Philosophy Chapter
Gromov Witten theory is a theory to find the number of curves on a manifold. This is a classical problem in algebraic geometry that every algebraic geometer knows.
Square 1: For lines of degree one curves there is 2875. This is a classical result in the 1880s
Square 2: In the 1980s the number of lines for d=2 conics was 609,250.
Square 3: For the number of curves by a cubic equation there was 317,206,375. Mathematicians needed a computer to find this number. Originally they discovered there was a problem in the computer code. Physicists asked them to redo the equation and they discovered the number.
square 4: For a manifold of degree four even a more massive effort was undertaken than with degree three. It was one of the most difficult problems in mathematics and took a huge amount of effort to discover. The fourth square is always different.
Square 5: By the time that physicists were trying to find the number of curves for degree five computer technology got to the point that there was no longer any effort to find the numbers and after finding degree four all of the numbers after four were found. Square 5 is always transcendent. The nature of this problem mirrors the nature of a child learning numbers, how he can learn the first four numbers having a difficult time and does not understand numbers, but by number five he understands all numbers and no longer has trouble learning numbers. There was a huge amount of effort to find the first four degrees in Gromov Witten theory. It took a century of mathematicians working tirelessly. At the fifth degree and beyond there was no more effort because high tech computers did it all effortlessly by that point.
This is not a coincidence. The nature of reality is it reveals the quadrant model pattern throughout. Groom Witten theory is essential for string theory, which I also described ultimately reflects the quadrant model pattern.
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STOCK (1979) indicated that the discourse on the ‘Categories‘ of Aristotle – which is treated in the first book of ‘De Divisione Naturae‘ (463A) – can be found in a slightly different form in the ‘Tractatus de Catagoriis Aristotelis’ (Decem Catagoriae). This treatise from the fourth century AD was written by a successor of Themistius, probably Agorius Praetextanus. The text gave continuity between the tetradic thoughts of Aristotle and the European interpretation of Eriugena. The resemblance is as follows (STOCK, 1979):
Eriugena Decem Categoriae (Aristotle)
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1: quae creat et non creatus in solo et in omni
2: quae et creatur et creat in solo et non in omni
3: quae creatur et non creat in omni et non in solo
4: quae nec creat nec creatur nec in solo nec in omni
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According to Aristotle of all the things that exist,
Some may be predicated[further explanation needed] of a subject, but are in no subject; as man may be predicated of James or John, but is not in any subject.
Some are in a subject, but cannot be predicated of any subject. Thus a certain individual point of grammatical knowledge is in me as in a subject, but it cannot be predicated of any subject; because it is an individual thing.
Some are both in a subject and able to be predicated of a subject, for example science, which is in the mind as in a subject, and may be predicated of geometry as of a subject.
Last, some things neither can be in any subject nor can be predicated of any subject. These are individual substances, which cannot be predicated, because they are individuals; and cannot be in a subject, because they are substances.
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A brief explanation (with some alternative translations) is as follows:
Substance (οὐσία, ousia, essence or substance).[6] Substance is that which cannot be predicated of anything or be said to be in anything. Hence, this particular man or that particular tree are substances. Later in the text, Aristotle calls these particulars “primary substances”, to distinguish them from secondary substances, which are universals and can be predicated. Hence, Socrates is a primary substance, while man is a secondary substance. Man is predicated of Socrates, and therefore all that is predicated of man is predicated of Socrates.
Quantity (ποσόν, poson, how much). This is the extension of an object, and may be either discrete or continuous. Further, its parts may or may not have relative positions to each other. All medieval discussions about the nature of the continuum, of the infinite and the infinitely divisible, are a long footnote to this text. It is of great importance in the development of mathematical ideas in the medieval and late Scholastic period. Examples: two cubits long, number, space, (length of) time.
Qualification or quality (ποιόν, poion, of what kind or quality). This determination characterizes the nature of an object. Examples: white, black, grammatical, hot, sweet, curved, straight.
Relative or relation (πρός τι, pros ti, toward something). This is the way one object may be related to another. Examples: double, half, large, master, knowledge.
Where or place (ποῦ, pou, where). Position in relation to the surrounding environment. Examples: in a marketplace, in the Lyceum.
When or time (πότε, pote, when). Position in relation to the course of events. Examples: yesterday, last year.
Being-in-a-position, posture, attitude (κεῖσθαι, keisthai, to lie). The examples Aristotle gives indicate that he meant a condition of rest resulting from an action: ‘Lying’, ‘sitting’, ‘standing’. Thus position may be taken as the end point for the corresponding action. The term is, however, frequently taken to mean the relative position of the parts of an object (usually a living object), given that the position of the parts is inseparable from the state of rest implied.
Having or state, condition (ἔχειν, echein, to have or be). The examples Aristotle gives indicate that he meant a condition of rest resulting from an affection (i.e. being acted on): ‘shod’, ‘armed’. The term is, however, frequently taken to mean the determination arising from the physical accoutrements of an object: one's shoes, one's arms, etc. Traditionally, this category is also called a habitus (from Latin habere, to have).
Doing or action (ποιεῖν, poiein, to make or do). The production of change in some other object (or in the agent itself qua other).
Being affected or affection (πάσχειν, paschein, to suffer or undergo). The reception of change from some other object (or from the affected object itself qua other). Aristotle's name paschein for this category has traditionally been translated into English as "affection" and "passion" (also "passivity"), easily misinterpreted to refer only or mainly to affection as an emotion or to emotional passion. For action he gave the example, ‘to lance’, ‘to cauterize’; for affection, ‘to be lanced’, ‘to be cauterized.’ His examples make clear that action is to affection as the active voice is to the passive voice — as acting is to being acted on.
The first four are given a detailed treatment in four chapters, doing and being-affected are discussed briefly in a single small chapter, the remaining four are passed over lightly, as being clear in themselves. Later texts by scholastic philosophers also reflect this disparity of treatment
Aristotle only really talks about the first four
The present information comes from Plotinus and Simplicius, with additional evidence from Plutarch of Chaeronea and Sextus Empiricus. According to both Plotinus and Simplicius there were four Stoic categories, to wit:
substance (ὑποκείμενον [ypokeímenon {"underlying"}])
The primary matter, formless substance (ousia) which makes up things.
quality (ποιόν [poión {"whom"}])
The way in which matter is organized to form an individual object. In Stoic physics, a physical ingredient (pneuma: air or breath) which informs the matter.
somehow disposed (πὼς ἔχον [pós échon {"how haves"]})
Particular characteristics, not present within the object, such as size, shape, action, and posture.
somehow disposed in relation to something (πρός τί πως ἔχον [prós tí pos échon {"why that having"}])
Characteristics which are related to other phenomena, such as the position of an object within time and space relative to other objects
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The term Stoic categories refers to Stoic ideas regarding categories of being: the most fundamental classes of being for all things. The Stoics believed there were four categories (substance, quality, disposition, relative disposition) which were the ultimate divisions. Since we do not now possess even a single complete work by Zeno of Citium, Cleanthes or Chrysippus what we do know must be pieced together from a number of sources: doxographies and the works of other philosophers who discuss the Stoics for their own purposes.
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Schoepenhaurs On the Basis of Morality is divided into four sections. The first section is an introduction in which Schopenhauer provides his account of the question posed by the Royal Danish Society and his interpretation of the history of western ethics. In the second section, Schopenhauer embarks on a criticism of Kantian ethics, which he viewed as the orthodoxy in ethics. The third section of the work is Schopenhauer's positive construction of his own ethical theory. The final section of the work provides a brief description of the metaphysical foundations of ethics
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Kant is considered the greatest modern philosopher. His works are purely tetrads.
Kant performs four paralogisms
One of the ways that pure reason erroneously tries to operate beyond the limits of possible experience is when it thinks that there is an immortal Soul in every person. Its proofs, however, are paralogisms, or the results of false reasoning.
The Soul is substance[edit]
Every one of my thoughts and judgments is based on the presupposition "I think." "I" is the subject and the thoughts are the predicates. Yet I should not confuse the ever-present logical subject of my every thought with a permanent, immortal, real substance (soul). The logical subject is a mere idea, not a real substance. Unlike Descartes who believes that the soul may be known directly through reason, Kant asserts that no such thing is possible. Descartes declares cogito ergo sum but Kant denies that any knowledge of "I" may be possible. "I" is only the background of the field of apperception and as such lacks the experience of direct intuition that would make self-knowledge possible. This implies that the self in itself could never be known. Like Hume, Kant rejects knowledge of the "I" as substance. For Kant, the "I" that is taken to be the soul is purely logical and involves no intuitions. The "I" is the result of the a priori consciousness continuum not of direct intuition a posteriori. It is apperception as the principle of unity in the consciousness continuum that dictates the presence of "I" as a singular logical subject of all the representations of a single consciousness. Although "I" seems to refer to the same "I" all the time, it is not really a permanent feature but only the logical characteristic of a unified consciousness.[31]
The Soul is simple[edit]
The only use or advantage of asserting that the soul is simple is to differentiate it from matter and therefore prove that it is immortal, but the substratum of matter may also be simple. Since we know nothing of this substratum, both matter and soul may be fundamentally simple and therefore not different from each other. Then the soul may decay, as does matter. It makes no difference to say that the soul is simple and therefore immortal. Such a simple nature can never be known through experience. It has no objective validity. According to Descartes, the soul is indivisible. This paralogism mistakes the unity of apperception for the unity of an indivisible substance called the soul. It is a mistake that is the result of the first paralogism. It is impossible that thinking could be composite for if the thought by a single consciousness were to be distributed piecemeal among different consciousnesses, the thought would be lost. According to Kant, the most important part of this proposition is that a multi-faceted presentation requires a single subject. This paralogism misinterprets the metaphysical oneness of the subject by interpreting the unity of apperception as being indivisible and the soul simple as a result. According to Kant, the simplicity of the soul as Descartes believed cannot be inferred from the "I think" as it is assumed to be there in the first place. Therefore, it is a tautology.[32]
The Soul is a person[edit]
In order to have coherent thoughts, I must have an "I" that is not changing and that thinks the changing thoughts. Yet we cannot prove that there is a permanent soul or an undying "I" that constitutes my person. I only know that I am one person during the time that I am conscious. As a subject who observes my own experiences, I attribute a certain identity to myself, but, to another observing subject, I am an object of his experience. He may attribute a different persisting identity to me. In the third paralogism, the "I" is a self-conscious person in a time continuum, which is the same as saying that personal identity is the result of an immaterial soul. The third paralogism mistakes the "I", as unit of apperception being the same all the time, with the everlasting soul. According to Kant, the thought of "I" accompanies every personal thought and it is this that gives the illusion of a permanent I. However, the permanence of "I" in the unity of apperception is not the permanence of substance. For Kant, permanence is a schema, the conceptual means of bringing intuitions under a category. The paralogism confuses the permanence of an object seen from without with the permanence of the "I" in a unity of apperception seen from within. From the oneness of the apperceptive "I" nothing may be deduced. The "I" itself shall always remain unknown. The only ground for knowledge is the intuition, the basis of sense experience.[33]
The Soul is separated from the experienced world[edit]
The soul is not separate from the world. They exist for us only in relation to each other. Whatever we know about the external world is only a direct, immediate, internal experience. The world appears, in the way that it appears, as a mental phenomenon. We cannot know the world as a thing-in-itself, that is, other than as an appearance within us. To think about the world as being totally separate from the soul is to think that a mere phenomenal appearance has independent existence outside of us. If we try to know an object as being other than an appearance, it can only be known as a phenomenal appearance, never otherwise. We cannot know a separate, thinking, non-material soul or a separate, non-thinking, material world because we cannot know things, as to what they may be by themselves, beyond being objects of our senses. The fourth paralogism is passed over lightly or not treated at all by commentators. In the first edition of the Critique of Pure Reason, the fourth paralogism is addressed to refuting the thesis that there is no certainty of the existence of the external world. In the second edition of the Critique of Pure Reason, the task at hand becomes the Refutation of Idealism. Sometimes, the fourth paralogism is taken as one of the most awkward of Kant's invented tetrads. Nevertheless, in the fourth paralogism, there is a great deal of philosophizing about the self that goes beyond the mere refutation of idealism. In both editions, Kant is trying to refute the same argument for the non-identity of mind and body.[34] In the first edition, Kant refutes the Cartesian doctrine that there is direct knowledge of inner states only and that knowledge of the external world is exclusively by inference. Kant claims mysticism is one of the characteristics of Platonism, the main source of dogmatic idealism. Kant explains skeptical idealism by developing a syllogism called "The Fourth Paralogism of the Ideality of Outer Relation:"
If that whose existence can be inferred only as a cause of given perceptions has only a doubtful existence.
And the existence of outer appearances cannot be immediately perceived but can be inferred only as the cause of given perceptions.
Then, the existence of all objects of outer sense is doubtful.[35]
Kant may have had in mind an argument by Descartes:
My own existence is not doubtful
But the existence of physical things is doubtful
Therefore, I am not a physical thing.
It is questionable that the fourth paralogism should appear in a chapter on the soul. What Kant implies about Descartes' argument in favor of the immaterial soul is that the argument rests upon a mistake on the nature of objective judgement not on any misconceptions about the soul. The attack is mislocated.[36]
These Paralogisms cannot be proven for speculative reason and therefore can give no certain knowledge about the Soul. However, they can be retained as a guide to human behavior. In this way, they are necessary and sufficient for practical purposes. In order for humans to behave properly, they can suppose that the soul is an imperishable substance, it is indestructibly simple, it stays the same forever, and it is separate from the decaying material world. On the other hand, anti-rationalist critics of Kant's ethics consider it too abstract, alienating, altruistic or detached from human concern to actually be able to guide human behavior. It is then that the Critique of Pure Reason offers the best defense, demonstrating that in human concern and behavior, the influence of rationality is preponderant.
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Kant presents the four antinomies of reason in the Critique of Pure Reason as going beyond the rational intention of reaching a conclusion. For Kant, an antinomy is a pair of faultless arguments in favor of opposite conclusions. Historically, Gottfried Leibniz and Samuel Clarke (Newton's spokesman) had just recently engaged in a titanic debate of unprecedented repercussions. Kant's formulation of the arguments was affected accordingly.[38]
The Ideas of Rational Cosmology are dialectical. They result in four kinds of opposing assertions, each of which is logically valid. The antinomy, with its resolution, is as follows:
Thesis: The world has, as to time and space, a beginning (limit).
Antithesis: The world is, as to time and space, infinite.
Both are false. The world is an object of experience. Neither statement is based on experience.
Thesis: Everything in the world consists of elements that are simple.
Antithesis: There is no simple thing, but everything is composite.
Both are false. Things are objects of experience. Neither statement is based on experience.
Thesis: There are in the world causes through freedom.
Antithesis: There is no freedom, but all is nature.
Both may be true. The thesis may be true of things-in-themselves (other than as they appear). The antithesis may be true of things as they appear.
Thesis: In the series of the world-causes there is some necessary being.
Antithesis: There is nothing necessary in the world, but in this series all is contingent.
Both may be true. The thesis may be true of things-in-themselves (other than as they appear). The antithesis may be true of things as they appear.
According to Kant, rationalism came to fruition by defending the thesis of each antinomy while empiricism evolved into new developments by working to better the arguments in favor of each antithesis.
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Kants Doctrine of Method contains four sections. The first section, Discipline of Pure Reason, compares mathematical and logical methods of proof, and the second section, Canon of Pure Reason, distinguishes theoretical from practical reason.
The Divisions of Critique of Pure Reason
Dedication
1. First and second Prefaces
2. Introduction
3. Transcendental Doctrine of Elements
A. Transcendental Aesthetic
B. Transcendental Logic
(1) Transcendental Analytic
a. Analytic of Concepts
i. Metaphysical Deduction
ii. Transcendental Deduction
b. Analytic of Principles
i. Schematism (bridging chapter)
ii. System of Principles of Pure Understanding
a. Axioms of Intuition
b. Anticipations of Perception
c. Analogies of Experience
d. Postulates of Empirical Thought (Refutation of Idealism)
iii. Ground of Distinction of Objects into Phenomena and Noumena
iv. Appendix on the Amphiboly of the Concepts of Reflection
(2) Transcendental Dialectic: Transcendental Illusion
a. Paralogisms of Pure Reason
b. Antinomy of Pure Reason
c. Ideal of Pure Reason
d. Appendix to Critique of Speculative Theology
4. Transcendental Doctrine of Method
A. Discipline of Pure Reason
B. Canon of Pure Reason
C. Architectonic of Pure Reason
D. History of Pure Reason
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The first part of Kant's book, the Critique of Aesthetic Judgment, discusses the four possible "reflective judgments": the agreeable, the beautiful, the sublime, and the good. Kant makes it clear that these are the only four possible reflective judgments, as he relates them to the Table of Judgments from the Critique of Pure Reason.
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In the Critique of Pure Reason, Kant claimed that the understanding was the ability to judge. The forms of judgments were said to be the basis of the categories and all philosophy. But in his Critique of Judgment, he called a new, different ability the faculty of judgment. That now resulted in four faculties: sensation, understanding, judging, and reason.
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Kant's divisions, however, are guided by his search in the mind for what makes synthetic a priori judgments possible.[55]
FUNCTION OF THOUGHT IN JUDGMENT CATEGORIES OF UNDERSTANDING PRINCIPLES OF PURE UNDERSTANDING
Square 1: Quantity Quantity
Universal
Particular
Singular Unity
Plurality
Totality Axioms of Intuition
square 2: Quality Quality
Affirmative
Negative
Infinite Reality
Negation
Limitation Anticipations of Perception
Square 3: Relation Relation
Categorical
Hypothetical
Disjunctive Of Inherence and Subsistence (substantia et accidens)
Of Causality and Dependence (cause and effect)
Of Community (reciprocity between the agent and patient) Analogies of Experience
Square 4: Modality Modality
Problematical
Assertorical
Apodeictical Possibility-Impossibility
Existence-Non-existence
Necessity-Contingence Postulates of Empirical Thought in General
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In the Transcendental Deduction, Kant aims to show that the categories derived in the Metaphysical Deduction are conditions of all possible experience. He achieves this proof roughly by the following line of thought: all representations must have some common ground if they are to be the source of possible knowledge (because extracting knowledge from experience requires the ability to compare and contrast representations that may occur at different times or in different places). This ground of all experience is the self-consciousness of the experiencing subject, and the constitution of the subject is such that all thought is rule-governed in accordance with the categories. It follows that the categories feature as necessary components in any possible experience.[26]
1.Axioms of intuition
2.Anticipations of perception
3.Analogies of experience
4.Postulates of empirical thought in general
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The dark triad is a group of three personality traits: narcissism, Machiavellianism and psychopathy. Use of the term "dark" implies that people scoring high on these traits have malevolent qualities:
Narcissism is characterized by grandiosity, pride, egotism, and a lack of empathy.
Machiavellianism is characterized by manipulation and exploitation of others, a cynical disregard for morality, and a focus on self-interest and deception.
Psychopathy is characterized by enduring antisocial behavior, impulsivity, selfishness, callousness, and remorselessness.
All three traits have been associated with a callous-manipulative interpersonal style. A factor analysis carried out at the Glasgow Caledonian University found that among the big five personality traits, low agreeableness is the strongest correlate of the dark triad, while neuroticism and a lack of conscientiousness were associated with some of the dark triad members.
Several researchers have suggested expanding the dark triad to contain a fourth dark trait. Everyday sadism, defined as the enjoyment of cruelty, is the most common addition. While sadism is highly correlated with the dark triad, researchers have shown that sadism predicts anti-social behavior beyond the dark triad.
The fourth square is always different and does not seem to belong
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Aulus Cornelius Celsus (c. 25 BC – c. 50 AD) was a Roman encyclopaedist, known for his extant medical work, De Medicina, which is believed to be the only surviving section of a much larger encyclopedia. The De Medicina is a primary source on diet, pharmacy, surgery and related fields, and it is one of the best sources concerning medical knowledge in the Roman world.
Aulus Cornelius Celsus is credited with recording the cardinal signs of inflammation known as "Celsus tetrad": calor (warmth), dolor (pain), tumor (swelling) and rubor (redness and hyperaemia). He goes into great detail regarding the preparation of numerous ancient medicinal remedies including the preparation of opioids. In addition, he describes many 1st century Roman surgical procedures which included removal of a cataract, treatment for bladder stones, and the setting of fractures.
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Gottfried Wilhelm von Leibniz’s university thesis ‘De Dissertatio de arte combinatoria’ (1666) was an appraisal of the work of Ramon Lull. Leibniz mentioned Lull only once in the synopsis of the ‘Arte Combinatoria’ together with the scholar Athenasius Kircher (1602 – 1680). The dissertation started with a ‘Demonstratio Existentiae Dei’. The diagram shows the relation between the four elements and the qualities, which were described by Aristotle in his ‘De Generatione et Corruptione’. It was added in a later print of the dissertation.
Leibniz expresses the quadrant image in his drawing.
A tetromino is a geometric shape composed of four squares, connected orthogonally. This, like dominoes and pentominoes, is a particular type of polyomino. The corresponding polycube, called a tetracube, is a geometric shape composed of four cubes connected orthogonally.
A popular use of tetrominoes is in the video game Tetris, where they have been called Tetriminos (spelled with an "i" as opposed to the "o" in "tetromino") since 2001.
Tetris is one of the most popular games of all time. It is no coincidence it is related to the number four.
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In computing, a nibble (often nybble or even nyble to match the vowels of byte) is a four-bit aggregation, or half an octet. It is also known as half-byte[2] or tetrade. In a networking or telecommunication context, the nibble is often called a semi-octet, quadbit, or quartet. A nibble has sixteen (24) possible values. A nibble can be represented by a single hexadecimal digit and called a hex digit.
A full byte (octet) is represented by two hexadecimal digits; therefore, it is common to display a byte of information as two nibbles. Sometimes the set of all 256 byte values is represented as a table 16×16, which gives easily readable hexadecimal codes for each value.
4-bit computer architectures use groups of four bits as their fundamental unit. Such architectures were used in early microprocessors and pocket calculators and continue to be used in some micro controllers
There are 16 nibbles representing the 16 squares of the quadrant model
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Two levers connected by a rod so that a force applied to one is transmitted to the second is known as a four-bar linkage. The levers are called cranks, and the fulcrums are called pivots. The connecting rod is also called the coupler. The fourth bar in this assembly is the ground, or frame, on which the cranks are mounted.
Linkages are important components of machines and tools. Examples range from the four-bar linkage used to amplify force in a bolt cutter or to provide independent suspension in an automobile, to complex linkage systems in robotic arms and walking machines. The internal combustion engine uses a slider-crank four-bar linkage formed from its piston, connecting rod, and crankshaft to transform power from expanding burning gases into rotary power. Relatively simple linkages are often used to perform complicated tasks.
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In kinematics, cognate linkages are linkages that ensure the same input-output relationship or coupler curve geometry, while being dimensionally dissimilar. In case of four-bar linkage coupler cognates, the Roberts–Chebyschev Theorem, after Samuel Roberts and Pafnuty Chebyshev, states that each coupler curve can be generated by three different four-bar linkages. These four-bar linkages can be constructed using similar triangles and parallelograms, and the Cayley diagram (named after Arthur Cayley).
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Johannes Scotus Eriugena (/dʒoʊˈhæniːz, -ˈhænɪs ˈskoʊtəsˌ ˈskɒtəs ɪˈrɪdʒənə/; c. 815 – c. 877) was an Irish theologian, neoplatonist philosopher, and poet. He wrote a number of works, but is best known today, and had most influence in subsequent centuries, for having translated and made commentaries upon the work of Pseudo-Dionysius.
John Scotus’ book – also called in Greek ‘Periphyseon’ – was, above all, an unmistakable sign, that tetradic thinking had reached visibility. Or, like HEER (1966) put it in a more roundabout way: ‘Eriugena united the Greek doctrine of deification (as in Clement, Origen and Dionysius) with Celtic-Germanic beliefs regarding rebirth and return’.
The fourfold division of nature is put forward on the first page of Book I of Eriugena’s book (and later repeated in Book II and III) by the Nutritor (Master), who speaks to the Alumnus (Disciple):
‘It is my opinion that the division of Nature by means of four differences results in four species, being divided first into that which creates and is not created (quae creat et non creatus), secondly into that which is created and also creates (quae et creatur et creat), thirdly into that which is created and does not create (quae creatur et non creat), while the fourth neither creates nor is created (quae nec creat nec creatur).’
DUHEM (1958, Tome III, p. 53) typified the work of Eriugena as neo-Platonic: ‘la philosophie neo-platonicienne de Scot Erigene s’inspire surtout de Chalcidius‘ (the neo-platonic philosophy of Eriugena, who was inspired by Chalcidius (and his commentary of the ‘Timaeus‘ of Plato). He is also portrayed as a ‘Greek’ mind in a ‘Latin’ world (LEFF, 1958).
It is perhaps apologetic to call every visualization of division thinking in the European cultural history ‘neo-platonic’, but the association of this term with the neo-platonic writers of the early centuries AD (like Ammonius Saccas (Saccas being a nickname meaning ‘uncertain interpretation’; WALLIS, 1972/1995), his pupil Plotinus, Jamblichus, Porphyrius, etc.) is an unhappy one. Furthermore, the connotation does not give credit to Aristotle, who might be regarded as the main architect of the tetradic mind. Robert O’NEILL (2011) wrote a very clarifying article on Neoplatonism.
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Eriugena's great work, De divisione naturae (Περί φύσεων), which was condemned by a council at Sens by Honorius III (1225), who described it as "swarming with worms of heretical perversity," and by Gregory XIII in 1585, is arranged in five books. The form of exposition is that of dialogue; the method of reasoning is the syllogism. Nature (Natura in Latin or physis in Greek) is the name of the most comprehensive of all unities, that which contains within itself the most primary division of all things, that which is (being) and that which is not (nonbeing). The Latin title refers to these four divisions of nature: (1) that which creates and is not created; (2) that which is created and creates; (3) that which is created and does not create; (4) that which is neither created nor creates. The first is God as the ground or origin of all things, the last is God as the final end or goal of all things, that into which the world of created things ultimately returns. The second and third together compose the created universe, which is the manifestation of God, God in process, Theophania; the second is the world of Platonic ideas or forms, and the third is a more pantheistic world, or a pandeistic one,[8] depending on the interference of God. Thus we distinguish in the divine system beginning, middle and end; but these three are in essence one; the difference is only the consequence of our finite comprehension. We are compelled to envisage this eternal process under the form of time, to apply temporal distinctions to that which is extra- or supra-temporal. It is in turn through our experience that the incomprehensible divine is able to frame an understanding of itself.
The Division of Nature has been called the final achievement of ancient philosophy, a work which "synthesizes the philosophical accomplishments of fifteen centuries." It is presented, like Alcuin's book, as a dialogue between Master and Pupil. Eriugena anticipates Thomas Aquinas, who said that one cannot know and believe a thing at the same time. Eriugena explains that reason is necessary to understand and interpret revelation. "Authority is the source of knowledge, but the reason of mankind is the norm by which all authority is judged."[9]
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De divisione naturae ("The division of nature") is the title given by Thomas Gale to his edition (1681) of the work originally titled by Eriugena Periphyseon. This work was the magnum opus of ninth century theologian Johannes Scotus Eriugena.
The work is arranged in five books. The form of exposition is that of dialogue; the method of reasoning is the syllogism. Natura is the name for the universal, the totality of all things, containing in itself being and non-being. It is the unity of which all special phenomena are manifestations. But of this nature there are four distinct classes:
Square 1: That which creates and is not created;
Square 2: That which is created and creates;
Square 3: That which is created and does not create;
Square 4: That which neither is created nor creates.
The first is God as the ground or origin of all things, the last is God as the final end or goal of all things, that into which the world of created things ultimately returns. The second and third together compose the created universe, which is the manifestation of God, God in process, Theophania; the second being the world of Platonic ideas or forms, and the third being a more panentheistic, pandeistic, or panendeistic world, depending on the post-creation scope and interference of God.
Scotus is considered one of the greatest philosophers of all time, and he pushed the idea that God is Being. In my quadrant model the seventeenth square is being. The seventeenth square is the fifth quadrant, which represents God (ultra transcendence) ((Although God is even beyond being you cannot even talk about God adequately any attempt is futile)
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Book I of the Topics is introductory, laying down a number of preliminary principles upon which dialectical argumentation proceeds. After defining dialectical reasoning (syllogism) and distinguishing it from demonstrative, contentious, and (one might say) "pseudo-scientific"[8] syllogism, Aristotle notes the utility of the art of dialectic, then sets out four bases (accident, property, genus, definition) from which invention of such reasoning proceeds. He next elucidates various senses of "sameness", as bearing directly upon the usual character of such arguments. Dialectical propositions and dialectical problems are characterized. Then, the ὄργανα (órgana) or means by which arguments may be obtained are described, in a four-fold summary, as:
the provision of propositions
discovery of the number of senses of a term
the discovery of differences
the investigation of similarities
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The Prior Analytics represents the first formal study of logic, where logic is understood as the study of arguments. An argument is a series of true or false statements which lead to a true or false conclusion.[9] In the Prior Analytics, Aristotle identifies valid and invalid forms of arguments called syllogisms. A syllogism is an argument that consists of at least three sentences: at least two premises and a conclusion. Although Aristotles does not call them "categorical sentences," tradition does; he deals with them briefly in the Analytics and more extensively in On Interpretation.[10] Each proposition (statement that is a thought of the kind expressible by a declarative sentence)[11] of a syllogism is a categorical sentence which has a subject and a predicate connected by a verb. The usual way of connecting the subject and predicate of a categorical sentence as Aristotle does in On Interpretation is by using a linking verb e.g. P is S. However, in the Prior Analytics Aristotle rejects the usual form in favor of three of his inventions: 1) P belongs to S, 2) P is predicated of S and 3) P is said of S. Aristotle does not explain why he introduces these innovative expressions but scholars conjecture that the reason may have been that it facilitates the use of letters instead of terms avoiding the ambiguity that results in Greek when letters are used with the linking verb.[12] In his formulation of syllogistic propositions, instead of the copula ("All/some... are/are not..."), Aristotle uses the expression, "... belongs to/does not belong to all/some..." or "... is said/is not said of all/some..."[13] There are four different types of categorical sentences: universal affirmative (A), particular affirmative (I), universal negative (E) and particular negative (O).
A - A belongs to every B
E - A belongs to no B
I - A belongs to some B
O - A does not belong to some B
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Depending on the position of the middle term, Aristotle divides the syllogism into three kinds: Syllogism in the first, second and third figure.[15] If the Middle Term is subject of one premise and predicate of the other, the premises are in the First Figure. If the Middle Term is predicate of both premises, the premises are in the Second Figure. If the Middle Term is subject of both premises, the premises are in the Third Figure.
"In Aristotelian syllogistic (Prior Analytics, Bk I Caps 4-7), syllogisms are divided into three figures according to the position of the middle term in the two premises. The fourth figure, in which the middle term is the predicate in the major premise and the subject in the minor, was added by Aristotle's pupil Theophrastus and does not occur in Aristotle's work, although there is evidence that Aristotle knew of fourth-figure syllogisms."
The fourth square is always different and does not seem to belong
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The fallacy of four terms (Latin: quaternio terminorum) is the formal fallacy that occurs when a syllogism has four (or more) terms rather than the requisite three. This form of argument is thus invalid.
Sometimes a syllogism that is apparently fallacious because it is stated with more than three terms can be translated into an equivalent, valid three term syllogism.[2] For example:
Major premise: No humans are immortal.
Minor premise: All Greeks are people.
Conclusion: All Greeks are mortal.
This EAE-1 syllogism apparently has five terms: "humans", "people", "immortal", "mortal", and "Greeks". However it can be rewritten as a standard form AAA-1 syllogism by first substituting the synonymous term "humans" for "people" and then by reducing the complementary term "immortal" in the first premise using the immediate inference known as obversion (that is, "No humans are immortal." is equivalent to "All humans are mortal.").
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The letter S is the subject of the conclusion, P is the predicate of the conclusion, and M is the middle term. The major premise links M with P and the minor premise links M with S. However, the middle term can be either the subject or the predicate of each premise where it appears. The differing positions of the major, minor, and middle terms gives rise to another classification of syllogisms known as the figure. Given that in each case the conclusion is S-P, the four figures are:
Figure 1 Figure 2 Figure 3 Figure 4
Major premise: M–P P–M M–P P–M
Minor premise: S–M S–M M–S M–S
(Note, however, that, following Aristotle's treatment of the figures, some logicians—e.g., Peter Abelard and John Buridan—reject the fourth figure as a figure distinct from the first. See entry on the Prior Analytics.)
This is the foundation of all logic
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the Nyaya school first codified and established a 'system of logic'. The Nyāya recognized four 'sources of knowledge' (pramana): perception, inference, comparison and testimony.
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Venn diagrams typically represent two or three sets, but there are forms that allow for higher numbers. Shown below, four intersecting spheres form the highest order Venn diagram that has the symmetry of a simplex and can be visually represented. The 16 intersections correspond to the vertices of a tesseract (or the cells of a 16-cell respectively)
According to the quadrant model the fourth is always different. Four sets are possible although they are very transcendent. The 16 cell reflects the image of the quadrant model (the 16 squares)
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In De Libero Arbitrio III.20 & 21 (circa 395 C.E.), when Augustine first attends to the question of the soul's origin in a manner that focuses upon particular possibilities, he does so as part of an anti-Manichean theodicy intended to show that it is the human soul rather than God that is responsible for the presence of moral evil in the world. Thus, as he later points out in Letter 143 (circa 412 C.E.), he is not concerned to adjudicate between these competing hypotheses, but merely to show that each is consistent with a non-Manichean, Neoplatonizing account of moral evil. Nonetheless, the four hypotheses he does advance are important evidence about how he understands the conceptual landscape [O'Daly 1987, pp. 15–20; Mendelson 1998, pp. 30–44], and the anti-Manichean polemic notwithstanding, it is instructive that he makes no attempt to choose between or even to offer a tentative ranking of them.
Interestingly enough, two of the four hypotheses require the soul's existence prior to embodiment. On the first, the soul is sent by God to administer the body (henceforth the “sent” hypothesis); on the second, the soul comes to inhabit the body by its own choice (henceforth the “voluntarist” hypothesis). In later presentations of these hypotheses (though not in De Libero Arbitrio III), Augustine treats the voluntarist hypothesis as involving both a sin on the soul's part and a cyclical process whereby the soul is subject to multiple incarnations [Letter 166.27]. The other two hypotheses, the “traducianist” and the “creationist,” do not involve pre-existence, but there is nonetheless a significant contrast between them. On the traducianist account, all souls are propagated from Adam's soul in a manner analogous to that of the body, thus linking each soul to all previous ones by a kind of genealogical chain. On the creationist hypothesis, however, God creates a new soul for each body, thus creating a kind of vertical link between God and each individual soul.
These hypotheses do not exhaust the logical possibilities, but they were the main contenders in Augustine's time. There remains controversy over the extent to which Augustine himself was inclined towards either of the hypotheses that required pre-existence [O'Connell 1968, O'Daly 1987, pp. 15–20; O'Donnell 1992 II.34–5], but there are passages in the Confessions [see Confessions I.6–8] and elsewhere [e.g. De Genesi Contra Manicheos 2.8 (circa 388–9 C.E.) and De Genesi ad Literam Imperfectus Liber 1.3 (circa 393 C.E.)] that have led some to regard it as a possibility he takes very seriously indeed, perhaps even preferring it, at least until the early part of the fifth century [O'Connell 1968; Teske 1991]
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The Four Branches of the Mabinogi or Y Pedair Cainc Mabinogi are the earliest prose literature of Britain. Originally written in Wales in Middle Welsh, but widely available in translations, the Mabinogi is generally agreed to be a single work in four parts, or "Branches." The interrelated tales can be read as mythology, political themes, romances, or magical fantasies. They appeal to a wide range of readers, from young children to the most sophisticated adult. The tales are popular today in book format, as storytelling or theatre performances; they appear in recordings and on film, and continue to inspire many reinterpretations in artwork and modern fiction.
Each Branch contains several tale episodes in a sequence, and each Branch is titled with the name of a leading protagonist. These titles are Pwyll, Branwen, Manawydan and Math, but this is a modern custom: the Branches are not titled in the mediaeval manuscripts. Only one character appears in all four Branches, Pryderi, though he is never dominant or central to any of the Branches.
Square 1: Pwyll Prince of Dyfed tells of the heroic and magical sojourn of Pwyll in Annwfn, his shapeshifting, chastity and a duel, which all establish a mighty alliance. The formidable Rhiannon courts him, and he helps her win her freedom to marry him. The strange abduction at birth of their baby son follows, with his rescue, fostering and restoration by the good lord Teyrnon of Gwent. The child is named Pryderi.
Square 2: Branwen Daughter of Llŷr follows Branwen's marriage to the King of Ireland, who abuses her due to insult by her half brother Efnisien. A tragically genocidal war develops fomented by Efnisien, in which a Cauldron which resurrects the dead figures, and the giant king Bran's head survives his death in an enchanted idyll. Pryderi is merely named as a war survivor, and Branwen dies heartbroken.
Square 3: Manawydan Son of Llŷr brother of Branwen, heir to the throne of Britain, becomes Pryderi's good friend during the war. Pryderi arranges his friend's marriage to Rhiannon. The land of Dyfed is devastated. Journeys in England setting up craft businesses follow. An enchanted trap removes Pryderi and Rhiannon: Manawydan becomes a farmer. He cannily negotiates their release, as well as the restoration of the land, by confronting the villain behind it all.
Square 4: Math Son of Mathonwy is a dark sequence of deception and treachery: war with Dyfed, the death of Pryderi, the double rape of a virgin girl, and the rejection of an unwanted hero son by proud Arianrhod. Gwydion her magician brother is the architect of all these destinies. He adds an artificially incubated pregnancy, and a synthetic woman. She, Blodeuedd, creates a treacherous love triangle, murder in a peculiar manner. Gwydion makes a shamanic journey of redemption.
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The local news station was interviewing an 80-year-old lady because she had just gotten married - for the fourth time.
The interviewer asked her questions about her life, about what it felt like to be marrying again at 80, and then about her new husband's occupation.
"He's a funeral director," she answered.
"Interesting," the newsman thought. He then asked her if she wouldn't mind telling him a little about her first three husbands and what they did for a living.
She paused for a few moments, needing time to reflect on all those years. After a short time, a smile came to her face and she answered proudly, explaining that she'd first married a banker when she was in her early 20s, then a circus ringmaster when in her 40s, later on a preacher when in her 60s, and now in her 80s, a funeral director.
The interviewer looked at her, quite astonished, and asked why she had married four men with such diverse careers.
She smiled and explained, "I married one for the money, two for the show, three to get ready, and four to go."
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Four guys are hanging out at a bar, and one gets up to go to the bathroom. While he is gone, one of the others sparks up a conversation about his son.
He says, "I was afraid to think of my son's future when he was working as a secretary for a Real estate agency, but when he left that job, he started his own agency, and he's so rich now, that he gave his best friend a new house for his birthday!"
Another man says, "I thought my son was going nowhere when he had a job getting coffee for a stockbroker, but when he left that job, he started playing the market, and now he's so rich, he gave his best friend a million dollars in stock for his birthday!"
Another man says, "I thought my son wasn't going anywhere with his job as a secretary in a car dealership, but now he owns his own dealership, and he gave his best friend a new Mercedes for his birthday!"
The fourth man returned from the bathroom, and they asked him about his son.
The fourth man replied, "Well, I fear for my son's future because he's a hair stylist, and last year, I found out that he was gay, but, on the plus side, his four boyfriends gave him a new house, a million in stock, and a Mercedes for his birthday."
Q: Whats 69 and 69?
A: Dinner for 4.
Did you know the toughest golf foursome to play behind?
A: It's Monica Lewinsky, OJ Simpson, Ted Kennedy, and Bill Clinton.
Q: Why?
A: Monica is a hooker. OJ is a slicer. Kennedy can't drive over water and Clinton doesn't know which hole to play.
Four nuns were standing in line at the gates of heaven. Peter asks the first if she has ever sinned. "Well, once I looked at a man's penis," she said.
"Put some of this holy water on your eyes and you may enter heaven," Peter told her.
Peter then asked the second nun if she had ever sinned. "Well, once I held a man's penis," she replied.
"Put your hand in this holy water and you may enter heaven," he said.
Just then the fourth nun pushed ahead of the third nun. Peter asked her, "Why did you push ahead in line?"
She said, "Because I want to gargle before she sits in it!"
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A turnstile antenna is a radio antenna consisting of a set of two identical dipole antennas aligned at right angles to each other and fed in phase quadrature; the two currents applied to the dipoles are 90° out of phase.The name reflects the notion the antenna looks like a turnstile when mounted horizontally. The turnstile antenna is often referred to as crossed dipoles. The antenna can be used in two possible modes. In normal mode the antenna radiates horizontally polarized radio waves perpendicular to its axis. In axial mode the antenna radiates circularly polarized radiation along its axis.
The turnstile antenna was invented by George Brown in 1935[1] and described in scholarship in 1936. The patent history reveals the popularity of the turnstile antenna over the years.
The turnstile antenna is the shape of a quadrant.
The fundamental requirement for the turnstile to function is ensuring each dipole's currents are of equal magnitude and in phase quadrature.[2] This is done with feed-line techniques or by adding reactance in series with the dipoles.
Quadrature feed
A popular method of feeding the two dipoles in a turnstile antenna is to split the RF signal from the transmission line into two equal signals with a two way splitter, then delay one by 90 degrees additional electrical length. Each phase is applied to one of the dipoles
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The Stokes parameters are a set of values that describe the polarization state of electromagnetic radiation. They were defined by George Gabriel Stokes in 1852, as a mathematically convenient alternative to the more common description of incoherent or partially polarized radiation in terms of its total intensity (I), (fractional) degree of polarization (p), and the shape parameters of the polarization ellipse. The effect of an optical system on the polarization of light can be determined by constructing the Stokes vector for the input light and applying Mueller calculus, to obtain the Stokes vector of the light leaving the system.
The relationship of the Stokes parameters S0, S1, S2, S3 to intensity and polarization ellipse parameters is shown in the equations below and the figure at right.
{\begin{aligned}S_{0}&=I\\S_{1}&=Ip\cos 2\psi \cos 2\chi \\S_{2}&=Ip\sin 2\psi \cos 2\chi \\S_{3}&=Ip\sin 2\chi \end{aligned}}
The Stokes parameters are defined by
{\begin{matrix}I&\equiv &\langle E_{x}^{2}\rangle +\langle E_{y}^{2}\rangle \\~&=&\langle E_{a}^{2}\rangle +\langle E_{b}^{2}\rangle \\~&=&\langle E_{l}^{2}\rangle +\langle E_{r}^{2}\rangle ,\\Q&\equiv &\langle E_{x}^{2}\rangle -\langle E_{y}^{2}\rangle ,\\U&\equiv &\langle E_{a}^{2}\rangle -\langle E_{b}^{2}\rangle ,\\V&\equiv &\langle E_{l}^{2}\rangle -\langle E_{r}^{2}\rangle .\end{matrix}}
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A four-bar linkage, also called a four-bar, is the simplest movable closed chain linkage. It consists of four bodies, called bars or links, connected in a loop by four joints. Generally, the joints are configured so the links move in parallel planes, and the assembly is called a planar four-bar linkage.
If the linkage has four hinged joints with axes angled to intersect in a single point, then the links move on concentric spheres and the assembly is called a spherical four-bar linkage. Bennett's linkage is a spatial four-bar linkage with hinged joints that have their axes angled in a particular way that makes the system movable.
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The Hoeckens linkage is a four-bar mechanism that converts rotational motion to approximate straight-line motion. It is named after Karl Hoecken (1874−1962).
The example to the right spends over half of the cycle in the near straight portion.
The Hoeckens linkage is a cognate linkage of the Chebyshev linkage.
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To many clinicians, it may appear that the function of the anterior cruciate and posterior cruciate ligaments (ALL and PLL) is to limit anterior and posterior shear of the knee, as well as prevent rotation of the tibia in relation to the femur. This is what we were taught in orthopedics as we learned to perform the drawer and Lachman's tests of the knee.
In reality, the function of these ligaments is more than merely their contribution to knee stability. These ligaments are vital in transferring power from the muscles of the hip and pelvis (particularly the gluteus maximus and medius) to the leg. This transfer of power is done through the four-bar mechanism created by the degree of tension of these ligaments, and the stiffness of the tibia and femur.1-4
A four-bar mechanism is a simple closed-chain linkage composed of four bars (also referred to as links) and joined by four pivoting connections.5 This mechanism provides efficiency of motion, strength and stability.
Examples of four-bar mechanisms in engineering include vise-grips, lever-armed water pumps, car jacks, oil well pumps, folding chair mechanisms, and umbrellas. This mechanism is so efficient that many of the more modern prosthetic knees (for above-the-knee amputations) are now made with four-bar linkages. Researchers are trying to emulate this naturally occurring mechanism in knee-replacement prostheses.
The four-bar mechanism of the knee is a relatively simple apparatus that transfers power while maximizing leverage and minimizing energy loss. It is part of a broader biotensegrity system, which combines contractile and non-contractile tissues to efficiently transfer power and motion through the musculoskeletal system with minimal energy expenditure.
The four links transfer power and motion from relatively distant sources of power through a driver. In the knee, the femur, which is the longest lever in the body, acts as the driver as it transfers power from the gluteal muscles through its stiffness and strength to create tension on the ALL and PLL. This tension moves the femur relative to the plane(s) of the tibial plateau.
(It should be noted that the four-bar mechanism of the knee does not exactly mirror man-made mechanical models of four-bar machines. The ACL and PCL are relatively stiff only while under load, and even when under load, they maintain some elasticity.)
Certainly the ALL and PLL do not work autonomously in transferring power. The lower extremity is a complex aggregate of structures that includes ligaments, muscles, joint capsules and fascia. There is a concert of activity between these structures during knee motion.
While each of these components is important, the gluteal muscles have a prominent role in both power transfer and protection of the knee.6-10 This knee-gluteal muscle relationship is particularly interesting since the gluteal muscles do not directly attach to or even reside near the knee.
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Steno, in his Dissertationis prodromus of 1669 is credited with four of the defining principles of the science of stratigraphy: the law of superposition: "... at the time when any given stratum was being formed, all the matter resting upon it was fluid, and, therefore, at the time when the lower stratum was being formed, none of the upper strata existed"; the principle of original horizontality: "Strata either perpendicular to the horizon or inclined to the horizon were at one time parallel to the horizon"; the principle of lateral continuity: "Material forming any stratum were continuous over the surface of the Earth unless some other solid bodies stood in the way"; and the principle of cross-cutting relationships: "If a body or discontinuity cuts across a stratum, it must have formed after that stratum."[32] These principles were applied and extended in 1772 by Jean-Baptiste L. Romé de l'Isle. Steno's ideas still form the basis of stratigraphy and were key in the development of James Hutton's theory of infinitely repeating cycles of seabed deposition, uplifting, erosion, and submersion
The first three Steno called principles and the last one he called a law. The fourth is always different.
During the Sui dynasty, stone and brick were introduced as material for building pagodas. The Four-Gates Pagoda was built from blocks quarried from a hard local rock. All extant older stone pagodas are sculptured pagodas or columns in the shape of a pagoda. The simple design of the Four Gates Pagoda is typical for one-storey, pavilion-style pagodas: It has a square cross-section delineated by plane side walls. All elements of the structure are symmetrical with four identical sides each facing one of the four cardinal directions. In the center of each wall is a door with straight sides and round arch on top (hence the name). The roof of the pagoda is pyramid shaped. It consists of 23 tiers of overlapping stone slabs and is supported by 5 tiers of stone eaves. The tip of the roof is occupied by a stone steeple. The overall shape of the steeple resembles a box-shaped pagoda which is carved with Buddhist scriptures and sits on its own Sumeru pedestal with stone corner decorations in the shape of banana leaves. The spire of the steeple is made up of 5 stone discs. The total height of the pagoda is 10.4 meters; each side is 7.4 meters long.
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The most common Qi circulating formulation and a treatment for the stress, anger, and frustration associated with Liver Qi Stagnation is known as the “Four Gates”. The Four Gates are the right and left side acupuncture points Lv 3-Liver 3 (Taichong) and LI 4-Large Intestine 4 (Hegu).
Together these four acupuncture points are thought to enhance the circulation of Qi and blood throughout the body and have a calming and analgesic effect.
Large Intestine 4 is located on the padded area of your hand between the thumb and index finger, between the first and second metacarpal bones. Massage the point with your thumb on both hands for approximately 30 seconds.
Liver 3 is located in a hollow on the top of your foot below the gap between your big toe and the next toe, between the bones that attach to the large and second toes and gently knead the point for approximately thirty seconds. Then switch sides to stimulate Lv 3 on your other foot.
Scientists and psychologists have studied that this treatment is actually effective.
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The Four Seas are point groupings which have a strong effect on their related system within the body (i.e. qi, blood, marrow, digestion).
The Sea of Qi Points (ST 9, CV 17, GV 15, GV 14) effect the amount and flow of Qi (energy) within the body. A person with excess Qi may experience problems of an excess nature in the upper body (headache, red face, fullness in the chest, etc.). A person with Qi deficiency may experience problems with fatigue, weakness, shortness of breath, etc.
The Sea of Blood Points (UB 11, ST 37, ST 39) effect the amount and flow of Blood (which constitutes more than the western idea of blood) within the body. Excesses in the Blood, according to the classics, may make someone feel larger than they are and make them aware of a subtle illness or imbalance within their body. Blood excess is not a primary diagnosis in TCM, whereas Blood stagnation is. Blood deficiency may lead to a variety of issues within a person such as dizziness, dryness, thinking problems, etc. Again, according to the classics, Blood deficiency may make someone feel smaller than they are, however, this doesn't seem to be a common complaint in modern clinical practice. For Blood issues, points such as UB 17, UB 18, UB 19, SP 10 and LV 8 are much more widely used.
The Sea of Water and Grain Points (ST 30, ST 36) effect digestion and appetite.
The Sea of Marrow Points (GV 20, GV 16) effect mental functioning and energy levels. When deficient a person may experience fatigue, tinnitus, weakness in the lower limbs, etc.
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Acupuncture has numerous approaches around the world, including virtually every Asian nation. However, approximately 600 years ago, the Koreans developed one of the most significant techniques of balancing the meridians. The procedure is virtually unknown to most acupuncturists except in Korea, extreme northern China and in the northern islands of Japan.
The technique requires the use of four specific acupuncture points for each meridian that is shown to be either too high or too low. In Chinese acupuncture, the utilization of the single "tonification" or "sedation" point is all that is classically used.
Even though simple tonification and sedation will suffice in most cases, for those stubborn conditions that are having great difficulty in establishing a balance, this Korean system is ideal. This technique will balance meridians when other procedures will not
The four steps for a "deficient" meridian are:
Tonify the horary point of the mother organ.
Tonify the mother organ's element point on the affected organ.
Sedate the horary point of the controlling meridian (KO cycle).
Sedate the controlling organ's element point on the affected organ.
The four steps for an "excessive" meridian are:
Tonify the horary point of the controlling organ (KO cycle).
Tonify the controlling organ's element point on the affected organ.
Sedate the horary point on the "son" organ.
Sedate the son organ's element point on the affected organ.
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The four estates are: politics, administration, judiciary, journalism.
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Abstract Master Cui’s Four Flowers point combination is a group of non-channel points specifically described for the purpose of applying moxibustion in severe vacuity conditions. Traditionally, this group of points was located using an unusual technique, but over time some doctors simplified the point location method or equated them with channel points.
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Two diagrams known as bagua (or pa kua) loom large in feng shui, and both predate their mentions in the Yijing (or I Ching).[citation needed] The Lo (River) Chart (Luoshu) was developed first,[42] and is sometimes associated with Later Heaven arrangement of the bagua. This and the Yellow River Chart (Hetu, sometimes associated with the Earlier Heaven bagua) are linked to astronomical events of the sixth millennium BC, and with the Turtle Calendar from the time of Yao. The Turtle Calendar of Yao (found in the Yaodian section of the Shangshu or Book of Documents) dates to 2300 BC, plus or minus 250 years.[44]
In Yaodian, the cardinal directions are determined by the marker-stars of the mega-constellations known as the Four Celestial Animals:
East
The Azure Dragon (Spring equinox)—Niao (Bird 鳥), α Scorpionis
South
The Vermilion Bird (Summer solstice)—Huo (Fire 火), α Hydrae
West
The White Tiger (Autumn equinox)—Mǎo (Hair 毛), η Tauri (the Pleiades)
North
The Black Tortoise (Winter solstice)—Xū (Emptiness, Void 虛), α Aquarii, β Aquarii
The diagrams are also linked with the sifang (four directions) method of divination used during the Shang dynasty.[45] The sifang is much older, however. It was used at Niuheliang, and figured large in Hongshan culture's astronomy. And it is this area of China that is linked to Huangdi, the Yellow Emperor, who allegedly invented the south-pointing spoon (see compass)
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The Year of the Four Emperors was a year in the history of the Roman Empire, AD 69, in which four emperors ruled in succession: Galba, Otho, Vitellius, and Vespasian.
The suicide of emperor Nero, in 68, was followed by a brief period of civil war, the first Roman civil war since Mark Antony's death in 30 BC. Between June of 68 and December of 69, Rome witnessed the successive rise and fall of Galba, Otho and Vitellius until the final accession of Vespasian, first of the Imperial Flavian dynasty, in July 69. The social, military and political upheavals of the period had Empire-wide repercussions, which included the outbreak of the Batavian rebellion.
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I discussed that the four fields of inquiry are science, religion, art, and philosophy. There is the questionable fifth, history. A lot of people say that history is a science so it is not a separate field of inquiry. There is a connection between the first square and the fifth. The first, science, is the light, the fifth, history, is the true light. Some historians argue that history is not a science because they say it cannot be replicated and studied (arguably). Also history, the fifth square, and philosophy, the fourth square, are very connected. Some historians and philosophers say that history and philosophy are the same thing. The fourth square always indicates the nature of the fifth. In the end of this book I am going to give some examples from history that fulfill the quadrant model pattern.
Regardless the fifth is always questionable. The fourth is different. Some say that philosophy should just be reduced to science. As I mentioned philosophy encompasses science art and religion, the nature of the fourth square. The fifth square is always questionable.
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Ancient historians tell us that Alexander the Great’s four generals divided his empire and assumed control of different parts. His four generals were Lysimachus, Cassander, Seleucus, and Ptolemy.
Square 1: Lysimachus received Thrace and most of Asia Minor.
Square 2: Cassander obtained Macedonia and Greece.
Square 3: Ptolemy was given Egypt, Palestine, Cilicia, Petra, and Cyprus while
Square 4:Seleucus controlled the rest of Asia: Syria, Babylon, Persia, and India.
After Alexander's death his empire was divided among these four parts
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In Japan, the four brings misfortune. They avoid to pronounce it because the same word means "the death". The fourth square is knowledge/death
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Amerindians, this number is the perfection: the prayers are repeated four times, the dances have four tempo, and the warriors do four pauses before to rush on their enemies.
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There are four opposed camps of the morality and nature of evil: moral absolutism, amoralism, moral relativism, and moral universalism.
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The Valley of Mexico can be subdivided into four basins, but the largest and most-studied is the area which contains Mexico City. This section of the valley in particular is colloquially referred to as the "Valley of Mexico".[3] The valley has a minimum altitude of 2,200 meters (7,200 ft) above sea level and is surrounded by mountains and volcanoes that reach elevations of over 5,000 meters (16,000 ft).[4] It is an enclosed valley with no natural outlet for water to flow and a gap to the north where there is a high mesa but no high mountain peaks. Within this vulnerable watershed all the native fishes were extinct by the end of the 20th century.[5] Hydrologically, the valley has three features. The first feature is the lakebeds of five now-extinct lakes, which are located in the southernmost and largest of the four sub-basins. The other two features are piedmont, and the mountainsides that collect the precipitation that eventually flows to the lake area. These last two are found in all four of the sub-basins of the valley.[1][3] Today, the Valley drains through a series of artificial canals to the Tula River, and eventually the Pánuco River and the Gulf of Mexico. Seismic activity is frequent here, and the valley is considered an earthquake prone zone.[6]
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Mexico cityIntercity buses[edit]
The city has four major bus stations (North, South, Observatorio, TAPO), which comprise one of the world's largest transportation agglomerations, with bus service to many cities across the country and international connections.
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The Project Management Triangle (called also Triple Constraint or the Iron Triangle) is a model of the constraints of project management. It is a graphic aid where the three attributes show on the corners of the triangle to show opposition. It is useful to help with intentionally choosing project biases, or analyzing the goals of a project.[1] It is used to illustrate that project management success is measured by the project team's ability to manage the project, so that the expected results are produced while managing time and cost.[2][3][4]
Like any human undertaking, projects need to be performed and delivered under certain constraints. Traditionally, these constraints have been listed as "scope" (features and quality), "time", and "cost".[5] These are also referred to as the "Project Management Triangle," where each side represents a constraint. One side of the triangle cannot be changed without affecting the others. A further refinement of the constraints separates product "quality" or "performance" from scope, and turns quality into a fourth constraint.
The fourth is always different
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In statistics, a contingency table is a type of table in a matrix format that displays the (multivariate) frequency distribution of the variables. They are heavily used in survey research, business intelligence, engineering and scientific research. They provide a basic picture of the interrelation between two variables and can help find interactions between them. The term contingency table was first used by Karl Pearson in "On the Theory of Contingency and Its Relation to Association and Normal Correlation",[1] part of the Drapers' Company Research Memoirs Biometric Series I published in 1904.
A crucial problem of multivariate statistics is finding (direct-)dependence structure underlying the variables contained in high-dimensional contingency tables. If some of the conditional independences are revealed, then even the storage of the data can be done in a smarter way (see Lauritzen (2002)). In order to do this one can use information theory concepts, which gain the information only from the distribution of probability, which can be expressed easily from the contingency table by the relative frequencies.
contingency tables sort of look like quadrants
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In the field of machine learning, a confusion matrix, also known as a contingency table or an error matrix [3] , is a specific table layout that allows visualization of the performance of an algorithm, typically a supervised learning one (in unsupervised learning it is usually called a matching matrix). Each column of the matrix represents the instances in a predicted class while each row represents the instances in an actual class (or vice-versa).[2] The name stems from the fact that it makes it easy to see if the system is confusing two classes (i.e. commonly mislabeling one as another).
Contents [hide]
1 Example
2 Table of confusion
3 See also
4 References
5 External links
Example[edit]
If a classification system has been trained to distinguish between cats, dogs and rabbits, a confusion matrix will summarize the results of testing the algorithm for further inspection. Assuming a sample of 27 animals — 8 cats, 6 dogs, and 13 rabbits, the resulting confusion matrix could look like the table below:
Predicted
Cat Dog Rabbit
Actual
class Cat 5 3 0
Dog 2 3 1
Rabbit 0 2 11
In this confusion matrix, of the 8 actual cats
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In predictive analytics, a table of confusion (sometimes also called a confusion matrix), is a table with two rows and two columns that reports the number of false positives, false negatives, true positives, and true negatives. This allows more detailed analysis than mere proportion of correct guesses (accuracy). Accuracy is not a reliable metric for the real performance of a classifier, because it will yield misleading results if the data set is unbalanced (that is, when the number of samples in different classes vary greatly). For example, if there were 95 cats and only 5 dogs in the data set, the classifier could easily be biased into classifying all the samples as cats. The overall accuracy would be 95%, but in practice the classifier would have a 100% recognition rate for the cat class but a 0% recognition rate for the dog class.
Assuming the confusion matrix above, its corresponding table of confusion, for the cat class, would be:
5 true positives
(actual cats that were
correctly classified as cats) 2 false positives
(dogs that were
incorrectly labeled as cats)
3 false negatives
(cats that were
incorrectly marked as dogs) 17 true negatives
(all the remaining animals,
correctly classified as non-cats)
The final table of confusion would contain the average values for all classes combined.
Let us define an experiment from P positive instances and N negative instances for some condition. The four outcomes can be formulated in a 2×2 contingency table or confusion matrix, as follows:
True condition
Total population Condition positive Condition negative Prevalence =
Σ Condition positive
/
Σ Total population
Predicted
condition Predicted condition
positive True positive False positive
(Type I error) Positive predictive value (PPV), Precision =
Σ True positive
/
Σ Test outcome positive
False discovery rate (FDR) =
Σ False positive
/
Σ Test outcome positive
Predicted condition
negative False negative
(Type II error) True negative False omission rate (FOR) =
Σ False negative
/
Σ Test outcome negative
Negative predictive value (NPV) =
Σ True negative
/
Σ Test outcome negative
Accuracy (ACC) =
Σ True positive + Σ True negative
/
Σ Total population
True positive rate (TPR), Sensitivity, Recall =
Σ True positive
/
Σ Condition positive
False positive rate (FPR), Fall-out =
Σ False positive
/
Σ Condition negative
Positive likelihood ratio (LR+) =
TPR
/
FPR
Diagnostic odds ratio (DOR) =
LR+
/
LR−
False negative rate (FNR), Miss rate =
Σ False negative
/
Σ Condition positive
True negative rate (TNR), Specificity (SPC) =
Σ True negative
/
Σ Condition negative
Negative likelihood ratio (LR−) =
FNR
/
TNR
Detection theory or signal detection theory is a means to quantify the ability to discern between information-bearing patterns (called stimulus in living organisms, signal in machines) and random patterns that distract from the information (called noise, consisting of background stimuli and random activity of the detection machine and of the nervous system of the operator). In the field of electronics, the separation of such patterns from a disguising background is referred to as signal recovery.[1]
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predicted condition negative condition negative true negative
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predicted condition positive condition negative false positive type 1 error
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predicted condition negative and condition positive is a false negative type two error
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predicted condition positive and condition positive is a true positive
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The confusion table has four squares based off of two dualities
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Signal detection theory (SDT) is used when psychologists want to measure the way we make decisions under conditions of uncertainty, such as how we would perceive distances in foggy conditions. SDT assumes that the decision maker is not a passive receiver of information, but an active decision-maker who makes difficult perceptual judgments under conditions of uncertainty. In foggy circumstances, we are forced to decide how far away from us an object is, based solely upon visual stimulus which is impaired by the fog. Since the brightness of the object, such as a traffic light, is used by the brain to discriminate the distance of an object, and the fog reduces the brightness of objects, we perceive the object to be much farther away than it actually is (see also decision theory).
To apply signal detection theory to a data set where stimuli were either present or absent, and the observer categorized each trial as having the stimulus present or absent, the trials are sorted into one of four categories:
Respond "Absent" Respond "Present"
Stimulus Present Miss Hit
Stimulus Absent Correct Rejection False Alarm
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Based on the proportions of these types of trials, numerical estimates of sensitivity can be obtained with statistics like the sensitivity index d' and A',[7] and response bias can be estimated with statistics like c and β.[7]
Signal detection theory can also be applied to memory experiments, where items are presented on a study list for later testing. A test list is created by combining these 'old' items with novel, 'new' items that did not appear on the study list. On each test trial the subject will respond 'yes, this was on the study list' or 'no, this was not on the study list'. Items presented on the study list are called Targets, and new items are called Distractors. Saying 'Yes' to a target constitutes a Hit, while saying 'Yes' to a distractor constitutes a False Alarm.
Respond "No" Respond "Yes"
Target Miss Hit
Distractor Correct Rejection False Alarm
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Bayes Criterion[edit]
In some cases, it is far more important to respond appropriately to H1 than it is to respond appropriately to H2. For example, if an alarm goes off, indicating H1 (an incoming bomber is carrying a nuclear weapon), it is much more important to shoot down the bomber if H1 = TRUE, than it is to send a fighter squadron to inspect a false alarm (i.e., H1 = FALSE, H2 = TRUE) (assuming a large supply of fighter squadrons). The Bayes criterion is an approach suitable for such cases.[8]
Here a utility is associated with each of four situations:
U_{11}: One responds with behavior appropriate to H1 and H1 is true: fighters destroy bomber, incurring fuel, maintenance, and weapons costs, take risk of some being shot down;
U_{12}: One responds with behavior appropriate to H1 and H2 is true: fighters sent out, incurring fuel and maintenance costs, bomber location remains unknown;
U_{21}: One responds with behavior appropriate to H2 and H1 is true: city destroyed;
U_{22}: One responds with behavior appropriate to H2 and H2 is true: fighters stay home, bomber location remains unknown;
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Evaluation of binary classifiers[edit]
Main article: Evaluation of binary classifiers
From the contingency table you can derive four basic ratios
There are many metrics that can be used to measure the performance of a classifier or predictor; different fields have different preferences for specific metrics due to different goals. For example, in medicine sensitivity and specificity are often used, while in information retrieval precision and recall are preferred. An important distinction is between metrics that are independent on the prevalence (how often each category occurs in the population), and metrics that depend on the prevalence – both types are useful, but they have very different properties.
Given a classification of a specific data set, there are four basic data: the number of true positives (TP), true negatives (TN), false positives (FP), and false negatives (FN). These can be arranged into a 2×2 contingency table, with columns corresponding to actual value – condition positive (CP) or condition negative (CN) – and rows corresponding to classification value – test outcome positive or test outcome negative. There are eight basic ratios that one can compute from this table, which come in four complementary pairs (each pair summing to 1). These are obtained by dividing each of the four numbers by the sum of its row or column, yielding eight numbers, which can be referred to generically in the form "true positive row ratio" or "false negative column ratio", though there are conventional terms. There are thus two pairs of column ratios and two pairs of row ratios, and one can summarize these with four numbers by choosing one ratio from each pair – the other four numbers are the complements.
The column ratios are True Positive Rate (TPR, aka Sensitivity or recall), with complement the False Negative Rate (FNR); and True Negative Rate (TNR, aka Specificity, SPC), with complement False Positive Rate (FPR). These are the proportion of the population with the condition (resp., without the condition) for which the test is correct (or, complementarily, for which the test is incorrect); these are independent of prevalence.
The row ratios are Positive Predictive Value (PPV, aka precision), with complement the False Discovery Rate (FDR); and Negative Predictive Value (NPV), with complement the False Omission Rate (FOR). These are the proportion of the population with a given test result for which the test is correct (or, complementarily, for which the test is incorrect); these depend on prevalence.
In diagnostic testing, the main ratios used are the true column ratios – True Positive Rate and True Negative Rate – where they are known as sensitivity and specificity. In informational retrieval, the main ratios are the true positive ratios (row and column) – Positive Predictive Value and True Positive Rate – where they are known as precision and recall.
One can take ratios of a complementary pair of ratios, yielding four likelihood ratios (two column ratio of ratios, two row ratio of ratios). This is primarily done for the column (condition) ratios, yielding likelihood ratios in diagnostic testing. Taking the ratio of one of these groups of ratios yields a final ratio, the diagnostic odds ratio (DOR). This can also be defined directly as (TP×TN)/(FP×FN) = (TP/FN)/(FP/TN); this has a useful interpretation – as an odds ratio – and is prevalence-independent.
There are a number of other metrics, most simply the accuracy or Fraction Correct (FC), which measures the fraction of all instances that are correctly categorized; the complement is the Fraction Incorrect (FiC). The F-score combines precision and recall into one number via a choice of weighing, most simply equal weighing, as the balanced F-score (F1 score). Some metrics come from regression coefficients: the markedness and the informedness, and their geometric mean, the Matthews correlation coefficient. Other metrics include Youden's J statistic, the uncertainty coefficient, the Phi coefficient, and Cohen's kappa.
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Sensitivity and specificity are statistical measures of the performance of a binary classification test, also known in statistics as classification function:
Sensitivity (also called the true positive rate, or the recall in some fields) measures the proportion of positives that are correctly identified as such (e.g., the percentage of sick people who are correctly identified as having the condition).
Specificity (also called the true negative rate) measures the proportion of negatives that are correctly identified as such (e.g., the percentage of healthy people who are correctly identified as not having the condition).
Thus sensitivity quantifies the avoiding of false negatives, as specificity does for false positives.
For any test, there is usually a trade-off between the measures. For instance, in an airport security setting in which one is testing for potential threats to safety, scanners may be set to trigger on low-risk items like belt buckles and keys (low specificity), in order to reduce the risk of missing objects that do pose a threat to the aircraft and those aboard (high sensitivity). This trade-off can be represented graphically as a receiver operating characteristic curve.
A perfect predictor would be described as 100% sensitive (e.g., all sick are identified as sick) and 100% specific (e.g., no healthy are identified as sick); however, theoretically any predictor will possess a minimum error bound known as the Bayes error rate.
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In general, Positive = identified and negative = rejected. Therefore:
True positive = correctly identified
False positive = incorrectly identified
True negative = correctly rejected
False negative = incorrectly rejected
Let us consider a group with P positive instances and N negative instances of some condition. The four outcomes can be formulated in a 2×2 contingency table or confusion matrix, as follows
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In statistics, polychoric correlation is a technique for estimating the correlation between two theorised normally distributed continuous latent variables, from two observed ordinal variables. Tetrachoric correlation is a special case of the polychoric correlation applicable when both observed variables are dichotomous. These names derive from the polychoric and tetrachoric series which are used for estimation of these correlations. These series' were mathematical expansions once but not anymore.
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Fisher's exact test[1][2][3] is a statistical significance test used in the analysis of contingency tables. Although in practice it is employed when sample sizes are small, it is valid for all sample sizes. It is named after its inventor, Ronald Fisher, and is one of a class of exact tests, so called because the significance of the deviation from a null hypothesis (e.g., P-value) can be calculated exactly, rather than relying on an approximation that becomes exact in the limit as the sample size grows to infinity, as with many statistical tests.
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The test is useful for categorical data that result from classifying objects in two different ways; it is used to examine the significance of the association (contingency) between the two kinds of classification. So in Fisher's original example, one criterion of classification could be whether milk or tea was put in the cup first; the other could be whether Dr Bristol thinks that the milk or tea was put in first. We want to know whether these two classifications are associated – that is, whether Dr Bristol really can tell whether milk or tea was poured in first. Most uses of the Fisher test involve, like this example, a 2 × 2 contingency table. The p-value from the test is computed as if the margins of the table are fixed, i.e. as if, in the tea-tasting example, Dr Bristol knows the number of cups with each treatment (milk or tea first) and will therefore provide guesses with the correct number in each category. As pointed out by Fisher, this leads under a null hypothesis of independence to a hypergeometric distribution of the numbers in the cells of the table.
A two by two table is a quadrant
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With large samples, a chi-squared test can be used in this situation. However, the significance value it provides is only an approximation, because the sampling distribution of the test statistic that is calculated is only approximately equal to the theoretical chi-squared distribution. The approximation is inadequate when sample sizes are small, or the data are very unequally distributed among the cells of the table, resulting in the cell counts predicted on the null hypothesis (the "expected values") being low. The usual rule of thumb for deciding whether the chi-squared approximation is good enough is that the chi-squared test is not suitable when the expected values in any of the cells of a contingency table are below 5, or below 10 when there is only one degree of freedom (this rule is now known to be overly conservative[4]). In fact, for small, sparse, or unbalanced data, the exact and asymptotic p-values can be quite different and may lead to opposite conclusions concerning the hypothesis of interest.[5][6] In contrast the Fisher exact test is, as its name states, exact as long as the experimental procedure keeps the row and column totals fixed, and it can therefore be used regardless of the sample characteristics. It becomes difficult to calculate with large samples or well-balanced tables, but fortunately these are exactly the conditions where the chi-squared test is appropriate.
For hand calculations, the test is only feasible in the case of a 2 × 2 contingency table. However the principle of the test can be extended to the general case of an m × n table,[7][8] and some statistical packages provide a calculation (sometimes using a Monte Carlo method to obtain an approximation) for the more general case.
For example, a sample of teenagers might be divided into male and female on the one hand, and those that are and are not currently dieting on the other. We hypothesize, for example, that the proportion of dieting individuals is higher among the women than among the men, and we want to test whether any difference of proportions that we observe is significant. The data might look like this:
Men Women Row total
Dieting 1 9 10
Non-dieting 11 3 14
Column total 12 12 24
The question we ask about these data is: knowing that 10 of these 24 teenagers are dieters, and that 12 of the 24 are female, and assuming the null hypothesis that men and women are equally likely to diet, what is the probability that these 10 dieters would be so unevenly distributed between the women and the men? If we were to choose 10 of the teenagers at random, what is the probability that 9 or more of them would be among the 12 women, and only 1 or fewer from among the 12 men?
Before we proceed with the Fisher test, we first introduce some notation. We represent the cells by the letters a, b, c and d, call the totals across rows and columns marginal totals, and represent the grand total by n. So the table now looks like this:
Men Women Row Total
Dieting a b a + b
Non-dieting c d c + d
Column Total a + c b + d a + b + c + d (=n)
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The formula above gives the exact hypergeometric probability of observing this particular arrangement of the data, assuming the given marginal totals, on the null hypothesis that men and women are equally likely to be dieters. To put it another way, if we assume that the probability that a man is a dieter is P, the probability that a woman is a dieter is p, and we assume that both men and women enter our sample independently of whether or not they are dieters, then this hypergeometric formula gives the conditional probability of observing the values a, b, c, d in the four cells, conditionally on the observed marginals (i.e., assuming the row and column totals shown in the margins of the table are given). This remains true even if men enter our sample with different probabilities than women. The requirement is merely that the two classification characteristics—gender, and dieter (or not) -- are not associated.
For example, suppose we knew probabilities P,Q,p,q with P+Q=p+q=1 such that (male dieter, male non-dieter, female dieter, female non-dieter) had respective probabilities (Pp,Pq,Qp,Qq) for each individual encountered under our sampling procedure. Then still, were we to calculate the distribution of cell entries conditional given marginals, we would obtain the above formula in which neither p nor P occurs. Thus, we can calculate the exact probability of any arrangement of the 24 teenagers into the four cells of the table, but Fisher showed that to generate a significance level, we need consider only the cases where the marginal totals are the same as in the observed table, and among those, only the cases where the arrangement is as extreme as the observed arrangement, or more so. (Barnard's test relaxes this constraint on one set of the marginal totals.) In the example, there are 11 such cases. Of these only one is more extreme in the same direction as our data; it looks like this:
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While Barnard retracted his test in a published paper,[5] most researchers prefer using Barnard's exact test over Fisher's exact test for analyzing 2×2 contingency tables. The only exception is when the true sampling distribution of the table is hypergeometric. Barnard's test can be applied to larger tables, but the computation time increases and the power advantage quickly decreases.[6] It remains unclear which test statistic is preferred when implementing Barnard's test; however, most test statistics yield uniformly more powerful tests than Fisher's exact test.[7]
The two by two table is the quadrant
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Barnard's test is used to test the independence of rows and columns in a contingency table. The test assumes each response is independent. Under independence, there are three types of study designs that yield a 2×2 table. To distinguish the different types of designs, suppose a researcher is interested in testing whether a treatment quickly heals an infection. One possible study design would be to sample 100 infected subjects, randomly give them the treatment or the placebo, and see if the infection is still present after a set time. This type of design is common in cross-sectional studies. Another possible study design would be to give 50 infected subjects the treatment, 50 infected subjects the placebo, and see if the infection is still present after a set time. This type of design is common in case-control studies. The final possible study design would be to give 50 infected subjects the treatment, 50 infected subjects the placebo, and stop the experiment once a set number of subjects has healed from the infection. This type of design is uncommon, but has the same structure as the lady tasting tea study that lead to R. A. Fisher creating the Fisher's Exact test. The probability of a 2×2 table under the first study design is given by the multinomial distribution; the second study design is given by the product of two independent binomial distributions; the third design is given by the hypergeometric distribution.
The difference between Barnard's exact test and Fisher's exact test is how they handle the nuisance parameter(s) of the common success probability when calculating the p-value. Fisher's test avoids estimating the nuisance parameter(s) by conditioning on the margins, an approximately ancillary statistic. Barnard's test considers all possible values of the nuisance parameter(s) and chooses the value(s) that maximizes the p-value. Both tests have sizes less than or equal to the type I error rate. However, Barnard's test can be more powerful than Fisher's test because it considers more 'as or more extreme' tables by not conditioning on both margins. In fact, one variant of Barnard's test, called Boschloo's test, is uniformly more powerful than Fisher's exact test.[3] A more detailed description
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chi squared statistical tests also involve quadrant tables
QMRThere are a variety of used by the Coptic Christians.
Old Coptic crosses often incorporate a circle which may vary in size depending on the representation. For the Coptic Church, the circle represents the eternal and everlasting love of God, as shown through Christ's crucifixion, Christ's halo and resurrection.[1]
The Coptic cross is widely used in the Coptic church and the Ethiopian and Eritrean churches. Many Copts have the cross tattooed on the inside of their right arm.[2] The Coptic cross in its modern and ancient forms is considered a sign of faith and pride to the Copts [3] The Ethiopians Christians wear it as a symbol of faith.[4]
In 1984, a Coptic Cross was given as a gift by the Coptic Orthodox Church and mounted on the top of the All Africa Conference of Churches building, since the Coptic Church is considered to be the mother church in Africa.[5]
One of the forms of the Coptic cross, which is referred to as the Ethiopian Coptic cross[6] was worn by Stevie Ray Vaughan.[7] Keith Richards [8] also wears an Ethiopian Coptic Cross.
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Ever since Sir William Thomson's vortex theory, mathematicians have tried to classify and tabulate all possible knots. As of May 2008, all prime knots up to 16 crossings have been tabulated. 16 is the squares of the quadrant number
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Jim Hoste, Jeff Weeks, and Morwen Thistlethwaite used computer searches to count all knots with 16 or fewer crossings. This research was performed separately using two different algorithms on different computers, lending support to the correctness of its results. Both counts found 1701936 prime knots (including the unknot) with up to 16 crossings.[1]
Starting with three crossings (the minimum for any nontrivial knot), the number of prime knots for each number of crossings is
1, 1, 2, 3, 7, 21, 49, 165, 552, 2176, 9988, 46972, 253293, 1388705, ..
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16 is the squares of the quadrant model
Dominican sisters carry on a number of apostolates. They are distinct from the nuns. The sisters are a way of living the vocation of a Third Order Dominican.[citation needed]
As well as the friars, Dominican sisters live their lives supported by four common values, often referred to as the Four Pillars of Dominican Life, they are: community life, common prayer, study and service. St. Dominic called this fourfold pattern of life the "holy preaching". Henri Matisse was so moved by the care that he received from the Dominican Sisters that he collaborated in the design and interior decoration of their Chapelle du Saint-Marie du Rosaire in Vence, France.
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Four Pillars of Manufacturing Engineering[edit]
The Four Pillars of Manufacturing Engineering
The four pillars of manufacturing engineering provides a model of fundamental knowledge required for manufacturing practitioners. The model was formally introduced at the Society of Manufacturing Engineers Annual Meeting June 4–7, 2011 in Bellevue, WA. The concept is supported by the Curricula 2015 Report.[9] Since then the model has been the subject of numerous scholarly papers and strategic reports.[10]
There are four fundamental pillars:
Materials and Manufacturing Processes
Product, Tooling and Assembly Engineering
Manufacturing Systems and Operations
Manufacturing Competitiveness.
Supporting the pillars are the foundation skills in mathematics and physical science, engineering science and a broad set of personal effectiveness skills.
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The Four Pillars is a research programme set up in 1987 by the Geneva Association, also known as the International Association for the Study of Insurance Economics. The aim of the Four Pillars research programme is to study the key importance in the new service economy of Social Security, Insurance, Savings and Employment. The programme focuses on the future of pensions, welfare and employment. The Geneva Association launched its Four Pillars research programme with a view to identifying possible solutions to the issue of the future financing of pensions and, more generally, to organising social security systems in our post-industrial societies. Demographic trends - especially increased life and health expectancy - could be seen as positive if we were able to devise ways of enabling "ageing in good-health populations" to make a valid economic and social contribution to the functioning of our service economies over the decades to come.
The concept of the Four Pillars owes its origin to the fact that in most countries the funding of pensions is based on three pillars:
The 1st pillar - the compulsory, pay-as-you-go, state pension;
The 2nd pillar - the supplementary (often funding-based) occupational pension;
The 3rd pillar - individual savings (personal pension and assets and life insurance).
The Geneva Association advocated in its publications and seminars a strengthening of the 2nd pillar and further development of 3rd pillar resources. However, the attention of the Geneva Association has focused above all on a 4th pillar i.e. the future need for a flexible extension of work-life, mainly on a part-time basis, in order to supplement income from the three existing pillars. The reorganization of end-of-career and the new age-management strategy - in which gradual retirement is destined to play a key role - involved in establishing this pillar, also correspond to many of the changes (e.g. in quality of work and the life cycle) that are specific to our contemporary service economies.[1
QMRThe book Geometrie der Lage (1847) was a landmark in projective geometry. As Burau (1976) wrote:
Staudt was the first to adopt a fully rigorous approach. Without exception his predecessors still spoke of distances, perpendiculars, angles and other entities that play no role in projective geometry.[1]
Furthermore, this book (page 43) uses the complete quadrangle to "construct the fourth harmonic associated with three points on a straight line", the projective harmonic conjugate.
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The semiotic square, also known as the Greimas square, 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, and of extending the relevant ontology.
The semiotic square, derived from Aristotle's logical square of opposition, was developed by Algirdas J. Greimas, a Lithuanian linguist and semiotician, who considered the semiotic square to be the elementary structure of meaning.
Greimas first presented the square in Semantique Structurale (1966), a book which was later published as Structural Semantics: An Attempt at a Method (1983). He further developed the semiotic square with Francois Rastier in "The Interaction of Semiotic Constraints" (1968).
The square has an x like a quadrant
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The Stoics were interested in Heraclitus' treatment of fire. In addition to seeing it as the most fundamental of the four elements and the one that is quantified and determines the quantity (logos) of the other three, he presents fire as the cosmos, which was not made by any of the gods or men, but "was and is and ever shall be ever-living fire."[66] Fire is both a substance and a motivator of change, it is active in altering other things quantitatively and performing an activity Heraclitus describes as "the judging and convicting of all things."[67] It is "the thunderbolt that steers the course of all things."[68] There is no reason to interpret the judgement, which is actually "to separate" (κρίνειν krinein), as outside of the context of "strife is justice" (see subsection above).
Fire is the forth square. Fire is always transcendent.
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The Radcliffe Quadrangle at Harvard University, formerly the residential campus of Radcliffe College, is part of Harvard's undergraduate campus, in Cambridge, Massachusetts, USA. Generally just called the Quad, it is a traditional college quad slightly removed from the main part of campus. It should not be confused with Radcliffe Yard or with Harvard Yard — where most classes are conducted.
In architecture, a quadrangle (or colloquially, a quad) is a space or courtyard, usually rectangular (square or oblong) in plan, the sides of which are entirely or mainly occupied by parts of a large building (or several smaller buildings). The word is probably most closely associated with college or university campus architecture, but quadrangles may be found in other buildings such as palaces. Most quadrangles are open-air, while a few have been roofed over (often with glass), to provide additional space for social meeting areas or coffee shops for students.
The word quadrangle was originally synonymous with quadrilateral, but this usage is now relatively uncommon.[1]
Some modern quadrangles resemble cloister gardens of medieval monasteries, called garths, which were usually square or rectangular, enclosed by covered arcades or cloisters. However, it is clear from the oldest examples (such as Mob Quad) which are plain and unadorned with arcades, that the medieval colleges at Oxford and Cambridge were creating practical accommodation for college members. Grander quadrangles that look like cloisters came later, once the idea of a college was well established and benefactors or founders wished to create more monumental buildings.[2]
In North America, Thomas Jefferson's design for the University of Virginia centered the housing and academic buildings in a Palladian form around three sides of the Lawn, a huge grassy expanse. Later, some American college and university planners imitated the Jeffersonian plan, the Oxbridge idea, Beaux-Arts forms, and other models. The University of Chicago's Gothic campus is also notable for its innovative use of quadrangles.[citation needed] All five barracks at The Citadel (military college) feature quadrangles with red-and-white squares (the colors of the South Carolina battle flag), which are used for formations by the Corps of Cadets.
Quadrangles are also found in traditional Kerala houses (Naalukettu) and is known as the Nadumittam ("Middle Space").[3]
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The Quadrangle is the common name for a cluster of museums and cultural institutions in Metro Center, Springfield, Massachusetts, on Chestnut Street between State and Edwards Streets.
The Dr. Seuss National Memorial Sculpture Garden, in the center of the Quadrangle, is surrounded by a park, a library, four active museums, a fifth museum due to open in 2016, and a cathedral. A second cathedral is just on the Quadrangle's periphery.
In mathematics, specifically projective geometry, a complete quadrangle is a system of geometric objects consisting of any four points in a plane, no three of which are on a common line, and of the six lines connecting each pair of points. Dually, a complete quadrilateral is a system of four lines, no three of which pass through the same point, and the six points of intersection of these lines. The complete quadrangle was called a tetrastigm by Lachlan (1893), and the complete quadrilateral was called a tetragram; those terms are occasionally still used.
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