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Topic: why do you like math?
Replies: 38   Last Post: Apr 25, 2006 2:00 AM

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Nico Benschop

Posts: 1,708
Registered: 12/6/04
Re: why do you like math?
Posted: Sep 10, 2001 5:34 AM
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Neo 1061 wrote:
>
> On Wed, 05 Sep 2001 10:59:59 +0200, Nico Benschop
> <n.benschop@chello.nl> sat on a tribble, which squeaked:


What is a 'tribble', and if it squeakes, what does that mean..?

> >[*]: Who does'nt hate the increase of Entropy ?
> > (there is no lossless process in Nature, except light-propagation;-)
> > http://home.iae.nl/users/benschop/ether.htm

>
> Here's something interesting. I came up with what seems to be a proof
> that if the universe is deterministic and its evolution computable,
> then entropy is constant.



'Proof' is based on transitive closure, hence your result is
self- fulfilling (resulting from axioms & method):
[..old stuff, fairly irrelevant, based on a non-realistic model..;-]
[ Entropy (chaos) increases generally: my foot.
[ So what are YOU doing here?-) Certainly a local aberration...]
[ Structure increases globally, seems to be more realistic, but HOW? ]
>
[ The more interesting stuff comes next, allowing the thought of
[ the future to have influence on the present: "anti-causal"...:-]
[ This very old Greek(?) idea does have value. Essential question:
[ _Where_ do your idea's come from ? -- especially the creative ones.]
[ BTW: what the hell are you doing in sci.math, with this open mind
[ attitude? You'll be dismissed as a crank in no time: Good for you! ]
>
> Of course our everyday observation is increasing entropy.
> This is unlikely to be a curious local phenomenon,
> so the universe's forward evolution is probably not computable.


Probably? Certainly!
How about computing you and me, starting with a hot gas cloud...

Creative structure building is as natural a process as gravity, I bet.
At the Univ. Twente (NL) some people developed an anti-entopy model,
based on non-elastic (lossy) collisions between particles:
Just by shaking (not stirring;-) a mass of bicycle bullets
(fiets kogeltjes) that are initially equally distributed over bins,
a final state arises with all kogeltjes in just ONE bin ! Funny,
the Maxwell demon DOES exist, and its name is (creative) FRICTION...

> That is intriguing because it
> allows things in the universe to do what Turing machines cannot, and
> many annoying limitations (halting problem, Godel incompleteness)
> are perhaps escapable as a result. (Godel incompleteness applies
> to deductive reasoning, noted for its being mechanizable, and thus
> relates in some deep way to computability.)


At a philisofical & common-sense level, Godel's result came surpisingly
late, just saying that every theory (as transitive closure of a finite
set of axioms, using logic/causality as generating principle) has its
context. Viz: TRUTH is relative to your assumptions (axioms), and math
in particular does not yield anything really NEW beyond their transitive
closure.

> If it is, then it's
> probably gotta be infinite, and the second law doesn't matter. The
> universe has infinitely far to fall before heat death. Otherwise, it
> isn't deterministic. Free will *drool*. If it's nondeterministic it
> might fail to be stochastically modelable. So much for the second law
> then, since it is a probabilistic statement with such a hidden
> assumption.


Vive les hidden assumptions!
Example: the ONLY perpetuum mobile in Nature is light-propagation
(viz: lossless; equivalent to another hidden assumption: interstellar
space is PURE VACUUM, not depriving fotons travelling for billions of
lightyears of ANY energy at all... hence the Doppler expansion to
explain the Redshift, and by time reversal: the Big Bang (=Christian
biblical model: Begin --> End;-)
Notice that magic (& unreal) LOSSLESS axiom, counter even to any
SCIENTIFIC attitude, closing your eyes to what you don't like,
so it does not exist. Each Natural process DOES loose eventually its
inital purpose/impetus: I bet the lifetime of an electron, proton,
foton is finite: death by friction. But:
they again arise, come to life, by a process with enough chaos that
exceeds a certain TRHESHOLD : non-linear creative process, like the
lossy collisons between bicyle 'fiets kogeltjes' (ball-baring balls?-)

Good old Fred Hoyle will have a longer life than expected, once the
creative anti-entopy process of structure building frictive collision
process is better understood. How about the Cosmic Background Noise:
the light traveling in (great) circles in the Universe, creating plenty
new electrons (= closed foton, with double-twisted donut structure *)
to replace those that died of old age
(*): J.Williamson, M. van der Mark:
"Is the electron a photon with toroidal topology?"
in: Annales de Fondation L.de Broglie, V22, N2 (1997) p133-160.

> The universe could also be acausal. (It probably is, in fact.)
> There goes the second law again -- an acausal but
> self-consistent universe can be forced by boundary conditions to
> contain surprising events (highly improbable seeming a priori, but
> caused by a future cause) -- read Robert Forward's Timemaster if you
> don't believe me. (Sorry, no evil Amazon URLs, but your local library
> is likely to have it -- mine does.) Otherwise, entropy is constant,
> and no futile heat death. (That doesn't matter much if there's a big
> crunch of course. And this finite deterministic computable universe
> will just mechanically enter a loop and start repeating configurations.
> Maybe heat death is better than that species of Hell.
> But I don't believe it for a second -- consciousness looks
> suspiciously non-computable thus far, and causality is suspect.)


Right on! http://www.iae.nl/users/benschop/math-use.htm
(on the self-fulfilling view of how efficient a causal
and predictable & mathematical model is)

[Now comes the interesting part;-]
>
> OK, anyone wondering why I consider causality suspect? Firstly, it's
> up there with gravitation and such in the list of laws of nature, but
> the justifications for it tend to be philosophical. Also, it's widely
> disbelieved, unlike, say, gravitation. Most mythologies and belief
> systems in the world have a healthy dose of the teleological.
> Teleology is shunned by scientists because it's a problem for being
> able to make repeatable experiments and the like, of course. As a
> result, causality seems to be justified mainly because it's tidy. It's
> also clearly approximately true: the events of our everyday lives are
> generally patterned into cause followed by effect. It lets us make
> useful predictions. Yet physics at its most fundamental consists
> mainly of time-symmetric processes. The one process that isn't
> time-symmetric is the mysterious collapse of the quantum wavefunction,
> and that seems to occur without a preceding cause.


Or any lossy process: entropy / chaos increasing: the arrow of time...
So if you don't like that (loss) then ignore it, hence the still
extremely popular group theory (=invertable processes: conservation
of rank, vs. rank-decreasing algebra in general: semigroups --
http://arXiv.org/abs/math.GM/0103112 )

> Particles decay spontaneously,

... and I bet: even electrons & protons have a finite lifetime.

> and the Big Bang has no preceding cause because there
> was no "preceding" at all! If one accepts that some events lack a
> cause, causality is called into question. If one demands that every
> event has a cause, at least one (the Big Bang) must have its cause lie
> in its own future and the illusion of causality is shattered. Why then
> do our everyday lives suggest causality? Some causal patterns exist --
> past causes and future consequences. These are those observations.
> Those consequences that preceded their cause are dismissed as
> "spontaneous" and modeled as environmental noise. Unfortunately,
> modeling them as noise doesn't explain them away and perhaps is a
> crutch that holds progress back.


" Real is: what you have to deal with,
what won't go away just because it does'nt fit your prejudices".
(in: Sources of the Self, by Charles Taylor, McGill-U, 1989, pg. 59)
http://home.iae.nl/users/benschop/simple.htm

On the fundamental principle of Threshold:
"Everything is so clear & logical" (after Analog-->Digital conversion;-)
The logic of the courtroom: answer with yes or no, please (and forget
about the environmental conditions: 'Law' as a binary A/D coverter)

> Any "noise" should have a hidden variable explanation.
> The uncertainties in the weather forecast are because of the butterfly
> effect acting on the smaller uncertainties in our observations.


But notice in all those satellite pictures: the recurring 'galactic'
spiral structures (around a depression, in NL always coming via UK;-(
Could an electron be a spiralling ether-whirl? (*)

> The positions and momenta and other info on tons of
> atoms and molecules are the hidden variables behind the weather
> forecast noise. But what of the quantum noise? Spontaneous decays,
> Heisenberg uncertainty and its consequences? Heisenberg uncertainty
> was shown early on to be fundamental, not a failure of resolving power
> of instrumentation. Now we know that none of the quantum fuzziness can
> be explained by hidden variables, even fundamentally unmeasurable
> ones, because of the Bell's Inequality results. Not causally, that is.
> Causality is assumed in the argument against hidden variables. Maybe
> the fuzziness can be explained in terms of a future state that is
> unknown, and a feedback loop in time, though. Consider this. In an
> EPR experiment, measuring a particle spin collapses the wavefunction
> nonlocally. In some sense, it fixes that spin through history, as well
> as that of the other entangled particle. It's like something reached
> back and "filled in the blanks" to make the book of the universe a
> self-consistent story, starting with the particles' entanglement and
> ending with the measurements made on them. Sure, EPR phenomena seem
> unusable to macroscopically violate causality, but then again, isn't
> that just semantic quibbling? It sure seems to have been violated
> microscopically, whether it has been macroscopically or not!
> -- Neo 1061


Keep speculating, something may blossom out of it, after all.
It's not the answers that count, but the questions...
Answers condense into Form, Questions explore beyond (present) form.

-- NB -- http://www.iae.nl/users/benschop






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