Comments on: Not THAT again http://jueseph.com/2007/01/not-that-again/ home Fri, 04 May 2012 06:09:28 +0000 hourly 1 http://wordpress.org/?v=3.3.2 By: Coconuts http://jueseph.com/2007/01/not-that-again/comment-page-1/#comment-18 Coconuts Thu, 01 Feb 2007 03:38:43 +0000 http://sh133.surpasshosting.com/~jueseph/blog/?p=43#comment-18 Yeah, and that's what did in reductionistic science! Apparently the 20th century was all about shattering massive intellectual projects: Heisenburg, Gödel, Derrida, errrrr...anyone else? Yeah, and that’s what did in reductionistic science! Apparently the 20th century was all about shattering massive intellectual projects: Heisenburg, Gödel, Derrida, errrrr…anyone else?

]]> By: More ramblings « Mumble Mumble… http://jueseph.com/2007/01/not-that-again/comment-page-1/#comment-19 More ramblings « Mumble Mumble… Thu, 01 Feb 2007 03:18:52 +0000 http://sh133.surpasshosting.com/~jueseph/blog/?p=43#comment-19 [...] 31Jan07 Jue’s got a neat post today about an experience in a bio lecture that got him thinking about emergence again, and what he [...] [...] 31Jan07 Jue’s got a neat post today about an experience in a bio lecture that got him thinking about emergence again, and what he [...]

]]> By: Wang http://jueseph.com/2007/01/not-that-again/comment-page-1/#comment-21 Wang Thu, 01 Feb 2007 03:14:13 +0000 http://sh133.surpasshosting.com/~jueseph/blog/?p=43#comment-21 Okay, I think I get it a little more now...I was trying to say "We can IN PRINCIPLE derive macroscopic behavior from molecular/atomistic understanding, BUT we can't know enough about molecular/atomistic properties." As Heisenberg (or Sir Mix-a-lot) might tell us, that is one huge "BUT," in fact so big that it renders the "IN PRINCIPLE" more or less meaningless. It doesn't matter that the derivation can hold, since you can't satisfy the assumptions you need. Okay, I think I get it a little more now…I was trying to say “We can IN PRINCIPLE derive macroscopic behavior from molecular/atomistic understanding, BUT we can’t know enough about molecular/atomistic properties.” As Heisenberg (or Sir Mix-a-lot) might tell us, that is one huge “BUT,” in fact so big that it renders the “IN PRINCIPLE” more or less meaningless. It doesn’t matter that the derivation can hold, since you can’t satisfy the assumptions you need.

]]> By: Coconuts http://jueseph.com/2007/01/not-that-again/comment-page-1/#comment-20 Coconuts Thu, 01 Feb 2007 03:00:40 +0000 http://sh133.surpasshosting.com/~jueseph/blog/?p=43#comment-20 hmm, that's long, I think I'll post it on mine, too... oh, and good luck with classes, we start tomorrow! hmm, that’s long, I think I’ll post it on mine, too…

oh, and good luck with classes, we start tomorrow!

]]> By: Coconuts http://jueseph.com/2007/01/not-that-again/comment-page-1/#comment-22 Coconuts Thu, 01 Feb 2007 02:59:55 +0000 http://sh133.surpasshosting.com/~jueseph/blog/?p=43#comment-22 Okay, lemme at it. First of all, the relationship between amount of information know about a system and how predictable it is has been studied pretty well in mathematics, under the guise of entropy. I've only looked at it in discrete (dynamical) systems, and not in continuous (differentiable) ones, but at least in dynamical systems there's an interesting relationship between the entropy of a transformation (i.e. rule describing how the system changes over time) and other important properties (like, does it "mix" the space up? is it "fundamental," that is, ergodic?) It turns out that the interesting ones, ones with ergodicity/mixing, all have positive entropy, which means that, as we extend our knowledge of the past further and further, the amount of new information about the present continues to grow at a positive rate that does not approach zero (I can send you the paper I wrote on this for my final last semester if you'd like). What this means, though, is that for all but the silliest, simplest processes, to predict the future with any real accuracy we'd need knowledge of the infinite past of the system, which essentially translates into perfect knowledge of the present state of the system and the rules governing its change over time. This is where the reductionistic program breaks down, because at the lowest levels (which you will ultimately have to go to, if you're a <i>serious</i> reductionist) knowledge is governed by the Heisenberg uncertainty principle, which basically says we can't have perfect knowledge of the position and momentum of a particle at the same time. So there's always a little bit of uncertainty in the state of the system, and that means that any predictions we make at the reductionistic level are basically moot, because of the positive entropy of, well, everything...is that thermodynamics? I don't know... Anyway, I don't know how this relates to the whole issue of the small reductionistic step that you're talking about here, although I do think that it shows that the general principle of reductionism is deeply flawed. I also think that the whole question of why, at higher levels of conceptual organization, systems suddenly become well-behaved, and that sensitive dependence on initial conditions can be sort of stepped around if we only look at the right, sufficiently abstract set of "initial conditions." Okay, lemme at it. First of all, the relationship between amount of information know about a system and how predictable it is has been studied pretty well in mathematics, under the guise of entropy. I’ve only looked at it in discrete (dynamical) systems, and not in continuous (differentiable) ones, but at least in dynamical systems there’s an interesting relationship between the entropy of a transformation (i.e. rule describing how the system changes over time) and other important properties (like, does it “mix” the space up? is it “fundamental,” that is, ergodic?) It turns out that the interesting ones, ones with ergodicity/mixing, all have positive entropy, which means that, as we extend our knowledge of the past further and further, the amount of new information about the present continues to grow at a positive rate that does not approach zero (I can send you the paper I wrote on this for my final last semester if you’d like).

What this means, though, is that for all but the silliest, simplest processes, to predict the future with any real accuracy we’d need knowledge of the infinite past of the system, which essentially translates into perfect knowledge of the present state of the system and the rules governing its change over time. This is where the reductionistic program breaks down, because at the lowest levels (which you will ultimately have to go to, if you’re a serious reductionist) knowledge is governed by the Heisenberg uncertainty principle, which basically says we can’t have perfect knowledge of the position and momentum of a particle at the same time.

So there’s always a little bit of uncertainty in the state of the system, and that means that any predictions we make at the reductionistic level are basically moot, because of the positive entropy of, well, everything…is that thermodynamics? I don’t know…

Anyway, I don’t know how this relates to the whole issue of the small reductionistic step that you’re talking about here, although I do think that it shows that the general principle of reductionism is deeply flawed. I also think that the whole question of why, at higher levels of conceptual organization, systems suddenly become well-behaved, and that sensitive dependence on initial conditions can be sort of stepped around if we only look at the right, sufficiently abstract set of “initial conditions.”

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