Thursday, February 24, 2011

Shape as Memory : A Geometric Theory of Architecture

I have yet to read the book.

What came to mind as I was looking at this has to do with the landscape of ideas.

It has to do with what is lying in those valleys. This may supply some understanding of how something can evolve from symmetry, as an expression of asymmetry geometrical objects. Pebbles on the side of mountains. So the idea then is that the memory is a form of geometrical expression of the energy. The object itself contains the information.

How do buildings store information and experience in their shape and form? Michael Leyton has attracted considerable attention with his interpretation of geometrical form as a medium for the storage of information and memory. In this publication he draws specific conclusions for the field of architecture and construction, attaching fundamental importance to the complex relationship between symmetry and asymmetry.


LIST OF CONTENT


1. Geometry and Memory 8
1.1 Introduction 8
1.2 Conventional Geometry: Euclid to Einstein 8
1.3 Special and General Relativity 10
1.4 New Foundations to Geometry 12
1.5 The Memory Roles of Symmetry and Asymmetry 15
1.6 Basic Procedure for Recovering the Past 18
1.7 Architecture 21

2. A Process-Grammar for Shape 24
2.1 Curvature as Memory Storage 24
2.2 General Symmetry Axes 25
2.3 Symmetry-Curvature Duality 26
2.4 The Interaction Principle 27
2.5 Undoing Curvature Variation 28
2.6 Extensive Application 29
2.7 A Grammatical Decomposition of the Asymmetry Principle 31
2.8 Process-Grammar and Asymmetry Principle 35
2.9 Scientific Applications of the Process-Grammar 36
2.10 Artistic Applications of the Process-Grammar 40
2.11 Architectural Applications of the Process-Grammar 41

3. Architecture as Maximal Memory Storage 54
3.1 Introduction 54
3.2 The Two Fundamental Principles 54
3.3 Groups 55
3.4 Generating a Shape by Transfer 56
3.5 Fiber and Control 58
3.6 Projection as Memory 59
3.7 Regularity in Classical Architecture 62
3.8 Breaking the Iso-Regularity 69
3.9 Reference Frames 70
3.10 New Theory of Symmetry-Breaking 70
3.11 Maximizing Memory Storage 72
3.12 Theory of Unfolding 75

4. Architecture and Computation 86
4.1 Introduction 86
4.2 New Foundations for Science 86
4.3 New Foundations for Art 89
4.4 New Foundations for Computation 90
4.5 What is a Building? 91

Tuesday, February 22, 2011

Keeping it Real


The first results on supersymmetry from the Large Hadron Collider (LHC) have been analysed by physicists and some are suggesting that the theory may be in trouble. Data from proton collisions in both the Compact Muon Solenoid (CMS) and ATLAS experiments have shown no evidence for supersymmetric particles – or sparticles – that are predicted by this extension to the Standard Model of particle physics. Will the LHC find supersymmetry Kate McAlpine ?

Thank you Tommaso Dorigo

If such propositions are ever moved to the project of LHC confirmations then the ideals of those who proposed should never be conceived as rats as a commentator writes. It's just not polite.

I would comment at your blog article but like Cosmic Variance I have been blocked. Oh well:)

This information is a form of responsible action toward experimental fundamentalism we take as one moves forward.

Atlas Experiment

Link on Title and internal "color reference links" will highlight links to subject locations. Well worth the visit.

 The ATLAS detector consists of four major components
(place your cursor over the links below to identify the location of the components):
  • inner detector (yellow) - measures the momentum of each charged particle
  • calorimeter (orange and green) - measures the energies carried by the particles
  • muon spectrometer (blue) - identifies and measures muons
  • magnet system (grey) - bending charged particles for momentum measurement
The interactions in the ATLAS detectors will create an enormous dataflow. To digest this data we need:

Thursday, February 10, 2011

New View of Family Life in the North American Nebula

This swirling landscape of stars is known as the North American nebula. In visible light, the region resembles North America, but in this new infrared view from NASA's Spitzer Space Telescope, the continent disappears. Image credit: NASA/JPL-Caltech


See: New View of Family Life in the North American Nebula


See Explanation.  Clicking on the picture will download 
 the highest resolution version available.
The North America Nebula
Credit & Copyright: Jason Ware

Explanation: Here's a familiar shape in an unfamiliar location! This emission nebula is famous partly because it resembles Earth's continent of North America. To the right of the North America Nebula, cataloged as NGC 7000, is a less luminous Pelican Nebula. The two emission nebula measure about 50 light-years across, are located about 1500 light-years away, and are separated by a dark absorption cloud. The nebulae can be seen with binoculars from a dark location. Look for a small nebular patch north-east of bright star Deneb in the constellation of Cygnus. It is still unknown which star or stars ionize the red-glowing hydrogen gas.

Wednesday, February 09, 2011

Quark Soup: Applied Superstring Theory

Author(s)
Alex Buche-University of Western Ontario / Perimeter Institute
Robert Myers-Perimeter Institute
Aninda Sinha-Perimeter Institute

It is believed that in the first few microseconds after the Big Bang, our universe was dominated by a strongly interacting phase of nuclear matter at extreme temperatures. An impressive experimental program at the Brookhaven National Laboratory on Long Island has been studying the properties of this nuclear plasma with some rather surprising results. We outline how there may be a deep connection between extra-dimensional gravity of String Theory and the fundamental theories of subatomic particles can solve the mystery of the near-ideal fluid properties of the strongly coupled nuclear plasma.

See Also:

Canadian Association of Physicists

***
Part of the understanding of the research goes back to the beginning of this QGP endeavor that brings us to today's level of understanding  enhanced by phenomenological positions now that allows us to move forward in our predictions and speculations. 

The Phenix


PHENIX, the Pioneering High Energy Nuclear Interaction eXperiment, is an exploratory experiment for the investigation of high energy collisions of heavy ions and protons. PHENIX is designed specifically to measure direct probes of the collisions such as electrons, muons, and photons. The primary goal of PHENIX is to discover and study a new state of matter called the Quark-Gluon Plasma.




Back in 2005, what is it we saw and what we building along the way experimentally had constraints which lead our birdseye view of the process  as if from a distance looking toward the specifics of collision processes,  allowed us to be taken ever closer to the beginnings of the universe in expression.

***
In summary, experiments at RHIC have shown that a very dense QCD medium is formed in high-energy heavy-ion collisions. Other measurements, namely elliptic flow and baryon-to-meson ratios, indicate that this medium is characterized by partonic degrees offreedom and that its expansion and cooling is well described by hydrodynamical models with high viscosity. Thus, this medium is more similar to a liquid than to a gas of gluons and quarks.Review on Heavy-Ion Physics

Triggering a Wave of Star Formation.

Arp 147 contains a spiral galaxy (right) that collided with an elliptical galaxy (left), triggering a wave of star formation. Credit: X-ray: NASA/CXC/MIT/S.Rappaport et al, Optical: NASA/STScI   

See:Triggering a Wave of Star Formation.

Monday, January 31, 2011

Liberal arts

The Pyramid(as an expression of Liberal Arts Encapsulated) is a combination of  the Trivium , and  the Quadrivium
My interest has been from a historical position about how such a system while it developed from that ancient perspective,  is still not about a "religious perspective" as to what is to be believed by Lee Smolin.

If we think outside of time, we believe these ideas somehow "existed" before we invented them. If we think in time we see no reason to presume that.Lee Smolin

I of course question what is relative by appointments from him as to what can  exist "within and out of time." Since this is a foundation approach with which his whole take depends on, his relative relationships as it is relegated toward perspective about the beginning and the end of the universe,  is a position with which one cannot ever assume, hence, the value in religious perspective one is suppose to have in relation to their science? I hope I get this right.

The idea that truth is timeless and resides outside the universe was the essence of Plato's philosophy, exemplified in the parable of the slave boy that was meant to argue that discovery is merely remembering. Lee Smolin

So I needed to put this in perspective, so it is understood that the issue here arises "from within" so that all expression without,  inside or outside of time become a relative issue about position and stances assumed and cannot be differentiated to such categories as to it significance as being religious.

Among contemporary cosmologists and physicists, proponents of eternal inflation and timeless quantum cosmology are thinking outside of time. Proponents of evolutionary and cyclic cosmological scenarios are thinking in time. If you think in time you worry about time ending at space-time singularities. If you think outside of time this is an ignorable problem because you believe reality is the whole history of the world at once. Lee Smolin

So, I provided some access to "Plato's Dialogues" so as to give you the the ability to discern what is assume by Lee is what is spoken by and through Plato's own words.

What did you gain by reading that you can now say that what is established as "foundations approached" to being realistic, wafts through the scientific community and distinguishes itself according to some category that allows you to believe that it is religious by inherent and that such searches have no basis according too?

Does he say that explicit....only you can say by such association and quotes, can I say then that I point toward that direction in my assumptions as well. I mean you have been given the opportunity so you decide.

My perspective is about that "Cognitive Tool Kit" and how leading to a "point source" is nothing more then the recognition of coming to a "point source" inside you,  that is inside time. What I am saying, is that such perfection is the containment of all that has ever existed, or will ever exist, you are connected to in time, so these thoughts about the before and after are not apart from what happens within in any universe, nor can birth and death be considered outside of it.

This recognition is "the measure of" with which one can assume their foundation. That is, how I see Lee's position. All scientist would agree in that such measure is appropriate, yet such thoughts about time and outside of time pertaining to the Cognitive Tool Kit is not part and parcel of a "religious context" that one could say, "eureka!"

Again, it leads to a Point Source. A "point source" inside time that contain vasts potential?

SEE:
***



The seven liberal arts – Picture from the Hortus deliciarum of Herrad von Landsberg (12th century)

The term liberal arts denotes a curriculum that imparts general knowledge and develops the student’s rational thought and intellectual capabilities, unlike the professional, vocational and technical curricula emphasizing specialization. The contemporary liberal arts comprise studying literature, languages, philosophy, history, mathematics, and science.[1]

Contents

History

In classical antiquity, the liberal arts denoted the education worthy of a free person (Latin: liber, “free”).[2] Contrary to popular opinion, freeborn girls were as likely to receive formal education as boys, especially during the Roman Empire—unlike the lack-of-education, or purely manual/technical skills, proper to a slave.[3] The "liberal arts" or "liberal pursuits" (Latin liberalia studia) were already so called in formal education during the Roman Empire; for example, Seneca the Younger discusses liberal arts in education from a critical Stoic point of view in Moral Epistle 88.[4] The subjects that would become the standard "Liberal Arts" in Roman and Medieval times already comprised the basic curriculum in the enkuklios paideia or "education in a circle" of late Classical and Hellenistic Greece.

In the 5th century AD, Martianus Capella defined the seven Liberal Arts as: grammar, dialectic, rhetoric, geometry, arithmetic, astronomy, and music. In the medieval Western university, the seven liberal arts were:[5]
  1. grammar
  2. logic
  3. rhetoric
  1. arithmetic
  2. astronomy
  3. music
  4. geometry

 Liberal arts in the United States

In the United States, Liberal arts colleges are schools emphasizing undergraduate study in the liberal arts. Traditionally earned over four years of full-time study, the student earned either a Bachelor of Arts degree or a Bachelor of Science degree; on completing undergraduate study, students might progress to either a graduate school or a professional school (public administration, business, law, medicine, theology). The teaching is Socratic,[citation needed] to small classes,[citation needed] and at a greater teacher-to-student ratio than at universities;[citation needed] professors teaching classes are allowed to concentrate more on their teaching responsibilities than primary research professors or graduate student teaching assistants, in contrast to the instruction common in universities.[original research?][dubious ] Despite the European origin of the liberal arts college,[6] the term liberal arts college usually denotes liberal arts colleges in the United States.

See also

 References

  1. ^ "Liberal Arts: Encyclopedia Britannica Concise". Encyclopedia Britannica.
  2. ^ Ernst Robert Curtius, European Literature and the Latin Middle Ages [1948], trans. Willard R. Trask (Princeton: Princeton University Press, 1973), p. 37. The classical sources include Cicero, De Oratore, I.72–73, III.127, and De re publica, I.30.
  3. ^ H. I. Marrou, A History of Education in Antiquity [1948], trans. George Lamb (London: Sheed & Ward, 1956), pp. 266–67.
  4. ^ Seneca Epistle 88 at Stoics.com
  5. ^ "James Burke: The Day the Universe Changed In the Light Of the Above".
  6. ^ Harriman, Philip (1935). "Antecedents of the Liberal Arts College". The Journal of Higher Education, Vol. 6, No. 2 (1935), pp. 63–71.

 Further reading

  • Blaich, Charles, Anne Bost, Ed Chan, and Richard Lynch. "Defining Liberal Arts Education." Center of Inquiry in the Liberal Arts, 2004.
  • Blanshard, Brand. The Uses of a Liberal Education: And Other Talks to Students. (Open Court, 1973. ISBN 0-8126-9429-5)
  • Friedlander, Jack. Measuring the Benefits of Liberal Arts Education in Washington's Community Colleges. Los Angeles: Center for the Study of Community Colleges, 1982a. (ED 217 918)
  • Joseph, Sister Miriam. The Trivium: The Liberal Arts of Logic, Grammar, and Rhetoric. Paul Dry Books Inc, 2002.
  • Pfnister, Allen O. "The Role of the Liberal Arts College." The Journal of Higher Education. Vol. 55, No. 2 (March/April 1984): 145–170.
  • Reeves, Floyd W. "The Liberal-Arts College." The Journal of Higher Education. Vol. 1, No. 7 (1930): 373–380.
  • Seidel, George. "Saving the Small College." The Journal of Higher Education. Vol. 39, No. 6 (1968): 339–342.
  • Winterer, Caroline.The Culture of Classicism: Ancient Greece and Rome in American Intellectual Life, 1780–1910. Baltimore: Johns Hopkins University Press, 2002.
  • Wriston, Henry M. The Nature of a Liberal College. Lawrence University Press, 1937.
  • T. Kaori Kitao, William R. Kenan, Jr. (27 March 1999). The Usefulness Of Uselessness. Keynote Address, The 1999 Institute for the Academic Advancement of Youth's Odyssey at Swarthmore College.

 External links

Quadrivium


The quadrivium comprised the four subjects, or arts, taught in medieval universities after the trivium. The word is Latin, meaning "the four ways" or "the four roads". Together, the trivium and the quadrivium comprised the seven liberal arts.[1] The quadrivium consisted of arithmetic, geometry, music, and astronomy. These followed the preparatory work of the trivium made up of grammar, logic (or dialectic, as it was called at the times), and rhetoric. In turn, the quadrivium was considered preparatory work for the serious study of philosophy and theology.

Contents

Origins

These four studies compose the secondary part of the curriculum outlined by Plato in The Republic, and are described in the seventh book of that work.[1] The quadrivium is implicit in early Pythagorean writings and in the De nuptiis of Martianus Capella, although the term was not used until Boethius early in the sixth century.[2] As Proclus wrote:
The Pythagoreans considered all mathematical science to be divided into four parts: one half they marked off as concerned with quantity, the other half with magnitude; and each of these they posited as twofold. A quantity can be considered in regard to its character by itself or in its relation to another quantity, magnitudes as either stationary or in motion. Arithmetic, then, studies quantities as such, music the relations between quantities, geometry magnitude at rest, spherics [astronomy] magnitude inherently moving[3].

Medieval usage

At many medieval universities, this would have been the course leading to the degree of Master of Arts (after the BA). After the MA the student could enter for Bachelor's degrees of the higher faculties (Theology, Medicine or Law). To this day some of the postgraduate degree courses lead to the degree of Bachelor (the B.Phil and B.Litt. degrees are examples in the field of philosophy, and the B.Mus. remains a postgraduate qualification at Oxford and Cambridge universities).

The study was eidetic, approaching the philosophical objectives sought by considering it from each aspect of the quadrivium within the general structure demonstrated by Proclus, namely arithmetic and music on the one hand,[4] and geometry and cosmology on the other.[5]

The subject of music within the quadrivium was originally the classical subject of harmonics, in particular the study of the proportions between the music intervals created by the division of a monochord. A relationship to music as actually practised was not part of this study, but the framework of classical harmonics would substantially influence the content and structure of music theory as practised both in European and Islamic cultures.

Modern usage

In modern applications of the liberal arts as curriculum in colleges or universities, the quadrivium may be considered as the study of number and its relationship to physical space or time: arithmetic was pure number, geometry was number in space, music number in time, and astronomy number in space and time. Morris Kline classifies the four elements of the quadrivium as pure (arithmetic), stationary (geometry), moving (astronomy) and applied (music) number.[6]

This schema is sometimes referred to as "classical education" but it is more accurately a development of the 12th and 13th centuries with recovered classical elements, rather than an organic growth from the educational systems of antiquity. The term continues to be used by the classical education movement.

See also


 References

  1. ^ a b Wikisource-logo.svg "Quadrivium". New International Encyclopedia. 1905.
  2. ^ Henri Irénée Marrou, "Les Arts Libéreaux dans l'Antiquité Classique", pp. 6-27 in Arts Libéraux et Philosophie au Moyen Âge, (Paris: Vrin / Montréal: Institut d'Études Médiévales), 1969, pp. 18-19.
  3. ^ Proclus, A commentary on the first book of Euclid's Elements, xii, trans. Glenn Raymond Morrow (Princeton: Princeton University Press) 1992, pp. 29-30. ISBN 0691020906.
  4. ^ Craig Wright, The Maze and the Warrior - Symbols in Architecture, Theology, and Music, Harvard University Press 2001
  5. ^ Laura Ackerman Smoller, History, Prophecy and the Stars: Christian Astrology of Pierre D'Ailly, 1350-1420, Princeton University Press 1994
  6. ^ Morris Kline, "The Sine of G Major", Mathematics in Western Culture, Oxford University Press 1953

Saturday, January 22, 2011

Plato's Problem and Meno: How Accurately Portrayed?

SOCRATES: Then he who does not know may still have true notions of that which he does not know?

MENO: He has.

SOCRATES: And at present these notions have just been stirred up in him, as in a dream; but if he were frequently asked the same questions, in different forms, he would know as well as any one at last?

MENO: I dare say.

SOCRATES: Without any one teaching him he will recover his knowledge for himself, if he is only asked questions?

MENO: Yes.

SOCRATES: And this spontaneous recovery of knowledge in him is recollection?

MENO: True.

SOCRATES: And this knowledge which he now has must he not either have acquired or always possessed?

MENO: Yes.

SOCRATES: But if he always possessed this knowledge he would always have known; or if he has acquired the knowledge he could not have acquired it in this life, unless he has been taught geometry; for he may be made to do the same with all geometry and every other branch of knowledge. Now, has any one ever taught him all this? You must know about him, if, as you say, he was born and bred in your house.

MENO: And I am certain that no one ever did teach him.

SOCRATES: And yet he has the knowledge?

MENO: The fact, Socrates, is undeniable.

SOCRATES: But if he did not acquire the knowledge in this life, then he must have had and learned it at some other time?

MENO: Clearly he must.

SEE:Meno by Plato
 ***

LEE SMOLIN
Physicist, Perimeter Institute; Author, The Trouble With Physics

Thinking In Time Versus Thinking Outside Of Time

One very old and pervasive habit of thought is to imagine that the true answer to whatever question we are wondering about lies out there in some eternal domain of "timeless truths." The aim of re-search is then to "discover" the answer or solution in that already existing timeless domain. For example, physicists often speak as if the final theory of everything already exists in a vast timeless Platonic space of mathematical objects. This is thinking outside of time.

Scientists are thinking in time when we conceive of our task as the invention of genuinely novel ideas to describe newly discovered phenomena, and novel mathematical structures to express them. If we think outside of time, we believe these ideas somehow "existed" before we invented them. If we think in time we see no reason to presume that.

The contrast between thinking in time and thinking outside of time can be seen in many domains of human thought and action. We are thinking outside of time when, faced with a technological or social problem to solve, we assume the possible approaches are already determined by a set of absolute pre-existing categories. We are thinking in time when we understand that progress in technology, society and science happens by the invention of genuinely novel ideas, strategies, and novel forms of social organization.
See:A "scientific concept" may come from philosophy, logic, economics, jurisprudence, or other analytic enterprises, as long as it is a rigorous conceptual tool that may be summed up succinctly (or "in a phrase") but has broad application to understanding the world.

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

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