God, Man and Physics

The God Hypothesis:
Discovering Design in our "Just Right" Goldilocks Universe
by Michael A. Corey
(Rowman & Littlefield, 256 pp., $27)

GOD'S EXISTENCE is not required by the premises of quantum mechanics or general relativity, the great theories of twentieth-century physics --but then again, it is not contravened by their conclusions either. What else can we do but watch and wait?

The agnostic straddle. It is hardly a posture calculated to set the blood racing. In the early 1970s Jacques Monod and Steven Weinberg thus declared themselves in favor of atheism, each man eager to communicate his discovery that the universe is without plan or purpose. Any number of philosophers have embraced their platform, often clambering onto it by brute force. Were God to exist, Thomas Nagel remarked, he would not only be surprised, but disappointed.

A great many ordinary men and women have found both atheism and agnosticism dispiriting--evidence, perhaps, of their remarkable capacity for intellectual ingratitude. The fact remains that the intellectual's pendulum has swung along rather a tight little arc for much of the twentieth century: atheism, the agnostic straddle, atheism, the agnostic straddle.

The revival of natural theology in the past twenty-five years has enabled that pendulum to achieve an unexpected amplitude, its tip moving beyond atheism and the agnostic straddle to something like religious awe, if not religious faith.

It has been largely the consolidation of theoretical cosmology that has powered the upward swing. Edwin Hubble's discovery that the universe seemed to be expanding in every direction electrified the community of cosmologists in the late 1920s, and cosmologists were again electrified when it became clear that these facts followed from Einstein's general theory of relativity. Thereafter, their excitement diminished, if only because the idea that the universe was expanding suggested inexorably that it was expanding from an origin of some sort, a big bang, as the astronomer Fred Hoyle sniffed contemptuously.

In 1963 Arno Penzias and Robert Wilson inadvertently noticed the background microwave radiation predicted by Big Bang cosmology; when Robert Dicke confirmed the significance of their observation, competing steady-state theories of creation descended at once into desuetude. And thereafter a speculative story became a credible secular myth.

But if credible, the myth was also incomplete. The universe, cosmologists affirmed, erupted into existence fifteen billion years ago. Details were available, some going back to the first three minutes of creation. Well and good. But the metaphoric assimilation of the Big Bang to the general run of eruptions conveyed an entirely misleading sense of similarity. The eruption of Mount Vesuvius took place in space and time; the Big Bang marks the spot at which time and space taper to a singularity and then vanish altogether.

It follows that the universe came into existence from nothing whatsoever, and for no good reason that anyone could discern, least of all cosmologists. Even the most ardent village atheist became uneasily aware that Big Bang cosmology and the opening chapters of the Book of Genesis shared a family resemblance too obvious profitably to be denied.

Thereafter, natural theology, long thought dead of inanition, began appearing at any number of colloquia in mathematical physics, often welcomed by the same physicists who had recently been heard reading its funeral obsequies aloud. In "The God Hypothesis: Discovering Design in our "Just Right" Goldilocks Universe," Michael A. Corey is concerned to convey their news without worrying overmuch about the details. His message is simple. There is a God, a figure at once omnipotent, omniscient, eternal, and necessary. Science has established his existence.

AT THE very heart of revived natural theology are what the physicist Brandon Carter called "anthropic coincidences." Certain structural features of the universe, Carter argued, seemed finally tuned to permit the emergence of life. This is a declaration, to be sure, that suggests far more than it asserts. Structural features? Finely tuned? Permit? When the metaphors are squeezed dry, what more is at issue beyond the observation that life is a contingent affair? This is not a thesis in dispute.

Still, it often happens that commonplace observations, when sharpened, prompt questions that they had long concealed. The laws of physics draw a connection between the nature of certain material objects and their behavior. Falling from a great height, an astrophysicist no less than an airplane accelerates toward the center of the earth. Newton's law of gravitational attraction provides an account of this tendency in terms of mass and distance (or heft and separation). In order to gain traction on the real world, the law requires a fixed constant, a number that remains unchanged as mass and distance vary. Such is Newton's universal gravitational constant.

There are many comparable constants throughout mathematical physics, and they appear to have no very obvious mathematical properties. They are what they are. But if arbitrary, they are also crucial. Were they to vary from the values that they have, this happy universe--such is the claim--would be too small or too large or too gaseous or otherwise too flaccid to sustain life. And these are circumstances that, if true, plainly require an explanation.

Carter was a capable physicist; instead of being chuckled over and dismissed by a handful of specialists, the paper that he wrote in 1974 was widely read, Fred Hoyle, Freeman Dyson, Martin Rees, Stephen Hawking, Paul Davies, Steven Weinberg, Robert Jastrow, and John Gribbin all contributing to the general chatter. Very few physicists took the inferential trail to its conclusion in faith; what is notable is that any of them took the trail at all.

THE ASTRONOMER Fred Hoyle is a case in point, his atheism in the end corrected by his pleased astonishment at his own existence. Living systems are based on carbon, he observed, and carbon is formed within stars by a process of nucleosynthesis. (The theory of nucleosynthesis is, indeed, partly his creation.) Two helium atoms fuse to form a beryllium intermediate, which then fuses again with another helium atom to form carbon. The process is unstable because beryllium intermediates are short-lived.

In 1953 Edwin Salpeter discovered that the resonance between helium and intermediate beryllium atoms, like the relation between an opera singer and the glass she shatters, is precisely tuned to facilitate beryllium production. Hoyle then discovered a second nuclear resonance, this one acting between beryllium and helium, and finely tuned as well.

Without carbon, no life. And without specific nuclear resonance levels, no carbon. And yet there he was, Hoyle affirmed, carbon based to the core. Nature, he said in a remark widely quoted, seems to be "a put-up job."

INFERENCES now have a tendency to go off like a string of firecrackers, some of them wet. Hoyle had himself discovered the scenario that made carbon synthesis possible. He thus assigned to what he called a "Supercalculating Intellect" powers that resembled his own. Mindful, perhaps, of the ancient wisdom that God alone knows who God is, he did not go further. Corey is, on the other hand, quite certain that Hoyle's Supercalculating Intellect is, in fact, a transcendental deity--the Deity, to afford Him a promotion in punctuation.

And Corey is certain, moreover, that he quite knows His motives. The Deity, in setting nuclear resonance levels, undertook his affairs "in order to create carbon based life forms."

Did He indeed? It is by no means obvious. For all we know, the Deity's concern may have lain with the pleasurable intricacies of nucleosynthesis, the emergence of life proving, like so many other things, an inadvertent consequence of his tinkering. For that matter, what sense does it make to invoke the Deity's long term goals, when it is His existence that is at issue? If nothing else, natural theology would seem to be a trickier business than physicists may have imagined.

AS IT HAPPENS, the gravamen of Corey's argument lies less with what the Deity may have had in mind and more with the obstacles He presumably needed to overcome. "The cumulative effect of this fine tuning," Corey argues, "is that, against all the odds, carbon was able to be manufactured in sufficient quantities inside stellar interiors to make our lives possible." That is the heart of the matter: against all the odds. And the obvious question that follows: Just how do we know this?

Corey does not address the question specifically, but he offers an answer nonetheless. It is, in fact, the answer Hoyle provides as well. They both suppose that something like an imaginary lottery (or roulette wheel) governs the distribution of values to the nuclear resonance levels of beryllium or helium. The wheel is spun. And thereafter the right resonance levels appear. The odds now reflect the pattern familiar in any probabilistic process--one specified outcome weighed against all the rest. If nuclear resonance levels are, in fact, unique, their emergence on the scene would have the satisfying aspect of a miracle.

It is a miracle, of course, whose luster is apt to dim considerably if other nuclear resonance levels might have done the job and thus won the lottery. And this is precisely what we do not know. The nuclear resonance levels specified by Hoyle are sufficient for the production of carbon. The evidence is all around us. It is entirely less clear that they are necessary as well. Corey and Hoyle make the argument that they are necessary because, if changed slightly, nucleosynthesis would stop. "Overall, it is safe to say"--Corey is speaking, Hoyle nodding--"that given the utter precision displayed by these nuclear resonances with respect to the synthesis of carbon, not even one of them could have been slightly different without destroying their precious carbon yield." This is true, but inconclusive. Mountain peaks are isolated but not unique. Corey and Hoyle may well be right in their conclusions. It is their argument that does not inspire confidence.

THE TROUBLE is not merely a matter of the logical niceties. Revived natural theology has staked its claims on probability. There is nothing amiss in this. Like the rest of us, physicists calculate the odds when they cannot calculate anything better. The model to which they appeal may be an imaginary lottery, roulette wheel, or even a flipped coin, but imaginary is the governing word. Whatever the model, it corresponds to no plausible physical mechanism. The situation is very different in molecular biology, which is one reason criticism of neo-Darwinism very often has biting power. When biologists speculate on the origins of life, they have in mind a scenario in which various chemicals slosh around randomly in some clearly defined physical medium. What does the sloshing with respect to nuclear resonance?

Or with respect to anything else? Current dogma suggests that many of the constants of mathematical physics were fixed from the first, and so constitute a part of the initial conditions of the Big Bang. Corey does not demur; it is a conclusion that he endorses. What then is left of the anthropic claim that the fundamental constants have the value that they do despite "all odds"? In the beginning there was no time, no place, no lottery at all.

MATHEMATICAL physics currently trades in four fundamental forces: gravity, electromagnetism, and the strong and weak forces governing the nucleus and radioactive decay. In general relativity and quantum mechanics, it contains two great but incompatible theories. This is clearly an embarrassment of riches. If possible, unification of these forces and theories is desirable. And not only unification, but unification in the form of a complete and consistent theoretical structure.

Such a theory, thoughtful physicists imagine, might serve to show that the anthropic coincidences are an illusion in that they are not coincidences at all. The point is familiar. Egyptian engineers working under the pharaohs knew that the angles of a triangle sum to more or less one hundred and eighty degrees. The number appears as a free parameter in their theories, something given by experience and experiment. The Greeks, on the other hand, could prove what the Egyptians could only calculate. No one would today think to ask why the interior angles of a Euclidean triangle sum to precisely one hundred and eighty degrees. The question is closed because the answer is necessary.

THE GRAND HOPE of modern mathematical physicists is that something similar will happen in modern mathematical physics. The Standard Model of particle physics contains a great many numerical slots that must be filled in by hand. This is never counted as a satisfaction, but a more powerful physical theory might show how those numerical slots are naturally filled, their particular values determined ultimately by the theory's fundamental principles. If this proves so, the anthropic coincidences will lose their power to vex and confound.

Nonetheless, the creation of a complete and consistent physical theory will not put an end to revived natural theology. Questions once asked about the fundamental constants of mathematical physics are bound to reappear as questions about the nature of its laws. The constants of mathematical physics may make possible the existence of life, but the laws of mathematical physics make possible the existence of matter. They have, those laws, an overwhelmingly specific character. Other laws, under which not much exists, are at least imaginable. What explanation can mathematical physics itself provide for the fact that the laws of nature are arranged as they are and that they have the form that they do? It is hardly an unreasonable question.

Steven Weinberg has suggested that a final theory must be logically isolated in the sense that any perturbation of its essential features would destroy the theory's coherence. Logical isolation is by no means a clear concept, and it is one of the ironies of modern mathematical physics that the logical properties of the great physical theories are no less mysterious than the physical properties of the universe they are meant to explain. Let us leave the details to those who cherish them.

The tactic is clear enough. The laws of a final theory determine its parameters; its logical structure determines its laws. No further transcendental inference is required, if only because that final theory explains itself.

This is very elegant. It is also entirely unpersuasive. A theory that is logically isolated is not necessarily a theory that is logically unique. Other theories may be possible, some governing imaginary worlds in which light alone exists, others worlds in which there is nothing whatsoever. The world in which we find ourselves is one in which galaxies wink and matter fills the cup of creation. What brings about the happy circumstance that the laws making this possible are precisely the laws making it real? The old familiar circle.

ALL THIS leaves us where we so often find ourselves. We are confronted with certain open questions. We do not know the answers, but what is worse, we have no clear idea--no idea whatsoever--of how they might be answered. But perhaps that is where we should be left: in the dark, tortured by confusing hints, intimations of immortality, and a sense that, dear God, we really do not yet understand.

----------------------------
David Berlinski is a senior fellow of Discovery Institute and the author of "A Tour of the Calculus" and "The Advent of the Algorithm." His most recent book is Newton's Gift (Free Press).

Nobel laureate Prigogine has already shown us in Order Out of Chaos that increased levels of order (i.e. complexity) are increasingly likely to self-form naturally as you remove useful energy from a system, but this trend runs against the axiom that increased levels of order require more energy for their very composition.

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.

I am not quite sure why you are failing to comprehend the difference between a "demonstration" and an "example" but please...

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?

...and your "example" of something like this actually taking place is?

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?

All due respect but you did not give an "example" of the process taking place. ...and after all of this, I believe you know that.

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.

Let's take this back to the very beginning i.e.. the first living cell in the ocean or wherever the first form of life was incubated. Did that cell not only evolve to include all animal life but also all plant life?

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.

"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."

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.

"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."

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...

"I will let you pick any source of randomness. It doesn't really matter as they will all produce any finite program in a finite amount of time. I can't believe that people are even arguing this point. It is ridiculous and founded in ignorance. People have done this at various times for decades (mostly at universities to prove a point), but it is a worthless proof because we can trivially prove it mathematically. So do you really question whether or not 2+2=4? How do you get on in the world? The mathematics of it is blatantly self-evident to me but apparently not to you. Perhaps you could take the time to read up on some elementary theorems of the subject we are talking about rather than insisting such things aren't so without the slightest clue one way or the other. Your mathematical position insists that no one can ever win the lottery, yet people do."

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")...

"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.

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.

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).

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).

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