the universal statement implies the particular statement. For instance, all men have penises is true. This implies that some men have penises.

*Square four: Contradictory. Universal affirmatives and particular negatives are contradictories. For instance, if every A is B, not some A is not B. An example of this is, every dog is an animal. Then it cannot be that some dogs are not animals; these are contradictories. It is interesting that the concept of contradictories has been questioned. The fourth square never seems to belong. Set theory has proposed a phenomena called, empty sets, where it is proposed that contradictories are possible. The fourth never seems to belong. These different propositions are often represented in pictorial forms by venn diagrams. Logic squares are the foundation of logic, and they fit the quadrant model pattern.

Aristotle’s logical relationships among propositions

Contraries	Sublanterns
Subcontraries	Contradictory

There are four primary operations in mathematics. They are: Square one: plus; square two: minus; square three: multiplication; square four: division.

Primary Operations of Mathematics

plus	multiplication
minus	division

At the beginning of every statistics book is described the four levels of measurement. They are

Square 1: Nominal. In nominal measurement numbers merely name something, as opposed to order it. For instance, jersey numbers on a basketball team measure at the nominal level. A person with jersey number 7 is not more than a person with a jersey number 2.

Square 2: Ordinal. In ordinal measurement attributes can be ranked, but the distance between the rankings makes no difference. For instance, one can measure education attainment as 1- high school degree 2- college degree 3- graduate degree. 3 is more than 1 and 2 is more than 3, but there is no reference in the ranking to how much more it is. Ordinal measurements simply measure order.

Square 3: Interval. Interval measurements is when the distance between measurements does have meaning. For instance when measuring temperature, the distance between intervals matters and makes a difference. The distance from 30-60 is the same as the distance from 20-50.

Square 4: Ratio. Ratio variables have a clear definition of 0. Weight and height are ratio variables, because they start with 0 and it is understood what zero is. Temperature is not because 0 is set arbitrarily, and there is negative temperatures.

The Four types of Databases objects are made up of several components which are tables, Forms, Queries, and report.

Behavioural attractors and sustainable development

Some commentaries on chaos theory have focused on its detection of four basic attractors that ensure a degree of order and patterning in 1 to 4 dimensions [more]:

1-dimensional -- point attractor: This could be understood in terms of the manner in which issues emerge for an individual or society and become the focus of 'points' on the agenda of conferences like that on sustainable development. Particular issues either attract or repel but in either respect they engender a form of order, notably within a conference environment where they are a basis for coalition formation, resolution and plan articulation.

2-dimensional -- cycle (or circuit) attractor: This could be understood as the way in which a person or group is successively attracted to one issue and then to another -- being attracted to the next and repelled by the last. The cycle may involve two or more points of attraction (see checklist). For policy-makers the cycle may involve a succession of switches between, for example, 'centralization' and 'decentralization' as panaceas for governance. Traditional farmers may use more complex cycles through crop rotation in order to ensure sustainable yields from their fields. Presumably the many cycles identified above could be understood in terms of a cycle attractor.

3-dimensional -- torus attractor: A torus attractor (like a donut or smoke ring) can be understood as defined by a spiralling cycles on many planes which may, or may not, eventually reconnect after completing one or more revolutions of the torus. Each cyclic revolution there is a movement forward, effectively a spiral movement -- repetition with difference, as in predator-prey relationships. Whilst not recognized as a 'torus', such phenomena may well be recognized in terms of 'spirals' or 'spiralling' (see below). It is possible that the somewhat predictable and repetitive manner in which issues of sustainable development are approached (through a succession of conferences) could be explored in this light.

4-dimensional -- strange attractor: This attractor cannot be described by any 3-dimensional geometric form because of its 4-dimensional nature. It has been recognized as basic to processes of self-organization. It is of no apparent order but the forms it takes have been explored in terms of some widely publicized fractal sets (eg Mandelbrot, Feigenbaum [more]). Elsewhere the question of whether human values can be usefully understood as strange attractors has been explored (Judge, 1993).

The above sequence illustrates the challenge for sustainable development, namely to encompass the transitions:

from a focus on point attractors (the focus of conventional conference agenda items and their conclusions),

through cycle attractors (as noted above and as basic to many responses to sustainble development, if only 'recycling'),

through torus attractors enabling recognition of the subtly repetitive nature of conference series on sustainable development (cf 'those who fail to learn from history are forced to repeat it'),

to strange attractors that are driving the process through the interplay of human values in relation to environment and development, in terms of both their individual and collective implications.

Arnold Keyserling [more] suggests that these may be understood as corresponding to the four Jungian psychological functions: sensing, thinking, feeling and willing (intuition). This correspondence works quite will in the case of sensing the issues and 'points' in relation to sustainable development, and to the intuitive understanding driving efforts to resolve them. It is however more ambiguous in the case of thinking and feeling. On the one hand policy thinking on any issue may oscillate cyclically between two or more approaches to an issue of sustainable development, but this may also reflect the cyclic nature of the waves and tides of public feeling in response to an issue.

Taleb's problem is about epistemic limitations in some parts of the areas covered in decision making. These limitations are twofold: philosophical (mathematical) and empirical (human known epistemic biases). The philosophical problem is about the decrease in knowledge when it comes to rare events as these are not visible in past samples and therefore require a strong a priori, or an extrapolating theory; accordingly predictions of events depend more and more on theories when their probability is small. In the fourth quadrant, knowledge is uncertain and consequences are large, requiring more robustness.

The Map

Now it lets see where the traps are:

First Quadrant: Simple binary decisions, in Mediocristan: Statistics does wonders. These situations are, unfortunately, more common in academia, laboratories, and games than real life—what I call the "ludic fallacy". In other words, these are the situations in casinos, games, dice, and we tend to study them because we are successful in modeling them.

Second Quadrant: Simple decisions, in Extremistan: some well known problem studied in the literature. Except of course that there are not many simple decisions in Extremistan.

Third Quadrant: Complex decisions in Mediocristan: Statistical methods work surprisingly well.

Fourth Quadrant: Complex decisions in Extremistan: Welcome to the Black Swan domain. Here is where your limits are. Do not base your decisions on statistically based claims. Or, alternatively, try to move your exposure type to make it third-quadrant style ("clipping tails").

Taleb's black swan is different from the earlier philosophical versions of the problem, specifically in epistemology, as it concerns a phenomenon with specific empirical and statistical properties which he calls "the fourth quadrant".[9] Taleb's problem is about epistemic limitations in some parts of the areas covered in decision making. These limitations are twofold: philosophical (mathematical) and empirical (human known epistemic biases). The philosophical problem is about the decrease in knowledge when it comes to rare events as these are not visible in past samples and therefore require a strong a priori, or an extrapolating theory; accordingly, predictions of events depend more and more on theories when their probability is small. In the fourth quadrant, knowledge is both uncertain and consequences are large, requiring more robustness.

Before Taleb,[citation needed] those who dealt with the notion of the improbable, such as Hume, Mill, and Popper focused on the problem of induction in logic, specifically, that of drawing general conclusions from specific observations. Taleb's Black Swan Event has a central and unique attribute, high impact. His claim is that almost all consequential events in history come from the unexpected—yet humans later convince themselves that these events are explainable in hindsight (bias).

Why are humans often caught off guard by or slow to recognize the rare and novel, partly because built into the very nature of our experience is the propensity to extend existing knowledge and experience to future events and experiences. To exacerbate this natural propensity much of our cultural education both formal and otherwise is built upon historical knowledge forced on us by others. Of course both the natural physiological propensity and the cultural phenomenon are somewhat a necessary precondition to learning, since complete openness to every event would be inefficient. Bertrand Russell observed, "An open mind is an empty mind." So we cannot be completely open, but we must guard against being completely closed as well. It would be most efficacious if we could find a balance between the known and unknown and the limits of our knowledge and experience. The effect of unexpected events likely is integral to finding this balance. Thus, the rare and unexpected is far more significant to our formation of knowledge than people often imagine.

Taleb argues that the proposition "we know", in many cases, is an illusion, albeit a necessary one; the human mind tends to think it knows, but it does not always have a solid basis for this delusion of "I know". This notion that we do not know is very old, dated at least as far back as Socrates. The Socratic method of questioning and avowal of ignorance is the type of corrective action to the delusion that we know something completely and truly.

Similarly, to those who might argue that the advancement of science has rendered the world well-known, Taleb argues that while science added knowledge, we always run the risk of experiencing the improbable, rare, and novel. We can be shocked by this knowledge and experience or we can be open to it. As with the dictum of Socrates, "the only thing I know is that I do not know", is as true as ever, Taleb concludes. Taleb further expands this idea of finite knowable worlds (e.g., a game) vs. infinite and thus unknowable worlds (our natural world) in what he calls the Ludic fallacy.

The Four Quadrants

The idea of classifying risk by distribution of observations (normal or fat-tailed) and our ability to understand the interconnectedness of the risk (simplicity or complexity) was suggested by Nassim Taleb. The classification concept is excellent, but we feel it has not been well developed. The main take-away is to “stay away from the fourth quadrant” where statistics and models fail. This paper is intended as a guide for assigning risks to quadrants and for risk managing them optimally.

Earlier four-quadrants risk literature classifies risk by significance of impact and likelihood of occurrence. Both metrics are useless since we frequently understand neither in advance.

QUADRANT 1 Predictable Gaussian World (Simplicity and Normal Distribution)

A Gaussian world is safe (no big surprises) and events and observations are normally distributed.

There are two categories of observations in the first quadrant:

1. Binary

a. Outcomes are of the yes/no, black/red, heads/tails variety.

b. In a heads/tails coin toss, a sufficient number of tosses (let’s say 1,000) will lead to a normal distribution – the classic bell-shaped curve.

c. No single outcome can dramatically change the mean.

2. Small Range

a. The distance from the minimum possible reading to the maximum possible reading is small.

b. Measure the height of enough MBA students (let say 1,000) and you will end up with a relatively small range and a normal distribution.

c. No single outcome can dramatically change the mean. Add the tallest MBA student in the world (213cm?) to the 1,000 student average of 178 cm, and the average increases to just 178.03 cm. No drama.

d. While height, weight and commuting time conform to this “no single reading can significantly change the average” concept, the wealth of individuals does not. The average net worth of a Mexican is $13,000. Take 1,000 Mexicans, add the $53 billion net worth Carlos Slim to the group, and the average net worth of the 1,001 sample jumps to $52.96 million. The distribution of wealth of individuals is not normal and therefore this data series does not belong in Q1. (Wealth tends to follow a power distribution).

Payoff

Distribution

Simple (win/lose)

Complex (almost anything)

Normal (Bell Curve)

Coin toss; Height

Fat-Tailed or Indeterminate

Everyone likes a Gaussian world – normally distributed and safe – where predictions without errors are easy. Such perfect environments are every risk manager’s dream.

Risks are binary or cover a small range of possibilities, and are not life-threatening. Only probability is important – not magnitude.

Much scientific and academic research is based on a Gaussian Quadrant 1 environment (Black-Sholes pricing model) due to the high degree of predictability.

Examples of Q1 Risks:

Binary • Roulette: Red/black • Coin toss: Heads/tails • Digital Options: Win/lose • Mortality: Life/death • Elections: Win/lose

Small range • Height or weight of people • Commuting time (subway uncertainty in the absence of terrorist threats) • Length of a movie • Daily temperature range in Singapore • Longevity • Automobile insurance claims

Q1 Checklist:

• One additional extreme reading cannot change the average significantly.

• No leverage exists.

• Out of 1,000 coin tosses, you can be extremely wrong many times (guessing tails or heads come up) and not be devastated.

• The payoff is “Simple” • The distribution is “Normal”

Risk Management Tools:

“At-Risk”-type (VaR) risk management models are perfect for such risks since probabilities derived from historical data work well. There are no “outliers” or surprises.

Or Fire your risk managers if you only play in Quadrant 1; you won’t need them.

QUADRANT 2 Risk Models CAN Work – Simple Payoffs with Fat or Indeterminate Tails

As with Q1, the payoff is simple. The anticipated outcome either happens, or it doesn’t. The difference with Q2 is that we don’t understand the distribution very well – numerous tame observations can be followed by one observation with a dramatic and potentially devastating impact. And we don’t know when that dramatic event will take place.

We don’t usually recognize the presence of a Q2 risk at first glance, though if we think about it for a second, the risk becomes apparent and we can define it. We can easily understand and estimate the possible outcomes of a potential tail event.

We just can’t predict HOW FAT the tail will be nor WHEN it will occur. If “size matters” and “timing is everything”, then we have a problem in Q2. The good news is that Q2 risks are manageable.

To compare Q2 to Q1, let’s look at two fruit trees:

Payoff

Distribution

Simple (win/lose)

Complex (almost anything)

Normal (Bell Curve)

Fat-Tailed or Indeterminate

Coconuts

Apple Tree (Q1)

Coconut Tree (Q2)

Number of fruits that can potentially fall

Several hundred to thousands

Ability to predict when they will fall

High – many per day when ripe

No idea. When you least expect it

Weight of fruit

150 gm

2,000 gm

Height of fruit on tree

25m

Impact if one hits you on the head

Surprise

Concussion or death

Risk management

Wear a hat, but really not necessary

Don’t sit under the coconut tree. Place a strong wire skirt around the tree trunk (high up) to catch falling coconuts

Simple or complex system

Simple – an apple either falls or it doesn’t

Simple – a coconut either falls or it doesn’t

Normal or fat-tailed or indeterminate distribution

Normal – one apple won’t hurt you

Fat–tailed or indeterminate – just one can kill you

Examples of Q2 Risks – an accident waiting to happen

• Coconut uncertainty • Most linear financial products (without leverage) • Wealth destruction from house burning down • Shark attack (discovery channel!) • Falling airplane parts • Tsunami • Nine eleven • Oil spills (BP in April 2010) • Ponzi schemes (Madoff) • Subway uncertainty (for cities where terrorism is a threat)

Risk Management Tools

• Know the risks – define them – raise awareness • Rules-based solutions – plan what to do, if and when • Reduce, cap, mitigate, avoid or

• Insure risks, but make sure the insurer can pay. Also ensure a sovereign government (reflecting social pressure) cannot retroactively uncap your insurance and make your potential liability infinite.

While the payoffs on Q2 are simple (happens/doesn’t happen), risk solutions are most often difficult. If the risk solutions are simple (avoidance – don’t go outside, don’t work in a high rise, don’t swim in the ocean) then there is often a significant opportunity cost.

Risk

Risk Management

Coconut uncertainty

Don’t sit under the tree

Skirts to catch falling coconuts

Linear financial products

Use a stop loss (weak)

Buy a “crash put” (strong)

House burning down

Install sprinkler system Build a moat

Buy fire insurance

Shark attack

Don’t swim in the water

Swim in a fenced/netted area

Falling airplane parts

Don’t go outside

Don’t live under air routes

Tsunami

When the tide goes way out, head for higher ground or stay in the water significantly offshore

Build your house or resort on a cliff.

Nine eleven

Don’t work in high-rises. Don’t teach flying students who don’t want to land.

Equip everyone above the 30th floor with a quick-release parachute.

Oil spills

Engineering building codes

Alternative energy sources

Ponzi schemes

Basic due diligence

If something is “too good to be true”, it probably isn’t true.

Subway uncertainty (where terrorism threat possible)

Don’t take the subway

Increase surveillance

QUADRANT 3 Complexity & Normal Distributions – Think Engineering

Quadrant 3 deals primarily with physical laws where normal distributions exist. The outcome can be predicted with a high degree of certainty. No leverage is involved. The consequences of being wrong are extreme, yet the likelihood of error is small. Errors are most often human, not physical (exceeding O-ring temperature guidelines in the Space Shuttle Challenger, pilots attempting to land in bad weather instead of diverting to a safer airport), so risk management involves hiring smart engineers, rational operators and making systems resilient.

Examples of Q3 Risks

Physics

In Quadrant 3, numerous independent parts work together to form a complex interdependent whole. The independent parts are usually mechanical in nature and conform well to traditional statistical methods.

Biology and Social Systems ARE NOT in Q3

Distributions can stray far from the bell-shaped “normal” where biological or social systems are concerned. The spread of SARS could be limited to Hong Kong one day, and then spread throughout Canada the next day after one infected Hong Kong carrier hopped on a plane to Toronto. The growth of Facebook connections looks much more exponential than normal. When a YouTube video goes “viral” power distributions are at work.

Q3 Auto Example

An automobile is made up of thousands of independent parts (nuts, bolts, hoses, wires) that form many independent systems (electrical, engine, fuel, cooling, drive train, and brakes) that interact to make a complex car. Each of the independent systems has simple statistical properties that can be replicated (mass produced) with tiny margins of error. The result is thousands of complex vehicles where the expected performance can be forecast with precision. The performance distribution is normal, yet the system is complex.

Payoff

Distribution

Simple (win/lose)

Complex (almost anything)

Normal (Bell Curve)

Moon Landing

Fat-Tailed or Indeterminate

Q3 Lunar Exploration Example

The first human landing on the moon – clearly a complex undertaking – involved the interaction of gravity, orbits, earth spin, pressure, oxygen, electrical, mechanical, propulsion engineering and numerous other parts and systems. Computing power was laughable by today’s standards. Yet the landing was precise and without incident. The lunar landing was a truly complex task where the expected result fell within a very small range of possibilities.

Risk Management Tools - Resilience and the Many R’s

The complex risks of Q3 can only be managed by introducing sufficient redundancy and fail- safe mechanisms.

The role of resilience in integrated risk management has gained much traction in recent years. As Walter Ammann noted in his presentation to the 2009 Global Risk Forum in Davos:

• “Resilient systems reduce the probability of failure, the consequences of failure and the time needed for recovery.

• Resilience reflects a concern for improving the capacity of physical and human systems to respond to and recover from extreme events.

• Resilience is both inherent strength and the ability to be flexible and adaptive after environmental shocks and disruptive events.”

The building blocks of a resilient system, referred to in various research papers as the 3, 4 or 5R’s, are;

• Redundancy • Reliability • Robustness • Resourcefulness • Rapid response • Regulation

Questions We Need to Ask:

Why are Quadrant 3 tails thin? Is it because we are truly playing in the land of normal distributions, or is there simply insufficient historical data or laboratory research to form a statistically significant distribution? Many distributions appear normal until the fat tail hits.

Are Q3 risks so safe that sound models, rational operators and resilient systems are sufficient to remove the risk of extreme events, or do we suffer from the illusion of control?

QUADRANT 4 Risk Models Don’t Apply – Complex Systems &Fat or Indeterminate Tails

• Q4 extreme risk events are infrequent, yet their impact is massive (same characteristics as our Q2 coconut). In fact, their infrequency often lulls us into a false sense of security and overconfidence in our ability to avoid catastrophe.

• The complexities and interconnectedness in Q4 are enormous, yet risks are often invisible or ignored.

• Leverage – often excessive – is usually present in Q4.

• Our ability to forecast the timing and magnitude of Q4 risk events is poor – approaching the impossible. The world is just too complex and too interconnected to figure out how a Q4 risk will materialize. So we mistakenly try to forecast harder, with more inputs and better models.

• Risk models don’t work in Q4.

• Since risk models don’t work, the modellers try to tweak and calibrate models to make them work better. (We have a tendency to make small incremental changes – iterations – in our attempt to find solutions instead of completely discarding bad models and starting afresh with a clean slate).

• Modellers try to modify and adapt risk measures that work in Q1 (VaR) to account for leverage, unpredictability and fat tails (expected loss), but they just introduce the illusion of control. We think we can model and risk manage fat-tailed Q4 risks, but we can’t.

• Nassim Taleb refers to Q4 as “Extremistan”.

• The social impact of a Q4 fat-tail event is enormous (people lose jobs, houses, retirement funds, have heart attacks, get arrested and spend time in jail, governments fail, new laws and regulations are introduced).

Examples of Q4 Risks

• Lehman – leveraged and interconnected financial system risks leading to a systemic meltdown. Few people knew that Lehman was a counterparty to so many trades. Without

Payoff

Distribution

Simple (win/lose)

Complex (almost anything)

Normal (Bell Curve)

Fat-Tailed or Indeterminate

Leveraged Finance

government action (printing money) almost all banks and investment dealers in the US (and many in parts of Europe) would probably have gone bankrupt and anarchy would have prevailed. A clear Q4 risk.

• AIG – agreed to insure credit risks that exceeded their capital by more than 10 times. The risk was simple (a debtor either defaults or it doesn’t), yet the conditions leading to defaults were unpredictable. Complexity and leverage – definitely Q4.

• Bubonic plague, SARS – any virus spread by air or contact. Fast, modern transportation allows viruses to spread more rapidly than ever before. Traditional statistics of mean and standard deviation cannot help us when the spread of viruses reaches the logarithmic or power distribution phase. Vaccines or isolation help where models fail.

• Economic systems are Q4 phenomena.

• Leveraged financial products. If you bought a Greek government bond at par with 10 time’s leverage, and the bond’s price drops (yields rise) by 10% within one month, your investment has gone to zero.

• Short gamma (short, short-dated options). • Complex or “structured financial products”. Even the issuers often fail to understand the

complexities of their products.

• Lloyds of London names. High net worth individuals wrote insurance policies for centuries and generated a substantial and steady income. When the US courts ruled in favour of asbestos-related injuries, which Lloyds names had insured in what are now regarded as badly-worded policies, names were “called” and many went bankrupt. A better-worded contract that capped claims would have placed Lloyds’ names in Q2.

• The internet – not all Q4 risks are bad. Many of the most influential inventions and innovations are Q4 surprises. Complex, interconnected systems, significant leverage and major impact. (think: the hand phone, fax machine, computer)

Risk Management Tools – Are There Solutions to Q4 Risks?

It is important to accept the fact that we cannot manage or model the risks in Q4. We must get out of Q4!

• Reduce the impact of relationships and complexities we do not understand. • Chop the tails:

− − −

Limit the downside contractually Buy “crash puts” Change the risk profile to that of Q2 or Q3.

• Many banks, hedge funds, businesses and individuals have gone to zero (or less) due to a misguided belief in their ability to model Q4 risks.

• Do NOT rely on statistics or models.

• Employ the resilience guidelines discussed in Q3 – build in redundancies. (humans have two kidneys but only need one), make your business robust (some parts of the business do well in an economic downturn), become resourceful and act quickly.

• Reduce leverage. A Simple Q4 Housing Scenario Identical houses are offered for sale in the same neighbourhood for $1 million each.

Conservative Joe from Q2 has been saving all his life and pays cash for his $1million house. He has bad memories of the 1993 Toronto real estate market when prices collapsed by 60%. Joe buys his house with 100% equity.

Aggressive Fabio from Q4 has no cash, applies for and receives a $1million mortgage from the local bank. Fabio has just finished reading a best-selling book on “How to Profit from the Coming Real Estate Boom with No Money Down”. This is a small town, and the bank has 10 depositors who have each placed their $100k retirement savings on deposit. Deposit insurance has not been invented. Fabio buys his house with 100% debt.

Housing prices collapse by 60%.

Q2 Joe is not happy, but his life doesn’t change. He still lives in his house. No drama.

The bank repossesses Q4 Fabio's house, and tries to sell it at auction in a falling market. The 10 bank depositors get wind of this, all try to withdraw their cash simultaneously and create a run on the bank. The bank has insufficient cash and declares bankruptcy. The depositors lose 60% of their retirement savings and will have to work longer, retire later and live in a depressing trailer park. Fabio buys a nice house for $300k at a forced auction.

Who wins and who loses in Q4?

The depositors thought they were being conservative by placing their money with a bank, but they took on leveraged and interconnected complex risk that was difficult to map. They had limited upside potential (the interest paid on their deposits), while their downside was the loss of all their savings. (If deposit insurance had been invented, the taxpayers would have borne the loss instead of depositors).

Fabio thought he was being aggressive, but he really just purchased a free call option on a house with tremendous appreciation potential. He had positive asymmetric risk – no downside and unlimited upside.

Over the course of history, many of the largest personal fortunes have been made by leveraged long real estate portfolios. And many of the most spectacular bank failures have been a result of mortgage lending. Both play in Q4.

Summary

A risk is either simple – a coconut falls and hits you on the head, or it doesn’t – or complex – AIG insures a credit risk, and then another, and then hundreds of billions more, which all go bad and destroy all US investment banks within a week and compel the government to spend trillions of taxpayers’ money that they don’t have, which threatens social systems, which gives people heart attacks, which starts congressional hearings, which destroys careers, which lands people in jail – well, we assume you get the picture.

And a risk is ether normally distributed – casinos rely on this Gaussian world – or fat-tailed where a small Mediterranean country with clear waters, sunny skies, sandy beaches, a long history, delicious olive oil, marginal wine and an excessive sovereign debt can potentially destroy the official currency of 16 nations

Astrology has used the concept of classical elements from antiquity up until the present. In Western astrology and Indian astrology four elements are used, namely Fire, Earth, Air and Water.

Four Classical Elements; this classic diagram has two squares on top of each other, with the corners of one being the classical elements, and the corners of the other being the properties

In Western tropical astrology, there are always 12 astrological signs; thus, each of the four elements is associated with 3 signs of the Zodiac which are always located exactly 120 degrees away from each other along the ecliptic and said to be in trine with one another. Most modern astrologers use the four classical elements extensively, (also known as triplicities) and indeed it is still viewed as a critical part of interpreting the astrological chart.

Beginning with the first sign Aries which is a Fire sign, the next in line Taurus is Earth, then to Gemini which is Air, and finally to Cancer which is Water. This cycle continues on twice more and ends with the twelfth and final astrological sign, Pisces. The elemental rulerships for the twelve astrological signs of the zodiac (according to Marcus Manilius) are summarised as follows:

Fire — 1 - Aries; 5 - Leo; 9 - Sagittarius - hot, dry, ardent

Earth — 2 - Taurus; 6 - Virgo; 10 - Capricorn - heavy, cold, dry

Air — 3 - Gemini; 7 - Libra; 11 - Aquarius - light, hot, wet

Water — 4 - Cancer; 8 - Scorpio; 12 - Pisces - wet, soft, cold

Elements in classical astrology[edit]

Triplicity rulerships[edit]

In traditional astrology, each triplicity has several planetary rulers, which change with conditions of sect – that is, whether the chart is a day chart or a night chart. Triplicity rulerships are an important essential dignity – one of the several factors used by traditional astrologers to weigh the strength, effectiveness and integrity of each planet in a chart.

Triplicity rulerships (using the "Dorothean system") are as follows:[1]

Triplicity Rulerships

Triplicity Day Ruler Night Ruler Participating Ruler

Fire (Aries, Leo, Sagittarius) Sun Jupiter Saturn

Earth (Taurus, Virgo, Capricorn) Venus Moon Mars

Air (Gemini, Libra, Aquarius) Saturn Mercury Jupiter

Water (Cancer, Scorpio, Pisces) Venus Mars Moon

"Participating" rulers were not used by Ptolemy, as well as some subsequent astrologers in later traditions who followed his approach.

Triplicities by season[edit]

In ancient astrology, triplicities were more of a seasonal nature, so a season was given the qualities of an element, which means the signs associated with that season would be allocated to that element. The seasonal elements of ancient astrology are as follows:

Spring (wet becoming hot) - Air - Aries, Taurus, Gemini

Summer (hot becoming dry) - Fire - Cancer, Leo, Virgo

Autumn (dry becoming cold) - Earth - Libra, Scorpio, Sagittarius

Winter (cold becoming wet) - Water - Capricorn, Aquarius, Pisces

Using the seasonal qualities accounts for the differences in expression between signs of the same element. All the fire signs are by their nature hot and dry. However, the addition of the elemental qualities of the seasons results in differences between the fire signs. Leo being the midsummer sign gets a double dose of hot and dry and is the pure fire sign, but Aries being a Spring sign is wetter (hot & dry, hot & wet), and Sagittarius being an Autumnal sign is colder (hot & dry, cold & dry).

In the Southern Hemisphere the seasonal cycle is reversed.[2]

This yields secondary and tertiary elements for each sign.

Sign Element Qualities Season: North Season: South

Aries Fire Hot & Dry Hot & Wet (Spring/Air) Cold & Dry (Autumn/Earth)

Taurus Earth Cold & Dry Hot & Wet (Spring/Air) Cold & Dry (Autumn/Earth)

Gemini Air Hot & Wet Hot & Wet (Spring/Air) Cold & Dry (Autumn/Earth)

Cancer Water Cold & Wet Hot & Dry (Summer/Fire) Cold & Wet (Winter/Water)

Leo Fire Hot & Dry Hot & Dry (Summer/Fire) Cold & Wet (Winter/Water)

Virgo Earth Cold & Dry Hot & Dry (Summer/Fire) Cold & Wet (Winter/Water)

Libra Air Hot & Wet Cold & Dry (Autumn/Earth) Hot & Wet (Spring/Air)

Scorpio Water Cold & Wet Cold & Dry (Autumn/Earth) Hot & Wet (Spring/Air)

Sagittarius Fire Hot & Dry Cold & Dry (Autumn/Earth) Hot & Wet (Spring/Air)

Capricorn Earth Cold & Dry Cold & Wet (Winter/Water) Hot & Dry (Summer/Fire)

Aquarius Air Hot & Wet Cold & Wet (Winter/Water) Hot & Dry (Summer/Fire)

Pisces Water Cold & Wet Cold & Wet (Winter/Water) Hot & Dry (Summer/Fire)

These associations are not given any great importance in modern astrology, although they are prominent in modern Western neopaganism, druidism and wicca

In the hills of Moray Peru, there are a series of 4 holes comprised of concentric terraced rings, built into the natural landscape of the terrain…so it appears. The experts are not sure what this site was used for. Speculation is that is served as a laboratory for the Inca botanists.

Some argue that you can see the fibbonaci spiral in the shape of the four holes of Moray

In Astrology, the Royal Stars of Persia were regarded as the guardians of the sky in approximately 3000 BCE during the time of the Ancient Persians in the area of modern day Iran.[1] The Persians believed that the sky was divided into four districts with each district being guarded by one of the four Royal Stars.[2] The stars were believed to hold both good and evil power and the Persians looked upon them for guidance in scientific calculations of the sky, such as the calendar and lunar/solar cycles, and for predictions about the future.

Although there is mention of the Royal Stars influencing the Ancient Egyptians in roughly 5,000 BCE, they were noted when the Ancient Persian Prophet Zarathustra, also known as Zoroaster in Greek, mentioned them in the Bundahishn, the collection of Zoroastrian Cosmogony and Cosmology, in approximately 1,500 BCE.[3] Zoroastrianism was a religion formed by Zarathustra, based upon the God Ahura Mazda and was native to Persia.

The four stars with their modern and ancient Persian names were:

Aldebaran (Tascheter) - vernal equinox (Watcher of the East)

Regulus (Venant) - summer solstice (Watcher of the South)

Antares (Satevis) - autumnal equinox (Watcher of the West)

Fomalhaut (Haftorang/Hastorang) - winter solstice (Watcher of the North)

The four dominant stars have an apparent magnitude of 1.5 or less.[4] The reason why they are called "Royal" is that they appear to stand aside from the other stars in the sky. The four stars, Aldebaran, Regulus, Antares, Fomalhaut, are the brightest stars in their constellations, as well as being part of the twenty five brightest stars in the sky, and were considered the four guardians of the heavens.[3] They marked the seasonal changes of the year and marked the equinoxes and solstices. Aldebaran watched the Eastern sky and was the dominant star in the Taurus constellation, Regulus watched the North and was the dominant star in the Leo constellation, Antares watched the West and was the alpha star in Scorpio, and Fomalhaut watched the Southern sky and was the brightest star in Piscis Austrinus (sharing the same longitude with the star Sadalmelik which is the predominant star in Aquarius). Aldebaran marked the vernal equinox and Antares marked the autumnal equinox, while Regulus marked the Summer Solstice and Fomalhaut the Winter Solstice. While watching the sky, the dominant star would appear in its season, each having a time of the year when most noticeable. Regulus was seen as the main star because it was in the constellation of Leo, giving it the power of the lion, signifying the strength of kings with large implications.[5]

The constellations of the Royal Stars were said to be fixed because their positions were close to the four fixed points of the sun's path.[5] The sun was then surrounded by four bright stars at the beginning of every season.[6] From this observation individuals began to denote them the Royal Stars.[6]

By 700 BCE the Nineveh and Assyrians had essentially mapped the ecliptic cycle because of the four stars and were in result able to map the constellations, distinguishing them from the planets and the fixed stars.[5] From this, in 747 BCE the Babylonian King Nabu-nasir adopted a calendar derived from information based on the four stars, one following an eight-year cycle and one a nineteen-year cycle (later adopting the nineteen-year calendar as standard).[7]

The Royal Stars were used primarily for navigation.They were also believed to govern events in the world. Major disasters, breakthroughs, and historical phenomenons were seen as caused by the stars and their alignment in the sky during the time in which the event occurred.[5] When the stars were aligned accordingly, favourable conditions followed, and when they were negatively aligned, disaster was predicted. Because Regulus was the most influential of the Royal Stars, events that took place while Regulus was in dominance were amplified and grave, foreshadowing destruction.

Regulus is known as the Ruler or the Lawgiver. In the dictionary, regulate means "to make regular; put in good order; adjust by rule. As the brightest star in the constellation of Leo, Regulus has been almost universally associated in ancient cultures with the concept of royalty and kingly power - the name Regulus comes from the Latin rex meaning king.

The star was known in the older cultures of the Akkadians, Hindus, Arabians, Babylonians, Persians, Greeks and Romans as the King of the Heavens or the Heart of the Lion. Regulus is one of the four royal stars of the heavens, the other three being Aldebaran in the constellation of Taurus - the Eastern Royal Star, Antares in the constellation of Scorpio - the Western Royal Star, Fomalhaut, in the constellation of Pisces – the Southern Royal Star and Regulus, in the constellation of Leo - the northern Royal Star.

These four royal stars are considered to be sentinels watching over other stars and form a fixed cross configuration in the heavens, to which a hidden has been attributed.

Characteristics of the One who was crucified on a fixed cross

This is outstandingly the Cross of the Soul. The person who is upon the Fixed Cross is becoming increasingly aware of its direction and influences, and does not respond as blindly as others who have not yet mounted this Cross. One does not mount this Cross of Right Direction until they have attained some measure of soul contact and have had some touch of illumination and of spiritual intuition—no matter how fleeting that touch may have been.

It is the Cross of "fixed vision and of that immovable intent which draws one from points of light to blazing solar radiance." The person upon the Fixed Cross says, “I am the soul and here I stand. Naught shall remove my feet from off the narrow place whereon I stand. I face the light. I am the Light and in that light shall I see Light.

It is the Cross whose four energies blend with and transmit the energies of the solar system itself. This it can do because the person upon the Fixed Cross is becoming increasingly conscious of issues which are larger than their own self, more engrossing than their previous interests, and those which concern humanity in its relation to solar forces and not just planetary forces. One is becoming sensitive to the larger whole. The energies of this Cross continue to evoke response until the time of the third initiation, the Tranfiguration.

It is called the Fixed Cross because one is stretched upon it by the directed choice and immovable intent of one's Soul. From that decision there is no turning back. [1]

Regulus lies at the base of the sickle of Leo, resembling a reversed question mark (esoterically, a sickle is used to cut out or cut down that which hinders the application of spiritual law and so hinders the flowering forth of the Soul). To modern sky watchers this sickle outlines the majestic head and mane of the great westward-facing lion, crouched in the regal pose of the king of the forest.

Regulus is only half a degree from the ecliptic and it happens that either the moon or one of the other bright planets pass close to Regulus, infrequently occulting it. Regulus lies in the heart of the Lion, which in esoteric language refers to the heart or the Christ consciousness, which is the Soul and therefore synonymous with love.

Prophecy from the Ageless Wisdom teachings: A certain relationship or configuration of stars ~ of which one is the star Regulus, in Leo ~ will bring about a situation where the reorientation of the attitude of the legal profession will take place; its functions and duties will be centralized for the purpose of world usefulness, and in this process legislation for children will assume great importance and be the motivating power.

16 is the squares of the quadrant model

Geomancy (Greek: γεωμαντεία, "earth divination") is a method of divination that interprets markings on the ground or the patterns formed by tossed handfuls of soil, rocks, or sand. The most prevalent form of divinatory geomancy involves interpreting a series of 16 figures formed by a randomized process that involves recursion followed by analyzing them, often augmented with astrological interpretations.

Geomancy requires the geomancer to create sixteen lines of points or marks without counting, creating sixteen random numbers. Without taking note of the number of points made, the geomancer provides the seemingly random mechanism needed for most forms of divination. Once the lines are produced, the geomancer marks off the points two by two until either one or two points remain in the line; mathematically, this is the same as producing two dots if the number is even or one dot if the number is odd. Taking these leftover points in groups of four, they form the first four geomantic figures and form the basis for the generation of the remaining figures. Once this is done, the "inspired"[6] portion of the geomantic reading is done; what remains is algorithmic calculation.

Traditionally, geomancy requires a surface of sand and the hands or a stick, but can be done equally well with a wax tablet and stylus or a pen and paper; ritualized objects may or may not be desired for use in divination. Often, when drawing marks or figures, geomancers will proceed from right to left as a tradition from geomancy's Arabic origins, although this is by no means mandatory. Modern methods of geomancy include, in addition to the traditional ways, computerized random number generators or thrown objects; other methods including counting the eyes on potatoes.[7] Some practitioners use specialized cards, with each card representing a single geomantic figure; in this case, only four cards are drawn after shuffling. Specialized machines have also been used to generate full geomantic charts.

The figures are entered into a specialized table, known as the shield chart, which illustrates the recursive processes reminiscent of the Cantor set[3] that form the figures. The first four figures are called the matres, or Mothers, and form the basis for the rest of the figures in the chart; they occupy the first four houses in the upper right-hand corner such that the first Mother is to the far right, the second Mother is to her left, and so on (continuing the right-to-left tradition). The next four figures, the filiae, or Daughters, are formed by rearranging the lines used in the Mothers: the first Daughter is formed by taking the first line from the first, second, third, and fourth Mothers in order and rearranging them to be the first Daughter's first, second, third, and fourth lines, respectively. The process is done similarly for the second Daughter using the second line from the Mothers, and so on. The Daughters are placed in the next four houses in order on the same row as the Mothers.

After the eight matres and filiae are formed, the four nepotes (or Nieces) are formed by adding those pairs of figures that rest above the houses of the respective Niece. Therefore, the first and second Mothers add to form the first Niece, the third and fourth Mothers add to form the second Niece, and so on. Here, addition involves summing the points in the respective lines of the parents: if the sum is an even number, then the resulting figure's line will have two points, and if the sum is odd then the line will have one point. Conceptually, this is the same procedure in mathematical logic as the exclusive or, where a line with two points is used instead of "false" and a line with one point instead of "true".[9]

From the four nepotes, the two testes (or Witnesses) are formed in the same manner as the nepotes: the first and second Nieces form the Right Witness, and the third and fourth Nieces form the Left Witness. From the Witnesses, using the same addition process, the iudex, or Judge, is formed. A sixteenth figure, the Reconciler or superiudex, is also generated by adding the Judge and the First Mother, although this has become seen as extraneous and a "backup figure" in recent times.

One division of the shield chart for interpretation involves triplets of the figures called triplicities.[10] Each triplicity contains two of the Mothers or two of the Daughters and the Niece that results from them. They can be interpreted in a manner similar to the Witnesses and Judge, in that the right parent represents the past, the child the present, and the left parent the future; another way to interpret such a triplet views the right parent as the querent's side, allies, resources, and opinions, the left parent as the quesited's side, and the child as the interaction of the two sides.

Triplicity Figures Involved Interpretation

First Triplicity First Mother, Second Mother, First Niece The querent's health, disposition, outlooks, and habits. Current trends in the querent's life.

Second Triplicity Third Mother, Fourth Mother, Second Niece The influences in the querent's life at the time of the reading. Factors that shape the querent's life and the situation surrounding the query.

Third Triplicity First Daughter, Second Daughter, Third Niece The places most frequented by the querent, including the home and the workplace. People and objects found at those places. Family, partners, and housemates of the querent.

Fourth Triplicity Third Daughter, Fourth Daughter, Fourth Niece Friends, associates, coworkers, colleagues of the querent, as well as people in authority over the querent. Situations and factors caused by external sources.

The four binary elements of each figure allow for 16 different combinations, each called a tableau. As each chart is generated from the four Mothers, there are a total number of 164, or 65,536, possible charts. Due to the mathematics of the chart, only figures that have an even number of points total can become Judges;[9] each of the eight Judges then has 8,192 charts associated with it. Traditional practitioners of geomancy use this knowledge as a type of parity check on the chart to ensure that no mistakes have been made while computing the figures.

In each chart, if all sixteen figures are observed (the four Mothers, the four Daughters, the four Nieces, the Witnesses, Judge, and Reconciler), at least two of the figures must be the same. However, as the Reconciler is usually termed an optional figure, 16 combinations of Mother figures can yield a chart where the Mothers, Daughters, Nieces, Witnesses, and Judge are all unique. Notably, Populus cannot appear in these charts, since mathematically it either requires two figures to be the same in order to be formed, or produces a duplicate figure when added to another figure. In such charts, the Judge will always be one of Conjunctio, Amissio, Carcer, or Acquisitio. The sixteen combinations of Mothers, in order from the First to the Fourth Mother, are

Puer, Caput Draconis, Tristitia, Albus

Conjunctio, Puella, Fortuna Major, Tristitia

Puella, Puer, Tristitia, Albus

Puella, Cauda Draconis, Tristitia, Albus

Rubeus, Laetitia, Puella, Puer

Rubeus, Laetitia, Cauda Draconis, Puella

Rubeus, Laetitia, Cauda Draconis, Caput Draconis

Rubeus, Laetitia, Caput Draconis, Puer

Acquisitio, Puella, Albus, Fortuna Major

Laetitia, Fortuna Minor, Puer, Conjunctio

Laetitia, Fortuna Minor, Acquisitio, Cauda Draconis

Cauda Draconis, Caput Draconis, Tristitia, Albus

Caput Draconis, Amissio, Fortuna Major, Tristitia

Caput Draconis, Carcer, Albus, Fortuna Major

Fortuna Minor, Rubeus, Puer, Amissio

Fortuna Minor, Rubeus, Carcer, Cauda Draconis

The Arabic tradition consists of sketching sixteen random lines of dots in sand. This same process survived virtually unchanged through its introduction to Europe in the medieval era, and survives to this day in various Arabic countries. Sikidy and other forms of African divination also follow techniques that have remained virtually unchanged.

In Africa one traditional form of geomancy consists of throwing handfuls of dirt in the air and observing how the dirt falls. It can also involve a mouse as the agent of the earth spirit. Ifá (which also had 16 figures), one of the oldest forms of geomancy, originated in West Africa, and uses the same sixteen geomantic figures as in Arabic and Western geomancy with different meanings and names; the process is shortened to using only two figures. In China, the diviner may enter a trance and make markings on the ground that are interpreted by an associate (often a young or illiterate boy). Similar forms of geomancy include scrying involving the patterns seen in rocks or soil.

The eight trigrams used in I Ching.

The Chinese divination practice of the I Ching has several striking similarities to geomancy. It includes a series of binary trigrams (as opposed to tetragrams used in geomancy) that are generated at random, the resulting figures of which are taken in combination. However, the figures are not added or reorganized as in geomancy, but are instead taken to form a single hexagram. While there are 23, or eight, trigrams, there are 26, or 64, hexagrams. This yields a smaller set of resulting charts than geomancy.

16 is the squares of the quadrant model

The 16 geomantic figures are the primary symbols used in divinatory geomancy. Each geomantic figure represents a certain state of the world or the mind, and can be interpreted in various ways based upon the query put forth and the method used to generate the figures. When geomancy was introduced to Europe in the Middle Ages, the figures acquired astrological meanings and new forms of interpretation. The figures bear superficial resemblance to the ba gua, the eight trigrams used in the I Ching, a Chinese classic text.

Each of the figures is composed of four lines, each line containing either one or two points. Each line represents one of the four classical elements: from top to bottom, the lines represent fire, air, water, and earth. When a line has a single point, the element is said to be active; otherwise, with two points, the element is passive. Because there are four lines, and since each line can be either active or passive, there are 24, or 16, different figures. The different combinations of elements yields different representations or manifestations of the figure's energy.

Each figure can be said to have a ruling element, whereby that element's energy and manifestations correlates most closely to the figure itself. With the exception of Populus, the ruling element for each figure is always represented as active (a single point in the corresponding line). For figures with only one active element, that element by default is its ruling element; other combinations of active and passive elements require more introspection to assign rulerships. Populus, consisting of all passive lines, is ruled by Water by its nature of being entirely passive and taking on the reflective qualities of water whenever an outside force acts upon it.

Ruling Element Figures Ruled

Fire Laetitia, Cauda Draconis, Fortuna Minor, Amissio

Air Puer, Rubeus, Acquisitio, Conjunctio

Water Populus, Via, Albus, Puella

Earth Fortuna Major, Tristitia, Caput Draconis, Carcer

While the elements just described are from the geomantic tradition, another set of elemental assignments are used based on the figures' astrological connections. These elements are assigned based on the zodiac sign of a given figure. The geomantic element is said to reflect the nature of a figure when viewed alone; the astrological element reflects its nature when acting with other figures.

Ruling Element Figures Ruled

Fire Puer, Fortuna Major, Fortuna Minor, Acquisitio, Cauda Draconis

Air Albus, Puella, Tristitia

Water Populus, Via, Rubeus, Laetitia

Earth Amissio, Conjunctio, Caput Draconis, Carcer

Another classification of the geomantic figures involves their quality, which is either stable or mobile. The quality of a figure represents its duration of effect or motion, such that a figure with a stable quality will represent a long-term situation or that a certain object remains where it was left, while a mobile figure represents a transient effect upon the real world. In simple "yes or no" style divinations, stable figures indicate a positive answer, while mobile figures indicate a negative one.

Quality Figures

Stable Acquisitio, Albus, Puella, Populus, Tristitia, Caput Draconis, Carcer, Fortuna Major

Mobile Laetitia, Cauda Draconis, Amissio, Fortuna Minor, Rubeus, Puer, Conjunctio, Via

Originally, the quality was shown in terms of entering or exiting figures, where, from the viewer's point of view, the figure would be pointing towards (downward) or away from (upward) the viewer. Entering figures have the stable quality, while the exiting figures have the mobile quality; when an entering figure is rotated upside-down, it becomes an exiting figure, and vice versa. However, based on this classification, the four figures that point in both directions regardless of rotation have the quality of both entering and exiting, and must be evaluated in terms of its neighbors or generating figures.

Direction Figures

Entering Acquisitio, Albus, Puella, Tristitia, Caput Draconis, Fortuna Major

Exiting Laetitia, Cauda Draconis, Amissio, Fortuna Minor, Rubeus, Puer

Both Populus, Via, Carcer, Conjunctio

In the generation of the geomantic charts, the primary answer is given by the figure called the Judge. Based upon the mathematics involved in generating the charts, the Judge figure must always have an even number of points. For this reason, all the figures that can appear as Judges (i.e. have an even number of points) are also termed impartial figures; they represent objective states of the world observable equally by any party. The ones with odd numbers of points are termed partial or personal due to their subjective and emotional nature.

Type Figures

Impartial Populus, Via, Carcer, Conjunctio, Amissio, Acquisitio, Fortuna Major, Fortuna Minor

Partial Laetitia, Tristitia, Rubeus, Albus, Cauda Draconis, Caput Draconis, Puella, Puer

In the Middle Ages, when geomancy was introduced to Europe where astrology was the foremost occult science, the geomantic figures obtained astrological correspondences to the Zodiac and to the planets. Based on their zodiacal correspondences, astrologers assigned new elemental rulerships (henceforth known as outer elemental rulers, whereas the previous elemental assignments will be known as inner elemental rulers) based on the element of their zodiacal ruler. The exceptions to the planetary rulerships were the figures Cauda Draconis and Caput Draconis, which were assigned to the northern and southern lunar nodes instead.

Planet Diurnal figure Nocturnal figure

Sun Fortuna Major Fortuna Minor

Moon Populus Via

Mercury Albus Conjunctio

Venus Puella Amissio

Mars Puer Rubeus

Jupiter Acquisitio Laetitia

Saturn Tristitia Carcer

Lunar nodes Caput Draconis Cauda Draconis

Traditionally, the energies and manifestations of the planets were different based on their declination or motion; for the planets Mercury, Venus, Mars, Jupiter, and Saturn, the diurnal energy represents the planet in direct motion, while the nocturnal energy refers to the retrograde motion of the planets. For the Moon, this was illustrated by the waxing or waning periods of the Moon, respectively; the Sun's figures were based on the Sun during the day (or northern declination) or during the night (southern declination). The zodiacal rulerships followed from the diurnal or nocturnal planetary rulership: nocturnal figures are assigned earth and water signs, while diurnal figures are assigned fire and air signs. The North Node is assigned, by Gerard of Cremona, to Sagittarius and the South Node to Virgo (for the sake of finding the ascendant in astrological traditions of geomancy). Once the zodiacal rulerships were agreed upon, all the following correspondences followed upon the geomantic figures, including what part of the body they each ruled over, different countries, planetary hours, body and character types, and so on.

The geomantic figures[edit]

Via[edit]

Geomantic via.svg

Latin for "the Way". The figure resembles a road or path. It is considered bad of most things, but good with concerns of roads, travels, or journeys. Astrologically it is associated with Cancer and the waning Moon, and both its inner and outer elements are water. All the elements in Via are active, and as such the figure indicates change more than any other figure. Regarding the outcome of the situation being divined, it is neutral, unless change by itself infers a positive or negative result. This figure inverts any figure when added, giving it another meaning of change. Its planetary ruler is Chashmodai, its Intelligence is the Intelligence of Intelligences Malkah beTarshishim ve-ad Ruachoth Shechalim, and its Spirit is the Spirit of Spirits is Shad Barshemoth ha-Shartathan. It is associated with the deities Diana and Mercurius, and the angels Gabriel and Muriel. It is associated with the stomach.

Cauda Draconis[edit]

Geomantic caudadraconis.svg

Latin for "the Tail of the Dragon" and the figure of the south node of the Moon. It is considered very bad in most situations, such that in older traditions if this was the first figure drawn the geomancy reading was stopped. It is only good in circumstances for ending or completing things, such as breaking up a relationship. It brings good with evil, and evil with good. It is associated with the malefic planets Saturn and Mars, and the astrological sign Virgo. Its inner and outer element are both fire. Its planetary intelligences are Agiel and Graphiel, and its spirits are Zazel and Bartzabel; it is associated with the deities Mavors, Saeturnus, and Athena, and the angels Cassiel, Samael and Malchidael. It is associated with the left arm.

Puer[edit]

Geomantic puer.svg

Latin for "the Boy". The figure is a representation of a sword or erect phallus and refers to male energies, primarily aggression and passion, but also war and male sexuality. It is bad in most cases, but good in situations where boys (in Antiquity and Medieval society) excelled: love and war. Astrologically it is associated with Aries and Mars. All elements are active except Water, the element of emotion; its inner element is air, but due to it being ruled by Mars, its outer element is fire. Its planetary intelligence is Graphiel and its spirit is Bartzabel; it is associated with the deities Mavors and Athena, and the angels Samael and Malchidael. It is associated with the head.

Fortuna Minor[edit]

Geomantic fortunaminor.svg

Latin for "the Lesser Fortune". The figure is symbolic of success coming down like beams of light from the Sun. Astrologically it is associated with Leo and the Sun in southern declinations; both its inner and outer elemental rulers are fire. It indicates a weakly positive outcome in nearly all questions, representing transient success that is dependent upon outside help. It favors situations that can be resolved quickly and do not need to be sustained. It is a figure of change and instability. Its planetary intelligence is Nakhiel and its spirit is Sorath; it is associated with the deities Apollo and Jupiter, and the angels Michael and Verchiel. It is associated with the spine.

Puella[edit]

Geomantic puella.svg

Latin for "the Girl". The figure is to resemble the vulva or a woman with exaggerated breasts. It is good in most situations, especially with women, beauty, or feminine situations. Astrologically it is associated with Libra and Venus; its outer element is air, but its inner element is water. It represents peace and passivity, which can be either positive or negative depending on the question being answered, though generally positive, requiring to be acted upon instead of it acting on a situation. It is the symbol of feminine sexuality, balancing the energy of Puer. Its planetary intelligence is Hagiel and its spirit is Kedemel; it is associated with the deities Venus and Vulcanus, and the angels Anael and Zuriel. It is associated with the kidneys, lower back, buttocks, and skin.

Amissio[edit]

Geomantic amissio.svg

Latin for "Loss". The figure is of two bowls or cups turned upside-down. Astrologically, it is associated with Taurus and Venus retrograde. Its inner element is fire but ruled outwardly by earth. In general, the figure is bad or negative figure for all charts except those for love (being a figure of Venus) or where loss is desired and denotes loss. Often it represents something outside of one's grasp. Its planetary intelligence is Hagiel and its spirit is Kedemel; it is associated with the goddess Venus, and the angels Anael and Asmodel. It is associated with the neck and throat.

Carcer[edit]

Geomantic carcer.svg

Latin for "the Prison". The figure is the outline of an enclosure, a link in a chain, or prison cell. It is usually bad in situations and denotes delays, setbacks, or bindings. Astrologically it is associated with Capricorn and Saturn retrograde; its inner and outer element is earth. It refers to immobility, and also thereby strength. Depending on the question it could indicate a restriction or a source of willpower. It is generally unfavourable, but can be favourable in questions involving stability or security. Its planetary intelligence is Agiel and its spirit is Zazel; it is associated with the deities Saeturnus and Vesta, and the angels Cassiel and Hanael. It is associated with the knees and skeletal system of the body.

Laetitia[edit]

Geomantic laetitia.svg

Latin for "Joy". The figure resembles an arch, fountain, or rainbow. It is good in situations that concern potential, joy, or happiness. Astrologically it is associated with Pisces and Jupiter retrograde. It is ruled externally by water, but inwardly by fire. It is a positive figure for nearly all questions, representing fast situations and construction. It indicates upward motion, happiness, or joy. Its planetary intelligence is Iophiel and its spirit is Hismael; it is associated with the deities Jove and Neptunus, and the angels Sachiel and Barchiel. It is associated with the feet.

Caput Draconis[edit]

Geomantic caputdraconis.svg

Latin for "the Head of the Dragon". The figure resembles the astrological symbol the north node of the Moon. It is neutral figure (good with good, evil with evil) but fortunate with starting or beginning new things. It is favourable for beginnings and profit, and otherwise favourable with other favourable figures, and unfavourable with unfavourable ones. It is associated with the benefic planets Jupiter and Venus, and assigned to the zodiac sign of Sagittarius; its outer element is fire due to its association with Sagittarius while its inner element is earth. Its planetary intelligences are Iophiel and Hagiel and its spirits are Hismael and Kedemel; it is associated with the deities Venus, Iove, and Vulcanus, and the angels Sachiel, Anael, and Zuriel. It is associated with the right arm.

Conjunctio[edit]

Geomantic conjunctio.svg

Latin for "the Conjunction". The figure resembles a crossroads or joining of two figures. The sign is neutral in meaning (good in good things, evil in evil), but good with joining or recovering things, especially marriage or relationships. Astrologically it is associated with Virgo and Mercury retrograde. It represents a combination of forces, for good or ill. By itself, it is neutral, only becoming favourable or not by other figures around it. Its outer element is earth, while its inner element is air. Its planetary intelligence is Tiriel and its spirit is Taphthartharath; it is associated with the deities Mercurius and Ceres, and the angels Raphael and Hamaliel. It is associated with the intestines and digestive system.

Acquisito[edit]

Geomantic acquisitio.svg

Latin for "Gain". The figure resembles two bowls or cups turned upright. It is good in almost all situations, especially for getting and obtaining things. Astrologically it is associated with Sagittarius and Jupiter, with its outer element ruled by fire and its inner element ruled by air. For most charts it is a positive figure, except where a loss is desired. It indicates a gain financially, mentally, or in any other form, or something within one's grasp. Its planetary intelligence is Iophiel and its spirit is Hismael; it is associated with the deities Jove and Diana, and the angels Sachiel and Adnachiel. It is associated with the hips and thighs.

Rubeus[edit]

Geomantic rubeus.svg

Latin for "Red". The figure is an overturned glass; an inversion, meaning good in all that is evil, and evil in all that is good. Like the Tail of the Dragon, the figure is considered so unfavourable that if it were the first in a reading, the reading would end. Astrologically it is associated with Scorpio and Mars retrograde; its inner element is ruled by air, and its outer element ruled by water. It represents passion, deception, violence, and vice. Its planetary intelligence is Graphiel and its spirit is Bartzabel; it is associated with the god Mavors, and the angels Samael and Barbiel. It is associated with the reproductive and excretory systems along with the genitals.

Fortuna Major[edit]

Geomantic fortunamajor.svg

Latin for "the Greater Fortune". The figure resembles blessings growing from the earth and being fruitful in the air. It is good in all situations in a best case scenario sense and represents great good fortune, especially in beginnings. Astrologically it is associated with Leo, like Fortuna Minor, but by the Sun in northern declinations. Its inner element is earth while its outer element is fire. It denotes power and success, and so is very favourable in conflicts and contests; being a figure of stability and long-term success, it also denotes hardship at the outset of an endeavor. Its planetary intelligence is Nakhiel and its spirit is Sorath; it is associated with the deities Apollo and Jupiter, and the angels Michael and Verchiel. It is associated with the heart and chest.

Albus[edit]

Geomantic albus.svg

Latin for "White". The figure resembles an upright glass or goblet. It is good in most situations, especially with good figures in company, but itself is a weak figure. Astrologically it is associated with Gemini and Mercury; even though its inner element is water, its outer element is air. It represents peace, wisdom and purity. It benefits beginnings and profit, or any situation where careful and deliberate planning is needed. Its planetary intelligence is Tiriel and its spirit is Taphthartharath; it is associated with the deities Mercurius and Apollo, and the angels Raphael and Ambriel. It is associated with the shoulders and lungs.

Tristitia[edit]

Geomantic tristitia.svg

Latin for "Sorrow". The figure resembles a broken arch or a stake being driven into the ground. It is bad in most cases and connotes sadness or mourning. Astrologically it is associated with Aquarius and Saturn. Tristitia is an unfavorable figure in almost all questions, usually representing pain and suffering. However, it is favorable in questions dealing with stability, building, or the Earth (such as agriculture). Its outer element is air and inner element is earth. Its planetary intelligence is Agiel and its spirit is Zazel; it is associated with the deities Saeturnus and Juno, and the angels Cassiel and Gabriel. It is associated with the ankles and lower legs.

Populus[edit]

Geomantic populus.svg

Latin for "the People". The figure resembles a bird's eye view of a group of people. The figure can mean that the outcome is based on the people of the situation, or represents a large number of people or peers. Astrologically it is associated with Cancer and the waxing Moon; both its inner and outer elements are water. It refers to a gathering or assembly of people and is very neutral, for though there may be a great deal of movement within the crowd, there is very little effect on the crowd as a whole. It is favorable with favorable figures, and unfavorable with unfavorable ones. Its planetary ruler is Chashmodai, its Intelligence is the Intelligence of Intelligences Malkah beTarshishim ve-ad Ruachoth Shechalim, and its Spirit is the Spirit of Spirits is Shad Barshemoth ha-Shartathan. It is associated with the deities Diana and Mercurius, and the angels Gabriel and Muriel. It is associated with the breasts and torso.

In the canonical I Ching, the hexagrams are arranged in an order dubbed the King Wen sequence after King Wen of Zhou, who founded the Zhou dynasty and supposedly reformed the method of interpretation. The sequence generally pair hexagrams with their upside-down equivalents, although in eight cases hexagrams are paired with their inversion.[50] Another order, found at Mawangdui in 1973, arranges the hexagrams into eight groups sharing the same upper trigram. But the oldest known manuscript, found in 1987 and now held by the Shanghai Library, was almost certainly arranged in the King Wen sequence, and it has even been proposed that a pottery paddle from the Western Zhou period contains four hexagrams in the King Wen sequence.[51] Whichever of these arrangements is older, it is not evident that the order of the hexagrams was of interest to the original authors of the Zhou yi. The assignment of numbers, binary or decimal, to specific hexagrams is a modern invention.

16 is the squares of the quadrant model

Ruling Element Figures Ruled

Fire Laetitia, Cauda Draconis, Fortuna Minor, Amissio

Air Puer, Rubeus, Acquisitio, Conjunctio

Water Populus, Via, Albus, Puella

Earth Fortuna Major, Tristitia, Caput Draconis, Carcer

Ruling Element Figures Ruled

Fire Puer, Fortuna Major, Fortuna Minor, Acquisitio, Cauda Draconis

Air Albus, Puella, Tristitia

Water Populus, Via, Rubeus, Laetitia

Earth Amissio, Conjunctio, Caput Draconis, Carcer

Quality Figures

Stable Acquisitio, Albus, Puella, Populus, Tristitia, Caput Draconis, Carcer, Fortuna Major

Mobile Laetitia, Cauda Draconis, Amissio, Fortuna Minor, Rubeus, Puer, Conjunctio, Via

Direction Figures

Entering Acquisitio, Albus, Puella, Tristitia, Caput Draconis, Fortuna Major

Exiting Laetitia, Cauda Draconis, Amissio, Fortuna Minor, Rubeus, Puer

Both Populus, Via, Carcer, Conjunctio

Type Figures

Impartial Populus, Via, Carcer, Conjunctio, Amissio, Acquisitio, Fortuna Major, Fortuna Minor

Partial Laetitia, Tristitia, Rubeus, Albus, Cauda Draconis, Caput Draconis, Puella, Puer

Planet Diurnal figure Nocturnal figure

Sun Fortuna Major Fortuna Minor

Moon Populus Via

Mercury Albus Conjunctio

Venus Puella Amissio

Mars Puer Rubeus

Jupiter Acquisitio Laetitia

Saturn Tristitia Carcer

Lunar nodes Caput Draconis Cauda Draconis

The geomantic figures[edit]

Via[edit]

Geomantic via.svg

Cauda Draconis[edit]

Geomantic caudadraconis.svg

Puer[edit]

Geomantic puer.svg

Fortuna Minor[edit]

Geomantic fortunaminor.svg

Puella[edit]

Geomantic puella.svg

Amissio[edit]

Geomantic amissio.svg

Carcer[edit]

Geomantic carcer.svg

Laetitia[edit]

Geomantic laetitia.svg

Caput Draconis[edit]

Geomantic caputdraconis.svg

Conjunctio[edit]

Geomantic conjunctio.svg

Acquisito[edit]

Geomantic acquisitio.svg

Rubeus[edit]

Geomantic rubeus.svg

Fortuna Major[edit]

Geomantic fortunamajor.svg

Albus[edit]

Geomantic albus.svg

Tristitia[edit]

Geomantic tristitia.svg

Populus[edit]

Geomantic populus.svg

Other famous mathematical problems that fit the quadrant model pattern are squaring a circle. The fourth squaring of a circle is different from the previous three. Also the four color theorem. It was known that any map could be colored with five colors. A computer proved that all maps can be colored with only four colors and no two territories would touch the same color. The other numbers, 2 and 3 and 1 did not need a computer to be proven. The forth is always different. Also the P versus NP problem contains elements for square 1: P. Square 2: NP Square 3: NP complete and Square 4: NP hard. The solving of this problem would have a reward of a billion dollars because it would help with quantum encryption.

Lagrange's four-square theorem states that every positive integer can be written as the sum of at most four square numbers. Three are not always sufficient; 7 for instance cannot be written as the sum of three squares

In mathematics and logic an extremely important concept is the concept of Truth Tables. Truth Tables take the quadrant model pattern. There are four possibilities in an atomic Truth Table.

*Square one: Proposition one is true, and proposition two is true.

*Square two: Proposition one is true, and proposition two is false.

*Square three: Proposition one is false, and proposition two is true.

*Square four. Proposition one is false, and proposition two is false.

There are five standard connectives used to form compound propositions from atomic propositions. These are:

*Square one: Disjunction--called inclusive OR statements. An example is, the player has to score 50 points per game or make five three pointers per game to be the MVP. The idea is if either the player scores 50 points per game, or makes five three pointers, then he will be the MVP. He does not need to do both; he must do only one. Proposition one is labeled P. Proposition two is labelled Q. If P is True and Q is true then the statement, R, is true. If P is True and Q is False then the statement R is true. If P is False and Q is true then the statement R is true. IF P is false and Q is false then the statement R is false.

*Square two: Conjunction--called AND statements. An example of a conjunction is if the player scores 50 points a game, P, and makes five three pointers per game, Q, then he will get the MVP. Again there are four possibilities. If P is true and Q is true, then R is true. If P is true and Q is false then R is false. If P is false and Q is true then R is false. If P is false and Q is false then R is false. Disjunctions, which are “or statements”, and conjunctions which are “and statements” are the duality.

*Square three: Conditionals--also called implications. These are if/then statements. For instance, if P, then Q. Another way to say it is, P implies Q. Examples would be, if the man scores 50 points it implies that the man made five three pointers. This is also called modus ponens. If P is true then Q must be true. It is impossible for Q to be false if P is true. If Q is false, P must be false. If P is false then Q can be true or false. P implies Q is always true if P is false. This is confusing, but these are the rules. The truth values are, if P is true

and Q is true then R is true. If P is true and Q is false then R is true. If P is false and Q is true then R is true. If P is false and R is false, Q is true.

*Square four: Biconditional. This is, if and only if, the fourth square. The fourth is always different. This is a statement of equivalence. If the truth values of P and Q are identical then the statement is true. If P is true and Q is true, R is true. If P is true and Q is false, R is false. If P is false and R is true then Q is false. If P is false and R is false then Q is true.

*Square five. Negation--a possible fifth square. It is very different from the previous four, and is questionable. It means “not”. There are two truth values for an atomic negation truth table. If P is true then not P is false. If P is false then not P is True.

Solving linear equations, quadratic equations, tertiary equations, and quartic equations by factorization into radicals is straightforward. Linear equations have xs, quadratic equations have an x squared, and tertiary equations have an x to the third power. Formulas for factoring these equations were discovered pretty easily. The fourth is always different. It took a very long time to come up with a quartic equation. It has been proven a formula for a quintic equation is impossible. But this has been proven. For any equation higher than this it is impossible. This fits the quadrant model pattern. The formula for a quadratic equation is x equals negative b plus or minus square root b squared minus four ac all over 2a. Every middle school student memorizes this formula.

The geometric nature of calculus also fits the quadrant model pattern. In statistics there are four options. These options fit the quadrant model pattern.

*Square one: You reject H not and H not is true. This is a type 1 error.

*Square two: You fail to reject H not and H not is true. This is no error.

*Square three: You reject H not and H not is false. This is no error.

*Square four: You fail to reject H not and H not is false. This is a type 2 error. This chart is the foundation of statistics, and the type of error that occurs determines statistical probabilities.

In probability theory and statistics, Bayes' theorem (alternatively Bayes' law or Bayes' rule) is the probability of an event, based on conditions that might be related to the event. For instance, let's say one is interested in whether Addison has cancer, and that she is 65. If cancer is related to age, information about Addison's age can be used to more accurately assess the probability of her having cancer using Bayes' Theorem.

Bayer' theorem is the central theorem of statistics. I sat in on statistics classes and this was the foundational formula. It has four parts

Square 1: P(A). This is the probability of A

Square 2: P(B). This is the probability of B. The first two squares are a reality.

Square 3:P(A | B), a conditional probability, is the probability of observing event A given that B is true. The third square is the doing/happening square.

Square 4:P(B | A), is the probability of observing event B given that A is true.

.i in the complex or cartesian plane. Real numbers lie on the horizontal axis, and imaginary numbers lie on the vertical axis. The complex plane in mathematics is a quadrant with these axes.

The imaginary number i is defined solely by the property that its squareis −1:

i^2 = -1 \ .

With i defined this way, it follows directly from algebra that i and −i are both square rootsof −1.

imaginary numbers are represented in a quadrant grid with i at the top -i at the bottom 1 on the right and -1 on the left

Mandelbrot studied the parameter space of quadratic polynomials in an article that appeared in 1980.[6] The mathematical study of the Mandelbrot set really began with work by the mathematicians Adrien Douady and John H. Hubbard,[1] who established many of its fundamental properties and named the set in honor of Mandelbrot.

the Mandelbrot set is the set of values of c in the complex plane for which the orbit of 0 under iteration of the complex quadratic polynomial

The Mandelbrot Set has ‘16‘ rays that can be indicated by the 16 red dots emanating out of the core/center. Overall there are 4 spokes of the Mandelbrot Set.

THe Mandelbrot Set is the most famous fractal of all fractals.

16 is the squares of the quadrant model

The Mandelbrot set is the set of complex numbers c for which the function f(z)=z²+c does not diverge when iterated, i.e., for which the sequence f(0), f(f(0)), etc., remains bounded.

The set is closely related to Julia sets (which produce similarly complex shapes). Its definition and its name is the work of Adrien Douady, in tribute to the mathematician Benoit Mandelbrot.[1]

Mandelbrot set images are made by sampling complex numbers and determining for each whether the result tends towards infinity when a particular mathematical operation is iterated on it. Treating the real and imaginary parts of each number as image coordinates, pixels are colored according to how rapidly the sequence diverges, if at all.

More precisely, the Mandelbrot set is the set of values of c in the complex plane for which the orbit of 0 under iteration of the complex quadratic polynomial.

The Mandelbrot Set began fractal mathematics and chaos theory which has led to the graphics in animation and many other inventions.

Immanuel Kant is considered to be one of the greatest philosophers of all time. He is known for his metaphysics, expanding on the work of Hume. His model fits the quadrant model pattern. He proposes the existence of two dichotomies. One is analytic and synthetic; the other is apriori and aposteriori. These dichotomies yield four results. An analytic proposition has a predicate concept is contained in its subject concept. An example of this is all bachelors are not married. The definition of bachelor is that he is unmarried. Synthetic propositions have predicate concepts not contained in the subject concept. An example of this is “all bachelors are unhappy”. A priori propositions are propositions known to be true without experiencing them. An experience of this is the statement, “If the king reigned for ten years then you know he reigned for nine years”. It is not necessary to experience the king's reign to know this is true. An aposteriori proposition is a proposition that needs to be experienced to be seen as true. An example of this is, “The king reigned from 1900 to 1910”. This must be examined and studied to know it is true. These two dichotomies yield four results.

*Square one: analytic apriori statements. These are statements that are known to be true by definition, with no need to experience them. For instance, “a male has a penis”. Males have penises by definition; there is no need to study the male to know this is true. This is the idealist. Analytic corresponds to abstract. Analytic is true based on definition. This corresponds to the mind, and relates to abstract. Apriori corresponds to cooperative. Cooperative people are not doers. They do not experience as much. They follow the rules more often.

*Square two: Synthetic apriori statements. Synthetic apriori is something known neither by definition, nor by experience. Kant said that an example of this is mathematical statements such as 7 + 5 equals 12. Kant said that the concept of 12 is not contained in 7 or 5, so it is synthetic. But he said that the knowledge is apriori in that you do not need to experience seven things and five things to know that this statement is true.

*Square three: Synthetic aposteriori. This is something that is not true based on definition, but must be experienced. An example is, “basketball players get more women”. The definition of basketball player is not getting women, and to find out if this is true one must experience it. Synthetic corresponds to concrete, aposteriori corresponds to utilitarian. This is the doing square.

*Square four: analytic aposteriori statements. Kant said that square four was impossible. This is something that is true based on definition, with need for experiencing it. The fourth never seems to belong. Recent philosophers, however, have said that there is such a thing as analytic aposteriori knowledge; perhaps everything is analytic aposteiroi. According to Plato’s model of the world of Forms, everything exists as an idea existing in a transcendent reality. There is nothing that is not true based on definition. Yet people must experience these things in order for them to be true. According to quantum mechanics some say that a person must experience something in order for it to exist. It has been proposed that analytic aposteriori propositions are possible, and not just possible but perhaps everything. The fourth always seems not to belong, but it encompasses the previous three.

Kant’s Metaphysics

analytic apriori	synthetic aposteriori
synthetic apriori	analytic aposteriori

Kant was famous for his four antinomies. These antinomies he used to show that science was limited in finding Truth and that philosophy could not be reduced to science. The four antinomies related to

Square 1: the limitation of the universe in respect of space and time,

Square 2: the theory that the whole consists of indivisible atoms (whereas, in fact, none such exist),

Square 3: the problem of free will in relation to universal causality

Square 4: the existence of a necessary being

One of Kant's central ideas was his analysis of duties. Kant is known as a philosopher for his analysis of ethics. In the categorical imperative, Kant's most important expression was his idea of the four duties. These four duties were derived from two dichotomies. One was duties to self/duties to Townes. The other was perfect duties/imperfect duties.Perfect duties are ones that must be fulfilled at every opportunity. Imperfect duties are ones that must be fulfilled at some point, but we are allowed to decide when and how this is done. The four types of duties fit the quadrant model pattern. They are
Square 1: perfect duties toward ourselves
Square 2: perfect duties toward others
Square 3:imperfect duties toward ourselves
Square 4:imperfect duties toward others
This is known as Kant's famous categorical imperative. This is what Kant became one of the most famous philosophers in history for
Kant gives four examples of each type of duty. They are
Square 1:To refrain from suicide is a perfect duty toward oneself.
Square 2:to refrain from making promises you have no intention of keeping is a perfect duty toward other
Square 3: to develop one's talents is an imperfect duty toward oneself
Square 4: to contribute to the happiness of others an imperfect duty toward others.

Here's another excerpt from qmr
Kant's table of judgement broke into four groups. These four groups fit the quadrant model pattern. They were
Square 1: quantity
Square 2: quality
Square 3: relation
Square 4: modality

John R. Searle is a world renowned philosopher who created a fourfold in his book The Construction of Social Reality. In my book I mention in the conclusion that epistemology is the study of knowledge. Ontology is the study of Being. Knowledge is the sixteenth square. Being is the seventeenth. Searle's fourfold is as follows

Square 1: Epistemologically subjective

Square 2: Epistemologically objective

Square 3: Ontologicaly objective

Square 4: Ontologically subjective

Richard McKeon's aspects of knowing fit the quadrant model pattern. It is based off of two dichotomies. One is between holoscopic principles and meroscopic principles. Holoscopic principles, looking at or seeing the whole, provide a coincidence of knowledge and known. Meroscopic principles, looking at or seeing the parts, separate the knower and the knowable from each other and from influence between each other. The other dichotomy is between notice interpretations and phenomenal interpretations. Ontic interpretations, between the knowable and knowledge, derive their character from a reality assumed to transcend or to underlie phenomena and statements. Phenomenal interpretations, between knower and the known, may reduce reality and values to aspects or consequences of phenomena.

They are

Square 1: Universal ontic holoscopic

Square 2: Universal phenomenal meroscopic

Square 3: Particular phenomenal holoscopic

Square 4: Particular ootice holoscopic

Being and Nothingness: An Essay on Phenomenological Ontology (French: L'Être et le néant : Essai d'ontologie phénoménologique), sometimes subtitled A Phenomenological Essay on Ontology, is a 1943 book by philosopher Jean-Paul Sartre.

Being is the 17th square of the quadrant model. Non Being is teh 18th

Being and Time (German title: Sein und Zeit), published in 1927, was Heidegger's first academic book. He had been under pressure to publish in order to qualify for Husserl's (to whom he dedicated the work) chair at the University of Freiburg and the success of this work ensured his appointment to the post.

It investigates the question of Being by asking about the being for whom Being is a question. Heidegger names this being Dasein (see above), and the book pursues its investigation through themes such as mortality, care, anxiety, temporality, and historicity. It was Heidegger's original intention to write a second half of the book, consisting of a "Destruktion" of the history of philosophy—that is, the transformation of philosophy by re-tracing its history—but he never completed this project.

Being and Time influenced many thinkers, including such existentialist thinkers as Jean-Paul Sartre (although Heidegger distanced himself from existentialism—see below).

Being is the 17th square of the quadrant model

In his "Building Dwelling Thinking" (in: "Poetry, Language, Thought") Martin Heidegger relates to his key concept of "fourfold" as a central aspect of dwelling (see previous part of the summary). The four elements of the fourfold are earth and sky, divinities and mortals. The fourfold is a kind of fullness which is a part of dwelling. This unity of the fourfold cannot be divided into its components and each one of these can only be what it is only when the others are kept in mind. Therefore, Heidegger claims, a man is not only a being in the world, but a part of the fourfold of earth, sky, divinities and mortals.

Earth

Earth is the supporting ground on which we stride. It supports us in the most physical sense and also by nurturing, watering and providing for us. Despite its perceived stability, the earth as part of the fourfold is an elusive element.

Sky

The sky as part of Heidegger's fourfold as the sky in their usual referential meaning but they have some additional layers of meaning. Human beings' gaze towards the sky gives birth the metaphors that reflect the fact that we are always both here but also "beyond". Therefore "sky" as a part of the fourfold are a spiritual component relating to eternity.

Mortals

The mortals in Heidegger's fourfold are human beings. Relating to mankind as mortals emphasizes our finiteness and instability of our existence. Only through "memto mori", the remembering of our inevitable death, can we come to terms with our essential nature. By this we can sustain a proper dwelling which leads, according to Heidegger, to a "good death" as human beings which in not nothingness but rather our essential nature.

Divinities

Following Holderlin, Heidegger understands the divinities as the most basic criterion of mankind. God for Heidegger is a poetic fiction, an anonymous creator and provider. And it is through his anonymity that god sets the standards for dwelling in the world, by his concealed presence in everything that surrounds us.

Heidegger's fourfold is the unity of earth, sky, mortals and divinities. It is part of our being in space and the site in which dwelling takes place. Human beings provide access to the fourfold by being a part of it and by their dwelling, sustaining the fourfold and its unity.

In this fourfold unity humans exist in their dwelling which is "done right" by "sparing the earth" and maintaining its true nature without exploiting it. Dwelling according the Heidegger is accepting the sky as sky, with their blessing and atrocities. Dwelling is also constituted by "awaiting the divinities as divinities" and by recognizing our limited existence.

Heideggers fourfold is again placed in a quadrant by Heideggar. He saw this as his most important work and the foundation for all of his work, and Heideggar is considered one of the greatest philosophers of all time. The dichotomy is tool v. broken tool, and something v something all. This yields

tool, specific something- Gods

broken tool, specific something sky

tool, something at all- Earth

broken tool, something at all, mortals.

I discussed Heideggers fourfold in the philosophy section. Graham analyzed this fourfold and developed his metaphysical quadruple object. Again, there is a dichotomy between sensual and real and qualities and objects. The fourfold fits the quadrant model pattern as such

Square 1: sensual qualities

Square 2: sensual object

Square 3: real object

square 4: real qualities

EJ Lowe is a philosopher who created a fourfold ontology

Square 1: attributes

Square2: kinds

Square 3: objects

square 4: modes

Fichtean Dialectics (Hegelian Dialectics) is based upon four concepts:

Square 1: Everything is transient and finite, existing in the medium of time.

Square 2: Everything is composed of contradictions (opposing forces).

Square 3: Gradual changes lead to crises, turning points when one force overcomes its opponent force (quantitative change leads to qualitative change).

Square 4:Change is helical (spiral), not circular (negation of the negation).

The concept of dialectic (as a unity of opposites) existed in the philosophy of Heraclitus, who stated that everything is in constant change. The history of the dialectical method is the history of philosophy

It was noted above that the first square field of inquiry is science, the second is religion, and third is art. The fourth square is philosophy. In Ken Wilber's quadrant model the existence of four levels of consciousness is proposed . This model deals with two dichotomies--the interior and exterior, and the individual and collective. The combinations of these yields four squares.

*Square one: Individual interior--labeled the “I”. It is also called the subjective square, the physiological, spiritual square. The fourth square of the first quadrant is self awareness. Idealists are first quadrant people. These people try to gain a sense of self, and tend to be very spiritual. The connotation of an aware person is a self-aware person who is spiritual.

*Square two: interior collective--”We”. This is the relational cultural square. Wilber calls it the intersubjective square. This is the Guardian square, and is about homeostasis. This is belief and faith which tie communities together.

*Square three: Exterior individual. Physiological behavioral. Wilber calls this the objective square. This is the doing square. It is about action. The third quadrant is about doing.

*Square four: Exterior collective. This structural social square is about systems, and puts people in a larger context. Wilber calls this the interobjective square. The fourth square puts things in a larger context. Becoming aware of a deep intimate connection with something takes a person outside the ego. Wilbur says the fourth square deals with systems, governments, networks, and technology. The third square is the ego square. In the fourth square transcends the ego. In the first square the search is to find the self. Once the self is found/established the move is into the second square, which is culture. The self exists only within a cultural context and a group context--the second square. After fitting in the culture and belonging, the search is to become an individual, and break out, which is to enter the third square--the doing square. The ego is now transcended, and a connection with a higher harmony emerges. The first square is the “I” experience. The second square is the “we” experience. The third square is the “what I do” experience. The fourth square is the “what we do”. These are the qualities of the squares of the quadrant model. By knowing this model a better understanding of the nature of each square in the quadrant model of reality is possible.

Ken Wilber’s Quadrant Model

Individual Interior- I- Subjective	Exterior Individual- Physiological Behavioral- Objective
Interior Collective We- Intersubjective	Exterior Collective- Structural Social-Interobjective

According to Aristotle there is a hierarchy of being. He describes that between the levels of the hierarchy there is huge chasms. Throughout history philosophers have referred to these different levels of being, especially religious philosophers Jewish, Christian, and Muslim. In "A Guide for the Perplexed", British philosopher and economist E. F. Schumacher says that the chasm between these levels of being has never been explained, and he thinks that the chasm are so huge that it refutes physicalist explanations for reality, because he does not believe that they can just emerge from natural processes. The creation of qualitatively new levels of existence in science is called emergence. The four levels of being according to Aristotle, are

Square 1: Mineral- rocks, metals and other lifeless things. The only goal which these things seek is to come to a rest. The first square is not yet the doing square. Idealists are not doers.

Square 2: Vegetative- plants and other wildlife. Vegetation is alive. Because plants seek nourishment and growth, they have souls and can be even said to be satisfied when they attain these goals. The first square wants to gain a soul and become the second square. The second square still is not a doer though. The second square is the guardian. Things in the vegetative level of existence would include trees, and fungi.

Square 3: Animal- These are the creatures in the animal kingdom. Animals seek pleasure and reproduction, and they have emotions. For instance, dogs can seem to be happy, and animals can seem to be scared or angry. The third square is emotion and doing. The third square is the artisan.

Square 4: Human- Aristotle sees what separates humans from animals to be reason. Aristotle sees humans as the emergence of a completely new level of being due to reason. According to Aristotle humans are capable of acting according to principles, and taking responsibility for their choices and blaming. The fourth square is the rational. The rational is known for his reason.

According to Rudolf Steiner there are four etheric forces or life forces or simply, ethers. In general, we can liken these forces that act on human beings the same way as the forces that act on the earth and the plants. Steiner is considered an outstanding snd remarkable philosophical and spiritual thinker. He is world renowned

Square 1:Warmth ether – this is described as very active quality and is represented by fire as the physical element, which always needs something it can burn. This involves time which is progressing and has the quality of ripening.

In the Human being, this is found in the will, such that if we are not doing something, the fire dies. Love enables the human being to be on fire which is borned our of the warmth of the heart.

In relation to a tree the warmth ether – leaves and flowers, and eventually fruits

2. Light ether – this represents polarities of darkness and light, with the physical element of air. This quality allows the distinction and makes visible boundaries of physical matter. It leads to the periphery and draws the viewer to feel as though as being sucked into that periphery. This also gives the quality of levity where there is an elongation / uprightness and overcoming of gravity. In relation to the tree the light ether gibes the height

3. Sound Ether / Tone – This exudes the quality of separation and connection. The physical element is water which is connected to the Life Ether and as such is recognized also as the chemical ether. It is in this sphere that one experiences harmony which is also related to all numbers and allows for analytical thinking. In relation to a tree the sound ether gibes the structure to the tree.

4. Life Ether – is the great healer. This allows physical processes which went “wild” to reintegrate itself back into the life processes to create the balance of health again. This has the quality of integrating and uniting.

HP Blavatsky said the following in her book the Secret Doctrine

page 98

"The Svastica is the most philosophically scientific of all symbols, as also the most comprehensible. It is the summary in a few lines of the whole work of creation, or evolution, as one should rather say, from Cosmo-theogony down to Anthro-pogony, from the indivisible unknown Parabrahm to the humble moneron of materialistic science, whose genesis is as unknown to that science as is that of the All-Deity itself. The Svastica is found heading the religious symbols of every old nation”

page 100

“It is the Alpha and the Omega of universal creative Force, evolving from pure Spirit and ending in gross Matter. It is also the key to the cycle of Science, divine and human; and he who comprehends its full meaning is for ever liberated from the toils of Mahamaya, the great Illusion and Deceiver”

More than the sum of the facts, the life ether, brings a holistic feeling and flexible thinking. Thus allowing one to look inside to see the world in you. (the whole is visible in each component).Life ether – forms the roots and branches

Itzhak Bentov’s name is a recognizable name in many, many circles.

Those that knew him well simply called him Ben.

Images were drawn by Ben.

Does God’s name in the original Hebrew text YHWH literally mean “He Causes to Become”?

And the text that accompanies these images on pages 50-51 of Bentov’s book A BRIEF TOUR OF HIGHER CONSCIOUSNESS states the following: (highlights in red have been added by me)

“This desire resulted in the process of creation, symbolized by the swastika within the creative center, representing a four-dimensional rotating universe.

It is interesting to note that if you merge your consciousness with that of the Creator, you discover within Him a rotating swastika.

In other words, swastika stands for both the Creator and the Creation – they are inseparable”

Bentov died in 1979 in an air accident

Itzhak wrote

“This desire resulted in the process of creation, symbolized by the swastika within the creative center, representing a four-dimensional rotating universe.

It is interesting to note that if you merge your consciousness with that of the Creator, you discover within Him a rotating swastika.

In other words, swastika stands for both the Creator and the Creation – they are inseparable”

Aristotle attributes the following four views to Thales:

The earth rests on water. (De Caelo 294a28)

Water is the archê of all things. (Metaph. 983b18)

The magnet has a soul. (De Anima 405a19)

All things are full of gods. (De Anima 411a7)

Zeno, one of the most famous ancient Greek philosophers, said that there were four stages in the process leading to true knowledge, which he illustrated with the example of the flat, extended hand, and the gradual closing of the fist:

Zeno stretched out his fingers, and showed the palm of his hand, – "Perception," – he said, – "is a thing like this."- Then, when he had closed his fingers a little, – "Assent is like this." – Afterwards, when he had completely closed his hand, and showed his fist, that, he said, was Comprehension. From which simile he also gave that state a new name, calling it katalepsis (κατάληψις). But when he brought his left hand against his right, and with it took a firm and tight hold of his fist: – "Knowledge" – he said, was of that character; and that was what none but a wise person possessed.

This is the event, his four stages to knowledge, that Zeno of Citium is most famous for.

The first quadrant is perception, the second quadrant is belief which is a sort of ascent, the third square is thinking which is comprehension. The first three parts Zeno has his right hand. The third part his hand is in a fist. The third square is the most solid. In the fourth he puts up his left hand. The fourth is always different. The fourth part Zeno said is knowledge. Knowledge is the fourth quadrant.

According to Epicurus the mind is composed of four different types of particles--fire, air, wind, and the "nameless element," which surpasses the other particles in its fineness. The fourth is always different.

Plutarch was a middle Platonist who wrote a work called parallel lives in which he made biographies of Greeks and Romans in parallel. But he is known for his "four unpaired lives".

In the SECI model of knowledge dimensions four modes of knowledge conversion were identified:

Square 1: Tacit to Tacit (Socialization) - This dimension explains Social interaction as tacit to tacit knowledge transfer, sharing tacit knowledge face-to-face or through experiences. For example, meetings and brainstorm can support this kind of interaction. Since tacit knowledge is difficult to formalize and often time and space specific, tacit knowledge can be acquired only through shared experience, such as spending time together or living in the same environment. Socialization typically occurs in a traditional apprenticeship, where apprentices learn the tacit knowledge needed in their craft through hands-on experience, rather than from written manuals or textbooks

Square 2: Tacit to Explicit (Externalization) - Between tacit and explicit knowledge by Externalization (publishing, articulating knowledge), developing factors, which embed the combined tacit knowledge which enable its communication. For example, concepts, images, and written documents can support this kind of interaction. When tacit knowledge is made explicit, knowledge is crystallized, thus allowing it to be shared by others, and it becomes the basis of new knowledge. Concept creation in new product development is an example of this conversion process

Square 3: Explicit to Explicit (Combination) - Explicit to explicit by Combination (organizing, integrating knowledge), combining different types of explicit knowledge, for example building prototypes. The creative use of computerized communication networks and large-scale databases can support this mode of knowledge conversion. Explicit knowledge is collected from inside or outside the organisation and then combined, edited or processed to form new knowledge. The new explicit knowledge is then disseminated among the members of the organization

Square 4: Explicit to Tacit (Internalization) - Explicit to tacit by Internalization (knowledge receiving and application by an individual), enclosed by learning by doing; on the other hand, explicit knowledge becomes part of an individual's knowledge and will be assets for an organization. Internalization is also a process of continuous individual and collective reflection and the ability to see connections and recognize patterns and the capacity to make sense between fields, ideas, and concepts.

The Information Space, or I-Space was developed by Max Boisot as a conceptual framework relating the degree of structure of knowledge (i.e. its level of codification and abstraction) to its diffusibility as that knowledge develops.

This results in four different types of knowledge.

Square 1: Public knowledge, such as textbooks and newspapers, which is codified and diffused.

Square 2: Proprietary knowledge, such as patents and official secrets, which is codified but not diffused. Here barriers to diffusion have to be set up.

Square 3: Personal knowledge, such as biographical knowledge, which is neither codified nor diffused.

Square 4: Common sense – i.e. what ‘everybody knows’, which is not codified but widely diffused.

The Cynefin framework has five domains. The first four domains are:

Obvious - replacing the previously used terminology Simple from early 2014 - in which the relationship between cause and effect is obvious to all, the approach is to Sense - Categorise - Respond and we can apply best practice.

Complicated, in which the relationship between cause and effect requires analysis or some other form of investigation and/or the application of expert knowledge, the approach is to Sense - Analyze - Respond and we can apply good practice.

Complex, in which the relationship between cause and effect can only be perceived in retrospect, but not in advance, the approach is to Probe - Sense - Respond and we can sense emergent practice.

Chaotic, in which there is no relationship between cause and effect at systems level, the approach is to Act - Sense - Respond and we can discover novel practice.

The fifth domain is Disorder, which is the state of not knowing what type of causality exists, in which state people will revert to their own comfort zone in making a decision. The fourth is transcendent and different frok the previous three. It points to the nature of the fifth. The cynefin model os the quadrant model pattern

In healthcare, Carper's fundamental ways of knowing is a typology that attempts to classify the different sources from which knowledge and beliefs in professional practice (originally specifically nursing) can be or have been derived. It was proposed by Barbara A. Carper, a professor at the College of Nursing at Texas Woman's University, in 1978.

The typology identifies four fundamental "patterns of knowing":

Square 1: Empirical

Factual knowledge from science, or other external sources, that can be empirically verified.

Square 2: Personal

Knowledge and attitudes derived from personal self-understanding and empathy, including imagining one's self in the patient's position.

Square 3: Ethical

Attitudes and knowledge derived from an ethical framework, including an awareness of moral questions and choices.

Square 4: Aesthetic

Awareness of the immediate situation, seated in immediate practical action; including awareness of the patient and their circumstances as uniquely individual, and of the combined wholeness of the situation. (Aesthetic in this sense is used to mean "relating to the here and now", from the Greek αἰσθάνομαι (aisthanomai), meaning "I perceive, feel, sense";[3] the reference is not to the consideration of beauty, art and taste).

The emphasis on different ways of knowing is presented as a tool for generating clearer and more complete thinking and learning about experiences, and broader self-integration of classroom education.

Philippe Descola is an anthropologist who delineated Four Ontologies. The demarcation is based off of two dualities. One is similar in inferiority v. dissimilar in inferiority. The other is similar in physicality and dissimilar in physicality. The four are

Square 1: similar in inferiority and dissimilar in physicality. Animism

Square 2: Dissimilar in inferiority and dissimilar in physicalist. Analogism

Square 3: Similar in inferiority and similar in physicality. Totemism

Square 4: Disimilar in inferiority and similar in physicality. Naturalism

Cynefin was chosen by the Welsh scholar Dave Snowden to describe a perspective on the evolutionary nature of complex systems, including their inherent uncertainty. The domains of the model fit the quadrant model pattern. They are

Square 1: Obvious - replacing the previously used terminology Simple from early 2014 - in which the relationship between cause and effect is obvious to all, the approach is to Sense - Categorise - Respond and we can apply best practice.

Square 2: Complicated, in which the relationship between cause and effect requires analysis or some other form of investigation and/or the application of expert knowledge, the approach is to Sense - Analyze - Respond and we can apply good practice.

Square 3: Complex, in which the relationship between cause and effect can only be perceived in retrospect, but not in advance, the approach is to Probe - Sense - Respond and we can sense emergent practice.

Square 4: Chaotic, in which there is no relationship between cause and effect at systems level, the approach is to Act - Sense - Respond and we can discover novel practice.

Ludwig von Bertalanffy outlines systems inquiry into three major domains: Philosophy, Science, and Technology. In his work with the Primer Group, Béla H. Bánáthy generalized the domains into four integratable domains of systemic inquiry:

Square 1: philosophy-the ontology, epistemology, and axiology of systems

Square 2:Theory-a set of interrelated concepts and principles applying to all systems

Square 3:Methodology the set of models, strategies, methods, and tools that instrumentalize systems theory and philosophy

Square 4:Application the application and interaction of the domains

In the version of Engaged theory developed by an Australian-based group of writers, analysis moves from the most concrete form of analysis – empirical generalization – to more abstract modes of analysis. Each subsequent mode of analysis is more abstract than the previous one moving across the following themes: 1. doing, 2. acting, 3. relating, 4. being.

This leads to the 'levels' approach as set out below:

Square 1: 1. Empirical analysis (ways of doing)

The method begins by emphasizing the importance of a first-order abstraction, here called empirical analysis. It entails drawing out and generalizing from on-the-ground detailed descriptions of history and place. This first level either involves generating empirical description based on observation, experience, recording or experiment—in other words, abstracting evidence from that which exists or occurs in the world—or it involves drawing upon the empirical research of others. The first level of analytical abstraction is an ordering of ‘things in the world’, in a way that does not depend upon any kind of further analysis being applied to those ‘things’. The first square is always sensation and perception.

For example, the Circles of Sustainability approach is a form of engaged theory distinguishing (at the level of empirical generalization) between different domains of social life. It can be used for understanding and assessing quality of life. Although that approach is also analytically defended through more abstract theory, the claim that economics, ecology, politics and culture can be distinguished as central domains of social practice has to be defensible at an empirical level. It needs to be useful in analyzing situations on the ground.

The success or otherwise of the method can be assessed by examining how it is used. One example of use of the method was a project on Papua New Guinea called Sustainable Communities, Sustainable Development.

2. Conjunctural analysis (ways of acting)

This second level of analysis, conjunctural analysis, involves identifying and, more importantly, examining the intersection (the conjunctures) of various patterns of action (practice and meaning). Here the method draws upon established sociological, anthropological and political categories of analysis such as production, exchange, communication, organization and inquiry. Behavior is patterns of action. Behavior is the second quadrant.

Square 3. Integrational analysis (ways of relating)

This third level of entry into discussing the complexity of social relations examines the intersecting modes of social integration and differentiation. These different modes of integration are expressed here in terms of different ways of relating to and distinguishing oneself from others—from the face-to-face to the disembodied. Here we see a break with the dominant emphases of classical social theory and a movement towards a post-classical sensibility. In relation to the nation-state, for example, we can ask how it is possible to explain a phenomenon that, at least in its modern variant, subjectively explains itself by reference to face-to-face metaphors of blood and place—ties of genealogy, kinship and ethnicity—when the objective ‘reality’ of all nation-states is that they are disembodied communities of abstracted strangers who will never meet. This accords with Benedict Anderson's conception of 'imagined communities', but recognizes the contradictory formation of that kind of community.

Square 4. Categorical analysis (ways of being)

This level of enquiry is based upon an exploration of the ontological categories (categories of being such as time and space). If the previous form of analysis emphasizes the different modes through which people live their commonalities with or differences from others, those same themes are examined through more abstract analytical lenses of different grounding forms of life: respectively, embodiment, spatiality, temporality, performativity and epistemology. At this level, generalizations can be made about the dominant modes of categorization in a social formation or in its fields of practice and discourse. It is only at this level that it makes sense to generalize across modes of being and to talk of ontological formations, societies as formed in the uneven dominance of formations of tribalism, traditionalism, modernism or postmodernism.

Kent Palmer's four levels of being in information space on the internet are:

Square 1: static being, that which is present, existent

Square 2: process being, that which is dynamic, changing, becoming

Square 3: hyper being, emergent, autopoietic being, that which achieves semi-stasis emergent from dynamics

Square 4: wild being, a meta-field of overlapping fields of stasis and dynamics, involving interaction of numerous emergent beings

According to Aristotle there are four types of economy. They are

Square 1: Royal economy – The simplest and most important. It has a king.

Square 2:Satrapic economy—The medium between the economies. It consists of the provincial governor.

Square 3:Political economy—Most varied and easiest. It is “The economy of the city”.

Square 4:Personal economy— Least important, quite varied

- Practiced by the individual

In the Poetics Aristotle defined four genres of literature. He said they were Comedy, tragedy, epic poetry, and lyric poetry

In Aristotle's Physics he discusses motion. He says motion is the passage of matter into form. He states there are four kinds of motion. They are

Square 1: motion which affects the substance of a thing, particularly its beginning and its ending

Square 2: motion which brings about changes in quality

Square 3: motion which brings about changes in quantity, by increasing it and decreasing it

Square 4: motion which brings about locomotion, or change of place. Of these the last is the most fundamental and important.

In Platos book, The Phaedo, the theme is that Socrates wants to prove the immortality of the soul. I already discussed that in the Meno socrates does this through geometry and ultimately draws 16 squares in the sand, or in other words, the quadrant model. He begins his argument by drawing a literal quadrant, which he calls the double square. In the Phaedo, he gives four arguments for the immortality of the soul

Square 1:The Cyclical Argument, or Opposites Argument says Forms are eternal and unchanging, and as the soul always brings life, then it must not die, and is necessarily "imperishable". As the body is mortal and is subject to physical death, the soul must be its indestructible opposite. Plato then suggests the analogy of fire and cold, saying if cold is imperishable, and fire, its opposite, was within its sphere, it would necessarily withdraw intact like the soul during death. This is similar to the idea of the opposite charges of magnets.

Square 2: The Theory of Recollection explains that humans have some non-empirical knowledge (e.g. The Form of Equality) at birth, implying the soul existed before birth to carry that knowledge. He also suggests this in the Meno.

Square 3: The Affinity Argument, explains that invisible, immortal, and incorporeal things are different from visible, mortal, and corporeal things. Humans' souls are invisible. Humans bodies are visible. When humans' bodies die and decay, our soul will continue to live.

Square 4: The Argument from Form of Life, or The Final Argument explains that the Forms, incorporeal and static entities, are the cause of all things in the world, and all things participate in Forms. Socrates says beautiful things participate in the Form of Beauty and he says the number four participates in the Form of the Even. The soul, Socrates says, participates in the Form of Life, which means the soul can never die.

In the dialogue lysis Socrates states that there are four types of friendship. They are

Square 1: Friendship between people who are similar, interpreted by Socrates as friendship between good men.

Square 2: Friendship between men who are dissimilar.

Square 3: Friendship between men who are neither good nor bad and good men.

Square 4: Gradually emerging: friendship between those who are relatives

In Plato's book Philebus, Socrates proclaims that there are four kinds of Being. They are

Square 1. The limitless. These are the types of things of which we make relative comparisons such as more or less.

2. The limited. These are the types of things which can be given a definite measurement of number.

3. The mixed kind of being is mixes the first two, limiting and various types of limitless beings in the "world of becoming" and change which people experience, or in any means that aspect of it which is not arbitrary and aimless, but a more genuine kind of becoming that aims at being.

4. The cause of such genuine mixture, which limits the unlimited beings and orders nature. Socrates argues this is reason itself - not only human reason, but the greater reason of nature itself.

In Plato's book Phaedra, Socrates argues that great philosophy and art come from madness. Socrates describes four types of madness. They are

Square 1: From Apollo, the gift of prophecy;

Square 2: From Dionysus, the mystic rites and relief from present hardship;

Square 3: From the Muses, poetry;

Square 4: From Aphrodite, love.

Plato said that there are four states of altered consciousness. They are

Square 1: oracle presided by apollo. The first square is intellectual

Square 2: literal dionyses

Square 3: ecstatic possession artistic muses. The third sauare is doing

Square 4: erotic aphrodite. The fourth square is knowledfe which is related tk sex and death

Ficino distinguishes four mnemonic metaphorical processes through which the external world is reimagined through the creation of psychological perspective:

wine, provides a metaphor for absorbing spirit from the earthy world around, drinking in food for the soul from the variability and fluidity of life in the moment. As a psychological participation in life, Moore contrasts such pleasure with conventional entertainment. (p. 78-83)
aromas, serve as placemarkers for nourishing memories of the past that continue to be able to move the soul. Using a pun, and stretching a point, Moore argues that 'Ficino calls for the revival of a neglected sense, an olfactory awareness used to make 'scents' out of this world' (p. 83-85)
music elicits reflections on the qualities of experiential time, abstracting from specific content to protray the dynamic patterns of life and of the soul. Moore argues that it is 'a kind of hermeneutic, a mode of interpreting life midway between blind experience and distant explanation.' We need to be musicians of the soul, with taste and a good ear. (p. 85-90)
light in the sense of transrational intelligence (the 'reason of light') offers a new quality of understanding (in-sight), suggesting the fruitfulness of life, the perspicacity of our senses, the certitude of our intelligence and the bountifulness of grace. 'In this psychology we are concerned not with turning the light of reason on the dark, unknown, and troubling phenomena...but rather to discover within events and within ourselves the reasons or patterns or seeds...of that inner light, that internal universe and vestal fire.' (p. 90-94)

In order to transcend what Moore terms the 'steady, monotonous hum of the sane adjusted life' (p. 97) that dulls the soul, 'we require inner figures associated with specific kinds of nonrational consciousness' the platonic 'frenzies' or forms of 'madness':

through the poetic imagination the soul is awakened and withdraws from literalism, establishing the basis for a psychological attitude;
through a mode of fantasy, 'sacerdotal madness', serious attention is given to this psychological attitude, bringing not only fantasies but the deepest structuring patterns of the soul, its true mysteries, into view;
through prophetic madness one experiences a shift in time perspective that moves attention away from discrete elements taking place in linear time to cyclic patterns and fragments of imagery that do not fit the linear scheme;
through erotic madness, beauty lures the soul away from concreteness and literalism, activating the deeper strata of the soul (p. 96-114)

Philo of Alexandria is considered one of the greatest ancient philosophers. He stated that there were diur tyoes of ecstasy. They are

Square 1: pathological

Square 2: extreme amazement

Square 3: passivity of mind

Square 4: divine possession

Philo claimed to be a prophet and gain divine knowledge from God, the fourth type, and that he claimed was the source of his writing.

The Hellenistic Jewish Biblical philosopher Philo Judaeus, born in Alexandria, (d. ca. 50 CE) presents his allegorical interpretation of the ladder in the first book of his De somniis. There he gives four interpretations, which are not mutually exclusive:[2]

The angels represent souls descending to and ascending from bodies (some consider this to be Philo's clearest reference to the doctrine of reincarnation).

In the second interpretation the ladder is the human soul and the angels are God's logoi, pulling the soul up in distress and descending in compassion.

In the third view the dream depicts the ups and downs of the life of the "practiser" (of virtue vs. sin).

Finally the angels represent the continually changing affairs of men.

The classic Torah commentaries offer several interpretations of Jacob's ladder. According to the Midrash, the ladder signified the exiles which the Jewish people would suffer before the coming of the Messiah. First the angel representing the 70-year exile of Babylonia climbed "up" 70 rungs, and then fell "down". Then the angel representing the exile of Persia went up a number of steps, and fell, as did the angel representing the exile of Greece. Only the fourth angel, which represented the final exile of Rome/Edom (whose guardian angel was Esau himself), kept climbing higher and higher into the clouds. Jacob feared that his children would never be free of Esau's domination, but God assured him that at the End of Days, Edom too would come falling down.

The fourth square is always transcendent.

Albinus (Greek: Ἀλβῖνος; fl. c. 150 AD) was a Platonist philosopher, who lived at Smyrna, and was teacher of Galen. He is known for his ideas on drama. He is famous for dividing the Dialogues of Plato into four classes,

Square 1: logical- the first square is mental

Square 2: critical- the second square is homeostasis and order and that involves criticality

square 3: physical- the third square is the physical doing square

Square 4:, ethical

and mentions another division of them into Tetralogies, according to their subjects. He advises that the Alcibiades, Phaedo, Republic, and Timaeus, should be read in a series.

He divides Platos works into tetralogies, or groups of four, harkening the quadrant

According to David Hume there are four circumstances, on which depend all, or the greatest part of the ills, that harm sensible creatures, that Hume thinks God could have done differently. Hume says these ills may be unavoidable.

Square 1: Hume says that there does not need to be pleasure and pain but humans could just feel varying degrees of pleasure. For instance, if something is harmful to somebody he does not need to feel pain but just could feel a lot less pleasure. Hume does not think that pain was necessary to produce. The first quadrant is the sensation and perception square and Hume's circumstance is related to sensation and perception

Square 2: Hume thinks that God could have made laws of nature that exterminated the capacity to do ill. Hume does not see for instance why God made it so it was necessary that if man fell off a cliff he would fall to his death. Hume thinks if God was benevolent he would have made laws that would protect humans from such things. For instance if a person fell from a cliff gravity could soften. The second quadrant is homeostasis and structure which is related to natural laws

Hume thinks that God could get rid of general laws of nature and just set things up so people are benefitted. For instance there are storms and droughts. Instead, Hume says, why does

A benevolent God not change the winds to help the sailor and reduce the uncertainty for the sailor? Why, if a man has a brain disorder caused by a random genetic defect that causes him to be a psychopath, does God not just make it so there is not so much uncertainty and make it so there is no psychopaths by making the genetic laws so that does not happen. This second square. The second square is involved with laws and homeostasis.

Square 3: Hume does not see why God is frugal in what he endows. Hume says that God gives an animal intelligence like humans but makes him week. He gives a creature speed but reduces its power. He makes a creature strong but makes it dumb. The third square is the doing square. Why not make humans as fast as a cheetah as string as a bear and as smart as a human? The third quadrant is the physical square and Hume questions why the physical endowments of creatures are frugally parceled. He thinks if it were not so frugal this would eliminate ills.

Square 4: Hume says that there is inaccurate workmanship are too many flaws in reality. There are tornadoes volcanoes and too many extremes. He thinks if God evened this out and fixed the flaws this would eliminate ills

The Fourth Way (1957) is a book about the Fourth Way system of self-development as introduced by Greek-Armenian philosopher G.I. Gurdjieff and is a compilation of the lectures of P. D. Ouspensky at London and New York, 1921–1946, published posthumously by his students in 1957.[1][2]

The term "The Fourth Way" has also come to be used as a general descriptive term for the body of ideas and teachings which Gurdjieff brought to the west from his study of eastern schools.[3]

Ouspensky was given the task of bringing these ideas to a wider audience in an unadulterated form by Gurdjieff. The Fourth Way is considered to be the most comprehensive statement of Gurdjieff's ideas as taught by Ouspensky.

The book consists of adaptations of Ouspensky's lectures, and the accompanying question and answer sessions.

The 'Fourth Way' to which the title refers is a method of inner development - "the way of the sly man," as Gurdjieff described it. This way is to be followed under the ordinary conditions of everyday life, as opposed from the three traditional ways that call for retirement from the world: those of the fakir, the monk, and the yogi, which Gurdjieff maintained could only result in partial, unbalanced development of man's potential.

Ouspensky died in Lyne Place, Surrey, in 1947. Shortly after his death, The Psychology of Man's Possible Evolution was published, together with In Search of the Miraculous. A facsimile edition of In Search of the Miraculous was published in 2004 by Paul H. Crompton Ltd. London. Transcripts of some of his lectures were published under the title of The Fourth Way in 1957; largely a collection of question and answer sessions, the book details important concepts, both introductory and advanced, for students of these teachings.

Ouspensky's papers are held at Yale University Library's Manuscripts and Archives department.

Teaching

After Ouspensky broke away from Gurdjieff, he taught the "Fourth Way", as he understood it, to his independent groups.

Fourth Way

Gurdjieff proposed that there are three ways of self-development generally known in esoteric circles. These are the Way of the Fakir, dealing exclusively with the physical body, the Way of the Monk, dealing with the emotions, and the Way of the Yogi, dealing with the mind. What is common about the three ways is that they demand complete seclusion from the world. According to Gurdjieff, there is a Fourth Way which does not demand its followers to abandon the world. The work of self-development takes place right in the midst of ordinary life. Gurdjieff called his system a school of the Fourth Way where a person learns to work in harmony with his physical body, emotions and mind. Ouspensky picked up this idea and continued his own school along this line.[21]

Ouspensky made the term "Fourth Way" and its use central to his own teaching of the ideas of Gurdjieff. He greatly focused on Fourth Way schools and their existence throughout history.

Pyotr Demianovich Ouspenskii (known in English as Peter D. Ouspensky, Пётр Демья́нович Успе́нский; 5 March 1878 – 2 October 1947),[1] was a Russian mathematician and esotericist known for his expositions of the early work of the Greek-Armenian teacher of esoteric doctrine George Gurdjieff, whom he met in Moscow in 1915.

His first book, The Fourth Dimension, appeared in 1909; his second book, Tertium Organum, in 1912. A New Model of the Universe, as explained by Ouspensky in the foreword of the second edition, was written and published as articles by 1914, updated to include "recent developments in physics" and republished as a book in Russian in 1917. It was assumed that Ouspensky was lost to the Revolution's violence, it was then republished in English without his knowledge in 1931. Since the earliest lectures this work attracted a who's who of the philosophy crowd (see below) and has been to this day a widely accepted authoritative basis for a study of metaphysics, or rather, to exceed the limits of the same by his "psychological method", which he defines as (paraphrasing p. 75.) "a calibration of the tools of human understanding to derive the actual meaning of the thing itself." This term is one of three high concepts of the material presented, along with "the esoteric method" which as he sums up (p. 76) depends on the first to derive the possibility of something beyond ordinary human effort entirely. In high concept terms: "The idea of esotericism ... holds that the very great majority of our ideas are not the product of evolution but the product of the degeneration of ideas which existed at some time or are still existing somewhere in much higher, purer and more complete forms." (p. 47) Ouspensky's reputation is presently degenerated to being a follower of Gurdjieff rather than a partner (see below) and the apex of esotericism, self-knowledge, and metaphysical thought. The title itself promises a model of the universe, or unified theory of everything, which it is. He also wrote the novel Strange Life of Ivan Osokin, which explored the concept of eternal recurrence or the eternal return.

He traveled in Europe and the East — India, Ceylon, and Egypt — in his search for knowledge. After his return to Russia and his introduction to Gurdjieff in 1915, Ouspensky spent the next few years studying with him, and supporting the founding of a school. According to Osho, when Ouspensky went to Gurdjieff for the first time, the latter was but an unknown fakir and Ouspensky made him well-known to his own reading public.[5]

Denying the ultimate reality of space and time in his book Tertium Organum,[6] he also negates Aristotle's Logical Formula of Identification of "A is A" and finally concludes in his "higher logic" that A is both A and not-A.[7]

Unbeknown to Ouspensky, a Russian émigré by the name of Nicholas Bessarabof took a copy of Tertium Organum to America and placed it in the hands of the architect Claude Bragdon who could read Russian and was interested in the fourth dimension.[8] Tertium Organum was rendered into English by Bragdon who had incorporated his own design of the hypercube[9][10] into the Rochester Chamber of Commerce building.[11] Bragdon also published the book and the publication was such a success that it was finally taken up by Alfred A. Knopf. At the time, in the early 1920s, Ouspensky's whereabouts were unknown until Bragdon located him in Constantinople and paid him back some royalties.

Ouspensky's lectures in London were attended by such literary figures as Aldous Huxley, T. S. Eliot, Gerald Heard and other writers, journalists and doctors. His influence on the literary scene of the 1920s and 1930s as well as on the Russian avant-garde was immense but still very little known.[12] It was said of Ouspensky that, though nonreligious, he had one prayer: not to become famous during his lifetime.

Ouspensky also provided an original discussion of the nature and expression of sexuality in his A New Model of the Universe; among other things, he draws a distinction between erotica and pornography.

During his years in Moscow, Ouspensky wrote for several newspapers and was particularly interested in the then-fashionable idea of the fourth dimension.[13] His first published work was titled The Fourth Dimension[14] and he explored the subject along the ideas prevalent at the time in the works of Charles H. Hinton,[15] the fourth dimension being an extension in space.[16][17] Ouspensky treats time as a fourth dimension only indirectly in a novel he wrote titled Strange Life of Ivan Osokin[18] where he also explores the theory of eternal recurrence.

Hume is famous for his four dissertstions

Hume provides four reasons to think that there has never been sufficient evidence in favor of a miracle to render it probable.

Square 1: First, no miracle is supported by testimony of a sufficient number of trustworthy people to rule out the possibility of falsehood. The first square is based off of sensation and perception. He is claiming there is not enough witnesses.

Square 2: Second, while we should normally believe that which most closely accords itself with past experience, the sensations of surprise and wonder often lead us to unreasonable beliefs. There are many examples of tall tales that are not from reasonable inquiry but from a love of wonder. The second square is the feeling/faith square, and Hume thinks that people want to believe in these things because it makes them feel good.

Square 3: Third, Hume states that most reports of miraculous events occur amongst barbarous or ignorant people, who may not be sophisticated enough to disbelieve fabricated testimony. The third square is the bad square, related to the artisan who is not considered the most polite and sophisticated in terms of being good.

Square 4: Fourth, since every religion claims the veracity of its own miracles but discredits the miracles of every other religion, the evidence of all other religions opposes the evidence in favor of a miracle in any one particular religion. For instance, what a Hindu might consider a miracle would be considered a heresy by anyone of different faith. The fourth square points to a larger context snd makes comparisons

Out of his analysis of miracles, Hume establishes that religion is not based on reason but faith. Faith is the second quadrant and religion is a second square field of inquiry

There are four works in the nag hamadi texts that are gospels. There are other works in the nag hamadi collection but the four primary works are these gospels. The Nag Hamadi Gospels are

Square 1: Gospel of Thomas- sayings if jesus. The first square is mental

Square 2: Gospel of truth- meditation on jesus ministry. Second square is himeostasia

Square 3: the Gospel of the Egyptians- a sacramental text about an initiation ritual. The third square is doing

Square 4: the Gospel of Philip- sayings and the sacrament of the mystery of the bride chamber. The fourth dquare is mental and doing

Qualia is a very important topic in philosophy and the study of consciousness. Daniel Dennett identifies four properties that are commonly ascribed to qualia. According to these, qualia are:

Square 1: ineffable; that is, they cannot be communicated, or apprehended by any other means than direct experience.

Square 2: intrinsic; that is, they are non-relational properties, which do not change depending on the experience's relation to other things.

Square 3: private; that is, all interpersonal comparisons of qualia are systematically impossible.

Square 4: directly or immediately apprehensible in consciousness; that is, to experience a quale is to know one experiences a quale, and to know all there is to know about that quale.

V. S. Ramachandran and William Hirsteinproposed three laws of qualia (with a fourth later added), which are "functional criteria that need to be fulfilled in order for certain neural events to be associated with qualia" by philosophers of the mind:

Square 1: Qualia are irrevocable and indubitable. You don't say 'maybe it is red but I can visualize it as green if I want to'. An explicit neural representation of red is created that invariably and automatically 'reports' this to higher brain centres.

Square 2: Once the representation is created, what can be done with it is open-ended. You have the luxury of choice, e.g., if you have the percept of an apple you can use it to tempt Adam, to keep the doctor away, bake a pie, or just to eat. Even though the representation at the input level is immutable and automatic, the output is potentially infinite. This isn't true for, say, a spinal reflex arc where the output is also inevitable and automatic. Indeed, a paraplegic can even have an erection and ejaculate without an orgasm.

Square 3: Short-term memory. The input invariably creates a representation that persists in short-term memory—long enough to allow time for choice of output. Without this component, again, you get just a reflex arc.

Square 4:Attention. Qualia and attention are closely linked. You need attention to fulfill criterion number two; to choose. A study of circuits involved in attention, therefore, will shed much light on the riddle of qualia

Nicolai Hartmann is considered one of the greatest metaphysicians of all time. He described four levels of reality. They are

Hartmann's levels of reality are

Square 1: the inorganic level (German: anorganische Schicht)

Square 2: the organic level (organische Schicht). The first two squares are the duality.

Square 3: the psychical/emotional level (seelische Schicht). The third square is related to action and emotion.

Square 4: the intellectual/cultural level (geistige Schicht). The fourth square is related to the rational and intellect. It is Wilber's culture square

Hartmann stated four laws that apply to the levels of reality.

Square 1: The law of recurrence: Lower categories recur in the higher levels as a subaspect of higher categories, but never vice versa.

Square 2: The law of modification: The categorial elements modify in their recurrence in the higher levels (they are shaped by the characteristics of the higher levels).

Square 3: The law of the novum: The higher category is made up of of a diversity of lower elements, but it is a specific novum that is not included in the lower levels.

Square 4: The law of distance between levels: Since the different levels do not develop continuously but in leaps, they can be clearly distinguished.

Fascinatingly, these laws apply to the squares and nature of my model the quadrant model.

The Quadrature of the Parabola (Greek: Τετραγωνισμὸς παραβολῆς) is a treatise on geometry, written by Archimedes in the 3rd century BC. Written as a letter to his friend Dositheus, the work presents 24 propositions regarding parabolas, culminating in a proof that the area of a parabolic segment (the region enclosed by a parabola and a line) is 4/3 that of a certain inscribed triangle.

Archimedes is considered one of the greatest mathematicians of all time. Archhimedes most famous proof culminates when he proves that 1/4 + 1/16 + 1/64 + ... = 1/3

To complete the proof, Archimedes shows that

1 \,+\, \frac{1}{4} \,+\, \frac{1}{16} \,+\, \frac{1}{64} \,+\, \cdots\;=\; \frac{4}{3}.

The formula above is a geometric series—each successive term is one fourth of the previous term. In modern mathematics, that formula is a special case of the sum formula for a geometric series.

Archimedes evaluates the sum using an entirely geometric method. Essentially what archimedes does is draw a quadrant and a quadrant within one square of that quadrant and a quadrant within one square of that quadrant making a square which has been dissected into an infinity of smaller squares. Each successive purple square has one fourth the area of the previous square, with the total purple area being the sum

\frac{1}{4} \,+\, \frac{1}{16} \,+\, \frac{1}{64} \,+\, \cdots.

However, the purple squares are congruent to either set of yellow squares, and so cover 1/3 of the area of the unit square. It follows that the series above sums to 4/3.

The way that archimedes does this is by drawing a quadrant, and then a quadrant within one square of that quadrant, and a quadrant within one square of that quadrant and so on. The proof reflects the quadrant model pattern.

This was Archimedes main proof and the one that he was most famous for.

Archimedes proofs regarding calculus represent the quadrant model pattern. The proofs of calculus themselves geometrically portray the quadrant model pattern.

The reason why students are required to memorize the quadratic equation is so that they can plot points on a cartesian coordinate grid. A cartesian coordinate grid is a quadrant and it is the foundation of all mathematics. Descartes created the Cartesian coordinate system and he claims that God gave him the inspiration to do so.

In mathematics, the quaternions are a number system that extends the complex numbers. They were first described by Irish mathematician William Rowan Hamilton in 1843 and applied to mechanics in three-dimensional space. A feature of quaternions is that multiplication of two quaternions is noncommutative. Hamilton defined a quaternion as the quotient of two directed lines in a three-dimensional space or equivalently as the quotient of two vectors.

Quaternions find uses in both theoretical and applied mathematics, in particular for calculations involving three-dimensional rotations such as in three-dimensional computer graphics, computer vision and crystallographic texture analysis.[5] In practical applications, they can be used alongside other methods, such as Euler angles and rotation matrices, or as an alternative to them, depending on the application.

In modern mathematical language, quaternions form a four-dimensional associative normed division algebra over the real numbers, and therefore also a domain. In fact, the quaternions were the first noncommutative division algebra to be discovered. The algebra of quaternions is often denoted by H (for Hamilton), or in blackboard bold by \mathbb H (Unicode U+210D, ℍ). It can also be given by the Clifford algebra classifications Cℓ0,2(R) ≅ Cℓ03,0(R). The algebra H holds a special place in analysis since, according to the Frobenius theorem, it is one of only two finite-dimensional division rings containing the real numbers as a proper subring, the other being the complex numbers. These rings are also Euclidean Hurwitz algebras, of which quaternions are the largest associative algebra.

Quaternions reflect the quadrant model pattern and are crucial in mathematics, considered one of the greatest mathematical findings ever.

Hamilton was looking for ways of extending complex numbers (which can be viewed as points on a 2-dimensional plane) to higher spatial dimensions. He failed to find a useful 3-dimensional system (in modern terminology, he failed to find a real, three-dimensional skew-field), but in working with four dimensions he created quaternions. According to Hamilton, on 16 October he was out walking along the Royal Canal in Dublin with his wife when the solution in the form of the equation

\displaystyle i^2 = j^2 = k^2 = ijk = -1

suddenly occurred to him; Hamilton then promptly carved this equation using his penknife into the side of the nearby Broom Bridge (which Hamilton called Brougham Bridge). This event marks the discovery of the quaternion group.

A plaque under the bridge, was unveiled by the Taoiseach Éamon de Valera (himself a mathematician and student of quaternions), on 13 November 1958.

Hamilton described a quaternion as an ordered four-element multiple of real numbers, and described the first element as the 'scalar' part, and the remaining three as the 'vector' part. The fourth part is always different from the previous three.

In mathematics, a regular 4-polytope is a regular four-dimensional polytope. They are the four-dimensional analogs of the regular polyhedra in three dimensions and the regular polygons in two dimensions.

Regular 4-polytopes were first described by the Swiss mathematician Ludwig Schläfli in the mid-19th century, although the full set were not discovered until later.

There are six convex and ten star regular 4-polytopes, giving a total of sixteen.

The sixteen are the sixteen squares of the quadrant model.

In geometry, a Kepler–Poinsot polyhedron is any of four regular star polyhedra.

They may be obtained by stellating the regular convex dodecahedron and icosahedron, and differ from these in having regular pentagrammic faces or vertex figures.

These figures have pentagrams (star pentagons) as faces or vertex figures. The small and great stellated dodecahedron have nonconvex regular pentagram faces. The great dodecahedron and great icosahedron have convex polygonal faces, but pentagrammic vertex figures.

The theorem on friends and strangers is a mathematical theorem in an area of mathematics called Ramsey theory. It is an extremely popular well known problem in mathematics.

The problem can be solved for up to four people and four lines. But with five people or five lines it cannot be solved even with complex computing. With four lines and four people the problem is difficult. With five it cannot be solved. The nature of the quadrant model is the fourth is always different. The fifth is questionable.

One philosophical theory is that everything is in a constant state of flux, therefore there is not really any thing, because the only constant is change-- “you can never step into the same river twice” according to Heraclitus. The principle behind everything is flux. Contemporary physicist say that particles are constantly going in and out of existence all the time. Biologist point out that a human constantly sheds skin, and cells in the humans body are constantly dieing and being replaced—a constant state of flux. Parmenides challenged this philosophy, saying that change is an illusion. Einstein was influenced by this idea; he was against the idea of quantum mechanics, which claimed that things were random and unknowable. Einstein said that he knew there was an order behind all things in the Universe--a perfect harmony, saying that “God does not play dice”. He called the universe a steady state. Einstein was said to be proven wrong when it was found that the Universe was expanding and accelerating in its expansion, and things are random, unknowable, and constantly changing, due to quantum mechanics. The constant used to discover the acceleration was a constant that Einstein had found. Einstein had discarded the constant, calling it a blunder, but it turned out to lead people to the idea that the Universe is accelerating. It turns out that maybe Einstein who said things are perfect and ordered and Bohr, who said they are random and disordered, may both be correct.

Melissus of Samos argued that the Universe must be eternal, using four statements that proved this. He said,

*Square one: Whatever comes to be must have a beginning

*Square two: The One did not have a beginning

*Square three: Therefore the One does not have a beginning

*Square four: Therefore the One is eternal

Melissus believed that there was one thing, or an Arche that underlies everything. This was a common notion among the pre-Socratics. This sounds like the notion of monotheism. Mellisus also argues that the One is incorporeal, changeless, and motionless, suggesting that he was aware of the quadrant model pattern. The quadrant model pattern is a changeless and eternal pattern that is a manifestation of the Form of Being. Nothing can “be” but the one Form of Being. There cannot be no thing. So the form must be eternal. It is also never changing because it is the only thing that can be.

Gorgias, another pre-Socratic philosopher, is labeled as a nihilist. He said that nothing can be known, and nothing exists. In the quadrant model the eighteenth square is non-being; Being is the seventeenth. Existence is an interplay between being and non-being--things are constantly going in and out of existence, and according to physicists so does the universe itself. According to the “Quadrant Model of Reality” nothing exists; everything is an expression of the quadrant Form of Existence. There is therefore no one thing. Everything is an illusion and connected to one formula/one form. The Gorgias argument fits the quadrant model pattern. He claims:

*Square one: Nothing exists

*Square two: Even if something exists, nothing can be known about it

*Square three: Even if something can be known about it, knowledge of it can not be communicated to others. The third premise is about communication. The third is always about doing.

*Square four: Even if it can be communicated, it cannot be understood. The fourth is knowledge and understanding, which points beyond the previous three.

The quadrant model points to Parmenides's philosophy--things seem different, and seem to change, but regardless there is one formula and one Being underlying everything. Zeno agreed with Parmenides. Zeno is famous for four main paradoxes, which he says describe the impossibility of motion. These four paradoxes fit the quadrant model pattern. They are

*Square one: the dichotomy paradox

*Square two: Achilles and the tortoise paradox.

*Square three: The Arrow paradox.

*Square four: The Stade paradox. The fourth paradox is different from the previous three. This is the nature of the quadrant model pattern.

Zenos’ Paradoxes

Dichotomy Paradox	Arrow Paradox
Achilles and the Tortoise Paradox	Stade Paradox

The missing square puzzle involves four figures.

The missing square puzzle is an optical illusion used in mathematics classes to help students reason about geometrical figures, or rather to teach them to not reason using figures, but only using the textual description thereof and the axioms of geometry. It depicts two arrangements made of similar shapes in slightly different configurations. Each apparently forms a 13×5 right-angled triangle, but one has a 1×1 hole in it.

A true 13×5 triangle cannot be created from the given component parts. The four figures (the yellow, red, blue and green shapes) total 32 units of area. The apparent triangles formed from the figures are 13 units wide and 5 units tall, so it appears that the area should be \textstyle {S={\frac {13\times 5}{2}}=32.5} units. However, the blue triangle has a ratio of 5:2 (=2.5), while the red triangle has the ratio 8:3 (≈2.667), so the apparent combined hypotenuse in each figure is actually bent. With the bent hypotenuse, the first figure actually occupies a combined 32 units, while the second figure occupies 33, including the "missing" square.

The amount of bending is approximately 1/28th of a unit (1.245364267°), which is difficult to see on the diagram of the puzzle, and was illustrated as a graphic. Note the grid point where the red and blue triangles in the lower image meet (5 squares to the right and two units up from the lower left corner of the combined figure), and compare it to the same point on the other figure; the edge is slightly under the mark in the upper image, but goes through it in the lower. Overlaying the hypotenuses from both figures results in a very thin parallelogram (represented with the four red dots) with an area of exactly one grid square, so the "missing" area.

Matsuyama has a missing square problem.

Mitsunobu Matsuyama's "Paradox" uses four congruent quadrilaterals and a small square, which form a larger square. When the quadrilaterals are rotated about their centers they fill the space of the small square, although the total area of the figure seems unchanged. The apparent paradox is explained by the fact that the side of the new large square is a little smaller than the original one. If a is the side of the large square and θ is the angle between two opposing sides in each quadrilateral, then the quotient between the two areas is given by sec2θ − 1. For θ = 5°, this is approximately 1.00765, which corresponds to a difference of about 0.8%.

Empedocles was a famous Greek pre-Socratic philosopher. He said that everything was based around the conflict of love and strife. He proposed a four stage cosmic cycle around the principal of love and strife.

*Square one: Pure domain of love, harmony. During this stage Empedocles says there is no life. This is the ideal stage. The first square is the Idealist. Life is bad, and in this stage there is not yet life.

*Square two: Contention between love and strife. During this stage there is a presence of life. There is a contention, but there is not yet any outright conflict. The second square is homeostasis. There is order in this square, but things are about to change.

*Square three: Pure domain of strife--chaos. Empedocles says in this stage there is outright conflict. The third square is the action square, it is bad and destructive. It is the doing square. There is no life in this stage, according to Empedocles.

*Square four: Contention between strife and love. Life is present in this stage. This is different from stage two in that in it love is fighting strife, and in stage four strife is fighting love. The fourth square is pointing beyond life to death.

The tetrapharmacon of the Greek Philosopher Epicurus was what Epircurus and the Epicureans were most known for. The four-way cure for moral health went as follows

Square 1: There is nothing to fear in God

Square 2: There is nothing to fear in death. The first two is the duality

Square 3: Good can really be attained.

Square 4: Evil can be readily endured

The Stoics held with four basic categories, all viewed as bodies (substantial and insubstantial): (1) substance in the sense of substrate, primary formless matter; (2) quality, matter's organization to differentiate and individualize something, and coming down to a physical ingredient such as pneuma, breath; (3) somehow holding (or disposed), as in a posture, state, shape, size, action, and (4) somehow holding (or disposed) toward something, as in relative location, familial relation, and so forth.

Plato was concerned with the creation of an ideal society. He said that governments undergo transformations. His description of the process of government change fits the quadrant model pattern. He calls this the five regimes.

*Square one: Timocracy--related to the Idealist. Plato says that timocracies are nice. The people in timocracies act as though they do not care about gold. Idealists often act as though they are spiritual and do not want to take part in the physical world. But idealists also want to belong, are conservative, and like the status quo. Plato says that people in timocracies secretly worship gold, but will not admit it. Socrates describes that that timocrats work on cultivating their virtues and intellects. This is the nature of the first square. But at the same time they are not content. Therefore timocracies become oligarchies. Asians are related to timocracies, sometimes acting as though they are not greedy, and are spiritual. Asians are the first square ethnicity.

*Square two: Oligarchy--distinguishes between the rich and the poor, making the rich their administrators. Keirsey's Guardians are related to oligarchies. Guardians are all about order and homeostasis. Guardians respect authority, hierarchy, and order. Guardians tend to be wealthy because they plan and are organized. Socrates thought that oligarch rulers make small armies so the poor will not rebel against them. Therefore oligarchies deteriorate because outside forces are too strong. Oligarchies degenerate into democracies.

*Square three: Democracy. The third square is about fun and doing. The third square is spontaneity. The third square is related to Keirsey's Artisan. Socrates describes that the supreme good in a democracy is labelled as freedom, but the poor get poorer and the rich get richer; everything becomes a popularity contest, and things are not decided by actual competence. Socrates says in a

democracy diversity is supreme, and people are allowed to do whatever they want, which leads to the downfall of democracy, as people begin to consume things that they do not need, becoming hedonistic, pursuing their desires and lusts, and nothing else. Inevitably disillusionment with democracy follows, creating an opening for a tyrant to emerge. Socrates says that the tyrant will be a smart man who is a philosopher. This leads to the fourth regime, the tyranny.

*Square four: Tyranny. The fourth is different from the previous three. The fourth is related to the Rational personality type. Rationals are philosophers, This leaves a power vacuum where a philosophical, intelligent tyrant seizes control. The tyrant must kill his enemies, which makes many enemies. Then the tyrant has to protect himself and his family with a lot of body guards. There are many people who want to kill him, and in order to not be killed the tyrant has to continue to kill his enemies. But in so doing he makes more enemies. The tyrant has such complete power that he begins to act lawlessly, becoming extremely blood thirsty. Socrates says that out of the tyranny emerges an aristocracy. The forth square is related to the philosopher and can be seen as bad.

*Square five: Aristocracy. Plato describes this as the ideal form of government, transcending all others. The fifth is related to God; the Kingdom of God. He makes a proposition of how a society can run in a three caste system, but realizes that this too will deteriorate. Finally he gives a metaphor of a perfect society, picturing each of the three castes as a type of animal. He says one is a human, one a lion, and one a bird. He said to put these three animals within a human, which represents the form of an ideal society. What Socrates described was the quadrant model pattern. Socrates put three elements within a fourth element; that is the nature of the quadrant model. In it there are three squares that are consumed by a fourth square. It is also interesting that philosophers note that this image is like a fractal image. It can be proposed that the human that these three elements are in is in another human with another lion and eagle. Then that human is another human with another lion and eagle next to it--so on and so forth, forever. Fractal mathematics is integral, physicists think, in the construction of reality. It is interesting that Plato may have intentionally drawn a fractal.

Platos’ governments

Timocracy	Democracy
Oligarchy	Tyrany

Aristocracy

Plato proposed the existence of four virtues that people possess. These virtues fit the quadrant model pattern. They are

*Square one: Wisdom. The first square is always related with the mind. This is related with Keirsey's Idealist temperament.

*Square two: Temperance--related with the Guardian. Temperance is the ability to control oneself.

*Square three: Courage. This is related to the Artisan temperament. Courage is related with doing. The third square is doing. Courageous people are willing to put themselves on the line, doing things that are dangerous, and often considered bad or destrictive.

*Square four: Justice--the consequence of the harmony of the other three

virtues. In other words, Justice involves the other three virtues. The fourth is always different, yet encompasses the previous three. Where there is synergy between wisdom, temperance, and courage, there is justice. Justice is related to the Rational temperament.

Cicero sketched and is famous for his scheme of ethics, which was based on the traditional cardinal virtues. The four-fold scheme consisted of:

Square 1; A life of wisdom or contemplation,

Square 2:A life of justice and beneficence,

Square 3: A life of courage of loftiness and strength of mind, and

Square 4: A life of temperance or moderation and propriety.

Plato’s Virtues

Wisdom	Courage
Temperance	Justice

Plato's famous allegory of the cave was designed to describe reality. He said that apparent reality is only a shadow of true reality, which he called the World of Forms, an eternal and unchanging reality. Socrates said that reality derived from One Form. The theory proposed by the Quadrant Model of Reality is that this form is the form of the cross.

Plato used an illustration called the divided line to describe the nature of reality. The divided line fits the quadrant model pattern.

*Square one: This is the square of imagining. According to Plato this is the square of sensation and perception. The first quadrant is the sensation and perception quadrant. Plato describes that the world that is sensed and perceived is an illusion' this level of knowledge is therefore unsatisfactory. Plato said that sensations and perceptions are just shadows of the true reality.

*Square two: Plato labels this section of the divided line belief. The second quadrant is belief and faith. Plato said that beliefs are about physical things in the physical world. He says that this section is also faith, that beliefs are not grounded in reality, and that physical things are not real.

*Square three: Plato labels this section of the divided line thinking. The third quadrant of the quadrant model is the thinking and doing quadrant. Plato describes that people at this level of knowledge perform mathematical reasoning. Mathematics is a form of doing; when you perform mathematics, a part of the performance is pointing and gesturing and writing itself. A part of thinking is actions performed with the body. This is the doing square.

Square four: Plato labels this square knowledge. The fourth quadrant of the quadrant model is the knowledge quadrant. Plato says that knowledge is recognition of the world of Forms, and that reality is a reflection of a true reality, which is a world of Ideas and Forms. He says that knowledge of this reality comes through conversations with people, which he calls dialectic. The fourth square is social, and points beyond itself. Plato's dialogues themselves are his written records of conversations between Socrates and other people. Socrates would often take an opposite viewpoint of another person, and in his argument eventually try to come up with the Truth. This contrasted with sophists who would argue to try to prove a point that they were trying to make and didn't care about discovering the Truth. Plato says that ultimate knowledge is knowledge of the Form of the Good; out of this Form everything derives. This form is the form of the cross and the quadrant model pattern which permeates from it.

Plato’s Divided Line

Imagining	Thinking
Belief	Knowledge

Plotinus is the father of Neoplatonism and gnostic belief. He is the most famous philosopher who came after Plato and Aristotle. According to Plotinus there are four levels of being. The levels fit the quadrant model. They are.

Square 1: matter. This is the sensible world which Plotinus declared was an illusion. The first square is sensation and perception.

Square 2: the soul. this is the world soul and the soul of humans. Plotinus said time is the life of the soul. The second square is time.

Square 3: the intellect. Plotinus said that this was the world of forms and the demiurge who was the first mover who fashions all being through intellect.Gnostic philosophers say the demiurge fashioned material existence but they say He is actually kind of evil because the world is a mind of prison and illusion.

Square 4. The one. This is the ineffable Form of the Good that Plato describes, says Plotinus. As I portrayed in this book that form is the quadrant. Plotinus was said to have achieved union with the One four times in his life.

Plato says that knowledge of geometry is essential to knowing the world of Forms. Geometry is mathematics dealing with shapes. Plato gives a mathematical statement which suggests that the first section of the divided line is smaller than the second section, and the third section is the same as the second section, and the fourth section is bigger than the third section. But he also says that each section is larger than the section previous to it. This is a contradiction because he previously says that the third and second sections are the same size. Some people thought that Plato made a mistake in his mathematics. Others said that he purposefully did this to get people to question him, and also to show that contradictions in reality are a part of the nature of reality. Plato may also have been trying to reveal that his model of the divided line is holistic, I propose. The quadrant model is holistic, each square building on the previous square, with each square containing the elements of the square before it, while also adding to it.

Plato is known for the five platonic solids. In the dialogue of the Timeaus Socrates hypothesizes that these perfect polyhedrons are related to the five elements. Kepler used the platonic solids to explain the distances of the planets from each other, although scientists today say that Kepler was incorrect in his mathematics. Euclid, a famous Greek Mathematician, wrote the criteria for the platonic solids. The criteria fit the quadrant model pattern. They are

*Square one: Each vertex of the solid must coincide with one vertex each of at least three faces.

*Square two: At each vertex of the solid, the total, among the adjacent faces, of the angles between their respective adjacent sides must be less than 360°.

*Square three: The angles at all vertices of all faces of a Platonic solid are identical: each vertex of each face must contribute less than 360°/3 = 120°.

*Square four: Regular polygons of six or more sides have only angles of 120° or more, so the common face must be the triangle, square, or pentagon. The platonic solids are Square one: tetrahedron; Square two: cube; Square three: octahedron; Square 4: dodecahedron; Square 5: icosahedron.

These solids are all connected to each other, and relate to each other. The dodecahedron was seen as divine, and its existence was kept secret. A fascinating thing is that some physicists have suggested that the shape of the Universe is a dodecahedron. A dodecahedron is like the shape of a soccer ball. It is interesting that biologist have discovered that viruses take shapes such as the shape of the icosahedron. Plato said each one represented one of the five elements. The fifth Plato said was transcendent and represented the Universe as a whole or God. It is interesting to note that physicists today do say that the Universe may be the shape of a dodecahedron, because evidence points to that. The fifth is always ultra transcendent. The dodecahedron was so transcendent that the Ancie philosophers like the Pythaogoreans said that its existence could not be known to the normal average human

Square 1: icosahedron. The icosahedron Plato said was air.

Square 2: octahedron. Plato said this was water.

Square 3:Cube. Plato said this was stable and related to Earth

Square 4:tetrahedron . Plato said it was pointy like fire.

Square 5: dodecahedron. Plato said it is the shape of the Universe and was like God. The fifth square is related to God.

The tetrahedron is the first manifested polyhedra,believed by Plato to equate with the element of fire.

in our Fibonacci circle,it is generated by the interaction of the star configuration formed by the 3,the 6 and the 9.

In qabalistic thinking,the tetrahedron is held to self-replicate into a star tetrahedron,as a primary manifestation of duality.In the instance of our device this means that it drops below and forms another tetrahedron from the remaining 3,6 and 9.

The vertices of this emergent star tetrahedron (the Merkaba) supply all the points of manifestation of the next two solids,The cube and the Octahedron,a pairing of solids which are held to manifest coterminously with each other

Pythagorean Tetrad

Four is the first number formed by the addition and multiplication of equals..

To the Pythagoreans this symbol and number represented justice as it is the first number that is divisible every way into equal parts.’’

Plato searched for an ideal form of government, and evoked a world of Forms for being the organizing principle behind reality. Aristotle used both his intuition as well as his experience to describe reality. He was very prolific in his ideas, even studying olympic athletes who won olympic events. Among other things, he is known for his four causes, which fit the quadrant model pattern. These four causes are causes of movement.

*Square one: Material cause--determined by the material of which it is composed. The material cause of a basketball might be rubber.

*Square two: Formal cause--related to the arrangement of a thing. Aristotle uses the example of octaves, and the 2:1 ratio of the string being the cause of the octave. The formal cause of a basketball might be its density and the way its texture is arranged. The second square is order and structure--the nature of the second square.

*Square three: Moving cause/efficient cause. The third square is the doing square; it is always related to movement. The moving cause according to Aristotle is something apart form the object being moved; it is interacting with the object, causing it to move. The efficient cause of a basketball may be a basketball player.

*Square four: Final cause--the purpose for which something is being moved. The purpose of moving a basketball is to have it go through a net. The purpose of a bullet might be to kill a living organism. These four causes inspired Tinbergen's four questions. Aristotle argued that there must be a primary mover that caused everything to move. Aristotle says that for every effect there was a cause, and there must have been a first cause. This, some scientists say is corroborated by the big bang theory. Physicists who study the multiverse and M theory suggest that the first cause might have been two primordial membranes colliding, the product of which was the big bang. Others say that this Universe was created from another Universe in the multiverse, which leaves a question regarding what created the multiverse that created this universe. Still Aristotle says there needs to have been a primary mover. Many have taken this to mean that Aristotle believed in a God that started everything.

A Hoberman sphere is not a true sphere, but a polyhedron known as an icosidodecahedron. The Hoberman sphere can be unfolded by allowing certain members to spread apart. This can be accomplished by feeding out a string or cable in the larger models. The operation of each joint is linked to all the others in a manner conceptually similar to the extension arm on a wall-mounted shaving mirror.

Clearly the shape of the swastika (6-leg version) plays a critical role in the operation of this sphere.

note the 16 point configuration is similar to the 16 wind Compass Rose that we find in St. Peter’s Square.

16 is the number of squares in the quadrant model

Aristotle’s causes

Material Cause	Moving Cause
Formal Cause	Final Cause

The four major philosophical arguments for the existence of God are

Square 1: the ontological argument

Square 2: the first cause argument

Square 3: the argument from design,

Square 4: the moral argument.

Franz Brentano held that any major philosophical period has four phases: (1) Creative and rapidly progressing with scientific interest and results; then declining through the remaining phases, (2) practical, (3) increasingly skeptical, and (4) literary, mystical, and scientifically worthless – until philosophy is renewed through a new period's first phase. (See Brentano's essay "The Four Phases of Philosophy and Its Current State"

C. S. Peirce, usually a trichotomist, discussed four methods for overcoming troublesome uncertainties and achieving secure beliefs: (1) the method of tenacity (policy of sticking to initial belief), (2) the method of authority, (3) the method of congruity (following a fashionable paradigm), and (4) the fallibilistic, self-correcting method of science (see "The Fixation of Belief", 1877); and four barriers to inquiry, barriers refused by the fallibilist: (1) assertion of absolute certainty; (2) maintaining that something is absolutely unknowable; (3) maintaining that something is absolutely inexplicable because absolutely basic or ultimate; (4) holding that perfect exactitude is possible, especially such as to quite preclude unusual and anomalous phenomena (see "F.R.L." [First Rule of Logic], 1899).

Paul Weiss built a system involving four modes of being: Actualities (substances in the sense of substantial, spatio-temporally finite beings), Ideality or Possibility (pure normative form), Existence(the dynamic field), and God (unity). (See Weiss's Modes of Being, 1958

John Boyd (military strategist) made his key concept the decision cycle or OODA loop, consisting of four stages: (1) observation (data intake through the senses), (2) orientation (analysis and synthesis of data), (3) decision, and (4) action. Boyd held that his decision cycle has philosophical generality, though for strategists the point remains that, through swift decisions, one can disrupt an opponent's decision cycle.

Richard McKeon outlined four classes (each with four subclasses) of modes of philosophical inquiry: (1) Modes of Being (Being); (2) Modes of Thought (That which is); (3) Modes of Fact (Existence); (4) Modes of Simplicity (Experience) – and, corresponding to them, four classes (each with four subclasses) of philosophical semantics: Principles, Methods, Interpretations, and Selections

Pythagoras was another pre-Socratic philosopher. He is credited for having discovered the pythagorean theorem, which says that the square of two sides of a right angle triangle equals the square of the hypotenuse of the triangle. It is also argued that one of his students made the discovery, but Pythagoras took the credit for it. He had his own academy, which resembled a cult--the group worshipped the tetragrammaton, a pyramid with one dot, then two dots, then three, then four. It is the set up of bowling pins, which resembles the quadrant model, in that there are four sections, each one building upon the next. The Pythagoreans worshipped this symbol. Another important symbol in ancient cultures was the tessellation of the isosceles triangle. This yielded an isosceles triangle within three isosceles triangles. This symbol was also seen as highly sacred, apparently because it represents the quadrant model Form of Existence. There are four squares, and the fourth is within the previous three, repeating the nature of the quadrant model pattern--the fourth encompasses the previous three.

The pythagoreans believed that the foundation of existence was mathematics. The Pythagoreans believed all mathematical science was to be divided into four parts, portraying the quadrant model pattern. The four parts were. Again, the pythagoreans envisioned a two fold. One dichotomy was quantity in regard to its character in itself and quantity in relation to others. The other was magnitude which was either stationary or in motion. These two dichotomies yielded the quadrivium, which was how the ancients divided the science.

Square 1: arithmetic is number in itself

Square 2: music is number in time

Square 3: geometry is number in space

Square 4: cosmology is number in space and time.

In Plato’s dialogue Meno, Socrates tries to prove the immortality of the soul by showing that knowledge was recalling. Socrates said that souls are originally from the world of forms, and when people learn things, they are not really learning, but are recalling what they already knew from the world of forms. To do this Socrates drew in the sand 16 squares and performed geometry with a slave boy. Socrates showed that the slave boy could understand the geometry despite having never received an education. Socrates said therefore the boy must be recalling what he knew from the world of forms. It is important to see though that to prove the immortality of the soul Socrates drew 16 squares into the sand. Socrates drew the quadrant model.

CHAPTER XXVII: The Pattern of Four in Political Spectrums

Political spectrums fit the quadrant model of reality. An example is the Nolan chart. The Nolan chart has two dichotomies. One is much political freedom and little political freedom. The other is much economic freedom and little economic freedom. This yields four types.

*Square one: Much personal freedom and little of economic freedom. These are liberals. Having much personal freedom allows for doing things like staying up late and partying and doing drugs. Liberals tend to fight for women’s rights to behave as they wish, having abortions if they want, and for minorities rights and gay rights. The first square corresponds with idealists, who are abstract, and thus open minded. Liberals are “politically correct”, but ironically they fight against people who are not politically correct. The first square is the Idealist personality type, who are abstract and cooperative. Being abstract corresponds with a desire for personal freedom and open mindedness and seeing everybody as one and thus having compassion for everybody, and being cooperative corresponds for a desire for government control over economic arenas. Liberals tend to be communists. The first square race is Asians. Asian cultures throughout Asia, including Russia, have been the most associated with being communist. People think communists are for equal rights for everybody, but really communists give considerable power to the state for economics, and the state discriminates against races, and helps the group in power. Communist nations have always brought about discrimination and oppression based on race. Idealists often act as though they are very compassionate and want equal rights for everybody, but really they have agendas and often in their desire to centralize power in the state, know that the power will be used to continue white supremacy. Idealists tend to like White people because White is the second square, and idealists are the first square. Liberals actually like the group in power, and by giving power to the state they help to maintain the status quo. Idealists love the status quo, and covertly worship the upper class, although they act as though they are compassionate for all people. Liberals do the same. Liberals tend to want economic controls to fight things like global warming and other issues, but they have other agendas. The first quadrant is awareness, and liberals are cautious of global problems. Idealists tend to be aware and perceptive, and want things like global warming and the harming of animals to be mitigated by economic controls. Szasz, a psychiatrist who is against psychiatry though, argues that liberals use their proclaimed politically correct desire for compassion for the less fortunate and all people to really harm the less fortunate. For instance, he describes that liberals like to state that they want to help “mentally ill people”, but really they use their proclaimed compassion to force people labelled mentally ill against their will to be “helped” through harmful medication that actually hurts them. He argues that liberals talk the same way about Black people, speaking to Black people and about Black people as if they are children and they want to help them, but then placing government programs and an environment that is not optimal for Black people.

*Square two: Little personal freedom and much economic control. These are statists. Little personal freedom corresponds with being concrete, and wanting much economic control corresponds with being cooperative. Unlike abstract liberals, the concrete statists are not concerned with political correctness, and are more against things like women’s rights to get abortions and peoples rights to do drugs. This square corresponds to the Guardian personality type. Guardians are concrete and cooperative Statists are associated with belonging; they all do the same things. The second quadrant is the belonging quadrant. The second square race is White people, who tend to be more into belonging and desire for everybody to have the same and correct belief system and behaviors and if you do not then they look down on you and employ insider outsider good guy bad guy consciousness. White is the second square race, and White countries throughout history have been associated with being statist. White people have the stereotype of being tight assed and like the status quo.

*Square three: Conservatives--want less personal freedom and more economic freedom. More economic freedom means that they want a free market. They want less personal freedom, because they are not abstract and open minded like liberals, but are more concrete and simple minded and ego driven. Conservatives corresponds with the Artisan who is concrete and utilitarian. Utilitarians want free markets. Artisans want to excel, have their own businesses, and care less about equality, and they want to do what they want. They are more independent individuals. But artisans are concrete. Abstract idealist people are open minded and like to act as though all people are equal and that women should be allowed to do what they want and minorities and everybody. Liberals are stereotypically sensitive and perceptive, and want government control to fight global warming and the harming of animals and other liberal agendas. Black is the third square race. Artisans and Black people stereotypically are not as sensitive and want freedom to do what they want to do economically, not caring about the environment, but they are stereotypically not as open minded and don’t see everything as one like abstract people, so they do not care about seeming politically correct as much, and rather than beating around the bush with their racism and desires to harm unwanted people of society, like Szasz says liberals do, they blatantly let people know how they feel and are not afraid to hurt peoples’ feelings. Black is the third square race, and Black people have the stereotype of being conservative. Black people stereotypically are not very concerned with things like global warming and wanting a centralized economic mechanism to determine what cars you can drive and being nice to everybody and so on and so forth. Liberals tend to be into things like environmentally friendly cars and eco friendly houses. Black people stereotypically are not too concerned and aware of such things. Black countries stereotypically are more conservative. It is the stereotype that African countries are not big fans of gay rights, or women’s rights like the right of abortion and to wear whatever you want, and so on and so forth. An explanation for why Black people might be more into economic freedom and less into personal freedom is there is a lot of genetic diversity among Blacks, so Blacks do not mind having non communistic societies where Blacks try to outdo other Blacks. But also they do not like personal freedoms like gay rights and freedom of abortion because each Black person wants to spread his genes as much as possible, and with abortion illegal each one has a higher chance of doing so. Also Blacks do not want to have gay children who will not spread their genes. Whites and Asians are more communal, wanting little economic freedom, perhaps because Whites and Asians are so genetically related, and there is little genetic diversity within the races, so they wqant equality among all of their members. This would be a biological explanation to explain the differences.

*Square four: Libertarians--favor both personal and economic freedom. This corresponds with the Rational, who is abstract and utilitarian. Libertarians are not worried about forced economic equality, so they are not into stifling economic freedom. They say that there is not a scarcity of resources. They point out things that are myths in the modern world, like when there is plenty in one place this causes scarcity in another. They say that this is a myth and that just because one group is thriving it does not mean it is because it is causing the groups that are not thriving not to thrive. So long as there is no global control system they say this is not true that one peoples prosperity causes another people’s lack of prosperity. So they fight against central economic controls, and do not want a central organization fighting things like global warming, which they say is a pretense for more sinister motivations. Libertarians do not want any economic controls, and feel that if there is a free market, then things will work out and the environment and problems like global warming will be naturally mitigated. They say there is not a limited amount of resources in the world and there does not need to be economic controls. Libertarians are abstract and are open minded, and they are politically correct and they do see everybody as one and want what is best for women, and the disenfranchised, and minorities, and so forth. They do not want laws stifling peoples’ personal freedoms, so they say that if women want abortions that should be ok, and if people want to do drugs they should be allowed to and if gays want to get married, let them. They argue that people should be allowed to do what they want. Szasz is a libertarian and argues that people should have the personal freedom to deny coerced medical treatment in psychiatry, and not be forced by liberals who want to “help” them to take the treatment they prescribe. But being utilitarian, libertarians feel the best way for a just society to be accomplished is with little government economic control. The race associated with the fourth square is brown people. Libertarians say that if people want to be racist they can, if they want to be for gay marriage they can, if they do not want to they can. Libertarians say that there should be personal freedom and no economic coercion. They point out that a lot of people say things like “fuck racism” but they employ the same consciousness that racism employs, good guy bad guy consciousness, pointing at people called racist and saying they are the bad guys like how racists look at people of a race and call them bad. Libertarians say that the government creates environments that produces racism and they say that governmental interference should be taken out and people would be happier. They say that the government creates environments where whites feel threatened by Blacks and this creates racism. For instance there are laws that say if a teacher says anything bad about Black he gets fired but they say that blacks can be racist against whites and there is less repercussions and they say that such laws facilitate racism. They point out that there is not a free market and the government helps corporations stay rich and the corporations contribute to atmospheres that maintain white supremacy and the status quo. For example, libertarians argue that corporations maintain organizations like bet that do not help Black people but harm the Black community. Libertarians believe that if the government stayed out of personal and economic freedoms and people didn't feel coerced to be certain ways people would be better off. For instance, libertarians say that Martin Luther King did not help blacks because he gave the government more power. The government was given more power to try to enforce integration, but this was the same government that enslaved blacks and benefitted off of white supremacy. So libertarians argue by giving the government more power, in fact what happened was the government implemented new legislation that maintained the status quo. Libertarians argue that the government should not have been given more power and blacks should have been allowed to decide whether they want to integrate or not and nobody should be forced to do something, because libertarians feel the government has sinister motivations. If you think about it, libertarianism kind of boils down the ideology of let people be what they want to be, whether it be conservative, liberal, or statist, and do not bother them. Again, the forth kind of encompasses the previous three.

The Nolan Political Spectrum Chart

liberals	conservatives
statists	libertarians

Another example of a political chart that fits the quadrant model pattern is the political compass. This chart is very similar to the Nolan chart. Another popular political chart is the Pournelle chart. This chart also fits the quadrant model pattern. There are two axis on this chart. One dichotomy is irrational vs. reason enthroned. This axis is called rationalism. The other dichotomy is state as the ultimate evil vs. state worship. This axis is called statism. These two dichotomies yield four results which resemble the quadrant model pattern. They are:

*Square one: Reason enthroned and state worship. According to Pournelle this includes welfare liberals, communists, and socialists. This corresponds with the idealist personality type. Reason enthroned corresponds with being abstract,

and state worship corresponds with being cooperative. Asians are the first square and Asians are associated with communism.

*Square two: Irrational and state worship. This is tied to the Guardian personality type. Irrational relates to being concrete, and state worship relates to being cooperative. This square, according to Pournelle, includes the Nazis and the fascists. It would also include an orthodox Jewish society. Nazism and Orthodox Judaism are very similar. People have made national socialism synonymous with evil, but really it is not. Europeans are the second square and Europeans are related with Nazism and fascism.

*Square three: Irrational and state as the ultimate evil. This relates with the Artisan personality type. Irrational relates to being concrete, and seeing the state as evil corresponds to being utilitarian. Utilitarians want to do what they want. They do not want people telling them what to do. Pournelle says that anarchists and the american counterculture fit into this category. Blacks are the third square race and Blacks are the most associated with anarchism and counterculture.

*Square four: Reason enthroned and state as the ultimate evil. This relates to the rational personality type. Reason enthroned relates to being abstract and state as the ultimate evil relates to being utilitarian. This model is exactly analogous to Nolan’s model. Again the Libertarians fit in this category. Pournelle says examples of systems that belong in this category are Libertarians, Max Stiner, and Ayn Rand. They encourage people to excel and think this is good for everybody ultimately, which is related to the concept of the flow. Brown people are the forth square race. The forth encompasses the previous three and brown people are in all of these types but are most associated with libertarianism.

In capitalist economic structures, supply and demand is an economic model of price determination in a market. It concludes that in a competitive market, the unit price for a particular good will vary until it settles at a point where the quantity demanded by consumers (at current price) will equal the quantity supplied by producers (at current price), resulting in an economic equilibrium for price and quantity.

The four basic laws of supply and demand are:[137]:37

If demand increases (demand curve shifts to the right) and supply remains unchanged, a shortage occurs, leading to a higher equilibrium price.

If demand decreases (demand curve shifts to the left) and supply remains unchanged, a surplus occurs, leading to a lower equilibrium price.

If demand remains unchanged and supply increases (supply curve shifts to the right), a surplus occurs, leading to a lower equilibrium price.

If demand remains unchanged and supply decreases (supply curve shifts to the left), a shortage occurs, leading to a higher equilibrium price.

Business cycle with it specific forces in four stages according to Malcolm C. Rorty, 1922

Revival

Prosperity

Liquidity

Depression

In 1860 French economist Clement Juglar first identified economic cycles 7 to 11 years long, although he cautiously did not claim any rigid regularity.[6] Later[when?], economist Joseph Schumpeter (1883–1950) argued that a Juglar Cycle has four stages:

expansion (increase in production and prices, low interest-rates)

crisis (stock exchanges crash and multiple bankruptcies of firms occur)

recession (drops in prices and in output, high interest-rates)

recovery (stocks recover because of the fall in prices and incomes)

The Soviet economist Nikolai Kondratiev (also written Kondratieff) was the first to bring these observations to international attention in his book The Major Economic Cycles (1925) alongside other works written in the same decade.[3][4] Two Dutch economists, Jacob van Gelderen and Samuel de Wolff, had previously argued for the existence of 50- to 60-year cycles in 1913.

In 1939, Joseph Schumpeter suggested naming the cycles "Kondratieff waves" in his honor.

Since the inception of the theory, various studies have expanded the range of possible cycles, finding longer or shorter cycles in the data. The Marxist scholar Ernest Mandel revived interest in long-wave theory with his 1964 essay predicting the end of the long boom after five years and in his Alfred Marshall lectures in 1979. However, in Mandel's theory, there are no long "cycles", only distinct epochs of faster and slower growth spanning 20–25 years.[citation needed]

The historian Eric Hobsbawm wrote of the theory: "That good predictions have proved possible on the basis of Kondratiev Long Waves—this is not very common in economics—has convinced many historians and even some economists that there is something in them, even if we don't know what." [5]

Characteristics of the cycle

Kondratiev identified three phases in the cycle: expansion, stagnation, recession. More common today is the division into four periods with a turning point (collapse) between the first and second phases. Writing in the 1920s, Kondratiev proposed to apply the theory to the 19th century:

1790–1849 with a turning point in 1815.

1850–1896 with a turning point in 1873.

Kondratiev supposed that, in 1896, a new cycle had started.

1. (1600–1780) The wave of the Financial-agricultural revolution

2. (1780–1880) The wave of the Industrial revolution

3. (1880–1940)Third square is doing. The wave of the Technical revolution

4. (1940–1985) The wave of the Scientific-technical revolution. The fourth is the rational..

5. (1985–2015) The wave of the Information and telecommunications revolution. The ultra transcendent

Karl Marx was the founder of the philosophy named after him, Marxism, which taught that the proletariat masses were exploited by the bourgeoise upper class, and therefore one day will revolt and establish a more just society. Central to Marx's theory was his notion of alienation. Marx declares that there are four types of alienation. They are

Square 1: Alienation of the worker from the work — from the product of his labour

Square 2: Alienation of the worker from working — from the act of producing

Square 3: Alienation of the worker from himself, as a producer — from his Gattungswesen (species-essence)

Square 4:IV) Alienation of the worker from other workers

It was out of this alienation, and the central tenet of Marx's theory was alienation of the workers, a revolution would be spawned

According to Marx, the mode of production which determines the general character of social, political, and spiritual processes of life is the main cause of social change.

As methods and techniques of production change the social relations which follow them also change. Against this background Marx describes four stages in history. They are:

a. Primitive Communism

b. Slavery

c. Feudalism

d. Capitalism

Machiavelli is one of the most famous political philosophers of all time. Machiavelli taught princes how to rule. He taught princes that their subjects should fear them, and he is said to have been very practical and pragmatic and historians call him a realist. Machiavelli side stepped Christian morality which would say that it is a virtue to be loved, and instead taught that it is better to be cruel than merciful, and to invoke fear on your subjects. However, some have proposed that Machiavelli was sardonic and was lampooning people with such views, and there are historians who say that there is evidence for this stance. Machiavelli, in his classic The Prince, models four types of principalities. They are

Square 1: Hereditary principalities, which are inherited by the ruler

Square 2: Mixed principalities, territories that are annexed to the ruler's existing territories

Square 3New principalities, which may be acquired by several methods: by one's own power, by the power of others, by criminal acts or extreme cruelty, or by the will of the people (civic principalities) The third is always bad.

Square 4: Ecclesiastical principalities, namely the Papal States belonging to the Catholic church. The fourth is transcendent.

In his book he also lays out the types of armies. They are

Square 1: Mercenaries or hired soldiers, which are dangerous and unreliable. They cannot be trusted because they are not fighting with fervor for their land and are just fighting for wages. The first square is not the doer and not that great at doing.

Square 2: Auxiliaries, troops that are loaned to you by other rulers—also dangerous and unreliable. These are better than mercenaries, but the second square still is not the doing square.

Square 3: Native troops, composed of one's own citizens or subjects—by far the most desirable kind. The third square is the doing square with the most ability

square 4: Mixed troops, a combination of native troops and mercenaries or auxiliaries—still less desirable than a completely native army. The fourth square encompasses the previous three. This is the nature of the quadrant model of reality.

The book itself is divided into four parts. They are

Square 1: Chapters 1-11 discuss the different types of principalities or states, Square 2: Chapters 12-14 discuss the different types of armies and the proper conduct of a prince as military leader,

Square 3: Chapters 15-23 discuss the character and behavior of the prince. The third square is the doing square

Square 4: Chapters 24-26 discuss Italy's desperate political situation.

George Orwells book 1984 was a classic novel about a dystopia future where a totalitarian regime new world order takes over and keeps the masses enslaved and worshipful of Big Brother, who represents the state which they are forced to revere. Orwells book 1984 , as well as his book animal farm, are critical looks at communism. Orwell notices that communistic regimes demand worship of the state, and while they offer nice sounding ideas, what they produce is detrimental. Instead of worshipping God, the people worship the state, and the state exploits them. In 1984 there are four ministries that control people's lives. Every aspect of people's lives is controlled. But there is no religious morality in the new world order. A fear that people have against communism is that it is liberal and replaces God with the state, and gets rid of morality. For instance, in this new world order pornocorp is funded by the state and gives its citizens porn, keeping the exploited masses appeased and dehumanized so that they will stay in their places. They four ministries actually do the opposite of what their names suggest. They are
Square 1: the ministry of peace which concerns itself with war, fighting any groups that seek to overthrow the communist regime. The end of the book raised the question of the wars are actually made up and fabricated in order to keep the citizens afraid and in their places.
Square 2: the ministry of truth which concerns itself with lies, teaching people falsehoods in order to keep them in their places and content
Square 3: the ministry of love which performs torture against dissidents of the state. Thomas Szasz is a psychiatrist who condemned communism because he felt that it's liberal ideologies were used to torture dissidents through psychiatry under the facade of helping them with "mental illnesses".
Square 4: the ministry of plenty which created starvation and lack of rations keeping the masses weak and unable to revolt.
A famous lie that is taught to the citizens of this new world order is 2 + 2 is 5. Two plus two is four is a truth that Socrates pointed out everybody knew. Two plus two is four is the make up of the quadrant model. But in this society people are taught that there is no truth. A fear of communism was that it was so liberal that it enforced that there was no truth in morality or anything.
People say that Orwell was lampooning modern society, and people cynically say that 1984 is the current world order.
George Orwell has another book about a dystopian future called a brave new world. In the book there is a four caste system, resembling the quadrant model pattern. In the Hindu Vedas there is a drug called soma. Again, in communist societies people are liberal so there is less strict moral codes, so people are encouraged to have orgies and take a drug called soma which keeps them pacified and sort of automatons for the state. Thomas Szasz again was hostile toward communistic ideology, seeing it as a liberal way of harming unwanted members of society while pretending to help them, Szasz would argue that the soma in today's world, which keeps the masses tranquilized and in their places is psychiatric medication. Orwell would see Kim

Jung ins North Korea as an example of the totalitarian state he fought against where the leader is worshipped and the masses are exploited.

The “9/11” disaster reveals the quadrant model as follows:

*Square one: World trade center tower one

*Square two: World trade center tower two. These two are the duality. To many throughout the world the world trade center represents greed and empire.

*Square three: Pentagon. The third is the most solid; it is a war building and a building for the United States military.

*Square four: The fourth plane landed on the ground and disappeared. The fourth always seems not to belong with the other three. The fourth always seems different and almost as if not to exist.

The Solonian Constitution was created by Solon in the early 6th century BC. At the time of Solon the Athenian State was almost falling to pieces in consequence of dissensions between the parties into which the population was divided. Solon wanted to revise or abolish the older laws of Draco. Solon promulgated a code of laws embracing the whole of public and private life, the salutary effects[2] of which lasted long after the end of his constitution.

Under Solon's reforms, all debts were abolished and all debt-slaves were freed.

Solon instituted a timocracy, and those who did not belong to the nobility received a share in the rights of citizens,according to a scale determined by their property and their corresponding services to the Athenian State. For this purpose he divided the population into four classes, founded on the possession of land.

Square 1: Pentacosiomedimni

Square 2: Hippeis

Square 3: Zeugitae

Square 4: Thetes. The fourth class was different from the other three, the nature of the quadrant model.

Solon's legislation only granted to the first three of these four classes a vote in the election of responsible officers, and only to the first class the power of election to the highest offices; as, for instance, that of archon. The first three classes were bound to serve as hoplites; the cavalry was raised out of the first two, while the fourth class was only employed as light-armed troops or on the fleet, and apparently for pay. The others served without pay. The holders of office in the State were also unpaid.

Each division had different rights; for example, the pentacosiomedimnoi could be archons, while thetes could only attend the Athenian assembly. The fourth class was excluded from all official positions, but possessed the right of voting in the general public assemblies (the Heliaia) which chose officials and passed laws. They had also the right of taking part in the trials by jury which Solon had instituted.

Solon established as the chief consultative body the Council of the Four Hundred, in which only the first three classes took part, and as chief administrative body the Areopagus which was to be filled up by those who had been archons.

The bible is full of 40s and 400s. I do not think it is a coincidence. It think numbers preceding in four are so important because they bring to mind the quadrant.

The stately quadrille is a term popularly used to describe the constantly shifting alliances between the Great Powers of Europe during the 18th century. The ultimate objective was to maintain the balance of power in Europe, and to stop any one alliance or country becoming too strong. It takes its name from the quadrille, a dance in which the participants constantly swap partners.

The most widely cited instance of this was in 1756 when Britain and Austria abandoned the long-standing Anglo-Austrian Alliance and instead made new alliances with former enemies Prussia and France respectively in what was known as the Diplomatic Revolution

Deming is best known in the United States for his 14 Points (Out of the Crisis, by W. Edwards Deming, Preface) and his system of thought he called the System of Profound Knowledge. The system comprises four components or "lenses" through which to view the world simultaneously:

Appreciating a system

Understanding variation

Psychology

Epistemology, the theory of knowledge

Deming advocated that all managers need to have what he called a System of Profound Knowledge, consisting of four parts:

Appreciation of a system: understanding the overall processes involving suppliers, producers, and customers (or recipients) of goods and services (explained below);

Knowledge of variation: the range and causes of variation in quality, and use of statistical sampling in measurements;

Theory of knowledge: the concepts explaining knowledge and the limits of what can be known.

Knowledge of psychology: concepts of human nature.

System of Magoroh Maruyama

(Mindscapes, social patterns and future development of scientific theory types. Cybernetica, 1980, 23, 1, pp. 5-25)

The system has four epistemological mindscapes:

1.1 H-mindscape (homogenistic, hierarchical, classificational): Parts are subordinated to the whole, with subcategories neatly grouped into supercategories. The strongest, or the majority, dominate at the expense of the weak (whether values, policies, problems, priorities, etc). Logic is deductive and axiomatic demanding sequential reasoning. Cause-effect relations may be deterministic or probabilistic.

1.2 I-mindscape (heterogenistic, individualistic, random): Only individuals are real, even when aggregated into society. Emphasis on self-sufficiency, independence and individual values. Design favours the random, the capricious and the unexpected. Scheduling and planning are to be avoided. Non-random events are improbable. Each question has its own answer; there are no universal principles.

1.3 S-mindscape (heterogenistic, interactive, homeostatic): Society consists of heterogeneous individuals who interact non-hierarchically to mutual advantages. Mutual dependency. Differences are desirable and contribute to the harmony of the whole. Maintenance of the natural equilibrium. Values are interrelated and cannot be rank-ordered. Avoidance of repetition. Causal loops. Categories not mutually exclusive. Objectivity is less useful than 'cross-subjectivity' or multiple viewpoints. Meaning is context dependent.

1.4 G-mindscape (heterogenistic, interactive, morphogenetic): Heterogeneous individuals interact non-hierarchically for mutual benefit, generating new patterns and harmony. Nature in continually changing requiring allowance for change. Values interact to generate new values and meanings. Values of deliberate (anticipatory) incompleteness. Causal loops. Multiple evolving meanings.

Maruyama has recently (54) compared his four types with an extensive survey of epistemological data grouped by O J Harvey into four "systems" (56).

System I: high absolutism, closedness of beliefs, high evaluativeness, high positive dependence on representatives of institutional authority, high identification with social roles and status position, high conventionality, high ethnocentrism.

System II: deep feelings of uncertainty, distrust of authority, rejection of socially approved guidelines to action accompanied by lack of alternative referents, psychological vacuum, rebellion against social prescriptions, avoidance of dependency on God and tradition.

System III: manipulation of people through dependency upon them, fairly high skills in effecting desired outcomes in his world through the techniques of having others do it for him, some autonomous internal standards especially in social sphere, some positive ties to the prevailing social norms.

System IV; high perceived self-worth despite momentary frustrations and deviation from the normative, highly differentiated and integrated cognitive structure, flexible, creative and relative in thought and action, internal standards that are independent of external criteria, in some cases coinciding with social definitions and in other cases not.

The two authors find that they agree on three types and differ on the nature of the fourth (which Jungian's would presumably consider as corresponding to a partially "repressed function" they have in common). It is much to be regretted that such surveys have not explored the epistemologies in "developing" countries to a greater degree, nor the extent towhich different epistemologies are co-present in the same culture, group, individual or life-cycle.

2. System of Geert Hofstede

(Culture's Consequences: international diffrences in work-related values. Sage, 1984)

Four indices of work-related values:

2.1 Power distance: Namely the attitude to human inequality. The index developed groups information on perceptions of an organizational superior's style, colleague's fear to disagree with the superior, and the type of decision-making that subordinates prefer in a superior.

2.2 Uncertainty avoidance: Namely the tolerance for uncertainty which determines choices of technology, rules and rituals to cope with it in organizations. The index developed groups information on rule orientation, employment stability and stress.

2.3 Individualism: Namely the relationship between the individual and the collectivity which prevails in a given society, especially as reflected in the way people choose to live and work together. The index distinguishes between the importance attached to personal life and the importance attached to organizational determination of life style and orientation.

2.4 Masculinity: Namely the extent to which biological differences between the sexes should or should not have implications for social activities that are transferred by socialization in families, schools, peer groups and through the media. The index developed measures the extent to which people endorse goals more popular with men or with women.

3. System of Kinhide Mushakoji

(Scientific revolution and interparadigmatic dialogue. Tokyo, United Nations University, GPID project, 1978)

Four modalities through which the human mind grasps reality:

3.1 Affirmation: Leading to affirmative action in the form of support, commitment, initiative, proposition, cooperation, consensus formation, empowering, 'opening'.

3.2 Negation: Leading to negative action in the form of sanction, withdrawal (of support), denial, disassociation, delimitation, criticism, opposition, promotion of dissent, disempowering, 'closing'.

3.3 Affirmation and negation: Leading to ambiguous action, non-violent resistance, 'dumb insolence', 'giving with one hand and taking with the other', 'double dealing', 'stick and carrot tactics', the 'yes but no' response of the frustrated cross-examinee.

3.4 Non-affirmation and Non-negation: Leading to action in the form of indifference, indecision, non-action (in the oriental sense), 'neither confirm nor deny', 'opening and closing'.

4. System of Will McWhinney

(Paths of Change: strategic choices for organizations and society. Sage, 1991)

Four modes of reality construction (resolution and change):

4.1 Analytic mode: Based on empirical thinking and depends on hypo-deductive and inductive methods, using all logics, theories and information available to the senses to identify possible solutions, predict implications, and evaluate outcomes. Currently associated with the scientific and quantitative methods. Provides no guide for the processes of change but determines (or predicts) outcomes. Change is driven by the sense of efficiency, of optimally organizing to produce that which can be produced.

4.2 Dialectic mode: Composed of a variety of methods which may appear to be totally distinct and arising from contrary world views based on unitary premises (and therefore held to be intimately related). Encompasses the mode of argument, of disputation among partisans of opposing views and of adversarial encounter -- all as methods of unification. Change serves to cleanse the system of error, correct for deviation from the norm, or protect the domain of truth. In the formation of synthesis, evolution occurs as a historically driven imperative that progressively cleanses the organization of impure functions.

4.3 Axiotic mode: Based on value exploration, resolving issues by developing new, and shared, evaluations of events. May work through 'recontexting' or 'transformation' of images by which an issue is 'dissolved'. Concerned with questions of morality, fairness and interpersonal behaviour as having value in and of themselves. Changes induced may affect the ideology of a system and thus be profoundly disturbing to and often blocked by those of unitary belief.

4.4 Mythic mode: Based on methods of symbolic creation. At the deepest level, mythic events create new meaning, literally producing something out of nothing. Resolution is produced by transcending existing structures and meanings that are given to words, situations, objects, and stories. Mythic inventions successful in engendering large scale change are those which are in tune with the needs of the cultural system into which they are injected. They are typically associated with charismatic leadership that captures the will and faith of the involved population. Major methods are those associated with creative endeavour, use of intuition and strong adherence to premises of the mythic reality.

5. System of S Pepper

(World Hypotheses: a study in evidence. University of California Press, 1942)

Four world hypotheses:

5.1 Formism: Grounded on the common sense experience of similarity and a correspondence theory of truth, expressed in the case of geography in a preoccupation with mapping.

5.2 Mechanism: Based on a causal adjustment theory of truth, taking the machine as the root metaphor, resulting in a preoccupation with special systems and functional mechanisms in the case of geography.

5.3 Organicism: Based on a coherence theory of truth, regarding every event as a more or less concealed process within an organic whole.

5.4 Contextualism: Based on an operational theory of truth, seeing the world as an arena of unique events.

6. System of Mary Douglas

(Natural Symbols: explorations in cosmology. Pelikan, 1973)

Four systems of natural symbols in which the image of the body is used in different ways to reflect and enhance each persons experience of society:

6.1 Body conceived as an organ of communication: 'The major preoccupations will be with its functioning effectively; the relation of head to subordinate members will be a model of the central nervous system, the favourite metaphors of statecraft will harp upon the flow of blood in the arteries, sustenance and restoration of strength.'

6.2 Body seen as a vehicle of life: As such 'it will be vulnerable in different ways. The dangers to it will come...from failure to control the quality of what it absorbs through its orifices; fear of poisoning, protection of boundaries, aversion to bodily waste products, and medical theory that enjoins frequent purging.'

6.3 Practical concern with possible uses of bodily rejects: As such it will be 'very cool about recycling waste matter and about the pay-off from such practices....In the control areas of this society controversies about spirit and matter will scarcely arise.'

6.4 Life seen as spiritual, and the body as irrelevant matter: 'In these types of social experience, a person feels that his personal relations, so inexplicably unprofitable, are in the sinister grip of a social system. It follows that the body tends to serve as a symbol of evil, as a structured system contrasted with pure spirit which by its nature is free and undifferentiated. The millennialist...believes in a Utopian world in which goodness of heart can prevail without institutional devices'.

In Microsoft Windows, the Calculator utility can be set to Scientific mode (called Programmer mode in some versions), which allows conversions between radix 16 (hexadecimal), 10 (decimal), 8 (octal) and 2 (binary), the four bases most commonly used by programmers. In Scientific Mode, the on-screen numeric keypad includes the hexadecimal digits A through F, which are active when "Hex" is selected. In hex mode, however, the Windows Calculator supports only integers.

The original calculators had four operations, plus minus multiplication, and division

The four division algebras R, C, H, O,

The Lo Shu Square is made up of quadrants.

Lo Shu Square (simplified Chinese: 洛书; traditional Chinese: 洛書; pinyin: luò shū; also written 雒書; literally: Luo (River) Book/Scroll), or the Nine Halls Diagram (simplified Chinese: 九宫图; traditional Chinese: 九宮圖; pinyin: jiǔ gōng tú), is the unique normal magic square of order three (every normal magic square of order three is obtained from the Lo Shu by rotation or reflection). Lo Shu is part of the legacy of the most ancient Chinese mathematical and divinatory (Yi Jing 易經) traditions, and is an important emblem in Feng Shui (風水), the art of geomancy concerned with the placement of objects in relation to the flow of qi (氣) "natural energy"

The odd and even numbers alternate in the periphery of the Lo Shu pattern; the 4 even numbers are at the four corners, and the 5 odd numbers (outnumbering the even numbers by one) form a cross in the center of the square. The sums in each of the 3 rows, in each of the 3 columns, and in both diagonals, are all 15 (the number of days in each of the 24 cycles of the Chinese solar year). Since 5 is in the center cell, the sum of any two other cells that are directly through the 5 from each other is 10 (e.g., opposite corners add up to 10, the number of the Ho Tu (河圖

One flat world 2D swastika can be reversed engineered geometrically i.e. taken apart and made into the shapes N Z which can easily be manipulated into two triangles which in turn can easily be manipulated into one 3D tetrahedron.

Thank you Bucky Fuller.

Types of cross

The Iron Cross (German: About this sound Eisernes Kreuz (help·info), abbreviated EK) was a military decoration in the Kingdom of Prussia, and later in the German Empire (1870–1918) and Nazi Germany (1939–1945). It was established by King Friedrich Wilhelm III of Prussia and first awarded on the 10th of March in 1813 during the Napoleonic Wars (EK 1813). The recommissioned Iron Cross was also awarded during the Franco-Prussian War (EK 1870), World War I (EK 1914), and World War II (EK 1939, re-introduced with a swastika added in the center). The Iron Cross was normally a military decoration only, though there were instances of it being awarded to civilians for performing military functions. Two examples of this were civilian test pilots Hanna Reitsch who was awarded the Iron Cross 2nd Class and 1st Class and Melitta Schenk Gräfin von Stauffenberg, who was awarded the Iron Cross 2nd Class, for their actions as pilots during World War II.

The design of the cross symbol was black with a white or silver outline. It was ultimately derived from the cross patty occasionally used by the Teutonic Order from the 13th century.[1] The black cross patty was also used as the symbol of the German Army from 1871 to March/April 1918, when it was replaced by the bar cross. In 1956, it was re-introduced as the symbol of the Bundeswehr, the modern German armed forces.

EM Miller theoriezed that the Celtic cross was a time telling device and that Jesus on the cross represented the flow, or time standing still.

According to legend, Constantine I adopted this Greek phrase, “εν τούτῳ νίκα”, (in this, win) as a motto after his vision of a chi rho on the sky just before the Battle of Milvian Bridge against Maxentiuson 28 October 312. The early Christian symbol consists of a monogram composed of the Greek letters chi (X) and rho (P), the first two letters in the name Christ (Greek: Χριστός). In later periods thechristogram “IHS” both stood for the first three letters of “Jesus” in Latinized Greek (Ιησούς, LatinizedIHSOVS) and “in hoc signo” from the legend.

Cross burning or cross lighting is a practice widely associated with the Ku Klux Klan, although the historical practice long predates the Klan's inception–as far back as Peter of Bruys (1117–1131), who burned crosses in protest of the veneration of crosses. In the early 20th century, the Klan burned crosses on hillsides or near the homes of those they wished to intimidate.

The simple theory of a `quadrant' balance is used to show how a balance of this type should be designed to give minimum variation of sensitivity over a given range of load. A form of the balance which is used for textile testing purposes is described, and figures are given to indicate the degree of accuracy which has been attained with four balances covering different ranges.

Sir William Thomson’s Quadrant Electrometer #10560

J. White, Glasgow

Thomson invented the quadrant electrometer in 1853. As with the electrostatic voltmeter, the quadrant electrometer utilizes the electrical force between charged electrodes. A butterfly-shaped electrode composed of two quadrants of a circular disk is supported by a torsion fiber inside a stationary circular box composed of four quadrants, opposite pairs of which are electrically connected. The rotation of the suspended electrode depends on the potentials applied to the various electrodes. A beam of light reflected from a mirror attached to the fiber is shown on a scale and is deflected as the fiber is rotated. The serial number of this instrument is 152.

The Victoria Cross (VC) is the highest military decoration awarded for valour "in the face of the enemy" to members of the armed forces of various Commonwealth countries, and previous British Empire territories.[3] It is first in the order of wear in the United Kingdom honours system, and takes precedence over all other orders, decorations, and medals, including the Order of the Garter. It may be awarded to a person of any military rank in any service and to civilians under military command. The VC is usually presented to the recipient or to their next of kin by the British monarch at an investiture held at Buckingham Palace.

A saltire is a heraldic symbol in the form of a diagonal cross, like the shape of the letter X in Roman type. Saint Andrew is said to have been martyred on such a cross.

The Camuni or Camunni were an ancient population located in Val Camonica during the Iron Age (1st millennium BC); the Latin name Camunni was attributed to them by the authors of the 1st century. They are also called ancient Camuni, to distinguish them from the current inhabitants of the valley (the Camuni or Camunians). The Camunni were among the greatest producers of rock art in Europe; their name is linked to the famous rock engravings of Valcamonica.

On it there is a swastika

The Swastika Stone is a stone adorned with a Swastika located on the Woodhouse Crag, on the northern edge of Ilkley Moor in West Yorkshire. The design has a double outline with five curved arms enclosing several so-called 'cup' marks, the like of which can be found on other stones nearby.

The design is unique in the British Isles, so its close similarity to Camunian rose designs in Italy have led some to theorise that the two are connected. In fact, the troops stationed in Ilkley during Roman occupation were recruited from the Celtic Lingones. This tribe was native to Gaul, but in around 400 BC, some migrated across the Alps to the Adriatic coast. Some believe the Ilkley Lingones were recruited from here rather than from Gaul. It is possible that the Italian Lingones passed through the Valcamonica region at some point, took on the swastika designs they found as part of their tribal symbolism, and carved it on the nearby moor when stationed in Ilkley.[1]

UK children's author Terry Deary has suggested the carving depicts a boomerang.[2]

The looped square resembles a quadrant

The looped square (⌘) is a symbol consisting of a square with outward pointing loops at its corners. It is referred to by this name, for example, in works regarding the Mississippian culture.[1] It is also known as the place of interest sign[2] when used on information signs, a practice which started in Nordic countries in the late 1960s.[3] Also, the symbol is known as Saint John's Arms or Saint Hannes cross (related to Swedish sankthanskors, Danish johanneskors, and Finnish hannunvaakuna), as Gorgon loop, and as command key symbol due to its use on the command key on Apple computer keyboards.

It is an ancient symbol used by several cultures, but remains in common use today. It belongs to a class of symbols which are called valknute in Norway.

The symbol appears on a number of old objects in Northern Europe. It features prominently on an image stone from Hablingbo, Gotland, Sweden, that was created between 400 and 600 AD.[5]

It is also similar to a traditional heraldic emblem called a Bowen knot.[6]

In Finland, the symbol was painted or carved on houses and barns, and domestic utensils such as tableware, to protect them and their owners from evil spirits and bad luck. The oldest surviving example is a pair of 1000-year-old (Finnish pre-Christian period) wooden skis decorated with the symbol.[7][8]

The looped square also appears on artifacts of the Mississippian culture of the southeastern United States.[1]

Modern use[edit]

In modern times, the symbol is commonly found in Ukraine, Belarus, Denmark, Estonia, Finland, Germany, Iceland, Lithuania, Norway, and Sweden as an indicator of locations of cultural interest, beginning in the Scandinavian countries in the late 1960s.[3] There has been modern speculation that it was chosen for its resemblance to an aerial view of Borgholm Castle;[9] however, the symbol is well-represented in Scandinavian artifacts that predate the current castle by centuries.[5]

The symbol later gained international recognition via computing. It is used on Apple keyboards as the symbol for the command key.[10]

The earliest known object with swastika-motifs is a bird made from the tusk of a mammoth from the paleolithic settlement of Mezine, Ukraine dated to 10,000 BCE.[15]

Among the earliest cultures utilizing swastika is the neolithic Vinča culture of South-East Europe (see Vinča symbols). More extensive use of the Swastika can be traced to Ancient India, during the Indus Valley Civilization.

The swastika is a repeating design, created by the edges of the reeds in a square basket-weave. Other theories attempt to establish a connection via cultural diffusion or an explanation along the lines of Carl Jung's collective unconscious.

The genesis of the swastika symbol is often treated in conjunction with cross symbols in general, such as the sun cross of pagan Bronze Age religion. Beyond its certain presence in the "proto-writing" symbol systems emerging in the Neolithic,[16] nothing certain is known about the symbol's origin. There are nevertheless a number of speculative hypotheses. One hypothesis is that the cross symbols and the swastika share a common origin in simply symbolizing the sun. Another hypothesis is that the 4 arms of the cross represent 4 aspects of nature - the sun, wind, water, soil. Some have said the 4 arms of cross are four seasons, where the division for 90-degree sections correspond to the solstices and equinoxes. The Hindus represent it as the Universe in our own spiral galaxy in the fore finger of Lord Vishnu. This carries most significance in establishing the creation of the Universe and the arms as 'kal' or time, a calendar that is seen to be more advanced than the lunar calendar where the seasons drift from calendar year to calendar year. The luni-solar solution for correcting season drift was to intercalate an extra month in certain years to restore the lunar cycle to the solar-season cycle. The Star of David is thought to originate as a symbol of that calendar system, where the two overlapping triangles are seen to form a partition of 12 sections around the perimeter with a 13th section in the middle, representing the 12 and sometimes 13 months to a year. As such, the Christian cross, Jewish hexagram star and the Muslim crescent moon are seen to have their origins in different views regarding which calendar system is preferred for marking holy days. Groups in higher latitudes experience the seasons more strongly, offering more advantage to the calendar represented by the swastika/cross. (Note relation to the sun cross.)

Alexander Cunningham suggested that the Buddhist use of the shape arose from a combination of Brahmi characters abbreviating the words su astí.

The Christian cross had been used as a symbol of Christianity from Late Antiquity. Beginning in the 11th century, and increasingly during the age of the Crusades, a variety of variant forms of cross symbols were developed for the purposes of the emerging system of heraldry.

The cross symbol was also used on flags from the medieval period, and in modern times also on numerous national flags.

The Cross of All Nations is a monumental cross located in Qanat Bakish, a locality close to the Lebanese town of Baskinta. The cross was built near a church dating back to 1898 on a land belonging to the Lebanese Maronite Order. At 73.8 metres (242 ft) tall, the Cross of All Nations is the largest illuminated cross in the world, it was inaugurated on September 13, 2010 on the eve of the Feast of the Exaltation of the Cross.[1] It was built by the Maronite Church and an organization of French Catholics the "Association Terre de Dieu" led by the brothers Jesus and Francois Ibanez. The inauguration was held after a Mass in the presence of Lebanese officials, the French ambassador to Lebanon Denis Pieton, high ranking clergy and thousands of believers. Following the ceremony, fireworks were set off and doves were released.

The Feast of the Exaltation of the Cross commemorates the discovery of the Cross of Christ by St. Helen, the mother of Roman emperor Constantine, on September 14, 326. In Lebanon the feast is celebrated each year in Christian towns and cities with crowded processions during which people carry torches and visit mountain tops where they plant crosses, hold prayer services and start bonfires.[1][2][3][4]

The cross is 73.8 metres (242 ft) tall (one tenth the height of mount Golgotha) and 37 metres (121 ft) wide. The cross's 8 metres (26 ft) deep base contains 500 cubic meters of concrete and 5 tons of steel, the cross's body itself is made up of 170 tons of steel and is lit by 1800 spotlights. Work on the monument started on 25 November 2008 and was done in 27 June 2010 and cost around 1.5 million USD mainly acquired through donations.[2][3][5] The cross is equipped with two elevators that allow up to 300 visitors to access a 300 square metres (3,200 sq ft) platform located at its vertical beam.[

The Ruckenkreuz (Rucken Cross) is an 8.4 metre tall, 2.80 metre wide memorial cross of reinforced concrete. It stands on a rocky mountain at Blaubeuren, Baden-Württemberg, Germany, in memory of the inhabitants of Blaubeuren killed in World War I. The Ruckenkreuz was completed on November 21, 1926.

Geographical coordinates: 48°24′38″N 9°47′30″E

Ostlandkreuz (German for "Eastern Lands Cross") or Kreuz des deutschen Ostens ("Cross of the German East") is the name of memorial crosses in Germany remembering the expulsion of Germans after World War II from the former Sudetenland areas of Czechoslovakia, from the so-called "Recovered Territories" of Poland and the Soviet part of the former Province of East Prussia. While most of these crosses stand in cemeteries, some are erected as landmarks on mountains.

A memorial cross (sometimes called an intending cross) is a cross, which was built as memorial to commemorate a special event; or it may be a simple form of headstone to commemorate the dead.

In England King Edward I had memorial crosses, the so-called Eleanor Crosses, erected in memory of his wife Eleanor of Castile who died in November 1290. Three of the original twelve crosses have survived.

In Germany today, the custom has arisen of erecting crosses (Unfallkreuze or "accident crosses") as roadside memorials at the spot where someone has been killed. These are maintained for shorter or longer periods of time and decorated e.g. with flowers or candles. In South Germany, especially in Bavaria, memorial crosses exist for those who died several generations ago. Some of these crosses are at very remote places. These, too, usually commemorate a fatal accident.

These roadside memorial crosses should not be confused with wayside crosses, which are erected in the Bavarian region on the edge of paths and tracks, and are there simply to give walkers the opportunity to say a short prayer.

Other memorial crosses commemorate war dead and victims of terrorism.

The largest memorial cross in the world is the Monumento Nacional de Santa Cruz del Valle de los Caidos near El Escorial in Spain. It has a height of 152.4 metres.

A khachkar, also known as an Armenian cross-stone[1] (Armenian: խաչքար, pronounced [χɑtʃʰˈkʰɑɾ], խաչ xačʿ "cross" + քար kʿar "stone") is a carved, memorial stele bearing a cross, and often with additional motifs such as rosettes, interlaces, and botanical motifs.[2] Khachkars are characteristic of Medieval Christian Armenian art.[1][3]

Since 2010, khachkars, their symbolism and craftsmanship are inscribed in the UNESCO list of Intangible Cultural Heritage.[4]

The current Basque coat of arms (Spanish: Escudo del País Vasco, Basque: Euskal autonomi erkidegoaren armarria[1]) is the official coat of arms of the Basque Country, Autonomous community of Spain. It consists of a party per cross representing the three historical territories of Álava, Gipuzkoa and Biscay, as well as a fourth, void quarter. The arms are ringed by a regal wreath of oak leaves, symbolic of the Gernikako Arbola. The fourth quarter constituted since the late 19th century the linked chains of Navarre; however, following a legal suit by the Navarre Government claiming that the usage of the arms of a region on the flag of another was illegal, the Constitutional Court of Spain ordered the removal of the chains of Navarre in a judgement of 1986.

The Southern Basque Country depicted in a publicity poster and including the original Laurak Bat coat of arms (1950s)

The Laurak Bat coat of arms used by the Basque Government until 1985

After the end of home rule in 1839-1841, the Basque governments started a mutual approach out of common concerns in face of their exposure to Spanish centralism. The movement intensified after 1866, and a motto was coined, the "Laurac bat", 'the four make one', echoing the "Irurac bat" of the Royal Basque Company, which in turn crystallized in a coat of arms including the four historic Basque districts in Spain (called variously the Sister Provinces, the Chartered Territories, the Basque Country, the Basque-Navarrese Country, etc.), to represent their common bonds, as claimed during that period by the chartered provincial governments,[4] or the 1931 draft Statute of the Basque Country.

In 1936, the Provisional Government of Euzkadi, presided over by the first president, José Antonio Aguirre, adopted the shield with the arms of the three provinces of Álava, Gipuzkoa, Biscay comprised in the 1936 Statute (the Basque Provinces, as established in the 1833 administrative design), and Navarre. The president of the government affirmed in the preamble to the Decree of 19 October 1936, and thereby approved, the emblem and flag that was to be used by the Basque Country. Thus the shield of the Government of Euzkadi contained the arms of Álava, Gipuzkoa, Biscay and Navarre in a single blazon of four quarters surrounded by a crown of oak leaves. The Provisional Government of Euzkadi stated that "the flag must be that which gathers Basque unity and which the use, ever more frequent in the Basque lands, has sanctioned as such symbol of their unity."[5]

As an official shield, like the 1936 Basque Autonomous Community, disappeared after the pro-Franco victory in the Spanish Civil War, but the coat of arms continued in unofficial use, it was even used in its flag by the rightist pro-rebel newspaper from Donostia El Diario Vasco during wartime (data for 2 May 1937). On 2 November 1978, the Consejo General del País Vasco (General Council of the Basque Country), restored the republican shield, albeit modified as follows:

The Álava quarter lost the motto "En aumento de la justicia contra malhechores"[6] and both the designs of the castle and of the arm with sword were changed. The castle is now on top of a grey rock and the arm and sword are light blue in colour.

In the Biscay quarter, the wolves of the arms of the Haro family were suppressed in 1986 and the field changed from gules to argent, the bordure from argent to gold, the crosses from sinople to gules, and the ground (terrase) from sinople to maroon.[7][8][9][10]

In the Gipuzkoa quarter, the field changed from argent to gold, and the ground (terrase) was removed, leaving only the trees and the waves.[11][12]

The fourth quarter once contained the linked chains of Navarre; however, following a legal suit by the Navarre government claiming that the usage of the arms of a region on the flag of another was illegal, the Constitutional Court of Spain forced the Basque government to remove the chains of Navarre, leaving the red background.[13]

In 1991 the Basque Government standardised the colours used in the shield.[14]

Basque nationalists, but not only, have used an unofficially recognised Basque coat of arms, the Zazpiak Bat. It has been argued that it differs from the original one by being divided into six squares and by including the coat of arms of the Basque regions in France.[15] The motto "Zazpiak bat" was coined by Antoine-Thomson d'Abbadie in the late 19th century

The lauburu or Basque cross (Basque: lauburu, "four heads") is a traditional Basque swastika with four comma-shaped heads. Today, it is a symbol of the Basque Country and the unity of the Basque people. It is also associated with Celtic peoples, most notably Galicians and Asturians. It can be constructed with a compass and straightedge, beginning with the formation of a square template; each head can be drawn from a neighboring vertex of this template with two compass settings, with one radius half the length of the other.

Flannel shirts are popular and are often comprised of quadrants.

Tartan kilt patterns: The set of many tartans highlights the way in which particular patterns emerge through being variously coloured. Each is however a particular pattern very much frozen in time. The concern here is with a visualization that would allow the particular arrangement of colours in a given tartan to emerge as part of a morphing process between all such tartan patterns -- rows moving backwards and forwards and changing colour and width, as with columns.

In Armenia swastika is called "arevakhach" and "kerkhach" (Armenian: կեռխաչ) and is the ancient symbol of eternity and eternal light (i.e. God). Swastikas in Armenia were found on petroglyphs. During the bronze age it was depicted on cauldrons, belts, medallions and other items. Among the oldest petroglyphs is the seventh letter of the Armenian alphabet - "E" (which means "is" or "to be") - depicted as half-swastika.

The earliest swastika in Armenia belongs to the Neolithic period of human cultural evolution, found on rock art dating back about 7000-5000 BC. The Indo-European ‘Aryan’ tribes who lived in what later came to be known as the Armenian Highlands were one of the earliest cultures to be using the swastika as a religious symbol. The main value of the Arevakhach is the sun, and the light, the movement of life, prosperity, joy, eternity and good luck.

Swastikas can also be seen on early Medieval churches and fortresses, including the principal tower in Armenia's historical capital city of Ani. The same symbol can be found on Armenian carpets, cross-stones (khachkar) and in medieval manuscripts, as well as on modern monuments as asymbol of eternity.

A terra-cotta found in a Phoenician tomb from Cyprus shows a Sun-priestess

having swastikas on her attire and carrying a vase

note it appears in the right thigh area we have 7 around 1 center dot = 8

left thigh area (viewer’s right) is a 8 around 1 dot scheme = 9

Ancient Greek architectural, clothing and coin designs are replete with single or interlinking swastika motifs. There are also gold plate fibulae from the 8th century BC decorated with an engraved swastika.[48] Related symbols in classical Western architecture include the cross, the three-legged triskele or triskelion and the rounded lauburu. The swastika symbol is also known in these contexts by a number of names, especially gammadion,[49] or rather the tetra-gammadion. The name gammadion comes from the fact that it can be seen as being made up of four Greek gamma (Γ) letters. Ancient Greek priestesses would tattoo the symbol, along with the tetraskelion, on their bodies. Ancient Greek architectural designs are replete with the interlinking symbol.

In Ancient Greece there is and image of Athena with swastikas on her robe in the thigh area

The swastika (sanskrit for: "well being") or tetra-gammadion (as it was called in ancient Greece), is a combination of four gimel (or "gammas" in Greek), which are symbols of movement towards reward or punishment.

Gimel is associated with a person in motion; symbolically, a rich man running after a poor man to give him charity, or divine assistance or retribution (some forms of the swastika suggest left facing gimel to be retribution). Either form of "gift" is for the well-being of the receiver (a form of regulation & balance), whether curse or blessing. This defines the swastika as a constant motion of the restoration and maintenance of life (or spiritual growth).

This is the basis for it's associations with the sun, and with Raphael (who is the angel of restoration, good will and blessing). Although it can easily be identified as a simple solar model, it's translation is more than portrait.

The "arms" of the symbol are either 3 or 4 in number. The "turning" impression that the symbol displays is a cycle of rejuvenation or return. Raphael is the angel over healing, because he is a personification of restoration. That is, restoration of anything to it's intended, created, or pure form. The symbol expresses this in it's cycle of "returning" & has been used as much to represent homecomings & migration, or the coming of spring in the year... etc.

All throughout history and all over the world, it has also been associated with travels (especially the "return home" - which is also a form of restoration), fortune, harvest and healing. All of these attributes are also properties of Raphael, and universal symbolisms of the sun.

The Wiphala (Quechua pronunciation: [wɪˈpʰɐlɐ]) is a square emblem, commonly used as a flag, representing some native peoples of all the Andes that include today's Bolivia, Peru, Ecuador and parts of Argentina, Chile and Colombia

It is made up of quadrant squares.

Here are some flags with crosses on them

Flag of England

Flag of Scotland and San Andres

Flag of Quebec

Flag of Nova Scotia

Flag of Red Cross

Flag of the Sovereign Military Order of Malta

Flag of the Navy, Italy

Arms of Schwyz, Switzerland

Flag of the Carabinieri gendarmerie, Italy

Arms of Kreuzlingen, Switzerland

Flag of Madeira Autonomous Region

Flag of Portugal (1095)

Southern cross appearing on a number of flag

Flag of the President of Finland includes the Cross of Liberty, 3rd Class in the canton and the same like design is also found in presidential decorations, as the Crand Cross of the White Rose of Finland with the fir cross Collar

The coat of arms of the Hungarian kingdom, from the 15th century

Flag of Rio de Janeiro

St Piran's Flag (Flag of Cornwall)

Victory Cross in the Flag of Asturias

16 major upanishads

Quadrant 1:

square 1: sensation

square 2: perceptions

square 3: response

square 4: awareness

Quadrant 2:

square 5: belief

square 6: faith

square 7: behavior

square 8: belonging

Quadrant 3

square 9: thinking

square 10: emotion

square 11: doing

square 12: dreaming

Quadrant 4:

square 13: contemplation

square 14: passion

square 15: flowing

square 16: knowing

Quadrant 5

square 17: being

square 18: nonbeing

square 19: becoming (ephemerality)

The Whole Quadrant Model

sensation	response	thinking	doing
perception	awareness	emotion	dreaming
belief	behavior	contemplation	flowing
faith	belonging	passion	knowing

nonbeing,

becoming

BEING

Conclusion- I just scratched the surface of the implications of the quadrant model and examples of the quadrant model in nature and reality. Existence is a manifestation of the quadrant model. I want to conclude with how I discovered the quadrant model. I sort of discovered it on accident. I was reading the Bible. I was on the chapter where Jesus was crucified. My Grandpa earlier that week had told me about Wilber’s personality model where he described thinkers, emoters, doers, and dreamers and described them in a quadrant. I thought about this model and I believed there should be only three personality types, thinkers, emoters, and doers, because I didn’t understand what it meant to be a dreamer. Then I thought about how dreaming is separate yet encompassed thinking emotion and doing. Then I immediately connected the idea of the quadrant to the idea of the cross. Coincidentally I was reading the chapter in the Bible which describes Jesus being crucified. I thought how thinking and emotion were a duality that were intricately connected. I realized doing was also interlinked with thinking and emotion. I believed these were all aspects of the same thing. I recognized that dreaming was separate from thinking, emotion, and doing, but encompassed them. Then I had the epiphanie that this pattern was seen in other things. I connected this pattern to the forces of nature and many other things. At that point I realized I was onto something. The next day in a biology class the class was watching a movie on Watson and Crick. I went to the bathroom and contemplated. When I came back I sat down and the contemplation, passion, flowing, and knowing quadrant came to me. I went to meet with my friend Michael and told him what I had discovered. Later that week I came up with the belief, faith, behavior, and belonging quadrant. Finally I came up with the sensation, perception, response, and awareness quadrant. During this whole period I had felt that I was in touch with the cosmos and connected to the cosmos in a sort of magical way. I felt that I was being guided to my realizations and so many coincidences and synchronicities and things that defy explanation were occurring that it was kind of incredible. Well before I discovered the quadrant model I would tell people that reality was an illusion and I would tell them that it is a metaphor of a True Reality, and I’m not sure that they knew what I meant and I wasn’t even 100 percent certain how to describe what I knew to be so. I remember knowing this though since I was extremely young, as long as I can remember. Now I think it has been proven. St. Paul said “we see through a mirror dimly, only then shall we see face to face”. In other words he described that in this realm people do not see things as they really are. The reality that I find myself in now is a shadow, it is a sort of illusion. Reality is merely a representation of the quadrant model pattern.

Summary

The Quadrant Model of Reality is a revolutionary book. It represents a paradigm shift in the way that people view reality. No longer can it be argued that reality is random. The Quadrant Model of Reality is a sort of theory of intelligent design. It states that nature is manifested around a principal pattern. This pattern is elucidated in the theory the quadrant model. Things in reality are often structured in layers or compartments or sections. There is often continuums in reality, but these continuums are also broken down into discrete sections. The quadrant model of reality argues that the ordering and structure of reality is not random but is based on a specific pattern. For instance the layers of the atmosphere are four and each level has certain qualities and characteristics. The layers of soil are also four and each layer embodies certain qualities and characteristics. The stomach is divided into compartments and each compartment has distinct characteristics. The particles of the Universe are ordered in a model called the standard model of particle physics. The quadrant model argues that the structure of the standard model, the atmosphere, the soil, the planets, the human eye, the forces of nature, the bible, the Vedas, and everything that is important is not accidental and random like a lot of scientists say, but is purposeful and based on a pattern, which is called the quadrant model pattern. Each square in the quadrant model embodies certain qualities and characteristics. There are 16 squares in all, and four quadrants in all. The book The Quadrant Model of Reality proposes that reality is organized along the basis of the quadrant model pattern. This book is a groundbreaking, earth shattering work that signals a brand new perspective on existence that completely defies and overpowers and subsumes any theory created before it, and the quadrant model theory is to this point the most accurate and successful explanation of the nature of existence. It seems almost impossible to believe that one simple model can explain all of existence exhaustively. Many have stated that they have come up with such theories, successful theories of everything, but they have not. There is a movie called the theory of everything describing Stephen Hawking's life, but his theory of everything is not really a theory of everything. His theory of everything is a theory of physics only. The quadrant theory of everything includes his theory within it as well as, well, everything else that is not in the domain of physics. The quadrant model of reality is the closest thing to a theory of everything ever devised. It seems unbelievable that there really can be one simple theory; one principle; one model that can explain existence perfectly and succinctly. But there is, and that theory is the quadrant model of reality. Hopefully you enjoy. Because this book signals a global consciousness shift, a sort of enlightenment, and one that is much needed in a world that many find to be confusing and overwhelming. And people are searching for answers and a way to make sense of a world that they are growing to believe is senseless. The quadrant model proposes that things aren't so complicated and complex as many would like you to believe, but that everything is centered around one organizing principle, and the cosmos which may seem to be random and chaotic, is really ordered beyond you can imagine. No this theory is not wishful thinking, or an attempt to simplify the cosmos in a way that is not intellectually honest. There is no attempt in this book to try to cram things conveniently into a theory where they don't belong. The theory doesn't involve searching for patterns and trying to force patterns where there is none. The quadrant model is not another example of Jim Carey's movie 23 where Mr.Carey is trying to prove his theory that the number 23 is everywhere and as a result tries to find the number 23 everywhere and believes he does. The quadrant model of reality is a descriptive theory of nature that proves the famous Ockam's razor- the most simple, elegant, and beautiful explanation is the one that is most likely to be correct. The quadrant theory is a metaphysical theory on the nature of being, and it answers the most important questions ever asked- What is being and why is being the way it is? Why do we exist and why do things exist the way they are? And the quadrant theory answers these questions in an amazingly simple way, and the simplicity of the model in no way detracts from its extraordinary accuracy and descriptive power. The quadrant model pattern is in fact the formula that underlies all of reality, and is the formula out of which reality reveals itself. The quadrant theory is the ultimate revelation, the final revelation of existence. This theory is the apocalypse- nothing has ever surpassed this and nothing ever will.

Quadrant Model of Reality

Monday, February 22, 2016

Quadrant Model of Reality Book 1 Philosophy

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