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

Quadrant Model of Reality

Tuesday, May 3, 2016

Quadrant Model of Reality Book 1 Philosophy

No comments:

Post a Comment