"Let no one ignorant of geometry enter"

Plato’s Motto

The scho­liast on Aelius Aris­tides 125.14 (Din­dorf, Vol. 3) says the fol­low­ing:

ἐπεγέγραπτο ἔμπροσθεν τῆς διατριβῆς τοῦ Πλάτωνος ὅτι ἀγεωμέτρητος μηδεὶς εἰσίτω· ἀντὶ τοῦ ἄνισος καὶ ἄδικος. ἡ γὰρ γεωμετρία τὴν ἰσότητα καὶ τὴν δικαιοσύνην τηρεῖ.

‘In front of Plato’s school had been inscribed, “Let noone enter un-​​geometried” rather than “unequal” or “unjust,” for geom­e­try main­tains equal­ity and justness.’


At any rate, Pseudo-​​Galen (post 2 A.D.?) quotes the phrase at the begin­ning of ‘On the divi­sions of phi­los­o­phy,’ and makes geom­e­try a pre­lim­i­nary to the­ol­ogy:

ὁ μὲν οὖν Πλάτων εἰς φυσιολογικὸν καὶ θεολογικὸν αὐτὸ διαιρεῖ· τὸ γὰρ μαθηματικὸν οὐκ ἠβούλετο εἶναι μέρος τῆς φιλοσοφίας, ἀλλὰ προγύμνασμά τι ὥσπερ ἡ γραμματικὴ καὶ ἡ ῥητορική· ὅθεν καὶ πρὸ τοῦ ἀκροατηρίου τοῦ οἰκείου ἐπέγραψεν ‘ἀγεωμέτρητος μηδεὶς εἰσίτω’. τοῦτο δὲ ὁ Πλάτων ἐπέγραφεν, ἐπειδὴ εἰς τὰ πολλὰ θεολογεῖ καὶ περὶ θεολογίαν καταγίνεται· συμβάλλεται δὲ εἰς εἴδησιν τῆς θεολογίας τὸ μαθηματικόν, οὗτινός ἐστιν ἡ γεωμετρία.

‘Plato divided it (the­o­ret­i­cal phi­los­o­phy) into phys­i­ol­ogy and the­ol­ogy. In fact, he did not want math­e­mat­ics to be a part of phi­los­o­phy, but a sort of pro­gym­nasma like gram­mar and rhetoric. That’s why, before his pri­vate lecture-​​room, he inscribed “Let no one enter un-​​geometried.” He inscribed this since he dis­coursed on the­ol­ogy in all mat­ters and dwelt on the­ol­ogy, and included math­e­mat­ics, of which geom­e­try is a part, into theology’s forms of knowledge.’ See:Plato’s Motto Written by Dennis McHenry. December 10, 2005

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Polish Society of St. Thomas Aquinas-Plato's Academy

Candidates for philosophy to be properly prepared.

Plato introduction to the philosophy of mathematics has made, highlighting the non-the usual benefits of studying mathematics in the improvement mind. At the front of the AP, as the legend goes, was engraved the inscription: "There is no WStE-pu anyone who does not know geometry. " In the Republic (VII 528 a) Plato classification mathematical sciences conducted on the basis of views Pythagoreans, who shared in the mathematical sciences depending on what questions to give answer: "How much?" - arithmetic and music, "how much?" - geometry and mechanical chanika. Plato arranges in order of mathematical sciences: arithmetic, geometry (distinguished by the geometry of the flat - planimetry and spatial geometry -stereometry), astronomy, music, and considers that these sciences are related to the relation-my formal, uwidocznionymi eg decreasing their abstractness. http://www.ptta.pl/pef/pdf/a/akademiaplaton.pdf

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If the late character of our sources may incite us to doubt the autheticity of this tradition, there remains that, in its spirit, it is in no way out of character, as can be seen by reading or rereading what Plato says about the sciences fit for the formation of philosophers in book VII of the Republic, and especially about geometry at Republic, VII, 526c8-527c11. We should only keep in mind that, for Plato, geometry, as well as all other mathematical sciences, is not an end in itself, but only a prerequisite meant to test and develop the power of abstraction in the student, that is, his ability to go beyond the level of sensible experience which keeps us within the "visible" realm, that of the material world, all the way to the pure intelligible. And geometry, as can be seen through the experiment with the slave boy in the Meno (Meno, 80d1-86d2), can also make us discover the existence of truths (that of a theorem of geometry such as, in the case of the Meno, the one about doubling a square) that may be said to be "transcendant" in that they don't depend upon what we may think about them, but have to be accepted by any reasonable being, which should lead us into wondering whether such transcendant truths might not exist as well in other areas, such as ethics and matters relating to men's ultimate happiness, whether we may be able to "demonstrate" them or not.See: Frequently Asked Questions about Plato by Bernard SUZANNE

Most certainly that given perspective about the reality of geometry in the context  of the abstract,  it is buried deep within ourselves that our creativity leads us that much closer to the truth and points to a depth of our being. Have you not ever been there to know, that by such mapping schematically, any direction lies under the sociological underpinnings of our associations and our dealings with reality?

On any road to self discovery it was apparent to me that by observing levels of awareness that we usually don't take the time to observe, the more I looked, a abstract math of let's say Game Theory, was apparent. When being lead through a mathematical landscape, could we arrive at our everyday dealings in society?

Economically, it had to make sense that such algorithms could be written and many of us as observers of the information world are unaware of the constrains we have applied to our everyday reading of the economic world?

Setting Time Aright

Time has no independent existence apart from the order of events by which we measure it. — Albert Einstein

While Event has since past, I hope the lecture itself will remain in public domain. It helps so as to see the context of the discussion provided by this conference with regard to that subject of time.




Video streaming by Ustream

See:Setting Time Aright

In 1952, in his book Relativity, Einstein writes:

Since there exists in this four dimensional structure [space-time] no longer any sections which represent "now" objectively, the concepts of happening and becoming are indeed not completely suspended, but yet complicated. It appears therefore more natural to think of physical reality as a four dimensional existence, instead of, as hitherto, the evolution of a three dimensional existence

.

Setting Time Aright

View more presentations from Sean Carroll

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  If man thinks of the totality as constituted of independent fragments, then that is how his mind will tend to operate, but if he can include everything coherently and harmoniously in an overall whole that is undivided, unbroken, and without a border then his mind will tend to move in a similar way, and from this will flow an orderly action within the whole. (David Bohm, Wholeness and the Implicate Order, 1980)


Lee Smolin:

I suspect this reflects the expectation many people have that time is not fundamental, but rather emerges only at a semiclassical approximation in quantum cosmology. If you believe this then you believe that the fundamental quantities a quantum cosmology should compute are timeless. This in turn reflects a very old and ultimately religious prejudice that deeper truths are timeless. This has been traced by scholars to the theology of Newton and contemporaries who saw space as “the sensorium” of an eternal and all seeing god. Perhaps the BB paradox is telling us it is time to give up the search for timeless probability distributions, and recognize that since Darwin the deep truths about nature cannot be divorced from time.

The alternative is to disbelieve the arguments that time is emergent-which were never very convincing- and instead formulate quantum cosmology in such a way that time is always real. I would suggest that the Boltzman Brain’s paradox is the reducto ad absurdum of the notion that time is emergent and that rather than play with little fixes to it we should try to take seriously the opposite idea: that time is real.

***

Bar of Lead Tungstate Source: A Quantum Diaries Survivor-Calorimeters for High Energy Physics experiments - part 1 April 6, 2008

Calorimeters measure the collective behavior of particles traveling along approximately the same path, and are thus naturally suited for the measurement of jets-Dorigo Tommaso

See: 

• FQXi Conference 2011
  
• The Reference Frame: Ten new things modern physics has learned about time

Utopia

Woodcut by Ambrosius Holbein for a 1518 edition of Utopia. The lower left-hand corner shows the traveler Raphael Hythlodaeus, describing the island.

Utopia (pronounced /juːˈtoʊpiə/) is a name for an ideal community or society possessing a seemingly perfect socio-politico-legal system.^[1] The word was invented by Sir Thomas More for his 1516 book Utopia, describing a fictional island in the Atlantic Ocean. The term has been used to describe both intentional communities that attempted to create an ideal society, and fictional societies portrayed in literature. It has spawned other concepts, most prominently dystopia.

The word comes from the Greek: οὐ, "not", and τόπος, "place", indicating that More was utilizing the concept as allegory and did not consider such an ideal place to be realistically possible. The English homophone Eutopia, derived from the Greek εὖ, "good" or "well", and τόπος, "place", signifies a double meaning.

It got my historical dithers up so as to pin down points of views that may have inspired cultures to look for new lands beyond the realms of thought each society was used too, and "hoped for" in some better form.

Utopia (book)

Utopia
Illustration for the 1516 first edition of Utopia.
Author	Thomas More
Translator	Ralph Robinson Gilbert Burnet
Country	Seventeen Provinces, Leuven
Language	Latin
Publication date	1516
Published in English	1551
Pages	134
ISBN	978-1-907727-28-3

Utopia (in full: Libellus vere aureus, nec minus salutaris quam festivus, de optimo rei publicae statu deque nova insula Utopia) is a work of fiction by Thomas More published in 1516. English translations of the title include A Truly Golden Little Book, No Less Beneficial Than Entertaining, of the Best State of a Republic, and of the New Island Utopia (literal) and A Fruitful and Pleasant Work of the Best State of a Public Weal, and of the New Isle Called Utopia (traditional).^[1] (See "title" below.) The book, written in Latin, is a frame narrative primarily depicting a fictional island society and its religious, social and political customs.

Despite modern connotations of the word "utopia," it is widely accepted that the society More describes in this work was not actually his own "perfect society." Rather he wished to use the contrast between the imaginary land's unusual political ideas and the chaotic politics of his own day as a platform from which to discuss social issues in Europe.

Why quest for new lands, planets for living?

Bacon's Utopia: The New Atlantis

Quote:

In 1623 Bacon expressed his aspirations and ideals in The New Atlantis. Released in 1627, this was his creation of an ideal land where "generosity and enlightenment, dignity and splendor, piety and public spirit" were the commonly held qualities of the inhabitants of Bensalem. In this work, he portrayed a vision of the future of human discovery and knowledge. The plan and organization of his ideal college, "Solomon's House", envisioned the modern research university in both applied and pure science.

Tommaso Campanella- See also:The City of the Sun

What contributions were idealistic set before those who signed the documents that one would have found reference from Raphael toward the Stanza's of the signatore's room in Rome?

The Room of the Segnatura contains Raphael's most famous frescoes. Besides being the first work executed by the great artist in the Vatican they mark the beginning of the high Renaissance. The room takes its name from the highest court of the Holy See, the "Segnatura Gratiae et Iustitiae", which was presided over by the pontiff and used to meet in this room around the middle of the 16th century. Originally the room was used by Julius II (pontiff from 1503 to 1513) as a library and private office. The iconographic programme of the frescoes, which were painted between 1508 and 1511, is related to this function. See Raphael Rooms

You had to understand the setting and the historical drama set forth?



School of Athens by Raphael

Quote:

In center, while Plato - with the philosophy of the ideas and theoretical models, he indicates the sky, Aristotle - considered the father of Science, with the philosophy of the forms and the observation of the nature indicates the Earth. Many historians of the Art in the face correspondence of Plato with Leonardo, Heraclitus with Miguel Angel, and Euclides with Twine agree.

So to set this up some background was needed?

Quote:

Plato and Aristotle, Up and Down by Kelley L. Ross, Ph.D. 

Rafael has Plato pointing up and Aristotle gesturing down to indicate the difference in their metaphysics. For Plato, true existence is in the World of Forms, in relation to which this world (of Becoming) is a kind of shadow or image of the higher reality. Aristotle, on the other hand, regards individual objects in this world as "primary substance" and dismisses Plato's Forms -- except for God as a pure actuality, without matter.

However, when it comes to ethics and politics, the gestures should be reversed. Plato, like Socrates, believed that to do the good without error, one must know what the good is. Thus, we get the dramatic moment in the Republic where Plato says that philosophers, who have escaped from the Cave and come to understand the higher reality, must be forced to return to this world and rule, so that their wisdom can benefit the state. Aristotle, on the other hand, says that the "good" is simply the goal of various particular activities, without one meaning in Plato's sense. The particular activities of most human affairs involve phronésis, "practical wisdom." This is not sophía, true wisdom, for Aristotle, which involves the theoretical knowledge of the highest things, i.e. the gods, the heavens, and God.

Thus, for philosophy, Aristotle should point up and would represent a contemplative attitude that was certainly more congenial to religious practices in the Middle Ages. By the same token, Aristotle's contribution to what we now think of as science was hampered by his lack of interest in mathematics. 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.

Therefore, caution is in order when comparing the meaning of the metaphysics of Plato and Aristotle with its significance for their attitudes towards ethics, politics, and science. Indeed, if the opposite of wisdom is, not ignorance, but folly, then Socrates and Plato certainly started off with the better insight.

Hope I didn't bore you with precursors of "new thoughts of how differing societies were formed?  How one may of attained such insight by helping one to realize the choice we have about how those new societies may have inspired?

Of course, "a science" evolved from it all?

Stargazers and Hill Climbers

AS with Einstein, who was Socrates daemon?:)

In Plato's Apology of Socrates, Socrates claimed to have a daimonion (literally, a "divine something")[6] that frequently warned him - in the form of a "voice" - against mistakes but never told him what to do

See:Fullerane and Allotropes

Some may even call "hills" mountains. Depends on where they think perspective is heighten in relation to where they see themself in the world, and where a better locations allows for a more expansive views of things. This is psychologically important to realize that inherent inside of us if one does follow the tenet of Know Thyself by Socrates. Such a plan would have been understood in the examination to see a relationship in continuity is topologically important with the world around them. Not be self-centred, but to move progressively in the world may call for understanding this relationship with the environment.

What shall proceed the understanding that the arche is fully understood as the central themes of characters, to see it exemplified in how you now approach the world in your own way? It becomes easier for you to understand, that this "imprint of the concrete in the painting I had selected of the Raphael" was to show such a school of thought, was exemplifying the truer principle of the wisdom seeking, while of course approaching the modern day world based on that Socratic method in science.

But I only show by example, and recognizing this facet of the nature of the individual is more the idea that what ever method you choose that it is consistent and recognizable, becomes second nature to the person seeking answers. Student of Science or Philosophy.

Death of Socrates by Jacques Davidthis picture depicts the closing moments of the life of Socrates. Condemned to death or exile by the Athenian government for his teaching methods which aroused scepticism and impiety in his students, Socrates heroicly rejected exile and accepted death from hemlock.

Self portrait of Jacques-Louis David, 1794, Musée du Louvre

Here the philosopher continues to speak even while reaching for the cup, demonstrating his indifference to death and his unyielding commitment to his ideals. Most of his disciplines and slaves swirl around him in grief, betraying the weakness of emotionalism. His wife is seen only in the distance leaving the prison. Only Plato, at the foot of the bed and Crito grasping his master's leg, seem in control of themselves.

See:Jacques-Louis David: The Death of Socrates

I think the idea is and can be unique, in that each can develop a process and means to an end( many travel far and wide while they should have never left home), that would allow this creative aspect of being "in the now" has potential. To be able to allow insight to manifest and spread across the mind in such lightning speed. It thusly leaves no doubt. This is a condensible feature of the complexity of information to be distill to it's essence. IN an abstract world, a rain drop can hold quite an lot of architectural meaning.

For Plato then it was the ideal city-state of Kallipolis

The Philosopher King

Plato defined a philosopher firstly as its eponymous occupation – wisdom-lover. He then distinguishes between one who loves true knowledge as opposed to simple sights or education by saying that a philosopher is the only man who has access to Forms – the archetypal entities that exist behind all representations of the form (such as Beauty itself as opposed to any one particular instance of beauty). It is next and in support of the idea that philosophers are the best rulers that Plato fashions the ship of state metaphor, one of his most often cited ideas (along with his allegory of the cave). "[A] true pilot must of necessity pay attention to the seasons, the heavens, the stars, the winds, and everything proper to the craft if he is really to rule a ship" (The Republic, 6.488d). Plato claims that the sailors (i.e., the people of the city-state over whom the philosopher is the potential ruler) ignore the philosopher's "idle stargazing" because they have never encountered a true philosopher before.

Stargazers by Paul Rossetti Bjarnson, Pg 102, Chapter XV

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Ever teacher has their progeny of students as has been exemplified in the context of our modern day scholars. Kip Thorne in relation to John Archibald Wheeler. Stephen Hawking and his doctoral students.

Dennis William Siahou Sciama FRS (November 18, 1926–December 18, 1999) was a British physicist who, through his own work and that of his students, played a major role in developing British physics after the Second World War.

Sciama also strongly influenced Roger Penrose, who dedicated his The Road to Reality to Sciama's memory. The 1960s group he led in Cambridge (which included Ellis, Hawking, Rees, and Carter), has proved of lasting influence.

I have already established this lineage and subsequent comments in relation to Penrose under this heading to exemplify the relationship and perspective in relation to each other externally in the progressive nature of moving forward in science.

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For Plato, it is no less an important feature that at Socrates bedside he sees the wisdom of his teacher become the "guiding light source" of all that must exchange between those who hold a value to "dimensional significance in abstract" in our current day, would be able to see the world in a most significant way. It's no less progressive then, that such an example was given to an extent that the thought process of the Gendankin, would be set before Plato's own students, as John Wheeler did for his, to see that Aristotle is most selectively announced as a most brilliant student by answering to Plato's analogy of the Cave. Who becomes an extension of the "arche in principle" as one end being science, and in a open sweeping hand, to all that is for ever exemplify in the "arche contained" in the heading of this blog above.

Plotinus

Plotinus (Greek: Πλωτῖνος) (ca. AD 204–270) was a major philosopher of the ancient world who is widely considered the founder of Neoplatonism (along with his teacher Ammonius Saccas). Much of our biographical information about him comes from Porphyry's preface to his edition of Plotinus' Enneads.

Plotinus Theory

Plotinus taught that there is a supreme, totally transcendent "One", containing no division, multiplicity or distinction; likewise it is beyond all categories of being and non-being. The concept of "being" is derived by us from the objects of human experience called the dyad, and is an attribute of such objects, but the infinite, transcendent One is beyond all such objects, and therefore is beyond the concepts that we derive from them. The One "cannot be any existing thing", and cannot be merely the sum of all such things (compare the Stoic doctrine of disbelief in non-material existence), but "is prior to all existents". Thus, no attributes can be assigned to the One. We can only identify it with the Good and the principle of Beauty. [I.6.9]

For example, thought cannot be attributed to the One because thought implies distinction between a thinker and an object of thought (again dyad). Even the self-contemplating intelligence (the noesis of the nous) must contain duality. "Once you have uttered 'The Good,' add no further thought: by any addition, and in proportion to that addition, you introduce a deficiency." [III.8.10] Plotinus denies sentience, self-awareness or any other action (ergon) to the One [V.6.6]. Rather, if we insist on describing it further, we must call the One a sheer Dynamis or potentiality without which nothing could exist. [III.8.10] As Plotinus explains in both places and elsewhere [e.g. V.6.3], it is impossible for the One to be Being or a self-aware Creator God. At [V.6.4], Plotinus compared the One to "light", the Divine Nous (first will towards Good) to the "Sun", and lastly the Soul to the "Moon" whose light is merely a "derivative conglomeration of light from the 'Sun'". The first light could exist without any celestial body.

While the arche then becomes a understanding and significant addition to ever place that self evident becomes real for the individual then how is it that such an relation cannot be seen in the world as a foundation principle to guarantee that they are on the right track. To see that "correlation of cognition" places a role in the factual attainment of information. No matter how insignificant or trivial the relation, as common knowledge, it becomes a reinforcing measure of how one is adapting and applying this model, which allows confidence to be built in pursuance of knowledge and truth.

Plato and Justice

A just society must be governed by men of reason.Inventing a new social myth to replace the old. Socrates calls those who rule for the benefit of the whole society and not to it's detriment golden men: in his myth they rightfully govern the men of silver and bronze.
This is the myth of metals(415a ff.) the centrepiece of a second accusation that has dogged Plato through the centuries. Plato made clear that merit and not heredity defined the gold man and that gold could be found in all parts of society. Nonetheless, Plato has never escaped the charge that he imposes upon society an elitist and authoritarian rule. The charge is pressed even though in Book IV Plato makes justice in the individual the condition of justice in society.--Pg 16, Para 2 and 3, of Plato the Republic Introduction by Richard W. Sterling and William C. Scott.

Plato prove that justice does not depend upon a chance, convention or upon external force. It is the right condition of the human soul by the very nature of man when seen in the fullness of his environment. It is in this way that Plato condemned the position taken by Glaucon that justice is something which is external. According to Plato, it is internal as it resides in the human soul. "It is now regarded as an inward grace and its understanding is shown to involve a study of the inner man." It is, therefore, natural and no artificial. It is therefore, not born of fear of the weak but of the longing of the human soul to do a duty according to its nature.

Plato's Concept Of Justice: An Analysis Bold was added by me for emphasis.

There is something extremely important about this term that comes from understanding it at a soul level then to think its administering is implied as external and there after, settles all accounts from what was done by telling lies stealing etc. It is an account expressed by Cephalus, Polymarchus, Thrasymachus and Glaucon, while Plato is the understanding of justice to imply it as a "human virtue' that makes a person self-consistent and good."


If the heart was free from the impurities of sin, and therefore lighter than the feather, then the dead person could enter the eternal afterlife

Now these are ancient notions about justice. It is something much more, when you understand what happens inside. What happens when you review your position to ask whether or not the heart is indeed "lighter then the feather." In these situations that one may extend themself beyond the issues of science here, to include the extensions of what is happening out there in our economies and our social institutions. It is very important to understand what the feather represent in that culture(truth) that would depict the plate for consideration, in line with, the concepts of Plato and what I feel is relevant to who you are and what happens inside.

It is even more real to have experienced this weighting process in one 's life when you know that to defy the mass consideration and physics therein, that a mind might consider to be lighter then, indeed such a state may have found that gravity no longer exists to keep the body home on earth. That it can float. Alas though no repeatability will ever the measure of in your case, so I cannot say this is a method with which you will ever experience, and will have thought better to let it arrive at the illusions of, then to sanction the validity of what is being presented here.


You would have to know of colour of gravity has been built throughout this site to know, that colour of gravity is a "real measure of the internal nature of the human being" that extends beyond it's home.

Scotch tape is nothing new Arun, and neither is Kirlian photography? It is not this external measure as to what one should weigh, but of what is inside, that leads to such colours.

Thus it is with some knowledge that Plato's pyramid is more the understanding of an "internal structure" and it's ascent, placing a value to the ephemeral nature of colour in the mind's evolution, and it's final discourse thoughtfully constructed as to who you are.

William Thurston

Xianfeng David Gu and Shing-Tung Yau
To a topologist, a rabbit is the same as a sphere. Neither has a hole. Longitude and latitude lines on the rabbit allow mathematicians to map it onto different forms while preserving information.

William Thurston of Cornell, the author of a deeper conjecture that includes Poincaré’s and that is now apparently proved, said, “Math is really about the human mind, about how people can think effectively, and why curiosity is quite a good guide,” explaining that curiosity is tied in some way with intuition.

“You don’t see what you’re seeing until you see it,” Dr. Thurston said, “but when you do see it, it lets you see many other things.”

Elusive Proof, Elusive Prover: A New Mathematical Mystery

Some of us are of course interested in how we can assign the relevance to perceptions the deeper recognition of the processes of nature. How we get there and where we believe they come from. As a layman I am always interested in this process, and of course, life's mysteries can indeed be a motivating factor. Motivating my interest about the nature of things that go unanswered and how we get there.


William Paul Thurston

(born October 30, 1946) is an American mathematician. He is a pioneer in the field of low-dimensional topology. In 1982, he was awarded the Fields medal for the depth and originality of his contributions to mathematics. He is currently a professor of mathematics and computer science at Cornell University (since 2003).

There are reasons with which I present this biography, as I did in relation to Poincaré and Klein. The basis of the question remains a philosophical one for me that I question the basis of proof and intuition while considering the mathematics.

Mathematical Induction

Mathematical Induction at a given statement is true of all natural numbers. It is done by proving that the first statement in the infinite sequence of statements is true, and then proving that if any one statement in the infinite sequence of statements is true, then so is the next one.

The method can be extended to prove statements about more general well-founded structures, such as trees; this generalization, known as structural induction, is used in mathematical logic and computer science.

Mathematical induction should not be misconstrued as a form of inductive reasoning, which is considered non-rigorous in mathematics (see Problem of induction for more information). In fact, mathematical induction is a form of deductive reasoning and is fully rigorous.

Deductive reasoning

Deductive reasoning is reasoning which uses deductive arguments to move from given statements (premises), which are assumed to be true, to conclusions, which must be true if the premises are true.[1]

The classic example of deductive reasoning, given by Aristotle, is

* All men are mortal. (major premise)
* Socrates is a man. (minor premise)
* Socrates is mortal. (conclusion)

For a detailed treatment of deduction as it is understood in philosophy, see Logic. For a technical treatment of deduction as it is understood in mathematics, see mathematical logic.

Deductive reasoning is often contrasted with inductive reasoning, which reasons from a large number of particular examples to a general rule.

Alternative to deductive reasoning is inductive reasoning. The basic difference between the two can be summarized in the deductive dynamic of logically progressing from general evidence to a particular truth or conclusion; whereas with induction the logical dynamic is precisely the reverse. Inductive reasoning starts with a particular observation that is believed to be a demonstrative model for a truth or principle that is assumed to apply generally.

Deductive reasoning applies general principles to reach specific conclusions, whereas inductive reasoning examines specific information, perhaps many pieces of specific information, to impute a general principle. By thinking about phenomena such as how apples fall and how the planets move, Isaac Newton induced his theory of gravity. In the 19th century, Adams and LeVerrier applied Newton's theory (general principle) to deduce the existence, mass, position, and orbit of Neptune (specific conclusions) from perturbations in the observed orbit of Uranus (specific data).

Deduction and Induction

Our attempt to justify our beliefs logically by giving reasons results in the "regress of reasons." Since any reason can be further challenged, the regress of reasons threatens to be an infinite regress. However, since this is impossible, there must be reasons for which there do not need to be further reasons: reasons which do not need to be proven. By definition, these are "first principles." The "Problem of First Principles" arises when we ask Why such reasons would not need to be proven. Aristotle's answer was that first principles do not need to be proven because they are self-evident, i.e. they are known to be true simply by understanding them.

Back to the lumping in of theology alongside of Atlantis. Rebel dreams, it is hard to remove one's colour once they work from a certain premise. Atheistic, or not.

Seeking such clarity would be the attempt for me, with which to approach a point of limitation in our knowledge, as we may try to explain the process of the current state of the universe, and it's shape. Such warnings are indeed appropriate to me about what we are offering for views from a theoretical standpoint.

The basis presented here is from a layman standpoint while in context of Plato's work, brings some perspective to Raphael's painting, "The School of Athens." It is a central theme for me about what the basis of Inductive and deductive processes reveals about the "infinite regress of mathematics to the point of proof."

Such clarity seeking would in my mind contrast a theoretical technician with a philosopher who had such a background. Raises the philosophical question about where such information is derived from. If ,from a Platonic standpoint, then all knowledge already exists. We just have to become aware of this knowledge? How so?

Lawrence Crowell:

The ball on the Mexican hat peak will under the smallest perturbation or fluctuation begin to fall off the peak, roll into the trough and the universe tunnels out of the vacuum or nothing to become a “something.”

Whether I attach a indication of God to this knowledge does not in any way relegate the process to such a contention of theological significance. The question remains a inductive/deductive process?

I would think philosophers should weight in on the point of inductive/deductive processes as it relates to the search for new mathematics?

Allegory of the Cave

For me this was a difficult task with which to cypher the greater contextual meaning of where such mathematics arose from. That I should implore such methods would seem to be, to me, in standing with the problems and ultimates searches for meaning about our place in the universe. Whether I believe in the "God nature of that light" should hold no atheistic interpretation to my quest for the explanations about the talk on the origins of the universe.

See:

The Sound of Billiard Balls

Mathematical Structure of the Universe

TagCrowd

Just thought I'd try it.

article aspect become blog brain clock context death dialogos eide energy exist experience flow further future given gravity human idea information life links manifest mapping method mind moments moves nature past physics plato points post present pulse quantum realities reference relation scheme self socratic solidification space subjective think understanding world

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The Socratic method

Death of Socrates by Jacques Davidthis picture depicts the closing moments of the life of Socrates. Condemned to death or exile by the Athenian government for his teaching methods which aroused scepticism and impiety in his students, Socrates heroicly rejected exile and accepted death from hemlock.

Self portrait of Jacques-Louis David, 1794, Musée du Louvre

Here the philosopher continues to speak even while reaching for the cup, demonstrating his indifference to death and his unyielding commitment to his ideals. Most of his disciplines and slaves swirl around him in grief, betraying the weakness of emotionalism. His wife is seen only in the distance leaving the prison. Only Plato, at the foot of the bed and Crito grasping his master's leg, seem in control of themselves.

See:Jacques-Louis David: The Death of Socrates

It was important people understood that even though there is this Glaucon who offers himself as a brother to Plato, it is the very "innate structure within the self" that I point too, as we search and quest our way in the world. It is about Creativity. Opening the doors not only to what has always existed but also realizing that such a stance is the provision for which the lightcone points to the now.

So what is of value is that we understand the dialogue can produce autonomous students whose strength are the understandings given, from compiling all the resources, and thusly, find of value that one may of found the discussion moved further by one more step?

Socratic Method

Socratic Method (or Method of Elenchus or Socratic Debate) is a dialectic method of inquiry, largely applied to the examination of key moral concepts and first described by Plato in the Socratic Dialogues. For this, Socrates is customarily regarded as the father of Western ethics or moral philosophy.

It is a form of philosophical inquiry. It typically involves two speakers at any one time, with one leading the discussion and the other agreeing to certain assumptions put forward for his acceptance or rejection. The method is credited to Socrates, who began to engage in such discussions with his fellow Athenians after a visit to the Oracle of Delphi. The Oracle of Delphi confirmed Socrates to be the wisest man in Athens. Socrates interpreted this as a paradox, and began utilizing the Socratic method in order to get his conundrum answered. Diogenes Laertius, however, wrote that Protagoras invented the “Socratic” method.[1][2]

Thus, I present the obvious in what Lee Smolin is trying( a picture perhaps of him writing the "Rovelli name," as an observable) a place in time, as he has positioned himself amongst particular views. That within every lecture, a telltale sign, that is continuously refined and pushed further, through his articulations. The realities, as he has come to believe of them?

So from within this context, I am referred back to the nature of the article by Bee of, "Every Now and Then," and the value placed on the Now. I will be posting a new post in regard to "The Problem of Time in Quantum Cosmology," for further consideration and relevance as extolled by the Backreactions article.


At 11:07 AM, May 04, 2008, Blogger Plato said...

The Socratic method

Most Socratic inquiries consist of a series of elenchai and typically end in aporia.

Frede (1992) insists that step #4 above makes nonsense of the aporetic nature of the early dialogues. If any claim has shown to be true then it can not be the case that the interlocutors are in aporia, a state where they no longer know what to say about the subject under discussion.

Aporia

Aporia (Ancient Greek: ἀπορία: impasse; lack of resources; puzzlement; embarrassment ) denotes, in philosophy, a philosophical puzzle or state of puzzlement, and, in rhetoric, a rhetorically useful expression of doubt.

So moving forward here is the understanding that "Ingenuity can find it's opening by creating a configuration space" for the "sum over path" and "all probabilities," while holding, the idea that these would not evolve further in time? I mention the idea I had about the calorimeters and the views in relation to the configuration space earlier, and in this context I see what cannot evolve further other then to look at the relevance in regards to cosmology's look into what Glast measures are saying, at the time of it's expression.

These are still held in context of the universe, and is part of the evolution of this universe, whether one agrees with it or not. It is part of the resulting talk pointing out the evidence of "boltzman brains" materializing in that space.

Realities of the Suppression of Present Moments

I thought I would pull the two comments I made in Backreactions thread,"Every Now and Then" to maintain the consistency, and direction the post was going. One called the "Socratic method" will become the subject of a new post. The other is listed below, and reference slides picked out to support statements made in blog post entry as well link to Joe Kapusta quote used to support contention, of what "Boltzman brain" and "the singularity" have in common.



At 12:40 PM, May 04, 2008, Blogger Plato said...

Realities of the Suppression of Present Moments

Of course I just finishing from having taken a look.

I found a place that I could actually upload it, and store it for a moment like this, since you last mentioned it. Mentioned again, I thought it important that I follow through. Surprise, surprise.

Rovellism's almost sounds like rebellionism:)




See, even Lee has to create his mythical figures for consideration. Now, of course we now know what the motivations are for the" every now and then," (a Boltzman brain in a configuration space) we can all now think "retrospect" of the lecture?



A Desitter phase space and temperature, signifying some heat death in the conscious unfoldment?




The comparative relation one may see in the singularity is what reality is asking of you when Joe Kapusta points out, "the idea of alien communications" in relation to the QGP?

The right spin for a neutrino superfluidCompiled by Steve Reucroft and John Swain, Northeastern University.

Kapusta points out that the condensation temperature would be well below the cosmic background temperature, so it would be quite a feat to make this superfluid. However, Kapusta also notes that a sufficiently advanced civilization might use pulses of neutrino superfluid for long-distance communications.

What is this world coming too?:)

Does Consciousness have it's own "heat death?" We would comparatively like to think that when it's done it's done, then, what use to think all those other universes, while we contend with this one alone?

Glaucon

Glaucon (Greek: Γλαύκων) (born circa 445 BC) son of Ariston, was the philosopher Plato's older brother. He is primarily known as a major conversant with Socrates in the Republic (Plato), and the questioner during the Allegory of the Cave. He is also referenced briefly in the beginnings of the dialogues of Plato Parmenides (Plato) and the Symposium (Plato).

While I of course understood this conversation between Plato and Glaucon, there is a statement of reference that needs to be explained. So that it is not misunderstood that "the object" and "state of the one who questions and the one questioned," are shown to be like "God as the Geometer?" It is an "innate feature to the state of enquiry." That it follows alongside mapping, which advanced my own position of "methodology by intuition." An accumulated to a state called"Correlation of Cognition."

So by introducing "this brother"( a figure in mind to advance the developmental methodology,) to create this "state of being" within us, is much like an artistic endeavour of a plot, a writer, since one may not have had this conversation other then to move this story forward. How?:)

So I am glad there is a Glaucon who would move the conversation for advancement.

As Socratic method requires both a questioner and one questioned to move forward, Glaucon, who is the most honest about his ignorance amongst the friends, will help “build” the ideal philosophical city by engaging Socrates without fighting his ideas.

Self Evident

We hold (they say) these truths to be self-evident: That all men are created equal. In what are they created equal? Is it in size, understanding, figure, moral or civil accomplishments, or situation of life?Benjamin Franklin-The Gentleman's Magazine, vol. 46, pp. 403–404)

Our attempt to justify our beliefs logically by giving reasons results in the "regress of reasons." Since any reason can be further challenged, the regress of reasons threatens to be an infinite regress. However, since this is impossible, there must be reasons for which there do not need to be further reasons: reasons which do not need to be proven. By definition, these are "first principles." The "Problem of First Principles" arises when we ask Why such reasons would not need to be proven. Aristotle's answer was that first principles do not need to be proven because they are self-evident, i.e. they are known to be true simply by understanding them.

"Deduction" is an interesting thing left on it's own. While we think it only as one avenue to the methodology of approach, it is not without pointing out that the "inductive part" is part of this philosophical adventure too. That it should leave one to understand that the "infinite regression" leaves one on a precipice of change. That what is self evident, becomes the "new stepping stone for advancement."

A VIEW OF MATHEMATICS by Alain CONNES

Most mathematicians adopt a pragmatic attitude and see themselves as the explorers of this mathematical world" whose existence they don't have any wish to question, and whose structure they uncover by a mixture of intuition, not so foreign from poetical desire", and of a great deal of rationality requiring intense periods of concentration.

Each generation builds a mental picture" of their own understanding of this world and constructs more and more penetrating mental tools to explore previously hidden aspects of that reality.

.......and again.

Alain Connes

Where a dictionary proceeds in a circular manner, defining a word by reference to another, the basic concepts of mathematics are infinitely closer to an indecomposable element", a kind of elementary particle" of thought with a minimal amount of ambiguity in their definition.

The Soul=λόγος,θυμος,ἔρως

21 Grams

The title of the movie comes from the work of Dr. Duncan MacDougall, who in the early 1900s sought to measure the weight purportedly lost by a human body when the soul departed the body upon death. MacDougall weighed dying patients in an attempt to prove that the soul was material, tangible and thus measurable. These experiments are widely considered to have little, if any scientific merit, and MacDougall's results varied considerably from 21 grams, but for some people this figure has become synonymous with the measure of a soul's mass [1].

When garnered to thinking about the soul, it's value in weight, always seems to occupy my mind. Even though the topic has been deemed foolish, by historical debate. It is the cornerstone of my relating "emotive colourations" to a value of our mind, tied to the current state of being.

Hall of Ma'at

In art, the feather was shown in scenes of the Hall of Ma'at. This hall is where the deceased was judged for his worthiness to enter the afterlife. The seat of the deceased's soul, his heart, was weighed on a balance against the feather of Ma'at. If the heart was free from the impurities of sin, and therefore lighter than the feather, then the dead person could enter the eternal afterlife. Other gods in the judgement hall who were part of the tribunal overseeing the weighing of the heart were also pictured holding a feather.

See:Egyptian Myths

You had to know of course what this picture above means from my own soul interpretation to understand what this blog is about. While of course speaking to everything science is and does, it never did answer the deeper questions I had about the soul. You had to know that given the set of circumstances in my youth that such motivation can be like Einstein's own, that this degree and direction of life, can have it's motivational factor determined. See "Einstein's compass"


God's Equation, by Amir D. Aczel, Pg 14

From a early age, young Albert showed great interest in the world around him. When he was five years old, his father gave him a compass, and the child was enchanted by the device and intrigued by the fact the needle followed a invisible field to point always in the direction of the north pole.Reminicing in old age, Einstein mentioned this incident as one of the factors that perhaps motivated him years later to study the gravitational field.

So you see such factors in our youth can determine something about our future. Is this quest "motivational and soulful enough" for such time to be taken. Sought as the soul's quest in this lifetime?

The soul, according to many religious and philosophical traditions, is the self-aware essence unique to a particular living being. In these traditions the soul is thought to incorporate the inner essence of each living being, and to be the true basis for sapience, rather than the brain or any other material or natural part of the biological organism. Some religions and philosophies on the other hand believe in the soul having a material component, and some have even tried to establish the weight of the soul. Souls are usually considered to be immortal and to exist prior to incarnation.

The concept of the soul has strong links with notions of an afterlife, but opinions may vary wildly, even within a given religion, as to what may happen to the soul after the death of the body. It also shares as a PIE root of spirit.

Socrates and Plato

Plato, drawing on the words of his teacher Socrates, considered the soul as the essence of a person, being, that which decides how we behave. He considered this essence as an incorporeal, eternal occupant of our being. As bodies die the soul is continually reborn in subsequent bodies. The Platonic soul comprises three parts:

1. the logos (mind, nous, or reason)
2. the thymos (emotion, or spiritedness)
3. the eros (appetitive, or desire)

Each of these has a function in a balanced and peaceful soul.

The logos equates to the mind. It corresponds to the charioteer, directing the balanced horses of appetite and spirit. It allows for logic to prevail, and for the optimisation of balance.

The thymos comprises our emotional motive, that which drives us to acts of bravery and glory. If left unchecked, it leads to hubris -- the most fatal of all flaws in the Greek view.

The eros equates to the appetite that drives humankind to seek out its basic bodily needs. When the passion controls us, it drives us to hedonism in all forms. In the Ancient Greek view, this is the basal and most feral state.

So in a sense we have a historical construction of the valuation being, that while developed from a philosophical view, I had found some relation to the way I'd awaken, my own Mind map. So by developing this model I wanted to be reminded of the integration of what lies outside of us physically(what is this field of endeavour?)

Logos (Greek λόγος) is an important term in philosophy, analytical psychology, rhetoric and religion. It derives from the verb λέγω legō: to count, tell, say, or speak.[1] The primary meaning of logos is: something said; by implication a subject, topic of discourse or reasoning. Secondary meanings such as logic, reasoning, etc. derive from the fact that if one is capable of λέγειν (infinitive) i.e. speech, then intelligence and reason are assumed.

Thumos

(also commonly spelled "thymos") (Greek: θυμος) is an Ancient Greek word expressing the concept of spiritedness. The word indicates a physical association with breath or blood. The word is also used to express the human desire for recognition.

In Homer's works, thumos was used to denote emotions, desire, or an internal urge. Thumos was a permanent possession of living man, to which his thinking and feeling belonged. When a Homeric hero is under emotional stress he may externalize his thumos, conversing with it or scolding it.[1]

Plato's dialogue Phaedrus and longer work The Republic discuss thumos as one of the three constituent parts of the human psyche, along with logos and eros. In the Phaedrus, Plato depicts logos as a charioteer driving the two horses of eros and thumos (i.e. desire and will were to be guided by rationality). In the Republic's Book IV, the soul is divided into nous ("intellect"), thumos ("passion"), and epithumia ("appetite"). Thumos is the emotional element in virtue of which anger and fear are felt.[2]

Eros

(ἔρως érōs) is passionate love, with sensual desire and longing. The Modern Greek word "erotas" means "(romantic) love". The term erotic is derived from eros.

See: Thematic Resolutions

Inside Out

3.1 As Cytowic notes, Plato and Socrates viewed emotion and reason as in a kind of struggle, one in which it was vitally important for reason to win out. Aristotle took a more moderate view, that both emotion and reason are integral parts of a complex human soul--a theory proposed by Aristotle in explicit opposition to Platonism (De Anima 414a 19ff). Cytowic appears to endorse the Platonic line, with the notable difference that he would apparently rather have emotion win out.

I am trying to "create a image" that will use the one above. It is important that the select quoted comment below is understood. This can't be done without some reference.

So while the exercise may be going on "inside" things are happening on the outside. Scientists have never been completely honest with themselves, while some may concern themselves with whose name said what?

I use Plato as a namesake obviously, because of what I saw of some of our influential minds speaking, all the while making inferences to Plato. When ever you read something that resonates with you, it is of value because it correlates to something that you already know. This is what I tried to get across in the previous post, about what is "self evident." Little do some people recognize that while I may have inferred the point of some philosophical foundations, it is not without recognizing that the "qualitative phrases" have to be reduced as well to a logic. To reason.

How do you do that? Well I'll tell you what I found and then you can think whether I understood reason in it's proper format. Whether I understood the "shadows of Plato" to mean something other then what could have been interpreted as being wrong. What is that analogy of the Cave really mean?

Our attempt to justify our beliefs logically by giving reasons results in the "regress of reasons." Since any reason can be further challenged, the regress of reasons threatens to be an infinite regress. However, since this is impossible, there must be reasons for which there do not need to be further reasons: reasons which do not need to be proven. By definition, these are "first principles." The "Problem of First Principles" arises when we ask Why such reasons would not need to be proven. Aristotle's answer was that first principles do not need to be proven because they are self-evident, i.e. they are known to be true simply by understanding them.

Yes I did not enter the halls of higher learning in the traditional ways. You can converse for many years, does not mean you become devoid of the lessons that spoken amongst the commentors. How is it you can think that while listening to scientists you cannot uncover the the processes they use? If I had given thirty years to study, what exactly had I studied? I am a doctor of nothing.:)

This is a torus (like a doughnut) on which several circles are located. Unlike on a Euclidean plane, on this surface it is impossible to determine which circle is inside of which, since if you go from the black circle to the blue, to the red, and to the grey, you can continuously come back to the initial black, and likewise if you go from the black to the grey, to the red, and to the blue, you can also come back to the black.

My quote at Backreaction on this and that, reveals not only part of the understanding gained through this "infinite regress," but also the understanding we have with the world around us. Some would be better served to see the image of the Klein bottle, but I wanted to show what is going on in a "abstract way" to what is happening inside of us, and at the same time, what is happening outside.



I had used the brain and head as a place of our conscious awareness within context of our environment, our bodies. The topological explanations of the numbers above, and used them in the next paragraph. There will be confusion with the colour lines, please disregard that.

While I talked of the emotive and mental realities. I included the spiritual development in the end. The way this interaction takes place, is sometimes just as the mental function(yellow). Other times, it is the emotive realization of the experience. It is coloured by our emotion(red).

While we interact with our environment, there is this turning inside out, continuously. Sometimes we may say that "1" is the emotive realization, while the number 2 is seen as a mental extension of the situation. While the areas overlap each other, an outward progression may mean that the spiritual progress is numbered 4, while the interaction of the emotive, mental and spiritual progression may be number 3. Ultimately the spiritual progression is 4 (Violet). All these colours can mix and are significant in themself. They reveal something about our very constitution.

While some may wonder how could any conceptualization ever integrate the "Synesthesia views" of the world when it sees itself presented with such a comparison? The journey of course leads to the "Colour of Gravity." Discard your body, and one will wonder about the "clear light." What it means, in the "perceptive state of existence." If one is prepared, then one shall not have "to much time on their hands" getting lost in the fog.

Plato and Aristotle, Up and Down by Kelley L. Ross, Ph.D.

Rafael has Plato pointing up and Aristotle gesturing down to indicate the difference in their metaphysics. For Plato, true existence is in the World of Forms, in relation to which this world (of Becoming) is a kind of shadow or image of the higher reality. Aristotle, on the other hand, regards individual objects in this world as "primary substance" and dismisses Plato's Forms -- except for God as a pure actuality, without matter.

However, when it comes to ethics and politics, the gestures should be reversed. Plato, like Socrates, believed that to do the good without error, one must know what the good is. Thus, we get the dramatic moment in the Republic where Plato says that philosophers, who have escaped from the Cave and come to understand the higher reality, must be forced to return to this world and rule, so that their wisdom can benefit the state. Aristotle, on the other hand, says that the "good" is simply the goal of various particular activities, without one meaning in Plato's sense. The particular activities of most human affairs involve phronésis, "practical wisdom." This is not sophía, true wisdom, for Aristotle, which involves the theoretical knowledge of the highest things, i.e. the gods, the heavens, and God.

Thus, for philosophy, Aristotle should point up and would represent a contemplative attitude that was certainly more congenial to religious practices in the Middle Ages. By the same token, Aristotle's contribution to what we now think of as science was hampered by his lack of interest in mathematics. 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.

Therefore, caution is in order when comparing the meaning of the metaphysics of Plato and Aristotle with its significance for their attitudes towards ethics, politics, and science. Indeed, if the opposite of wisdom is, not ignorance, but folly, then Socrates and Plato certainly started off with the better insight.

It is good that you go to the top of the page of the linked quotes of Kelley L. Ross. You must know that I developed this site without really understanding the extent Mr. Ross had taken this issue. There is much that is familiar, and with him, an opposing view too.

See:

Induction and Deduction
Intuitively Balanced: Induction and Deduction