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Posted on 02/19/2002 2:59:38 PM PST by Cameron
The irony here is that Prigogine showed mathematically how complex systems could self-organize out of diffuse chaotic environments. You apparently never even read the abstracts of his papers or at the very least didn't have a clue as to what they actually said.
You are very confused. You are mixing and matching mathematics and engineering concepts willy nilly in ways that are never proscribed. For example, in algorithm complexity (what we are talking about, whether you knew it or not), there is no concept of "energy". None at all. It isn't a mathematical concept. Energy does apply to the computing hardware (which is used to feed the entropy pump), but that is utterly irrelevant to what you posited. The computing hardware doesn't change its energy characteristics whether you are pumping random bits or a Fourier transform through it. Bits are bits.
Clearly there is a point at which a system must have more energy removed, than would be required to comprise a certain high level of order, rendering that chaotic system wholly incapable of creating said level of order naturally.
This is a variant of the very tired (and fundamentally ignorant) argument trying to mix axioms of information theory and thermodynamics. First, nothing in information theory requires energy to generate order or the lack thereof. A word processing program 100kBytes in length require the exact same amount of energy to create as a stream of random noise of the same size. Period. As I noted above, information theory does not create any physical laws with respect to energy. Thermodynamics does have a number of rules regarding entropy (Note: "order" is a meaningless term; there is either more or less entropy in a system). As has been mentioned many, many times: local reductions in entropy are permissible in thermodynamics in the presence of an enthalpy gradient. This is absolutely true of every biological system we have evidence of. In fact, the definition of life in most biology texts alludes to this (all living things have a metabolism).
As I have stated in previous posts, don't address heavyweight mathematical topics with pedestrian definitions of the relevant terms. You are not understanding the mathematics at all and are engaged in a very common misapplication of these concepts. Worse, you whip out sources like Prigogine which actually refute your position. Fortunately, this discussion touches on an area of mathematics that just happens to be my field of expertise so I am pretty damn confident about the basic and elementary definitions that I am using. It would be easier to have a useful discussion if we weren't arguing ancient mathematical definitions that can be looked up in any decent and relevant mathematics text.
First of all, your voicing magic perspectives about what I do or do not hypothesize smacks of "muddying the water".
Now...
I am not quite sure why you are failing to comprehend the difference between a "demonstration" and an "example" but please...
An example will suffice.
You keep repeating the same thing, but you aren't saying anything. Let me phrase the exact same mathematical problem a different way, with a real live "example" included.
Last week a woman picked a sequence of Lotto numbers in the state lottery. The random ball drawing machine (which is required to be mathematically random) pulled the exact same sequence of numbers that the woman had selected out of the entire combinatorial space. Furthermore, the random ball drawing machine is capable of pulling all possible combinations of numbers that anyone could possibly choose. And if you played the same numbers over and over again, eventually the random ball drawing machine would draw your numbers (although "eventually" is longer than the average human lifespan in all probability). I assume you agree with all this since it is how the lotto system actually works for the most part.
Now assume that the numbers that the woman selected are actually decimal opcodes for a computer architecture (a number is a number) and the sequence she selected is the opcode sequence for a useful program. Are you telling me that the lotto ball machine is suddenly incapable of randomly returning her sequence of numbers because the sequence of numbers she chose is "useful" in another context?
A lady did win the lottery. And people do every day. By the rules of that game, all possible sequences can be drawn (and will be drawn eventually), even if the sequences also happen to be a valid opcode sequence. Would you like me to look through the state lottery drawings for a valid opcode sequence? It wouldn't take long to find one. There are a very large number of valid sequences, though some do more things than others. DNA is actually even more likely to produce good results automatically, since unlike the lottery example, DNA has constructive/destructive reinforcement mechanisms at work (i.e. it isn't truly random in the conventional sense).
So there is an example of a random process generating an intentionally predefined sequence of symbols (a "program" for the pedestrians). What's the problem?
...and after all of this, I believe you know that.
Thanks, I need no more.
:)
Apparently because you have no idea what the hell you are asking for. What do you want an example of that hasn't been provided? I was giving examples of a proven theorem of mathematics for which there are no exceptions in the real world (math works that way and no one has ever found an exception in any case). You still doubt elementary theorems of mathematics? I've given ample examples of the mathematics in action, even though you could have simply cracked open a decent math text and read this stuff yourself. Clearly you do not understand my explanations of the mathematics, although I don't think it can be put in any simpler terms. I actually do know of at least one honest example of a "useful" randomly generated program, but other than saying "it happened", it is technically beyond those who can't grasp the math in the first place so it isn't like specific examples would gain any traction. I already know that is a futile direction.
At this point, all I can say is that a few of the people I am arguing with on this forum have a woefully inadequate education in the field of mathematics and apparently have no interest in correcting the situation. So be it.
Yes, all living organisms come from the same cellular lineage, and there is evidence for this in the comparative DNA. Another piece of evidence in this regard is that all living things have DNA. There are a number of chemical systems that can do what DNA does in cells i.e. DNA has no intrinsic importance to living organisms. The fact that all organisms do use DNA substantially reduces the probability that they emerged independently though it is certainly possible.
Did plant life come into being spontaneously or did a mutant blade of grass grow into a tree?
Plant life evolved from chloroplast containing microorganisms I think. But I am not a biologist, so I can't say for sure. My interest in the thread is mostly to correct really bad mathematics.
What drove that cell evolve in the first place? What possible pressures could have been put on that organism to change since by it's very uniqueness it had no natural enemies or threat to it's existence? Natural selection requires an outside threat or need to force an adaptation or evolution true or false?
Evolution doesn't happen to a cell, it shows up by comparing mutations in successive generations. Even in the absence of predators, there are tons of selection pressures. For example, many simple organisms can only live in specific temperature bands which vary depending on what proteins they use. It would take a relatively minor mutation (caused by stray alpha radiation for example) for a microorganism to have a survival preference for a different temperature band than its parents. This could mean that at some temperatures, only one of the two strains could survive. What happens is that you have the case where variations of the simple organism live at different locations in a temperature gradient with slightly different environmental differences as a side-effect of location. Wash-rinse-repeat, and you have an exponential take off in variation. Note that this exact same effect can be observed in organic chemistry as well, where a temperature gradient will generate complex variation and separation along the gradient (hence why temperature gradients are not desirable for reactions where we want only one end product) just by the nature of the types of reactions that are occurring. There also quite a number of chemicals (some proteins for example) that are quite capable of self-replicating in a rich environment. As the complexity of the chemistry increases, the chemical processes that are occurring also tend to increase in complexity, but unfortunately for us the computational complexity becomes intractable relatively quickly for molecules that can bootstrap themselves and we literally lack the computing power right now to figure out precisely what is going on beyond a certain point. All we can do then is observe the properties of the results.
So to answer a question, evolution will occur in any system that has both variation/mutation and selection; we don't even have to be talking about living organisms for this to be true. Mutations happen in single celled organisms regardless of whether or not there is a selection pressure because of things like radiation which are always in the environment. You don't have evolution unless you also have a selection mechanism, which can be any parameter that can kill the organism (changes in temp, radiation, chemistry, etc). So in practice, mutation is always occurring but selection happens intermittently. Note that sexual reproduction is a form of mutation as well, as the resulting DNA is always unique. Of course, once living organisms started to flourish they created yet another selection pressure when they started competing with themselves, but this was merely another selection pressure in a long line of selection pressures.
IT isn't ironic, it was my point. Prigogine does indeed show how complex systems can self-organize out of chaotic, natural environments. He points out that as useful energy is removed from a system, higher levels of organizational complexity become increasingly more possible to self-form.
But his pre-requisite, the removal of energy from a physical system, limits the potential upper-boundary of maximum possible complexity that a system can support. This limit is axiomatically in place (at the very least) because the maximum upper levels of organized structures possible for the system will require more energy for their composition than exist in said system after quantities of useful energy are removed.
Conversely, this means is that infinite (or even maximum system) levels of complex order will NOT self-form in any chaotic natural system.
Likewise, this disproves the folklore (and rest assured, what you've been trying to call mathematics is certainly not scientifically proven) that a million monkeys typing on a million keyboards for a million years will create a pristine copy of Shakespear's greatest works.
First of all, you have clearly overlooked what I had considered to be obvious: that we were comparing the physical characteristics of DNA coding to that of the electrical characterics of human computer programming, hence the mixing of engineering and mathematics (which go hand in hand, by the way).
Second, whether one pumps random bits through a computer - or whether one pumps Fourier Transform equations through a machine will make an enormous difference in behavior in the computerize machinery attached, as one will necessitate random movements yet the other will enable feedback and control to be introduced into said system. The feedback characteristic alone insures that the very electricity inside the system has a different characteristic than in a non-feedback, random bit application.
"This is a variant of the very tired (and fundamentally ignorant) argument trying to mix axioms of information theory and thermodynamics. First, nothing in information theory requires energy to generate order or the lack thereof."
Nonsense! All forms of order require some amount of energy for their very composition. If you don't have enough energy in your system for a certain composition of order, then you can't have that composition in your system; it would be impossible.
Perhaps you simply didn't comprehend my simple, original point above...
That's incorrect. The reason that you can't show an example of a useful computer program self-forming in a random environment is because complex levels of organization can often be beyond what is possible for a random, chaotic system to create (we don't have infinite time, after all).
Likewise, your lottery example is flawed. A winning lottery ticket might be comprised of 6 two-digit numbers, yet 6 two-digit numbers is vastly insufficient for any modern, useful software program. Perhaps a simplified software program could be comprised of 20,000 two-digit numbers. A similar lottery would require hundreds of billions of years before a winner was ever found (i.e. far older than our existing universe).
Except, even when that winning number was hit in the random, chaotic, physical world of either DNA or computer programs, it would just be one organizational structure inside a mass of useless data in a place unable to to either execute (in the case of a computer program) or activate (i.e. abiogenesis) and survive (in the case of DNA), much less replicate, mutate, and form new generations of programs and life.
So no, you can't point to an example of a computer program self-forming from any chaotic, random environment (even though you absurdly pretend that such an exercise is "trivial")...
This is true. And life on this planet has had a virtually unlimited supply of external energy for as long as we have had evidence life existed. Therefore, there is no contradiction in the premise that arbitrarily large amounts of spontaneous entropy reduction are possible in living organisms. This is a core point; entropy (or lack thereof) in organisms is only relevant in the absence of vast external enthalpy gradients. Since such gradients exist, the reduction in entropy in living organisms has never been a hurdle to their existence.
That's fundamentally incorrect and logically flawed.
We have variation, mutation, and selection in automobiles, but we know that the cars aren't self-evolving (rather, it is the Designers of cars who make the changes to the cars via Intelligent Intervention).
In fact, we don't have natural, unaided, unintelligent Evolution occur in many systems wherein Intelligent Intervention is present. For example, computer programs don't self-evolve (unless designers tell them to), even though the designers outside said systems might.
Did you actually intend to say "Since such gradients exist, the increase in entropy in living organisms has never been a hurdle to their existence?"
I've noticed a couple times that you are using "finite but extremely large" and "infinite" interchangeably, when the mathematical consequences are utterly different. Everything we have been talking about is in the realm of "finite but extremely large". Also, the computers we have today are unbelievably slow compared to theory for the amount of matter involved. There is literally more potential computing power in a grain of sand than man has produced in total in his CPU fabs. The problems we are discussing are "intractable", not "impossible", due mostly to the primitive and inefficient nature of our computers. Current engineering limits and theoretical engineering limits don't come remotely close to each other in this domain. Nonetheless, you act as though current engineering limits ARE a theoretical limit.
In a sense you are correct that it is difficult to extract large programs from unbiased noise streams, but this is only generally true on current systems, there are no intrinsic engineering, mathematical, or scientific limitations that mean this will always be the case. Quite the opposite in fact; there is substantial evidence that we will approach that capability much sooner than later. It is also true that a "sufficiently large" program may not be reasonably extractable from an unbiased noise stream in our universe.
Fortunately or unfortunately depending on how you look at it, there is a flaw in the above reasoning if we are trying to apply it to DNA that actually makes the scenario look far more improbable than it is. "Unbiased noise stream" makes the mathematics clean and easy, but has nothing to do with chemistry. In chemistry, the combinatorial probabilities are extremely biased (if it wasn't, chemical reactions of all types would almost never happen), and the probabilities of some specific sequences occurring are vastly higher than others. Throw in a feedback loop and the emergence of stable sequences become far more reasonable and probable. Incidentally, the calculations for probabilities in biased chaotic systems is far more complicated than the naive calculations that are only valid for unbiased combinatorics. In fact, the use of simple combinatorics for calculating probability in chemistry seems to be a very common error in these threads. We aren't discussing this, but I am merely pointing out the fact that what we ARE discussing isn't even particularly relevant to DNA (which is nominally what we were talking about).
I meant what I said, but I suppose it is subject to a perspective of the system. A better way to say it is that the issue of entropy is irrelevant to the existence of living organisms on this planet due to the existence of a vast enthalpy gradient. The enthalpy gradient makes entropy a non-issue for the sake of discussion.
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