{"id":446,"date":"2007-06-20T14:45:13","date_gmt":"2007-06-20T14:45:13","guid":{"rendered":"http:\/\/scientopia.org\/blogs\/goodmath\/2007\/06\/20\/dembskis-buddy-part-2-murphys-law-and-poincare-recurrence\/"},"modified":"2007-06-20T14:45:13","modified_gmt":"2007-06-20T14:45:13","slug":"dembskis-buddy-part-2-murphys-law-and-poincare-recurrence","status":"publish","type":"post","link":"http:\/\/www.goodmath.org\/blog\/2007\/06\/20\/dembskis-buddy-part-2-murphys-law-and-poincare-recurrence\/","title":{"rendered":"Dembski's Buddy (part 2): Murphy's Law and Poincare Recurrence"},"content":{"rendered":"

Part two of our crackpot’s babblings are actually more interesting in their way, because they touch on a fascinating mathematical issue, which, unfortunately, Mr. Brookfield is compeletely unable to understand: the Poincare recurrence theorem. <\/p>\n

Brookfield argues that the second law of thermodynamics in not<\/em> really a law, since it’s statistical, and that there must therefore be some real<\/em> law underlying the statistical behavior normally explained by the second law. Here’s his version – be prepared to giggle:<\/p>\n

\n

“The second law of thermodynamics has a rather different status than that of other laws
\nof science, such as Newton’s law of gravity, for example, because it does not hold
\nalways<\/b>, just in the vast majority of cases.”\n<\/p><\/blockquote>\n

Well, if it is a “law” then it must hold always by definition<\/b>. If it “does not hold always”
\nthen it is not<\/b> a law, period. If it is a “pseudo law” then that is fine for pseudo science, but
\nI am not interested in doing pseudo science. Hawking says that the thermodynamic arrow
\nis reversible because.. <\/p>\n

\n“…The probability of all the gas molecules in a box being found in one half of the box at
\na later time is many millions of millions to one, but it can happen.”\n<\/p><\/blockquote>\n

The type of event that Hawking is referring to here is known as “Poincare\u0301 Recurrence”–
\nnamed after the French mathematician Henri Poincare\u0301. The result of any such occurrence
\nwill indeed reverse the thermal characteristics of the box contents, violating the internal
\nthermodynamic arrow. This internal reversal however will not (in my opinion) reverse
\nthe real arrow — the unrelenting order to disorder movement of the total physical system.\n<\/p>\n<\/blockquote>\n

Yes, folks – Brookfield is a real scientist<\/em>, doing real science<\/em>; Steven Hawkings and his ilk are all just pseudo-scientists studying psuedo-laws; real<\/em> scientists like Brookfield throw out hopeless pseudo-laws like the second law of thermodynamics in favor of Murphy’s law. And yes, that<\/em> Murphy’s law. Brookfield really tries to argue for the use of Murphy’s law as a better statement of the principle of the second law. But we’ll get to that later.<\/p>\n

<\/p>\n

Poincare’s recurrence<\/a> is a real thing, and it is a real problem. There are some attempts to explain it, but it’s still somewhat of an open issue. Here’s the short
\nversion:<\/p>\n

Take a fixed set of particles with a fixed amount of energy in a fixed amount of
\nfinite space. With no external influence, given a sufficiently long period of time, those particles will return to a state arbitrarily similar to the initial state.<\/p>\n

The proper statement of it is somewhat more complicated than that: it talks in terms of the phase space of the system, and behavior of the system in terms of its dynamics in the phase space. In a dynamic finite system, the phase volume is fixed; and the phase trajectories within that space don’t intersect. So if you think about the system over time, it’s sweeping out paths through its phase space, and since paths can’t intersect, the volume is constantly being decreased. Eventually, it’s going to run out of places to go – except for returning to its starting point, and creating a loop.<\/p>\n

Yet another statement of this is based on topology: take a topological space, (T,τ), which is second-countable (that is, the base of the space is a countable set) and Hausdorff<\/a> (a space where you can separate things in terms of neighborhood inclusion). If there is a Borel algebra on (T,τ) (that is, an algebra operating on subsets of T which is closed under complementation and countable unions). If f : T→T is a function representing measure-preserving state transitions, then f has full measure<\/em>, which means that all points are recurrent: f will trace loops through (T,τ).<\/p>\n

So why is this a problem? Suppose that you take a finite space – a box, filled with a collection of gas particles. And you start with it in a very low<\/em> entropy state – like a state where all of the gas particles are in one corner of the box. Then the process of interactions in the box should result in an increase in entropy as the particles disperse. But the recurrence means that there’s a path where the entropy must decrease<\/em>, to return back to that initial state. (Note: this paragraph originally contained an incredibly stupid error: I wrote high entropy where I should have written low.)<\/em><\/p>\n

There are a couple of suggestions for why this isn’t a problem. The least hand-wavy explanation that I’ve is that you can’t isolate a subspace from its environment – so environment noise breaks things so that paths through the phase space do<\/em> intersect, which violates one of the premises of the proof of the theorem. So by this argument, finite sub-<\/em>spaces of the universe aren’t subject to it; they’re perturbed by the environment. And the entire space of the universe – even if it’s fixed, it’s expanding<\/em> – so it’s not a constant volume, and so it isn’t subject to recurrence. If the universe were finite and not expanding, or expanding with a maximum limit, then the universe as a whole could be cyclic.<\/p>\n

That explanation might be satisfactory; I don’t find that explanation to be entirely convincing given my level of knowledge, but since I have pretty much no expertise in dynamical systems, I really don’t know enough to judge it. We’re talking about some very difficult advanced math here: to really criticize it, you need to fully understand the proof – which would in the best possible case, take me at least<\/em> several weeks to months of studying dynamical systems to be able to really understand. (And I stress the “at least” above. I don’t know enough to know how much I don’t know about this, so that “weeks to months” is a lower bound.) What is clear is that it’s not<\/em> clear how Poincare recurrence applies to the physical world. We don’t have complete phase-space models of real (not completely isolated) systems that are precise enough to let us figure out exactly whether or not Poincare recurrence applies, or what the timescale of the recurrence is.<\/p>\n

Anyway – now you know a bit of what the Poincare recurrence is, and why it’s a problem. In fact, you know more about it that Brookfield. But that’s OK, because he’s not really interested in understanding it. He thinks he already knows everything he needs to – not a diffeq in sight, but he’s come to his conclusions that the Poincare recurrence theorem is completely incompatible with the second law of thermodynamics, and that this means that 2LOT is wrong<\/em>.<\/p>\n

\n

\tSuch obvious inconsistency causes me to believe that Hawking’s Second “Law” of
\nThermodynamics, with its statistical formulation, is not a real law but merely a good
\napproximation to a genuinely real 100% valid physical law. <\/p>\n

\tWhen ID theorists speak of the Second Law of Thermodynamics my feeling is that they
\nare almost always referring to its design (order) implications — the real arrow and not its
\nisolated thermal implications. Thus, we really need a name for this new, profound and all
\npowerful cosmic law, lurking just behind the Second “Law” of Thermodynamics. <\/p>\n

\tI had originally been afraid to bring this “new law” idea forward due to the likelihood of
\nits name turning out to be “Brookfield’s First Law of Irreversible Cosmic Catastrophe”
\nor equivalent. I then realized, however, to my enormous relief that we already have a
\npossible second name “Murphy’s Law.” <\/p>\n<\/blockquote>\n

Brookfield gets one<\/em> thing right: when IDists talk about 2LOT, they’re always talking about its implications in terms of order and chaos, not its actual thermodynamic meaning. The problem is, Brookfield thinks that they’re right<\/em> to do that. But
\nthermodynamics doesn’t<\/em> talk about order and chaos: it talks about entropy<\/em>. Entropy can sometimes<\/em> be informally described as chaos, but that’s just a metaphor. The 2LOT is about thermodynamic behavior and a specific measure
\nof a key thermodynamic property called entropy – it’s not about order versus chaos, or design versus randomness.<\/p>\n

But the second part of that is where it becomes truly laughable. Yes, the infamous Murphy’s law – “If anything can possibly go wrong, it will” is Brookfield’s model for a “correct” replacement for what he calls the second pseudo-law.<\/p>\n

\n

Luckily we now have Murphy’s law that states “if something can go wrong, it will.” Or
\nmore scientifically “If left to its own devices, the universe is doomed!” <\/p>\n

Other Murphylian statements might include; <\/p>\n

“The physical universe is on a collision course with itself!” <\/p>\n

“The universe’s matter is just mindlessly crashing around inside its space!” <\/p>\n

Let us now re-examine Hawking’s box in the light of our new “Murphylian” knowledge.
\nNow what could possibly go wrong? Well, for starters, during “Poincare\u0301 recurrence”
\nthere exists an absolute pressure differential between the part of the box that contains no
\nparticles (zero pressure) and the part of the box that contains all of the particles (all
\navailable pressure concentrated). If this pressure difference (or movement) either
\ndamages or destroys the box then this is certainly in keeping with Murphy’s Law. <\/p>\n<\/blockquote>\n

His argument against the Poincare recurrence is: “Yeah, well, if it happened, it would break things”, and since breaking things is in keeping with Murphy’s law, then he concludes that a Poincare recurrence doesn’t break his new and improved second law.<\/p>\n

\n

During “recurrence,” the physical box is put in the most uncomfortable situation of being
\ntwo sizes at once. If the structural damage incurred by this anti-thermal spike is sufficient
\nto keep “Murphy’s Arrow” on the “straight and narrow,” then Murphy’s Law is the more
\nscientific (realistic) of the two. Also, if the physical system in question (the box, the
\ntypewriter, the monkey, etc.) has sustained any damage between recurrences then these
\nlocal “recurrences” are illusory in terms of the system as a whole. Remember the inner
\nwalls of the box are constantly being hit by flying particles. During Hawking’s (particular
\ntype of recurrence) one side of the box is spared, but the other side is hit with double the
\nintensity. <\/p>\n

The Poincare\u0301 “recurrence” example is not telling us that physical systems can be ordered
\n— by accident — by chance — by randomness (the opposite of order). It is telling us
\ninstead that any such internal statistical analyses are incomplete and that such narrow
\nassumptions can only lead us to illogical “order by randomness” “light by darkness” type
\nconclusions. <\/p>\n

The orderly box is being constantly assaulted from inside by energized particles at all
\nlevels from microscopic to macroscopic. Given enough time, its destruction is inevitable.
\nAs long as every configuration state, including Poincare\u0301 “recurrence,” is doing its equal
\npart to bring about the eventual destruction of the box, then Murphy’s Arrow is perfectly
\nstraight. <\/p>\n

So while the internal system’s state during recurrence is indeed a violation of
\n“Maxwellian Distribution” (in which all particles “should” be spread evenly over the
\ninternal system space) it is completely consistent with *Murphylian Distribution (in
\nwhich the system’s self-destructive potential (stress) is spread evenly over all of the
\nsystem’s available configuration states). <\/p>\n<\/blockquote>\n

And there, folks, is the crowning glory of his work. To refute a beautiful mathematical
\nproof of an amazing and profound theorem with unknown implications on the real world, all it takes is an argument that “the box would break”, combined with the knowledge that order never emerges from randomness. Not a diffeq for miles to be scene – not an equation of any time, not a bit of mathematical analysis, not a refutation of any part of the proof of the theorem. All that stuff is unnecessary in the light of the brilliance of a mind like
\nBrookfield! Pinheads like Hawking might need that math stuff – but Brookfield can
\ndisprove it with a wave of the hands, and a snap of the fingers: “Poincare recurrence of a collection of gas molecules in a box would make the box break”, and poof! no more problem.<\/p>\n

Brookfield of course then needs to explain to us why none of those bozo scientists were able to see something as glaringly obvious as his argument:<\/p>\n

\n

So Steven Hawking (and apparently the entire scientific community) have missed out on
\ndiscovering “Devolution” by mistakenly assuming the following; <\/p>\n

#1. An orderly finite box (the universe is not a box{it is an infinite non-recurring
\nsystem}) <\/p>\n

#2. A perfectly strong box (no box is perfectly strong). <\/p>\n

#3. A perfect “bounce” (no bounce is a perfect bounce). <\/p>\n

In the real world, boxes are not perfectly strong, nor perfectly elastic and the physical
\nuniverse was never a box in the first place. <\/p>\n

So, if ones “order to disorder” model of the universe, is that of an order-adulterated gas
\ninside box, <\/p>\n

…but the real universe is not a box and its contents are subsequently not thus constrained, <\/p>\n

…then such a model cannot accurately represent the universe, nor properly display a
\ncosmic law of order and disorder — of constraint and absence of constraint. <\/p>\n<\/blockquote>\n

Now… Read that, and compare it to an explanation of Poincare’s recurrence and the
\nexplanations of why we don’t know how\/if it applies to the real universe. Brookfield has
\nre-invented a shabby non-mathematical version of one<\/em> of the possible explanations
\nwhy Poincares recurrence theorem doesn’t really work in the real world. One of the
\nextremely<\/em> well-known explanations. An explanation which no one who studies
\nthermodynamics could possibly have missed. But he thinks that the entire scientific
\ncommunity has missed this obvious<\/em> fact – and he thinks that his “collapsing box”
\nexplanation takes care of the problem in terms of his “new” law.<\/p>\n

And that’s the final piece of patheticness here. The second law of thermodynamics
\ndoes not<\/em> say “Disorder always increases.” It does not<\/em> not say
\n“The entropy of an isolated system not in equilibrium will tend to increase over time, approaching a maximum value at equilibrium.”. What it really says is: ∫(∂:Q\/T)&geq;0, where Q and T are well-defined terms about heat energy and time; and that Q is defined for the macro-state of a system in terms of a combination of the microstates of the components of that system. (That second part is what Brookfield objects to: the use of the statistical combination of microstates to explain the thermodynamic behavior of macrostates.) The fact that it’s really a precisely defined mathematical equation is important: it’s what makes it useful<\/em>, and what makes it a law<\/em>. It means that it’s a precise statement, with measurable implications, and which can be used to make precise predictions. Brookfield’s “replacement” for the supposedly flawed second law is not<\/em> a physical law; it’s not a scientific statement of any kind. It’s a mishmash built on undefined terms that produces the result that he wants, while not being able to actually precisely predict or describe anything<\/em>.<\/p>\n","protected":false},"excerpt":{"rendered":"

Part two of our crackpot’s babblings are actually more interesting in their way, because they touch on a fascinating mathematical issue, which, unfortunately, Mr. Brookfield is compeletely unable to understand: the Poincare recurrence theorem. Brookfield argues that the second law of thermodynamics in not really a law, since it’s statistical, and that there must therefore […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"jetpack_post_was_ever_published":false,"_jetpack_newsletter_access":"","_jetpack_dont_email_post_to_subs":false,"_jetpack_newsletter_tier_id":0,"_jetpack_memberships_contains_paywalled_content":false,"_jetpack_memberships_contains_paid_content":false,"footnotes":"","jetpack_publicize_message":"","jetpack_publicize_feature_enabled":true,"jetpack_social_post_already_shared":false,"jetpack_social_options":{"image_generator_settings":{"template":"highway","default_image_id":0,"font":"","enabled":false},"version":2}},"categories":[31],"tags":[],"class_list":["post-446","post","type-post","status-publish","format-standard","hentry","category-intelligent-design"],"jetpack_publicize_connections":[],"jetpack_featured_media_url":"","jetpack_shortlink":"https:\/\/wp.me\/p4lzZS-7c","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"http:\/\/www.goodmath.org\/blog\/wp-json\/wp\/v2\/posts\/446","targetHints":{"allow":["GET"]}}],"collection":[{"href":"http:\/\/www.goodmath.org\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"http:\/\/www.goodmath.org\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"http:\/\/www.goodmath.org\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"http:\/\/www.goodmath.org\/blog\/wp-json\/wp\/v2\/comments?post=446"}],"version-history":[{"count":0,"href":"http:\/\/www.goodmath.org\/blog\/wp-json\/wp\/v2\/posts\/446\/revisions"}],"wp:attachment":[{"href":"http:\/\/www.goodmath.org\/blog\/wp-json\/wp\/v2\/media?parent=446"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/www.goodmath.org\/blog\/wp-json\/wp\/v2\/categories?post=446"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/www.goodmath.org\/blog\/wp-json\/wp\/v2\/tags?post=446"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}