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Author Topic:   Is mathematics a science?
Chiroptera
Inactive Member


Message 31 of 48 (239918)
09-02-2005 11:11 AM
Reply to: Message 25 by cavediver
09-02-2005 7:11 AM


quote:
Ph.D. was related to fixed point properies on topological groups.
Cool! My life seemed to revolve around topological groups for several years (though usually Lie groups in my case).
My graduate studies was done at an institution that was predominantly algebraists, with a small geometry/toplogy contingent. Yet, somehow, I managed to leave without learning any more algebra than was necessary to pass the qualifying exams. Weird place.

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 Message 25 by cavediver, posted 09-02-2005 7:11 AM cavediver has replied

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 Message 32 by cavediver, posted 09-02-2005 11:32 AM Chiroptera has replied

  
cavediver
Member (Idle past 3644 days)
Posts: 4129
From: UK
Joined: 06-16-2005


Message 32 of 48 (239923)
09-02-2005 11:32 AM
Reply to: Message 31 by Chiroptera
09-02-2005 11:11 AM


I could never understand the algebraic topologists who had no need to draw pictures. How they could calculate smash products without at least a sketch? I guess that I could never quite beat the physicist out of me
The only way that I could convince myself that we weren't all deranged in applied maths and theo physics was to walk next door into pure maths and math' statistics It almost made me feel normal. Then again, if you want REALLY weird, you want to try Oxford and Penrose's crowd. Off the planet!

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cavediver
Member (Idle past 3644 days)
Posts: 4129
From: UK
Joined: 06-16-2005


Message 33 of 48 (239925)
09-02-2005 11:38 AM
Reply to: Message 29 by crashfrog
09-02-2005 10:14 AM


That the axiomatic conditions that mathematical reasoning depends on are ultimately arbitrary?
Of course, and the Platonic Realm holds all of them
their position seems to be based more on a need for their work not to simply be logic puzzles and symbol games rather than an actual "math" that exists somewhere in the universe.
Odd comment. It's those of us in theo physics that tend to get converted to at very least a weak Platonism because we keep finding all of the maths supposedly reserved for "logic puzzles and symbol games" firmly embedded in the universe.
The 1st Law of String Theory: no area of mathematics is sacred

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 Message 35 by Chiroptera, posted 09-02-2005 11:43 AM cavediver has replied

  
Chiroptera
Inactive Member


Message 34 of 48 (239928)
09-02-2005 11:39 AM
Reply to: Message 32 by cavediver
09-02-2005 11:32 AM


What I meant by "weird" was the way people didn't seem very interested in discussing their research -- which is why I, not being an algebraist, could avoid learning any algebra. It seems very different than when I was studying physics -- where everyone was always talking about their research -- but maybe this is more typical of departments of mathematics.

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 Message 43 by Brad McFall, posted 09-03-2005 8:26 AM Chiroptera has replied

  
Chiroptera
Inactive Member


Message 35 of 48 (239931)
09-02-2005 11:43 AM
Reply to: Message 33 by cavediver
09-02-2005 11:38 AM


Hee hee hee -- I couldn't resist!
quote:
It's those of us in theo physics that tend to get converted to at very least a weak Platonism because we keep finding all of the maths supposedly reserved for "logic puzzles and symbol games" firmly embedded in the universe.
Yeah, I can see how the illusion that your work has something profound to say about reality is even stronger for the theoretical physicists.

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 Message 36 by cavediver, posted 09-02-2005 12:23 PM Chiroptera has replied

  
cavediver
Member (Idle past 3644 days)
Posts: 4129
From: UK
Joined: 06-16-2005


Message 36 of 48 (239945)
09-02-2005 12:23 PM
Reply to: Message 35 by Chiroptera
09-02-2005 11:43 AM


Re: Hee hee hee -- I couldn't resist!
Oh yeah? Well, what about all the stuff you wouldn't have without us theo physicists? Wormholes? Warp drive? Teleport? Holodeck?
Hmmm... that's Star Trek isn't it? It's so hard drawing a distinction sometimes

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Chiroptera
Inactive Member


Message 37 of 48 (239963)
09-02-2005 1:17 PM
Reply to: Message 36 by cavediver
09-02-2005 12:23 PM


I know the feeling.
quote:
Hmmm... that's Star Trek isn't it? It's so hard drawing a distinction sometimes
I understand. Everytime I read the news, I feel like I'm in a film noir.

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nwr
Member
Posts: 6408
From: Geneva, Illinois
Joined: 08-08-2005
Member Rating: 5.1


Message 38 of 48 (239965)
09-02-2005 1:22 PM
Reply to: Message 28 by Chiroptera
09-02-2005 9:13 AM


Re: wrong question for this board!
Chiroptera writes:
Are you saying that microevolution cannot lead to macroevolution given enough time? Yow!
That's a strange way of putting it.
No, I'm not saying that. But I am saying that microevolution cannot lead to macroevolution unless there is selection.

This message is a reply to:
 Message 28 by Chiroptera, posted 09-02-2005 9:13 AM Chiroptera has replied

Replies to this message:
 Message 39 by Chiroptera, posted 09-02-2005 1:38 PM nwr has replied
 Message 40 by PurpleYouko, posted 09-02-2005 1:53 PM nwr has replied

  
Chiroptera
Inactive Member


Message 39 of 48 (239968)
09-02-2005 1:38 PM
Reply to: Message 38 by nwr
09-02-2005 1:22 PM


Re: wrong question for this board!
I would think that the selection process would be the person writing the proof.
Not being a Platonist, I would say that theorems don't prove themselves.

This message is a reply to:
 Message 38 by nwr, posted 09-02-2005 1:22 PM nwr has replied

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PurpleYouko
Member
Posts: 714
From: Columbia Missouri
Joined: 11-11-2004


Message 40 of 48 (239971)
09-02-2005 1:53 PM
Reply to: Message 38 by nwr
09-02-2005 1:22 PM


Re: wrong question for this board!
Isn't selection already a part of the definition of all evolution?

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 Message 38 by nwr, posted 09-02-2005 1:22 PM nwr has replied

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nwr
Member
Posts: 6408
From: Geneva, Illinois
Joined: 08-08-2005
Member Rating: 5.1


Message 41 of 48 (240027)
09-02-2005 3:31 PM
Reply to: Message 40 by PurpleYouko
09-02-2005 1:53 PM


Re: wrong question for this board!
Isn't selection already a part of the definition of all evolution?
Selection is part of the mechanism, not part of the definition.
Presumably one could have micro-evolution as a result of neutral drift (as in the neutral theory).

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nwr
Member
Posts: 6408
From: Geneva, Illinois
Joined: 08-08-2005
Member Rating: 5.1


Message 42 of 48 (240032)
09-02-2005 4:10 PM
Reply to: Message 39 by Chiroptera
09-02-2005 1:38 PM


Re: wrong question for this board!
Chiroptera writes:
I would think that the selection process would be the person writing the proof.
Sure. It's artificial selection.
Not being a Platonist, I would say that theorems don't prove themselves.
Not being a platonist, I would agree.
I suspect platonists would also agree. I guess they might say that the proof exists in some platonist sense, but needs to be discovered.

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Brad McFall
Member (Idle past 5033 days)
Posts: 3428
From: Ithaca,NY, USA
Joined: 12-20-2001


Message 43 of 48 (240221)
09-03-2005 8:26 AM
Reply to: Message 34 by Chiroptera
09-02-2005 11:39 AM


"/&/ "as genes? math or biology? normal rxns??
Some day I expect the shapes of the symbols in rings will affect biological signing but still it is the multiple "///" tones that matter in e/c. I really dont know that this must be not math. It seems like math when a notion of theoretical biology is sustained. I dont think that that the "////" can be blinking lights as Stu Kaufmann was motivated to think (that he could not "do" Kant etc).
Now that I know yous gls are really good math people I might try to figure out how the 70s' advances in group theory might be science via math in biogeography. Later.
Weyl wrote
quote:
Another point of debate is the question whether the numbers are independent objects or whether arithmetic is concerned merely with the concrete numerical symbols, "whose shape is recognizable by us with certainty independently of place and time, of the particular conditions of their manufacture, and of trifling differences in their execution" (Hilbert). Thus e.g. Helmholtz(Zahlen und Messen, loc. cit., p 359):"I consider arithmetic, or the theory of pure numbers, as a method built upon purely psychological facts, by which the consistent application of a system of symbols of unlimited extent and unlimited possibility of refinement is taught. In particular, arithmetic investigates what different modes of combination of these symbols (numerical operations) lead to the same result." Only recently Hilbert carried this point of view consistently into effect (compare Section 10), in a manner unassailable even by the crticism directed against it by Frege (Grundgesetze der Arithmetik, 1893). A succession of strokes ('ones') offers itself as a suitable symbol. If I hear a sequence of tones, I put down a stroke upon hearing each one, placing one stroke after another: ////. A second time I proceed similarly, again obtaining a symbol consisting of a succession of strokes. If I were immediately able to judge the equality or disparity of the 'shape' of the two symbols, a numerical comparison would be accomplished. Here the representation of data by strokes has the function of putting the data into a 'normal' form of such a kind that a difference in shape at once indicates a difference in number.
I always considered Mandelbrot's discussion of the word "fractal" to point to this problem of what FORM other than 'normal' such sounds heard in science might be maths for.
quote:
(For a directly given whole, number is meant to describe a relation between the whole and parts of it as are considered as units...)
both quotes of Weyl, page 35 in PHILOSOPHY OF MATHEMATICS AND NATURAL SCIENCE
I am torn between determining transfinte e-numbers or reflecting on groups further for the permutable subtraction I think evolution remands biologically from n! no matter the divisions. I really do think that whatever that "math" is it is pure in itself no matter how it sorts difference of natural and artifical selection in the statistical normal distribution approximation.

This message is a reply to:
 Message 34 by Chiroptera, posted 09-02-2005 11:39 AM Chiroptera has replied

Replies to this message:
 Message 46 by Chiroptera, posted 09-05-2005 6:41 PM Brad McFall has replied

  
crashfrog
Member (Idle past 1467 days)
Posts: 19762
From: Silver Spring, MD
Joined: 03-20-2003


Message 44 of 48 (240307)
09-03-2005 7:46 PM
Reply to: Message 37 by Chiroptera
09-02-2005 1:17 PM


Everytime I read the news, I feel like I'm in a film noir.
Well, maybe your problem is the way you read the news by having someone toss spinning newspapers right at your face:

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Replies to this message:
 Message 45 by Brad McFall, posted 09-05-2005 8:23 AM crashfrog has replied

  
Brad McFall
Member (Idle past 5033 days)
Posts: 3428
From: Ithaca,NY, USA
Joined: 12-20-2001


Message 45 of 48 (240521)
09-05-2005 8:23 AM
Reply to: Message 44 by crashfrog
09-03-2005 7:46 PM


to speak a langugage or not, is that a question?
Hey froggy,
I am not tempted to think of it "a priori" as a language or lingo.
What would happen if some one other than me (rhetorically speaking (I am not spitting venom here) figured out what Brown's letters "S" and "T" mean in terms of my annotation on his questioning? The three strokes I attached in my side comments WOULD NOT BE LEIXICALLY a language or even a part of it but only a pure mathematical thought that would have implementations differently than is currently being taught in biology because of evolutioanry influence I contenD. I met and spoke with Brown on a few occassions and even talked with him about set theory once. Compared with other mathematicians at Cornell (some coming from Harvard etc except one who left for Berkely) he is really an OK kind of guy.
The back cover of the book
contains my notes on how to relate group operations to biology but this is done in terms of human teleology. Weyl clearly indicated(I speaking for the entire book PHILOSOPHY OF MATHEMATICS AND NATURAL SCIENCE, not a part or trap of it inversly) that teleology could connect into math DIFFERENTLY than evolution by force as it was DISCUSSED in the late 40s. I suppose I will only lurch you if I show how the "business cycle" of teaching evolution is only the alternative "phase" of matter that Wright explicitly did not include & show that macroevolution is not within a collective aggregate of that supply. Oh, well......I suppose I will have to do that by enlaring this "thumbnail" above but that is not math as science but science as itself. If Theus ever decides to respond I'll pick that up with 'him'.
The "apriority" of which you write seems to me, if I understand you well enough, to be the result of probabalisms (no matter how reflected on) not any DETERMINATION made from a prior mathmatical mind whether only revealing a statstical regularity or regularity as law etc (in nature by nuture etc etc). So,,, I have to disagree with you and agree with some others in this thread.

This message is a reply to:
 Message 44 by crashfrog, posted 09-03-2005 7:46 PM crashfrog has replied

Replies to this message:
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