Plato at the Googleplex

Rebecca Goldstein: "Plato at the Googleplex" | Talks at Google

The Form of the Good

SOCRATES:  Tell me then, by Zeus, what is that excellent [págkalon, "all beautiful"] aim [érgon, "work, deed"] that the gods achieve, using us as their servants?
 
Plato, Euthyphro, 13e, translated by G.M.A. Grube [Hackett Publishing, 1981, p.19; Greek text, Plato -- Euthryphro, Apology, Crito, Phaedo, Phaedrus, Loeb Classical Library, Harvard, 1914-1956, pp.50-52]

In the Republic, Plato sets aside a direct definition of the "good itself" (autò t'agathón). Socrates says that instead we will get something in the nature of the "offspring" (ékgonos) or "interest" (tókos) on the good [Republic, 506 E]. For this "offspring," Plato offers an analogy:  The Good is to the intelligible world, the world of Being and the Forms, as the sun is to the visible world. As light makes vision possible in the material world, and so also opinion about such objects, the Form of the Good "gives their truth to the objects of knowledge and power of knowing to the knower..." [Loeb Classical Library, Plato VI Republic II, translated by Paul Shorey, Harvard University Press, 1935-1970, pp.94-95]. Furthermore, the objects of knowledge derive from the Form of the Good not only the power of being known, but their "very existence and essence" (tò eînaí te kaì hè ousía) [509B], although the Good itself "transcends essence" in "dignity and power" [ibid. pp.106-107]. The word here translated "essence" is ousía, which in Aristotelian terminology is the essence (essentia) of things, i.e. what they are. If Plato has something similar in mind, then the objects of knowledge derive from the good both their existence and their character. See: A Lecture on the Good,  by
Kelley L. Ross, Ph.D.

***

This below was a earlier attempt to define the idea of the Good and Form in context of the painting called Betrayal of Images" by Rene Magritte. 1929 painting on which is written "This is not a Pipe"

                    Probabilties
                 (The Fifth Dimension)
                         |
                         |
                  Idea of the pipe
                        / \
                       /   \
                      /     \
                 Picture of the pipe
                    /         \
                   /           \
                  /             \
               The real pipe and form  
                                         

The fifth dimension was a attempt by myself to explaining the dimensional shift from the four dimension(space-time) to the fifth. Four leads into three was an ancient idea(Quadrivium ad Trivium) that came to mind that we may seek to explain as humanities attempt at perfecting. But at the same time such a descendent from the heaven into the mind of humanity, as the idea. A effective expression of the idea into form.

So such truths were important to me as to how we discover them. I am saying that this is a capable feature in all of us, and it was an attempt to explain how this is done. Deductive Logic while a representation of Aristotle, Aristotle pointed the way toward Plato. Aristotle pointed the way to Plato's explanation of the Good as it may have meant to Plato and what Aristotle may of disagreed with.

Plato's use of Socrates in the dialogues was specific to Plato's explaining what he meant by heaven. This is not a theological revelation for Christianity in my view as to the principles of Plato, as to what heaven meant. But something quite capable as to what heaven may mean as we grasp the understanding of the Good and inspection as to the Theory of Forms.

Indirectly, Aristotle then introduce the idea then of the universal and the particulars?

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Distances” Determine Geometry
Describe an object with a table of distances between points.
Describe spacetime with a table of intervals between events
It is not my purpose in this discussion to represent the general theory of relativity as a system that is as simple and as logical as possible, and with the minimum number of axioms; but my main object here is to develop this theory in such a way that the reader will feel that the path we have entered upon is psychologically the natural one, and that the underlying assumptions will seem to have the highest possible degree of security.
—Albert Einstein

http://www.eftaylor.com/pub/chapter2.pdf

***

"Symmetry breaking illustrated": – high energy levels (left) the ball settles in the center, and the result is symmetrical. At lower energy levels (right), the overall "rules" remain symmetrical, but the "Mexican hat" potential comes into effect: "local" symmetry inevitably becomes broken since eventually the ball must roll one way (at random) and not another.

If one recognizes such a state as to imply that Heaven exists in such perfection and beauty, then what causes the asymmetry to be broken? Moving into a dualistic notion of operation, would signify a symmetry breaking?

The term “symmetry” derives from the Greek words sun (meaning ‘with’ or ‘together’) and metron (‘measure’), yielding summetria, and originally indicated a relation of commensurability (such is the meaning codified in Euclid's Elements for example). It quickly acquired a further, more general, meaning: that of a proportion relation, grounded on (integer) numbers, and with the function of harmonizing the different elements into a unitary whole. From the outset, then, symmetry was closely related to harmony, beauty, and unity, and this was to prove decisive for its role in theories of nature. In Plato's Timaeus, for example, the regular polyhedra are afforded a central place in the doctrine of natural elements for the proportions they contain and the beauty of their forms: fire has the form of the regular tetrahedron, earth the form of the cube, air the form of the regular octahedron, water the form of the regular icosahedron, while the regular dodecahedron is used for the form of the entire universe. The history of science provides another paradigmatic example of the use of these figures as basic ingredients in physical description: Kepler's 1596 Mysterium Cosmographicum presents a planetary architecture grounded on the five regular solids.Symmetry and Symmetry Breaking -The Concept of Symmetry

Symmetry Breaking, means to measure.

***

One may need to recognize some aspect of consciousness and its capabilities, and thus, the parameters by which one thinks of how their consciousness operates, can become the limitations that that one applies to all(deluded). This then becomes "an application" to self.

An analogy to this situation might be what is thought to happen to the forces of nature in modern physics, where a single, original, unified force is separated into several forces by "spontaneous symmetry breaking." The form of consciousness as, according to Brentano and Husserl, the intentional relationship of subject and object, itself represents an asymmetry, breaking the symmetry of an existence where there is no distinction between subject and object. Existence as such is thus broken by the form of consciousness, and it becomes the forms of value, good and evil, right and wrong, the beautiful and the ugly, etc., as these vary independently over and against the simple factual existence of objects in the phenomenal world, or even against each other in the phenomenon of moral dilemmas (i.e. doing right results in evils, while doing wrong results in goods). A Lecture on the Good -http://www.friesian.com/good.htm

Bold added for emphasis by me.

The connection between superfluidity and symmetry breaking has had a glorious history. It has left us a rich legacy of fertile ideas, that seems far from exhaustion. PG 60 Superfluidity and Symmetry Breaking

You have to know what your doing when you apply those constraints to yourself. So maybe, there is this bigger picture.

Pierre Curie (1894): “Asymmetry is what creates a phenomenon.”

First Alcibiades

Papyrus fragment of Alcibiades I, section 131.c-e.

The First Alcibiades or Alcibiades I (Ancient Greek: Ἀλκιβιάδης αʹ) is a dialogue featuring Alcibiades in conversation with Socrates. It is ascribed to Plato, although scholars are divided on the question of its authenticity.

Contents 1 Content 2 Authenticity 3 Dating 4 References 5 Bibliography 6 External links

Content

In the preface Alcibiades is described as an ambitious young man who is eager to enter public life. He is extremely proud of his good looks, noble birth, many friends, possessions and his connection to Pericles, the leader of the Athenian state. Alcibiades has many admirers but they have all run away, afraid of his coldness. Socrates was the first of his admirers but he has not spoken to him for many years. Now the older man tries to help the youth with his questions before Alcibiades presents himself in front of the Athenian assembly. For the rest of the dialogue Socrates explains the many reasons why Alcibiades needs him. By the end of Alcibiades I, the youth is much persuaded by Socrates' reasoning, and accepts him as his mentor.

The first topic they enter is the essence of politics – war and peace. Socrates claims that people should fight on just grounds but he doubts that Alcibiades has got any knowledge about justice. Prodded by Socrates’ questioning Alcibiades admits that he has never learned the nature of justice from a master nor has discovered it by himself .

Alcibiades suggests that politics is not about justice but expediency and the two principles could be opposed. Socrates persuades him that he was mistaken, and there is no expediency without justice. The humiliated youth concedes that he knows nothing about politics.

Later Alcibiades says that he is not concerned about his ignorance because all the other Athenian politicians are ignorant. Socrates reminds him that his true rivals are the kings of Sparta and Persia. He delivers a long lecture about the careful education, glorious might and unparalleled richness of these foreign rulers. Alcibiades has got cold feet which was exactly the purpose of Socrates’ speech.

After this interlude the dialogue proceeds with further questioning about the rules of society. Socrates points to the many contradictions in Alcibiades’ thoughts. Later they agree that man has to follow the advise of the famous Delphic phrase: gnōthi seautón meaning know thyself. They discuss that the "ruling principle" of man is not the body but the soul. Somebody's true lover loves his soul, while the lover of the body flies as soon as the youth fades. With this Socrates proves that he is the only true lover of Alcibiades. "From this day forward, I must and will follow you as you have followed me; I will be the disciple, and you shall be my master", proclaims the youth. Together they will work on to improve Alcibiades' character because only the virtuous has the right to govern. Tyrannical power should not be the aim of individuals but people accept to be commanded by a superior.

In the last sentence Socrates expresses his hope that Alcibiades will persist but he has fears because the power of the state "may be too much" for both of them.
 

Authenticity

 

In antiquity Alcibiades I was regarded as the best text to introduce one to Platonic philosophy, which may be why it has continued to be included in the Platonic corpus since then. The authenticity of the dialogue was never doubted in antiquity. It was not until 1836 that the German scholar Friedrich Schleiermacher argued against the ascription to Plato.^[1] Subsequently its popularity declined. However, stylometrical research supports Plato's authorship,^[2] and some scholars have recently defended its authenticity.^[3]

Dating

 

Traditionally, the First Alcibiades has been considered an early dialogue. Gerard Ledger's stylometric analysis supported this tradition, dating the work to the 390's.^[4] Julia Annas, in supporting the authenticity of Rival Lovers, saw both dialogues as laying the foundation for ideas Plato would later develop in Charmides.

A later dating has also been defended. Nicholas Denyer suggests that it was written in the 350's BC, when Plato, back in Athens, could reflect on the similarities between Dionysius II of Syracuse (as we know him from the Seventh Letter) and Alcibiades—two young men interested in philosophy but compromised by their ambition and faulty early education.^[5] This hypothesis requires skepticism about what is usually regarded as the only fairly certain result of Platonic stylometry, Plato's marked tendency to avoid hiatus in the six dialogues widely believed to have been composed in the period to which Denyer assigns First Alcibiades (Timaeus, Critias, Sophist, Statesman, Philebus, and Laws).^[6]


R.S. Bluck, although unimpressed by previous arguments against the dialogue's authenticity, tentatively suggests a date after the end of Plato's life, approximately 343/2 BC, based especially on "a striking parallelism between the Alcibiades and early works of Aristotle, as well as certain other compositions that probably belong to the same period as the latter."^[8]

References

 

1. ^ Denyer (2001): 15.
2. ^ Young (1998): 35-36.
3. ^ Denyer (2001): 14-26.
4. ^ Young (1998)
5. ^ Denyer (2001): 11-14. Cf. 20-24
6. ^ Denyer (2001): 23 n. 19
7. ^ Pamela M. Clark, "The Greater Alcibiades," Classical Quarterly N.S. 5 (1955), pp. 231-240
8. ^ R.S. Bluck, "The Origin of the Greater Alcibiades," Classical Quarterly N.S. 3 (1953), pp. 46-52

 

Bibliography

 

• Denyer, Nicholas, "introduction", in Plato, Alcibiades, Nicholas Denyer (ed.) (Cambridge: Cambridge University Press, 2001): 1-26.
• Foucault, Michel, The Hermeneutics of the Subject: Lectures at the Collège de France, 1981–1982 (New York: Picador, 2005).
• Young, Charles M., "Plato and Computer Dating", in Nicholas D. Smith (ed.), Plato: Critical Assessments volume 1: General Issues of Interpretation (London: Routledge, 1998): 29-49.

 

External links

 

• Greek text: Greek Wikisource, HODOI (with French translation and concordance)
• First Alcibiades, trans. Benjamin Jowett (Project Gutenberg)

The Ganzfeld effect

The  Ganzfeld effect (from German for “complete field”) is a phenomenon of visual perception caused by staring at an undifferentiated and uniform field of color. The effect is described as the loss of vision as the brain cuts off the unchanging signal from the eyes. The result is "seeing black"^[1] - apparent blindness.

History 

 

In the 1930s, research by psychologist Wolfgang Metzger established that when subjects gazed into a featureless field of vision they consistently hallucinated and their electroencephalograms changed.

The Ganzfeld effect is the result of the brain amplifying neural noise in order to look for the missing visual signals. The noise is interpreted in the higher visual cortex, and gives rise to hallucinations. This is similar to dream production because of the brain's state of sensory deprivation during sleep.

The Ganzfeld effect has been reported since ancient times. The adepts of Pythagoras retreated to pitch black caves to receive wisdom through their visions^[2], known as the prisoner's cinema. Miners trapped by accidents in mines frequently reported hallucinations, visions and seeing ghosts when they were in the pitch dark for days. Arctic explorers seeing nothing but featureless landscape of white snow for a long time also reported hallucinations and an altered state of mind.

The effect is a component of a Ganzfeld experiment, a technique used in the field of parapsychology.
The artist James Turrell (partly inspired by clear blue skies) has created many such "Ganzfelds" throughout his oeuvre.

See also

• Sensory deprivation
• Ganzfeld experiment
• Dark retreat
• Floatation tank
• Hypnagogia

 

References

1. ^ Ramesh B. Ganzfeld Effect.
2. ^ Ustinova, Yulia.Caves and the Ancient Greek Mind: Descending Underground in the Search for Ultimate Truth, Oxford University Press US, 2009. ISBN 0199548560

• Wolfgang Metzger, "Optische Untersuchungen am Ganzfeld." Psychologische Forschung 13 (1930) : 6-29. (the first psychophysiological study with regard to Ganzfelds)

 EGG: Did you reach this conclusion through more traditional media, like painting or sculpture?

JT: I haven't had anything to do with either sculpture or painting. I have done works that look painted or works that have form and look like sculpture. I make these spaces that apprehend light for your perception. In a way, it's like Plato's cave, where we are sitting in the cave looking at the reflection of reality with our backs to reality. I make these spaces where the spaces themselves are perceivers or in some way pre-form perception. It's a little bit like what the eye does. I mean, I look at the eye as the most exposed part of the brain, as something that is already forming perception. I make these rooms that are these camera-like spaces that in some way form light, apprehend it to be something that's physically present.

EGG: What happens when you use space this way?

JT: This results in an art that is not about my seeing, it's about your direct perception of the work. I'm interested in having a light that inhabits space, so that you feel light to be physically present. I mean, light is a substance that is, in fact, a thing, but we don't attribute thing-ness to it. We use light to illuminate other things, something we read, sculpture, paintings. And it gladly does this. But the most interesting thing to find is that light is aware that we are looking at it, so that it behaves differently when we are watching it and when we're not, which imbues it with consciousness. Often people say that they want to touch some of the work I do. Well, that feeling is actually coming from the fact that the eyes are touching, the eyes are feeling. And this happens because the eyes are quite sensitive only in low light, for which we were made. We're actually made for this light of Plato's cave, the light of twilight. See: Interview with James Turrell

psychomanteums

The room is set up to optimize psychological effects such as trance. Its key features are low light or near-darkness, flickering light, and a mirror. The dimness represents a form of visual sensory deprivation, a condition helpful to trance induction, the undifferentiated colour without horizon producing the Ganzfeld effect^[4], a state of apparent "blindness". The Ganzfeld experiment replicates the conditions of a psychomanteum where a state of trance may be induced by a uniform field of vision. In the way of strobe or flashing light, stimulus is provided by indirect, moving light in the psychomanteum. Flickering candles or lamps are sometimes recommended to induce hallucination. It is supposed the indeterminate depth of the mirror’s darkness allows the eyes to relax and become unfocused, a state that reduces alertness.^[2]

Dr. Raymond Moody, author of the 1981 book about near death experiences, Life After Life, included the psychomanteum in his research trialling 300 subjects which he recorded in his 1993 book, Reunions. Moody viewed the room as a therapeutic tool to heal grief and bring insight.^[2]

Model Building in Life

"...underwriting the form languages of ever more domains of mathematics is a set of deep patterns which not only offer access to a kind of ideality that Plato claimed to see the universe as created with in the Timaeus; more than this, the realm of Platonic forms is itself subsumed in this new set of design elements-- and their most general instances are not the regular solids, but crystallographic reflection groups. You know, those things the non-professionals call . . . kaleidoscopes! * (In the next exciting episode, we'll see how Derrida claims mathematics is the key to freeing us from 'logocentrism'-- then ask him why, then, he jettisoned the deepest structures of mathematical patterning just to make his name...)

* H. S. M. Coxeter, Regular Polytopes (New York: Dover, 1973) is the great classic text by a great creative force in this beautiful area of geometry (A polytope is an n-dimensional analog of a polygon or polyhedron. Chapter V of this book is entitled 'The Kaleidoscope'....)"

I just wanted to show you what has been physically reproduced in cultures. This in order to highlight some of the things that were part of our own make up,  so you get that what has transpired in our societies has been part of something hidden within our own selves.

As I have said before it has become something of an effort for me to cataloged knowledge on some of  the things I learn.  The ways in which to keep the information together. I am not saying everyone will do this in there own way but it seems to me that as if some judgement about our selves is hidden in the way we had gathered information about our own lives then it may have been put together like some kaleidoscope.

Online Etymology Dictionary-1817, lit. "observer of beautiful forms," coined by its inventor, Sir David Brewster (1781-1868), from Gk. kalos "beautiful" + eidos "shape" (see -oid) + -scope, on model of telescope, etc. Figurative meaning "constantly changing pattern" is first attested 1819 in Lord Byron, whose publisher had sent him one.

So to say then past accomplishments were part of the designs, what had we gained about our own lives then?  What page in the book of Mandalas can you have said that any one belonged to you? It was that way for me in that I saw the choices. These I thought I had built on my own, as some inclination of a method and way to deliver meaning into my own life. Then through exploration it seem to contain the energy of all that I had been before as to say that in this life now, that energy could unfold?

Scan of painting 19^th century Tibetan Buddhist thangka painting

Maṇḍala (मण्डल) is a Sanskrit word meaning "circle." In the Buddhist and Hindu religious traditions their sacred art often takes a mandala form. The basic form of most Hindu and Buddhist mandalas is a square with four gates containing a circle with a center point. Each gate is in the shape of a T.^[1][2] Mandalas often exhibit radial balance.^[3]


These mandalas, concentric diagrams, have spiritual and ritual significance in both Buddhism and Hinduism.^[4][5] The term is of Hindu origin and appears in the Rig Veda as the name of the sections of the work, but is also used in other Indian religions, particularly Buddhism. In the Tibetan branch of Vajrayana Buddhism, mandalas have been developed into sandpainting. They are also a key part of anuttarayoga tantra meditation practices.


In various spiritual traditions, mandalas may be employed for focusing attention of aspirants and adepts, as a spiritual teaching tool, for establishing a sacred space, and as an aid to meditation and trance induction. According to the psychologist David Fontana, its symbolic nature can help one "to access progressively deeper levels of the unconscious, ultimately assisting the meditator to experience a mystical sense of oneness with the ultimate unity from which the cosmos in all its manifold forms arises."^[6] The psychoanalyst Carl Jung saw the mandala as "a representation of the unconscious self,"^{[citation needed]} and believed his paintings of mandalas enabled him to identify emotional disorders and work towards wholeness in personality.^[7]


In common use, mandala has become a generic term for any plan, chart or geometric pattern that represents the cosmos metaphysically or symbolically, a microcosm of the Universe from the human perspective.^{[citation needed]}

So what does this mean then that you see indeed some subjects that are allocated toward design of to say that it may be an art of a larger universal understanding that hidden in our natures the will to provide for something schematically inherent? Our nature,  as to the way in which we see the world. The way in which we see science. What cosmic plan then to say the universe would unfold this way, or  to seek the inner structure and explanations as to the way the universe began. The way we emerged into consciousness of who you are?

 The kaleidoscope was perfected by Sir David Brewster, a Scottish scientist, in 1816. This technological invention, whose function is literally the production of beauty, or rather its observation, was etymologically a typical aesthetic form of the nineteenth century - one bound up with disinterested contemplation. (The etymology of the word is formed from kalos (beautiful), eidos (form) and scopos (watcher) - "watcher of beautiful shapes".) The invention is enjoying a second life today - as the model for many contemporary abstract works. In Olafur Eliasson's Kaleidoscope (2001), the viewer takes the place of the pieces of glass, producing a myriad of images. In an inversion of the situation involved in the classic kaleidoscope, the watcher becomes the watched. In Jim Drain's Kaleidoscope (2003), the viewer is also plunged physically inside the myriad of abstract forms, and his image becomes a part of the environment. Spin My Wheel (2003), by Lori Hersberger, also forms a painting that is developed in space, spilling beyond the frame of the picture, its projected image constantly changing, dissolving the surrounding world with an infinite play of reflections in fragments of broken mirror. The viewer becomes one of the subjects of the piece. (Not the subject, as in Eliasson's work, but one of its subjects.)
See: The End of Perspective-Vincent Pécoil.

Would there be then some algorithmic style to the code written in your life as to have all the things you are as some pattern as to the way in which you will live your life? I ask then what would seem so strange that you might not paint a picture of it? Not encode your life in some mathematical principle as to say that life emerge for you in this way?

Although Aristotle in general had a more empirical and experimental attitude than Plato, modern science did not come into its own until Plato's Pythagorean confidence in the mathematical nature of the world returned with Kepler, Galileo, and Newton. For instance, Aristotle, relying on a theory of opposites that is now only of historical interest, rejected Plato's attempt to match the Platonic Solids with the elements -- while Plato's expectations are realized in mineralogy and crystallography, where the Platonic Solids occur naturally.Plato and Aristotle, Up and Down-Kelley L. Ross, Ph.D.

See Also:

• The Nobel Prize in Physics 1914 Max von Laue
• Quasicrystal: Prof. Dan Shechtman
•  Quasicrystal and Information

Plato's Cave(Animated Version)

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Hyperreality is used in semiotics and postmodern philosophy to describe a hypothetical inability of consciousness to distinguish reality from fantasy, especially in technologically advanced postmodern cultures. Hyperreality is a means to characterize the way consciousness defines what is actually "real" in a world where a multitude of media can radically shape and filter an original event or experience. Some famous theorists of hyperreality include Jean Baudrillard, Albert Borgmann, Daniel Boorstin, and Umberto Eco.

Photomontage of 16 photos which have been digitally manipulated in Photoshop to give the impression that it is a real landscape

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The medium is the message is a phrase coined by Marshall McLuhan meaning that the form of a medium embeds itself in the message, creating a symbiotic relationship by which the medium influences how the message is perceived. See: The medium is the message (phrase)

Know Thyself (γνώθι σεαυτόν )

A stained glass window with the contracted version γνωθι σαυτόν.

The saying "Know thyself" may refer by extension to the ideal of understanding human behavior, morals, and thought, because ultimately to understand oneself is to understand other humans as well. However, the ancient Greek philosophers thought that no man can ever comprehend the human spirit and thought thoroughly, so it would have been almost inconceivable to know oneself fully. Therefore, the saying may refer to a less ambitious ideal, such as knowing one's own habits, morals, temperament, ability to control anger, and other aspects of human behavior that we struggle with on a daily basis.

It may also have a mystical interpretation. 'Thyself', is not meant in reference to the egotist, but the ego within self, the I AM consciousness.

***

Delphi became the site of a major temple to Phoebus Apollo, as well as the Pythian Games and the famous prehistoric oracle. Even in Roman times, hundreds of votive statues remained, described by Pliny the Younger and seen by Pausanias. Supposedly carved into the temple were three phrases: γνωθι σεαυτόν (gnothi seauton = "know thyself") and μηδέν άγαν (meden agan = "nothing in excess"), and Εγγύα πάρα δ'ατη (eggua para d'atē = "make a pledge and mischief is nigh"),[6] as well as a large letter E.[7] Among other things epsilon signifies the number 5. Plutarch's essay on the meaning of the “E at Delphi" is the only literary source for the inscription. In ancient times, the origin of these phrases was attributed to one or more of the Seven Sages of Greece,[8] though ancient as well as modern scholars have doubted the legitimacy of such ascriptions.[9] According to one pair of scholars, "The actual authorship of the three maxims set up on the Delphian temple may be left uncertain. Most likely they were popular proverbs, which tended later to be attributed to particular sages

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"Let no one destitute of geometry enter my doors." Plato (c. 427 - 347 B.C.E.)

"[Geometry is] . . . persued for the sake of the knowledge of what eternally exists, and not of what comes for a moment into existence, and then perishes, ...[it] must draw the soul towards truth and give the finishing touch to the philosophic spirit."

***

 

III: The "Geometrical Problem" in the Meno.

Further along in the Meno occurs the celebrated case of the Geometrical Example at Meno 87, which in contrast to the previous mathematical illustration, has been twisted, tortured, and intentionally passed over for two centuries. Jebb said (loc.cit.) asven over a century ago:

The hypothesis appears to be rather trivial and to have no mathematical value. . . (which Raven echoes in 1965)

and here follow some barely intelligible geometrical details".

Bluck however, in 1961 devotes an excursus of some sixteen pages to a complete review of views on the problem, which include an array or barely intelligible geometrical details. The passage is made more difficult of interpretation by the fact that Socrates introduces the geometrical example in a very summary manner, which some have felt was an indication or its relative unimportance.

 I believe on the contrary that the almost schematic reference implies that the topic and the example were well known to the Platonic audience, and did not need explanation. Plato knows how to explain in full, and when he refrains we must understand the matter to be common knowledge. The problem as it occurs at Meno 87 a is briefly this:

We will proceed from here on like the geometer who when asked if a given triangle can be inscribed in a given circle, will say:

'I can't say, but let us proceed hypothetically or experimentally, draw out one leg, swing the other two and see if it falls short or exceeds the rim of the circle.'

In making this paraphrase I have added the word "experimentally" for obvious reasons, and I have taken the noun chorion correctly as area (not rectangle or a triangle, as has been said, which means nothing) in a sense very well attested. So apparently with these conditions, the words themselves are not obscure or really unintelligible, although as yet the meaning has not yet come to the surface.

See: Plato: Mathematician or Mystic ?

***

You might think the loss of geometry like the loss of, say, Latin would pass virtually unnoticed. This is the thing about geometry: we no more notice it than we notice the curve of the earth. To most people, geometry is a grade school memory of fumbling with protractors and memorizing the Pythagorean theorem. Yet geometry is everywhere. Coxeter sees it in honeycombs, sunflowers, froth and sponges. It's in the molecules of our food (the spearmint molecule is the exact geometric reaction of the caraway molecule), and in the computer-designed curves of a Mercedes-Benz. Its loss would be immeasurable, especially to the cognoscenti at the Budapest conference, who forfeit the summer sun for the somnolent glow of an overhead projector. They credit Coxeter with rescuing an art form as important as poetry or opera. Without Coxeter's geometry as without Mozart's symphonies or Shakespeare's plays our culture, our understanding of the universe,would be incomplete.

See: γνώθι σεαυτόν

A Holograpical Universe

Plato likened our view of the world to that of an ancient forebear watching shadows meander across a dimly lit cave wall. He imagined our perceptions to be but a faint inkling of a far richer reality that flickers beyond reach. Two millennia later, Plato’s cave may be more than a metaphor. To turn his suggestion on its head, reality—not its mere shadow—may take place on a distant boundary surface, while everything we witness in the three common spatial dimensions is a projection of that faraway unfolding. Reality, that is, may be akin to a hologram. Or, really, a holographic movie.

The journey to this peculiar possibility combines developments deep and far-flung—insights from general relativity; from research on black holes; from thermodynamics, quantum mechanics, and, most recently, string theory. The thread linking these diverse areas is the nature of information in a quantum universe.

Physicists Jacob Bekenstein and Stephen Hawking established that, for a black hole, the information storage capacity is determined not by the volume of its interior but by the area of its surface. But when the math says that a black hole’s store of information is measured by its surface area, does that merely reflect a numerical accounting, or does it mean that the black hole’s surface is where the information is actually stored? It’s a deep issue and has been pursued for decades by some of the most renowned physicists. The answer depends on whether you view the black hole from the outside or from the inside—and from the outside, there’s good reason to believe that information is indeed stored at the event horizon. This doesn’t merely highlight a peculiar feature of black holes. Black holes don’t just tell us about how black holes store information. 
Black holes inform us about information storage 
in any context. See:Our Universe May Be a Giant Hologram

See Also: Physics and Philosophie Pay attention too, #8. (And Stefan submits: What is the ontological status of AdS/CFT?)[also pay attention to comments relating to #8]

Plato's Problem

Plato's problem is the term given by Noam Chomsky to the gap between knowledge and experience. It presents the question of how we account for our knowledge when environmental conditions seem to be an insufficient source of information. It is used in linguistics to refer to the "argument from poverty of the stimulus" (APS). In a more general sense, Plato’s Problem refers to the problem of explaining a "lack of input." Solving Plato’s Problem involves explaining the gap between what one knows and the apparent lack of substantive input from experience (the environment). Plato's Problem is most clearly illustrated in the Meno dialogue, in which Socrates demonstrates that an uneducated boy nevertheless understands geometric principles.

Contents 1 Introduction 2 Plato (427 B.C. – 347 B.C.) 2.1 Background 2.2 Early work 2.3 Socrates (470 B.C. - 399 B.C.) 2.3.1 Socratic method 2.4 Meno 2.4.1 Innate knowledge 3 Contemporary parallels 3.1 Linguistics 3.1.1 Universal grammar 3.2 Perception and attention 3.2.1 Visual 3.2.2 Auditory 3.2.3 Subliminal priming 3.3 Long-term memory (LTM) 4 Implications 5 References 6 External links

Introduction

What is knowledge? What is experience? How do they interact? Is there a correlational, causal, or reciprocal relationship between knowledge and experience? These and other related questions have been at the forefront of investigation by problem solvers, scientists, psychologists, and philosophers for centuries. These questions, but particularly the problem of how experience and knowledge interrelate, have broad theoretical and practical implications for such academic disciplines as epistemology, linguistics, and psychology (specifically the subdiscipline of thinking and problem solving). Gaining a more precise understanding of human knowledge, whether defined as innate, experiential, or both, is an important part of effective problem solving.

Plato was the first philosopher who systematically inquired into issues such as those noted above. He wrote many dialogues, such as Euthyphro and the Apology, but it is from the Meno that the modern instantiation of Plato’s Problem is derived. In the Meno, Plato theorizes about the relationship between knowledge and experience and provides an explanation for how it is possible to know something that one has never been explicitly taught. Plato believed that we possess innate ideas that precede any knowledge that we gain through experience.

As formulated by Noam Chomsky,[1] accounting for this gap between knowledge and experience is "Plato’s Problem." The phrase has a specific linguistic context with regard to language acquisition but can also be used more generally.

Plato (427 B.C. – 347 B.C.)

Plato

Background

Plato was born into an aristocratic Athenian family. When Plato was a young man, Athens was defeated in the Peloponnesian War, a tragedy he attributed to the democracy (Russell). Plato was principally opposed to democracy, as he believed "democracy passes into despotism" [2]. Several of the political calamities of the day led Plato to propose an ideal form of government in his most famous work, The Republic, which still has profound influences on modern Western political philosophy.

Early work

Plato’s early philosophical endeavors involved poetry discussing many ideas, such as the differences between knowledge and opinion, particulars and universals, and God and man. These early dialogues do not utilize conventional notions of reason. Rather, they appeal to the emotions, the allegorical, the spiritual, and the mythological interests of an ancient speculative mind.

Controversy surrounds the early dialogues in how they are to be interpreted. Some claim that Plato was truly trying to discover objective reality through these mystical speculations while others maintain that the dialogues are stories to be interpreted only as parables, allegories, and emotional appeals to religious experience. Regardless, Plato would come to formulate a more rigorous and comprehensive philosophy later in his life, one that reverberates in contemporary Western thought to this day.

Some of Plato’s famous works are Phaedo, the Crito, and, as noted earlier, the Meno. Within these works are found a comprehensive philosophy that addresses epistemology, metaphysics, ethics, aesthetics, theology, and logic. As noted, most of the writing is in the form of dialogues and arguments to pursue answers to difficult questions and concepts. Plato’s teacher and mentor, Socrates, always plays a significant and formative role in these dialogues.

Socrates (470 B.C. - 399 B.C.)

Socrates

 

Most of Plato’s philosophical ideas were communicated through his beloved teacher Socrates as a presence in the dialogues. Though Socrates never wrote anything himself, it is evident through Plato’s works that Socrates had an incredible ability to explore the most intense analytical discussions. However, for some there is controversy regarding how much historical fact can be derived from Plato’s Socrates (Russell). Some doubt Socrates ever existed. Others are skeptical as to the accuracy of some of Plato’s dialogues but nonetheless maintain that we can learn a substantial amount of historical information about Socrates from the dialogues. Still others take practically everything Plato wrote about Socrates as veridical history. Regardless, it may be safe to say that Plato never meant to record Socrates verbatim and it may plausibly be concluded that his general ideas were communicated in the dialogues.

Socratic method

As delineated in various writings, the meticulousness, articulation, and sophistication with which Socrates spoke supplies an outstanding problem solving technique – the Socratic Method. The Socratic method may be described as follows: it usually involves others with whom Socrates directly engages (not merely pontificating to an audience), it involves a deep philosophical or ethical question to which an answer was sought, and it usually involves Socrates asking questions either to affirm his understanding of others or to seek their understanding.

If someone disagreed with him, Socrates would execute this process in order to bring about his interlocutor’s reluctant admission of inconsistencies and contradictions. Either Socrates would ask his debators questions about their claims that would lead them to admit their fallacy or Socrates would answer questions by posing questions meant to lead the other to answer their own query.

The Socratic Method

Meno

One such dialogue of Plato’s that utilized the Socratic Method was the Meno. The participants were Socrates, Meno, Anytus, and one of Meno’s slave boys. The dialogue begins with Meno asking Socrates whether virtue can be taught. Socrates responds by stating that he does not know the definition of virtue. Meno replies by stating the characteristics of a virtuous man, to which Socrates responds that the characteristics of a virtuous man may be the by-products of virtuousness but they by no means define virtue. Meno is obliged to agree; to wit, he tries to modify his explanation of virtue. Socrates counters each attempt by pointing to inconsistencies and circular arguments.
Meno seems to commit two fallacies when trying to define virtue. He either defines it using some form of the word itself, or he defines it using other words that call for definitions and explanations themselves. Eventually, Meno is lead to confess his shortcomings as he tries to define the enigmatic term (the Socratic Method is the mechanism that brings about this confession). Socrates claims that a definition of virtue must consist of common terms and concepts that are clearly understood by those in the discussion.
A crucial point in the dialogue is when Socrates tells Meno that there is no such thing as teaching, only recollection of knowledge from past lives, or anamnesis. Socrates claims that he can demonstrate this by showing that one of Meno’s servants, a slave boy, knows geometric principles though he is uneducated. Socrates states that he will teach the boy nothing, only ask him questions to assist the process of recollection. Socrates proceeds to ask the slave boy a series of questions about the size and length of lines and squares, using visual diagrams to aid the boy in understanding the questions. The crucial point to this part of the dialogue is that, though the boy has no training, he knows the correct answers to the questions – he intrinsically knows the Pythagorean proposition.

Innate knowledge

Shortly before the demonstration of Pythagoras’ theorem, the dialogue takes an epistemological turn when the interlocutors begin to discuss the fundamental nature of knowledge. The general question asked is how one can claim to know something when one does not even know what knowledge is. Via the Socratic method, it is shown that the answer to the question posed is innateness - one possesses a priori knowledge.

This is derived from Socrates’ belief that one’s soul existed in past lives and knowledge is transferred from those lives to the current one. "These [ideas] were revealed in a former state of existence, and are recovered by reminiscence (anamnesis) or association from sensible things" [3]. The claim is that one does not need to know what knowledge is before gaining knowledge, but rather one has a wealth of knowledge before ever gaining any experience.

Contemporary parallels

There are contemporary contexts that provide input for the various questions posed here: how to account for the gap between experience and knowledge, what are some of the sources of knowledge, or how much knowledge is possessed prior to experience or without conscious awareness. There are many areas in contemporary linguistics and psychological research that have relevance to these epistemological questions. Linguistic analysis has provided some strong evidence for innate cognitive capacities for language and there are many areas of cognitive psychology that yield hard data from investigations into sources of knowledge. In addition, there are some claims in the Meno that have connections to current research on perception and long-term memory (LTM).

Linguistics

Noam Chomsky

 

Linguistics is the scientific study of language. Chomskian linguistics (an inclusive, though perhaps informal, label for the theories and methodologies of linguistic study spearheaded by Noam Chomsky, meant to encompass his extensive work and influence in the field) includes everything from Chomsky’s earliest work in transformational grammar to more recent work in the Minimalist Program. More exactly, it is the study of the structure of language, or grammar. Chomskian linguistics is defined by a particular theoretical foundation and methodological approach that sets it apart from other linguistic perspectives, such as those described by functional grammar or structuralism (per Leonard Bloomfield) for example. This particular approach to the study of language is also often referred to as Generative linguistics, which is attributed to Chomsky and his early generative grammar work.

Universal grammar

There are several concepts important to the Chomskian (or generativist) approach to linguistics. The most fundamental of these ideas is the theory of universal grammar (UG). Simply put, and as implied by the name, UG refers to those grammatical properties thought to be shared by all (to be universal to all) derivations of human language (anything from Amharic to Zhuang).

Per this conceptualization, UG is innate to all humans – people come "pre-wired" with this universal grammatical structure. A person’s individual grammar (that which is unique to the person) develops from the interaction between the innate universal grammar and input from the environment, or primary linguistic data. This "analytic triplet" (McGilvray, ed., 2005, p. 51), UG + input = grammar, is the functional core of the theory.

Language acquisition

Several questions (or problems) motivate linguistic theorizing and investigation. Two such taken up in Chomskian linguistics are the process of language acquisition in children, and "Plato’s Problem." These subjects are interrelated and viewed as evidence in support of the theory of UG.

One of the simplest ways to approach the concept of universal grammar is to pose a hypothetical question about an aspect of language acquisition in children – why does a child learn the language that it does. As a specific example, how can a child of Asian descent (say, born of Chinese parents) be set down in the middle of Topeka, Kansas and acquire "perfect English?" The answer is that the child does not start with "Chinese," or any other conventionally defined language, in its head. The child does start with general grammatical rules that determine linguistic properties.

Children come equipped with universal grammar, from which any natural human language will develop – without instruction. All that is needed is passive input. If what the child predominantly hears (or sees via sign) as it is maturing through the critical period (in linguistics, that period within which a child must have necessary and sufficient exposure to human language so that language acquisition occurs; without sufficient exposure to primary linguistic data, the UG does not have the necessary input required for the development of an individual grammar; this period is commonly recognized as spanning from birth to adolescence, generally up to 12-years-old, though a shorter or longer critical period is possible on a person-by-person basis) is the English spoken in Topeka, Kansas, then that is what the child will acquire. This is why, regardless of a child’s ethnic/racial background (or any other of a variety of non-relevant factors), the child will know Cockney English, Egyptian Arabic, or isiZulu if the child’s primary linguistic input is Cockney English, Egyptian Arabic, or isiZulu, respectively.

The hypothetical question posed addresses a common misconception about what, exactly, is instantiated in the mind/brain of an individual when it comes to language. It does not address the "logical problem" of language acquisition, i.e., how children transition from ostensibly having no knowledge of language to having full knowledge, in what may be described as a very limited time with apparently limited input.

Plato's problem

To address the issue of apparently limited input, one must turn to what is possibly the most quoted of all arguments in support of universal grammar and its nativist interpretation – Plato’s Problem. The phrase refers to the Socratic dialogue, the Meno; Noam Chomsky is often attributed with coining the term. Plato's Problem particularly refers to a point in the dialogue when Socrates is talking with an uneducated servant and shows, through this interaction, that the servant knows the Pythagorean Theorem though he has never been explicitly taught any geometry. How does the servant know without having ever been taught? Plato’s suggestion is, essentially, that people have innate knowledge.

In the field of linguistics, Plato’s Problem is the problem of finding an explanation for how a child acquires language though the child does not receive explicit instruction and the primary linguistic data (input, or stimuli, from the environment; PLD is necessary for the development of an individual's grammar - language - via input into UG) a child does receive is limited. This limited