freecounterpoint: You schmucks know this?

Friday, November 21, 2008

You schmucks know this?

How do you think it relates to Arnol'd's silliness you posted a while back, AI?

22 comments:

Arelcao Akleos said...: Well, I've read it before. It's the sort of claim that tends to make a bigger splash with philosophers or historians of science than with most practicing scientists. After all, many practicing scientists tend to say "Whaddya gabbing about, Schmuck [as JJ would put it]? Of course it's reasonable, that's why it's so goddamned effective".
The tussle is not new, either. Plato and Aristotle seemed to have been readier to strangle each other over this issue than any other. Plato emphasizing mathematics' effectiveness, and trying to make it essential--never mind reasonable-- that it be so. Aristotle having grave doubts as to how widely effective it is, never mind reasonable, and trying to develop alternative foundations for effective enquiry into nature.
Mathematics approximating mathematics? You betcha.; 11/20/2008 4:56 PM
Mr roT said...: References, please. (I guess you're talking about Plato saying the Universe was a giant triangle--what a Greek schmuck); 11/20/2008 8:24 PM
Arelcao Akleos said...: Wigner knew more, having through his "genius" calculated his birth a couple of millenium later. But his was the brain of a gerbil compared to a Plato or Aristotle, or an Archimedes, Apollonius, Hipparchus, or Ptolemy
If he didn't amount to a hill of beans, we could throw him in with Pythagoras.; 11/20/2008 8:31 PM
Arelcao Akleos said...: JJ, you asking for references other than Plato or Aristotle on Plato or Aristotle? References from Plato and Aristotle on Planto or Aristotle? References from Philosophers or Historians of Science on Wigner's "The Unreasonable Effectiveness of Mathematics"? References on Schmucks by Schmucks or Non-Schmucks? References on Practicing Scientists Who Use The Word Schmuck But Do Not Think the Effectiveness of Mathematics is Unreasonable, or Do Think the Reasonable Mathematics is Ineffective, or Do Think the Effective Mathematics is Reasonably Unreasonable, or Don't Think They Give a Texas Desert Rat's Behind About Mathematics Because They Have Chinese Slaves To Do Their Grunt Lab Work, or...
C'mon guy, take time out from determining the pinkness of Plato's Triangle to ascertain what these references are to refer to. Capisce, Siracusan?; 11/20/2008 8:39 PM
Mr roT said...: Wigner the gerbil? Read his paper on the reps of the Poincaré group in the Annals. More meat in it than any of those sodomite agoraphiliacs.

Refs online if you can find them.; 11/20/2008 10:14 PM
Arelcao Akleos said...: Then simplicity itself, JJ. To read Plato, read Plato. To read Aristotle, read Aristotle. Geez, dude, Tejas got you to far away from your Timeo?; 11/20/2008 10:42 PM
Mr roT said...: I ain't gonna read all that gay stuff. Which parts?; 11/20/2008 10:50 PM
Arelcao Akleos said...: OK, enough facetiousness. For works on Plato in relation to mathematics, try these as a start. [From the Dialogues, besides the Timaeus, the Laws, the Republic, Gorgias, Parmenides, Theatetus, for instance, have long passages on mathematics and its role in Plato's conception of his theory of forms. The first book below has great references]

[1] The Mathematics of Plato's Academy: A New Reconstruction by David H. Fowler

[2] Plato's Philosophy of Mathematics. by Anders Wedberg

[3]Plato's philosophy of mathematics (International Plato studies) by Paul Pritchard

[4]Philosophy and Mathematics from Plato to the Present by Robert J. Baum

[5]Plato's Universe by Gregory Vlastos and Luc Brisson

[6]The birth of mathematics in the age of Plato by Francois Lasserre

[7] Translation of Arthur Ahlvers Zahl Und Klang Bei Platon/Number and Sound in Plato (Studies in the History of Philosophy, 67) by Arthur Ahlvers

[8] Theon of Smyrna: Mathematics Useful for Understanding Plato Or, Pythagorean Arithmatic, Music, Astronomy, Spiritual Disciplines (Secret doctrine reference series)

[9] Plato's Parmenides (The Joan Palevsky Imprint in Classical Literature) by Samuel Scolnicov

[10]Platonism and Anti-Platonism in Mathematics by Mark Balaguer

[11] History of Greek Mathematics: Volumes 1& 2. by Thomas Little Heath [Particularly Vol.1, "From Thales to Euclid"]

[12]Plato's Forms: Varieties of Interpretation by William A.Welton

[13]Euclid's Phanomena: A Translation and Study of a Hellenistic Treatise in Spherical Astronomy (History of Mathematics)

[14] The significance of the mathematical element in the philosophy of Plato by Irving Elgar Miller

[15]Science and Mathematics in Ancient Greek Culture by Lewis Wolpert, C. J. Tuplin, and T. E. Rihll

[16]Mathematics and the Divine: A Historical Study by Teun Koetsier and Luc Bergmans

[17] Plato's Cosmology: The Timaeus of Plato Translated with a Running Commentary by Francis MacDonald Cornford; 11/20/2008 11:12 PM
Arelcao Akleos said...: For Aristotle, and his views on mathematics [which contrast strongly with the mainstream view of Plato's Academy] his/his school's comments on it are mostly to be found in his physics, meterologia, de anima, the mechanical problems, and in a less direct way in his metaphysics and logic. The collected works would have all these. The first two references below are very very useful.

[1] Mathematics in Aristotle. by Thomas Heath

[2] Aristotle's Physics: A Guided Study (Masterworks of Discovery) by Joe Sachs and Aristotle

[3] Mechanics from Aristotle to Einstein by Michael J. Crowe

[4] Aristotle and Mathematics: Aporetic Method in Cosmology and Metaphysics (Philosophia Antiqua) by John J. Cleary

[5] Aristotle's Philosophy of Mathematics. by Hippocrates George Apostle

[6] Semio Physics: A Sketch by Rene Thom

[7] Essays on Plato and Aristotle by J. L. Ackrill

[8]John Philoponus Criticism of Aristotle's Theory of Aether (Peripatoi) by Christian Wildberg

[9] Ancient Mathematics (Sciences of Antiquity) by Serafina Cuomo

[10]The treatises of Aristotle on the parts and progressive motion of animals, the problems, and his treatise on divisible lines by Aristotle and Thomas Taylor

[11]Science and Religion, 400 B.C. to A.D. 1550: From Aristotle to Copernicus by Edward Grant

[12]One and Many in Aristotle's Metaphysics: The Central Books by Edward C. Halper

[13] Mathematics As a Science of Quantities by Hippocrates G. Apostle, Arnold M. Adelberg, and Elizabeth A. Dobbs

[14]Universal Mathematics in Aristotelian-Thomistic Philosophy: The Hermeneutics of Aristotelian Texts Relative to Universal Mathematics. by Charles Bonaventure Crowley

[15]Aristotle's "De Anima": A Critical Commentary by Ronald Polansky

[16]The Application of Mathematics to the Sciences of Nature by Claudio Pellegrini

[17 ]Form, Matter, and Mixture in Aristotle by Frank A. Lewis and Robert Bolton

[18 ]History of Free Fall: Aristotle to Galileo With an Epilogue on Pie in the Sky by Stillman Drake

[19]The Treatises of Aristotle, on the Heavens, on Generation and Corruption, and on Meteors: Translated from the Greek; 11/20/2008 11:38 PM
Mr roT said...: Oh, really Timeo? I thought you were joking. But where's the fight between Plato and Aristotle about the unreasonable effectiveness?; 11/21/2008 12:55 AM
Mr roT said...: Wow. What a list. OK, will look into this.; 11/21/2008 12:56 AM
Arelcao Akleos said...: The fight was not about "unreasonable" effectiveness, the fight was if it was reasonable to claim that mathematics was essentially effective [Pythagoras, Plato in his later years] or it was not reasonable [The Sophists, Aristotle]. Since mathematics and the "Natural Philosophy" of the ancient world were so bound together, and consciously so [with the Greeks, at least] through the concepts of Logos or of Rationality, that it would have been highly unlikely for someone-say, Archimedes or Heron, to have said: "hey, this geometry stuff is mighty useful. Yet for the life of me I'm flummoxed as to why".
.; 11/21/2008 9:55 PM
Mr roT said...: So they didn't see any difference between what was going on in their heads and what was going on in the world?
Seems silly. They didn't think physics was a model somehow (though their math was probably too primitive to model anything anyway).; 11/21/2008 10:19 PM
Arelcao Akleos said...: Uh, the idea of "model" certainly existed among the Greeks. The very concept of "Saving the Phenomena" allowed for the notion of alternative mathematical schemes to explain the same problem. Compare Hipparchus' earth-centered "World System" [later to be adumbrated and fleshed out by Ptolemy] with Aristarchus' sun-centered alternative. Both were trying to propose a scheme which "best fit" the evidence, and to all accounts did so with full awareness that this mathematical scheme could be one of "useful convention" [as opposed to what may in truth be the case]. The Church called upon this history in its attempt to convince Galileo to label the Copernican scheme as "probable hypothesis" as opposed to speaking as if it was a confirmed truth. Galileo's "Book of Nature is written in Mathematics" riff came across [accurately, I think] as emphasizing Truth rather than "Saving of the Phenomena". And this was a radical break with the ancients.
Of course, as has been already mentioned, there were also Greeks who held to a fixed unity between mathematics and the Universe. Besides the usual suspects, Pythagoras and the elder Plato, it's pretty striking to me how Euclid, for example, in his Optics [if he really was the author] writes as if certain of his theorems on "optical rays" are describing actual and previously unknown properties of nature [and not simply being fitted to be consistent with known observations]. And I wish to hell Archimedes had written a little more on this, or if he did that it had survived. Because his mathematical "natural philosophy" shines through and through with confidence he is discovering true things about the Universe when he proves his theorems on areas/volumes, or the stability of ships, just as much as he is confident in his "mechanical method" that he is being led to mathematical truths through examination of what is possible in nature.
The height of ancient mathematics was roughly on par with that of the height of Europe at the end of the 16th century [there is very little in Kepler which is not there with Archimedes or Ptolemy. The one exception being his late use of logarithms, then just recently discovered by Napier]. And every perspective on the relation between mathematics and nature that we can see in, say, Galileo or Descartes or Newton, is immediately there with the run from Pythagoras to,say, Pappus.......; 11/21/2008 10:59 PM
Mr roT said...: The last statement is false. Galileo first pushed the idea of natural (mathematically formulated) law and he also had a pretty good vague idea what an ODE was. None of the Greeks had either.

They were doing geometry, not physics.; 11/21/2008 11:19 PM
Arelcao Akleos said...: Hmmmm... This is not so. Remember that the sentence refers to "perspective on the relation between mathematics and nature", JJ, and not about mathematical technique to make use of in investigating nature. After all, as far as mathematical technique goes, it is the period of roughly 1590 to 1620 which sees the movement from "roughly on par" with the ancients to "this is something really new, and going further, boys". Soon enough, by the time Galileo is finished scribbling his two great books, young Fermat, Descartes, Hudde, and so on, have pinned down various alternative notions of the derivative and have gone far into developing the "Analytic Art".
But if you read Galileo, Descartes, Fermat etc... there is no broad perspective on the relationship between mathematical truth and natural truths which cannot be found with the ancients. Except for the "revealed religion" aspect, the debate between "Nature is Mathematical. Mathematics hits the Truth" and "Nature only appears Mathematical because men agree to measure it that way to save the phenomena" and "Nature only appears to be mathematical in a very limited way. Mathematical misses the essential" that plays back and forth through the period of Cusa to Newton [to pick convenient endpoints] is a stunning renaissance of a debate that ran from Pythagoras to, at the very least, the Library at Alexandria to the coming of the Romans.

As for "law", for Galileo, I take it you mean a mathematical relation which offers a proportion between two physical magnitudes which can vary [say, as with Galileo, time and distance]. It is a huge debate among historians of ancient science whether or not folks like Archimedes and Euclid and Ptolemy etc... had ever attained this notion. The debate centers on the very particular point of the notion of "varying" magnitude. Certainly the few ancient thinkers who worked succesfully on mathematizing astronomy, map-making ["geography"], engineering/strength of materials, and optics did know full well they were using mathematics to study nature-- not just doing mathematics per se. [hence the whole distinction between "saving the phenomena" vs natural truth vs the truths of mathematics]. They set out physical magnitudes, made assumptions/hypotheses as to the nature of light, states of matter, etc... as related to the problems they investigated, and they set out principles relating these physical magnitudes in proportions which allowed them to solve in a geometric language what, by 1638, can now be done by analytic geometry and the various proposed ways of handling "rates of change". But, the claim is, instead of using language of "variation of magnitudes" they used language of "general position". Which, the claim continues, separates the notion of "law" as Galileo had it from what came in the 16th century, never mind antiquity. The contrarians ask, basically, "why is the language of Galileo taken to define what is meant by "law'?" They argue that if you knowingly seek out physical magnitudes, and bind them in mathematial relationships, and seek to deduce the consequences and predictions of those relationships, then you have "law". And the question of a "dynamic' mathematical perspective vs a "static" mathematical perspective is simply a different issue....

Your last sentence gets to the nub of the issue. I take it your claiming either: [a] that they had no sense of the separation between doing mathematics and investigating Nature, and confused doing math with doing "physics", or [b] they did recognize the separation, and just limited themselves to doing mathematics and ignored any attempt at understanding the Universe through it.
Well, to those who upheld the unity of mathematics and the Universe, that would be [a]. Although they weren't confused, given their assumption they were clear on the concept. Setting aside the issue of whether their assumption was right or wrong, certainly you'd admit there are physicists/mathematicians today who hold to that credo, and act accordingly. It is not a question of ancient vs modern, it is a question of contending lines of thought, which originated in the ancient world, weaving through to our modern world. These lines have developed great sophistication and fundamental depth as the modern world has shot far past what antiquity had been able to reach.... but the basic problem "Is the Universe fundamentally mathematical or not? " stubbornly persists [just for the record, had I been around in the days of the Library of Alexandria, my money would have been on the "non". Today my [oh so little] money is on the "is". I'm a shameless creature of the Day that way]
As for [b], although some individuals certainly may have thought that way [Apollonius?], many clearly did not. Read Archimedes or Heron or Hipparchus or Aristarchus etc.. and then tell me they were not trying to understand the Universe through mathematics. Even Aristotle, who sought to establish his Logic and Metaphysics as the firmer and higher ground for understanding the Universe, saw a (limited) role for using mathematics to understand Natural phenomena....

Hey, JJ, I have to take an MTEL exam tomorrow. Need sleep. Later!.....
Damn, wish you were up here and could hash this out over good beer as opposed to this dry electronic bar of ours.; 11/22/2008 12:26 AM
Mr roT said...: Yes, beer.

First couple ideas struck. Yeah, I mean the Greeks didn't have any dynamics, as far as I know. Maybe you can't have any without the derivative to really make good sense of dynamics. As far as I am concerned, you really aren't talking about physics until you have rates of quantities (maybe need even that the qties have different units) being related.

$F=ma$ is physics. $C=2\pi r$ is not.

I read somewhere that I can't find ever that Galileo, trying to figure out the velocity-dependence of air resistance on a cannonball did remarkable thing. He understood enough about the derivative and differential equations (fucking $F=ma$!) to throw out candidate theories because of the qualitative behaviors of solutions the corresponding odes had!

That is fucking badass. No one did that before him and without it, you're jerking off, not doing physics.

The reason I am sensitive to this is partly personal. I am sick about not doing physics anymore and doing this immensely difficult perhaps beautiful shit I do. I want somehow to think of it as physics but it is not. It is geometry in spates. It is analysis, yes. Group representation theory, certainly. PDE, functional analysis, yes, yes. But it is junk at the end of the day. There's no $\partial/\partial t$.

Everyone, Omnes! agrees?

OK, not really related, but wanted the Latin pun.; 11/22/2008 1:33 AM
Pepe le Pew said...: Be careful you two: you almost sound educated.; 11/22/2008 4:06 AM
Pepe le Pew said...: sorry, I meant i meant ejookated.; 11/22/2008 10:59 AM
Mr roT said...: Go Sarah 2012!; 11/22/2008 11:31 AM
Pepe le Pew said...: You are hopeless.; 11/22/2008 1:45 PM
Mr roT said...: rah rah rah; 11/22/2008 4:14 PM