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Irreducible Complexity in Mathematics, Physics and Biology

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There is a new paper on Irreducible Complexity by renowned mathematician Gregory Chaitin: The Halting Probability Omega: Irreducible Complexity in Pure Mathematics Milan Journal of Mathematics, Vol. 75, 2007.

Ω is an extreme case of total lawlessness; in effect, it shows that God plays dice in pure mathematics.

On the surface Chaitin’s notion of Irreducible Complexity (IC) in math may seem totally irrelevant to Irreducible Complexity (IC) in ID literature. But let me argue that notion of IC in math relates to IC in physics which may point to some IC in biology…

First, of consider this article archived at Access Research Network (ARN) by George Johnson in the NY Times on IC in physics:

Challenging Particle Physics as Path to Truth

Many complex systems — the very ones the solid-staters study — appear to be irreducible.

The concept of “irreducible complexity” has been used by Alan Turing, Michael Behe, and perhaps now by physicists. Behe’s sense of irreducible is not too far from the sense of irreducible in the context of this physics. If biological systems take advantage of irreducible phenomena in physics (for example, what if we discover the brain uses irreducible physical phenomena ) we will have a strong proof by contradiction that there are no Darwinian pathways for biolgoical systems to incorporate that phenomena.

The possibility of IC in physics may be tied to IC in math and this may have relevance to IC in biology.

For the reader’s benefit here is a bit of a tutorial on the idea of IC in physics:

In science’s great chain of being, the particle physicists place themselves with the angels, looking down from the heavenly spheres on the chemists, biologists, geologists, meteorologists — those who are applying, not discovering, nature’s most fundamental laws. Everything, after all, is made from subatomic particles. Once you have a concise theory explaining how they work, the rest should just be filigree.

Even the kindred discipline of solid-state physics, which is concerned with the mass behavior of particles — what metals, crystals, semiconductors, whole lumps of matter do — is often considered a lesser pursuit. “Squalid state physics,” Murray Gell-Mann, discoverer of the quark, dubbed it. Others dismiss it as “dirt physics.”

Recently there have been rumblings from the muck. In a clash of scientific cultures, some prominent squalid-staters have been challenging the particle purists as arbiters of ultimate truth.

“The stakes here are very high,” said Dr. Robert B. Laughlin, a Stanford University theorist who shared a Nobel Prize in 1998 for discoveries in solid-state physics. “At issue is a deep epistemological matter having to do with what physics is.”

Many complex systems — the very ones the solid-staters study — appear to be irreducible. Made of many interlocking parts, they display a kind of synergy, obeying “higher organizing principles” that cannot be further simplified no matter how hard you try.

Carrying the idea even further, some solid-state physicists are trying to show that the laws of relativity, long considered part of the very bedrock of the physical world, are not platonic truths that have existed since time began.

particle physicists have reason to be wary. The squalid-staters are challenging them in a debate over how the universe is made and how science should be done.

The particle physicists’ ultimate goal is “grand unification” — recovering the primordial symmetry in the form of a single law — a few concise equations, it is often said, that could be silk-screened onto a T- shirt.

This approach, in which the most complex phenomena are boiled down to a unique underlying theory, is called reductionism.

The problem, the solid-staters say, is that many forms of matter — ranging from the exotic like superconductors and superfluids to the mundane like crystals and metals — cannot be described in terms of fundamental particle interactions. When systems become very complex, completely new and independent laws emerge. “More is different,” as the Nobel laureate Philip W. Anderson put it in a landmark paper in 1972. To the solid-staters, it would take something the size of a circus tent to hold all the equations capturing the unruliness of the physical world.

Like Aristotle, they lean toward the notion that it is the equations that flow from nature instead of the other way around. Mathematics is just a tool for making sense of it all.

“For at least some fundamental things in nature, the theory of everything is irrelevant,” declared Dr. Laughlin and Dr. Pines in the Jan. 4, 2000 issue of The Proceedings of the National Academy of Sciences. “The central task of theoretical physics in our time is no longer to write down the ultimate equations but rather to catalog and understand emergent behavior in its many guises, including potentially life itself.”

There may not be a theory of everything, they say, just a lot of theories of things. This is exactly the kind of squalor the particle physicists abhor.

Dr. Grigori E. Volovik, a solid- state physicist at the Helsinki University of Technology in Finland, champions an idea he calls “anti- grand unification.” In a review article last year (xxx.lanl.gov/abs /gr-qc/0104046), he ventured that the universe may have begun not in a state of pristine symmetry but in one of lawlessness. The laws of relativity and perhaps quantum mechanics itself would have emerged only later on.

The notion of emergent laws is not radical in itself. A flask of gas consists of trillions of molecules randomly colliding with one another. From this disorder, qualities like temperature and pressure emerge, along with laws relating one to the other.

So take that idea a level deeper. Physicists now believe that the vacuum of space is, paradoxically, not vacuous at all. It seethes with energy, in the form of “virtual particles” constantly flitting in and out of existence. So perhaps, Dr. Volovik suggests, even laws now considered fundamental emerged from this constant subatomic buzz.

Solid-state physics offers clues to how something like this might occur. The atomic vibrations that ripple through matter are, like all quantum phenomena, carried by particles — called, in this case, phonons.

Just as photons carry light and gravitons carry gravity, phonons carry the subatomic equivalent of sound. Like bubbles in a carbonated beverage, phonons — physicists call them “quasi particles” — appear only when the medium is disturbed.

In the world of solid-state physics, quasi particles abound. In some substances, like the semiconductors used to make computer chips, the displacement of an electron leaves behind a “hole” that behaves like a positively charged particle. An electron and a hole can sometimes stick together to form a chargeless quasi particle called an exciton. Other such ephemera include magnons and polarons.

Evanescent though they are, quasi particles act every bit like elementary particles, obeying the laws of quantum mechanics. This has led some mavericks to wonder whether there is really any difference at all. Maybe elementary particles are just quasi particles — an effervescence in the vacuum.

Particularly intriguing is a phenomenon, occurring at extremely low temperatures, called the fractional quantum Hall effect. In certain substances, quasi particles appear that act curiously like electrons but with one-third the normal charge. (Dr. Laughlin won his Nobel Prize for a theory explaining this.)

Quarks, the basic building blocks of matter, also carry a one-third charge, a coincidence that has fueled speculation that emergence may be somehow fundamental to the very existence of the physical world.

A stumbling block to carrying this idea further has been that the quantum Hall effect seems to work only in two-dimensions — on the surface of a substance. But in a paper published in the Oct. 26 issue of Science, Dr. Zhang and his student Jiangping Hu showed how to extend the phenomenon. In their scheme, the physical world would be a three-dimensional “surface” of a four-dimensional “quantum liquid” — an underlying sea of particles that can be thought of as the vacuum.

Analyzing the ripples that would appear in such a medium, the two scientists were surprised to find that they mathematically resembled electromagnetic and gravitational waves. But there are problems with the model. At this point, the hypothetical photons and gravitons that emerge from the equations do not interact with other particles, as they do in the real world.

“The coupling is zero, so apples are weightless, as is everything else,” said Dr. Joseph Polchinski, a string theorist at the University of California at Santa Barbara, who recently discussed the model with Dr. Zhang.

And there is what the theory’s inventors concede is an “embarrassment of riches” — the equations predict hordes of exotic particles that do not exist.

“The hope is that some modification of the theory, not yet specified in detail, will remove the extra fields and turn on the coupling,” Dr. Polchinski said. “Whether this can be done is at this point a guess. Overall my attitude now is interest with a high degree of skepticism.”

If the theory can be made to work, it may point to a new way of unifying quantum mechanics and relativity. But Dr. Zhang is careful not to oversell what he considers a work in progress.

“Our work only made a tiny step toward this direction,” Dr. Zhang said, “but it seems to indicate that the goal may not be impossible to reach.” At the very least, he said, his work may inspire more collaboration between particle physicists and solid-staters.

Ultimately, though, the two sides know that they are talking across a divide. Taken to its extreme, emergence suggests that all the fundamental laws, even quantum mechanics, may be secondary — that at the base of reality is random noise.

Dr. Polchinski said he found that idea discouraging.

“To me, the history of science seems to be a steady progression toward simpler and more unified laws, and I expect to see this continue and to contribute to it. Things may take many surprising twists and turns,” he said, “but we reductionists are still quite happily and busily reducing.”

Back to the paper on Irreducible Complexity in Mathematics by Chaitin:
The Halting Probability Omega: Irreducible Complexity in Pure Mathematics Milan Journal of Mathematics, Vol. 75, 2007

On the surface this may seem totally decoupled from Irreducible Complexity (IC) in the ID literature. In fact, Hubert Yockey furiously criticized Behe’s notion of IC and contrasted it with Turing notion of IC.

But let us not be to hasty to say the two notions of IC can have nothing to do with each other. Let me suggest, IC in math will permeate physics and therefore biology! There has been a suggestion that emergent IC phenomena in physics are tied to Godel’s incompleteness, thus we ought to expect irreducible systems in physics! And as I pointed out if biology exploits such irreducible phenomena, we have strong theoretical evidence there are not Darwinian pathways to creation of such systems. More nails in the coffin Darwin’s theories.

See this paper:

Emergence and Computability

This paper presents a discussion of the possible influence of incomputability and the incompleteness of the mathematics as a source of apparent emergence in complex systems. The suggestion is made that the analysis of complex systems as a specific instance of a complex process may be subject to inaccessible “emergence”. We discuss models of computation associated with transcending the limits of
traditional Turing systems, and suggest that inquiry into complex systems in the light of the potential limitations of incomputability and incompleteness may be worthwhile.

We suggest that what we intuitively define as (strongly) emergent systems may include processes which are not computable in a classical sense. We ask how incomputable processes would appear to an observer and, via a thought experiment, show that they would display features normally defined as ‘emergent’.

If this conjecture is correct, then two important corollaries follow: first, some emergent phenomena can neither be studied nor modelled via classical computer simulations and second, there may be classes of emergent phenomena which cannot be detected via standard physical measurements unless the process of measurement exhibits super-Turing properties in its own right. Borrowing from recent literature in
computer science we then show that tools which enable us to break the classical computational barrier are already available and suggest some directions for a novel approach to the problem.

[...] 3. To learn more reasons why reductionism fails to explain complex design, see: 2007 Irreducible Complexity in Mathematics, Physics and Biology and From Italy, Mathematics and the origin-of-life problem [...] Michael Lynch: Darwinism is a caricature of evolutionary biology | Uncommon Descent
[...] I recently posted on Irreducible Complexity in Mathematics, Physics and Biology. That thread generated interest in a well-written article by ID proponents in Italy. The article touches on the work of Turing, Chaitin, von Neumann and relates it to ID-sympathetic literature by Dembski, Behe, Voie, Trevors and Abel. The article was so well written and informative, that I felt it deserved its own thread. Our readers can learn much about ID through this article! [...] From Italy, Mathematics and the origin-of-life problem | Uncommon Descent
I think I'm writing a "message in a bottle". For me, the best definition of science was by physicist Joe Rosen in his book, The Capricious Cosmos . He wrote:
Science is our attempt to understand the reproducible and predictable aspects of nature.
He then defined the terminology, Nature meaning the material universe in which we interact, reproducible means experiments that can be repeated by other investigators, (of course, I am condensing his argument significantly here), predictability involves laws that can be formulated, predicting results. Now, in my opinion, since the cosmologists always are "surprised" by what is observed in the universe and consistently invent ever new ad hoc concepts, such as dark energy, matter, etc., and that the big bang is neither reproducible or observable, it fails; it is founded on an assumption, which is not necessarily falsifiable. And obviously, so is Darwinism. Rosen believes the "universe" was a quantum fluctuation; it was, as another scientist wrote, "one of those things" that just happen! To me, what is interesting about the debate about cosmology or Darwin is what it reveals about the debaters. For the advocates of Einstein, who to me belongs in the company of Darwin, Marx, and Freud, those stopped clocks right two times a day, his ideas are beyond question. Yet his "god" of the limitation on the "speed of light" is contradicted. And while I shall present later some concepts that some may find compelling, I think we, as human beings, should attempt to perfect ourselves, our character, and our conduct, and worry less about the nature of things, which I fear our ultimately beyond the ability of the human mind to comprehend. My earlier citations of the work of Simon Berkovich revealed his discomfort with the current state of affairs, and I find his assumption of a "holographic" universe compelling. However, while some are comfortable with David Bohms' "implicate order" hypothesis, I think an electrical model fits the observations better. Berkovich sees "God" as an information systems designer; he talks of design, but doesn't believe "metaphysics" belongs in the purview of science. There is tremendous evidence that the "universe" is not material. My unanswerable question is on the nature of human beings; "God" to me is an epic poet, and not a mathematician. Rupert Sheldrake wrote in his A New Science of Life :
The concept of genetic programming is based on an analogy with the programmes that direct the activities of computers. It implies that the fertilized egg contains a pre-formed programme which specifies the organism's morphogenic goals and co-ordinates and controls its development towards them. But the genetic programme must involve something more than the chemical structure of DNA, because identical copies of DNA are passed on to all cells; if all cells are programmed identically, they could not develop differently. So what exactly is it? In response to this question, the idea can only disintegrate into vague suggestions about physio-chemical interactions somehow structured in time and space; the problem is merely re-stated. ...But if it is argued that genetic programmes are not analagous to ordinary computer programs, but to those of self-reproducing, self-organising computers, the problem is such computers don't exist. And even if they did, they would have to be programmed in the most elaborate way by their inventors to start with...Indeed, the properties [neo-Darwinists] attributed to genetic programmes are remarkably similar to those which vitalists endowed their vital factors; ironically, the genetic programme seems to be like a vital factor in a mechanistic guise.
Life encompasses all the disciplines, does it not? Humans specialize -- physicists, molecular biologists, etc. but the universe is a coherent whole. I think Rosen's definition is apt; I agree with Berkovich that a new "paradigm" is needed, but I do not know if human beings are ready for it, or they would ultimately become better human beings with greater understanding. As to what makes more sense to me, personally, than superstrings, dark matter, dark energy, and "God" particles, consider the following:
If we deal with the real universe of our senses, augmented by modern technology, we stand the best chance of developing the physical concepts leading to a "real theory of everything." Here "everything" is limited in the sense of "everything we can detect and know about at present." For there is a limit to what we can detect and know, not only at the smallest and the largest of scales but also with regard to what we pay attention to and what we overlook at all scales. Neither Einstein's relativity nor quantum mechanics are physics so we cannot use them as a foundation for our new model (although we should find that the mathematics that works in the real world still applies). We have to discard "modern" physics and return to the classical physics of a century ago. This, perhaps, is the greatest hurdle – to discard our training and prejudices and to approach the problem with a beginner's mind. The "something absolutely fundamental" that is missing in our explanation of gravity and quantum behavior is the electrical structure of matter. Here we are not talking about negative electrons and positive atomic nuclei. We must "go down" one more level and propose that all subatomic particles, including the electron, are resonant structures of electric charges of opposite sign that sum to the charge on that particle. The electron is not a fundamental, point-like particle.4 It must have structure to provide its dipole magnetic field. There must be orbital motion of charges within the electron to generate the magnetic dipole. The transfer of electrical energy between the charges in their orbits must be resonant and near-instantaneous for the electron to be a stable particle. The same model applies to the proton and the neutron. This model satisfies Einstein's view that there must be some lower level of structure in matter to cause resonant quantum effects. We cannot have a theory of everything until we have a workable concept of the structure of matter that satisfies the observation that inertial and gravitational mass are equivalent. When we accelerate electrons or protons in an electromagnetic field they become less responsive to the fields the more they are accelerated. This has been interpreted as an increase in mass. However, charges have no mass. So how do they give the electron, proton and neutron the property of mass? The accelerating electromagnetic field will distort the orbits of charges within the electron or proton. It seems the more distorted a particle becomes, the more easily the energy supplied to accelerate the particle is assimilated in further distortion rather than in acceleration. Hence the apparent increase in mass. The inertial mass of a particle is a measure of the degree to which it responds to an electric field by distorting rather than accelerating. It implies the charge centers of a proton at rest have to be separated more than those in an electron at rest. That allows the proton to distort more readily than an electron in the same electric field and accounts for their differences in size and mass. “What we call mass would seem to be nothing but an appearance, and all inertia to be of electromagnetic origin.” – Henri Poincaré, Science and Method. A neutron combines the charges from a proton and an electron in a barely stable resonance, which decays in minutes. Its decay must have a cause and may involve an interaction with a neutrino. However, when combined with protons it seems neutrons form a new stable resonant structure that serves to bind the protons electrically despite the overall positive charge on the nucleus. The notion that matter can be annihilated when normal matter meets antimatter is a confusion of language. Matter can neither be destroyed nor created nor can matter be exchanged for energy. Einstein's E = mc2 refers to mass, a property of matter, not matter itself. The mathematical relationship represents the restructuring of resonant systems of charge. What seems to happen in "annihilation" is that the complementary resonant charge structures of a particle and its antiparticle combine so that almost all of the internal energy is radiated away and the combined charges form a new collapsed particle of low internal energy. The most collapsed form of matter is the neutrino, which has a vanishingly small mass. However, the neutrino must contain all of the charges required to form two particles – a particle and its antiparticle. This symmetry explains why a neutrino is considered to be its own anti-particle. A neutrino may accept energy from a gamma ray to reconstitute a particle and its anti-particle. "Empty space" is full of neutrinos. They are the repositories of matter in the universe, awaiting the burst of gamma-radiation to expand them to form the stuff of atoms. The weird "zoo" of short-lived particles created in particle accelerators and seen in cosmic rays are simply unstable resonant systems of charge. The equivalence of inertial and gravitational mass implies that gravity is also an electrical force. Before Einstein, some noted scientists were suggesting that the gravitational force between neutral particles might ultimately be due to electrical polarization within the particles. In 1882, Friedrich Zöllner wrote in the introduction to his book, Explanation of Universal Gravitation through the Static Action of Electricity and The General Importance of Weber's Laws, "…we are to conclude that a pair of electrical particles of opposite signs, i.e. two Weberian molecular pairs attract each other. This attraction is Gravity, it is proportional to the number of molecular pairs." Indeed, gravity can be represented as the sum of the radially aligned electric dipoles formed by all subatomic particles within a charged planet or star. This new electrical concept suggests that Newton's "universal constant of gravitation," or "G," is a dependent variable. G depends upon the charge distribution within a celestial body. Highly charged objects like comets look like solid rock, yet they have a gravitational field that suggests they are fluff-balls. And as they discharge they suffer what is euphemistically called "non-gravitational" accelerations. The extreme weakness of the force of gravity, compared to the electric force, is a measure of the minuscule electric dipolar distortion of nucleons. Gravity cannot be shielded by normal electrostatic shielding because all subatomic particles within the gravitational field respond to the dipolar distortion, whether they are metals or non-metals. What about magnetism? Ampere's law for the magnetic force between two current carrying wires is found to be equivalent to the transverse electric force caused by the distortion of electrons in an electric field. This distortion causes them to form tiny collinear electric dipoles. That is, the magnetic force is simply another manifestation of the electric force. This simple electrical model of matter has the great virtue of reducing all known forces to a single one – the electric force. However, it has a price. We must abandon our peculiar phobia against a force acting at a distance. And we must give up the notion that the speed of light is a real speed barrier. It may seem fast to us, but on a cosmic scale it is glacial. Imposing such a speed limit and requiring force to be transmitted by particles would render the universe completely incoherent. If an electron is composed of smaller subunits of charge orbiting within the classical radius of an electron, then the electric force must operate at a speed far in excess of the speed of light for the electron to remain a coherent object. In fact, it has been calculated that if released, the subunits of charge in the electron could travel from here to the far side of the Andromeda galaxy in one second! We have direct evidence of the superluminal action of the electric force, given that gravity is a longitudinal electric force. Indeed, Newton's celebrated equation requires that gravity act instantly on the scale of the solar system. It has been calculated that gravity must operate at a speed of at least 2x1010 times the speed of light, otherwise closely orbiting stars would experience a torque that would sling them apart in mere hundreds of years. Similarly, the Earth responds to the gravitational pull of the Sun where it is at the moment, not where the Sun was 8 minutes ago. If this were not so, the Earth and all other planets in the solar system would be slung into deep space within a few thousand years. Gravity is therefore an electrical property of matter, not a geometrical property of space... The implications for biological systems in this electrical model of matter are profound. A method of near-instantaneous signalling between resonant molecular structures within cells and on cell walls seems plausible and may provide a way of looking at the mind-body connection and other communications external to the body. It may provide a link between classical physics and the pioneering work of the biologist, Rupert Sheldrake, in biological morphogenesis and telepathy.
J. Parker
In reference to the Mathematics and origin of life article... "If H(p) is almost equal to "i" we stand in front of a poor quality and useless theory. In practice it does not tell us anything more that the input observation data tell us yet from the beginning." this was something that always bothered me about Darwinian evolution and its adjuncts (punctuated eqilibrium etc.) they always seemed to be little more than descriptions of data rather than a theory with any predictive power. For a quick, introductory read on emergence I'll plug Laughlin's book- A Different Universe: Reinventing Physics from the Bottom Down (2005, Pub. Basic Books) devilsadvocate
[...] In a blaze of ten posts per hour, I linked to an Uncommon Descent post on irreducible complexity in biology/physics, despite a warning signal in the back of my brain about the material. So here Evolutionblog comments on the article: Irreducible Complexity in Mathematics, Physics and Biology In his paper, Chaitin observes that, as important as Godel’s theorem is, it does not really tell us how serious a problem incompleteness is. In other words, Godel showed that there must be certain propositions that are true but unprovable. But to do this he had to conjure up a pretty bizarre, self-referential kind of statement. Not exactly the usual, humdrum kind of statements with which mathematicians generally concern themselves. The way mathematicians undertook their work was ultimately little affected by Godel’s discovery. It was possible for professional mathematicians to pretty much ignore what Godel did. [...] Darwiniana » IC in biology/physics: update
Salvador, Very interesting discussion again and enjoyed the last link. Besides an easy, accessible read and summary of Gödel, Turing, Chaitin, and Von Neumann's insights on biology, ProgettoCosmo reminded me of the great Italian seafood in Rimini, the wines of San Marino and walks along the mountains and coatal areas :) Good memories and Good science. Int Ping! Michaels7
Courtesy a good friend, here is an article that touches on Chaitin's work and IC in biology: Mathematics and the origin-of-life problem It may be important in enough I'll post a separate weblog. Salvador scordova
I wanted to post this thread because there are interesting developments in Math and Physics that are poised to shatter reductionism. Mechanical reductionism tends to favor Darwinism.... Even though I think one can argue successfully that the definitions of IC in math, physics, and biology are distinct, these definitions are unified in their rejection of reductionism. Darwinism relies heavily on some sort of reductionism. That complex problems can be incrementally reduced to smaller pieces. A classic illustration of this is the micro evolution of finch beaks on the Galapogos islands. Dry environments favored thicker beaks. The problem of getting a thicker beak could be incrementally reduced and decomposed into smaller pieces which gave feedback toward the optimal solution. IC systems are not so friendly to this reductionistic approach. Consider your computer passwords. Can a hacker, in general, get a sense he's getting closer to finding your password via a Darwinian pathway. No. All of the nearest attempted passwords (passowrds that are only one character off) are just as ineffective at logging in as the one that are farthest (attempted passwords many characters off). The bigger problem can't be reduced (or scaled) into self-similar smaller parts. That is the nature of IC. Passwords are a good illustration of IC. What if we find in biology, certain features that exploit IC phenomena in physics? There is no provable Darwinian pathway to that physical phenomena, since by definition, an IC phenomena in physics will not have a gradualistic pathway. That may be the case because the underlying math of physics has many IC phenomena as well (see the article above connecting emergent phenoma in physics to Godel's incompleteness). Thus, physics and Darwinism probably don't mix.... Have we found such IC systems in biology which use IC in physics? I don't think so, yet. But we might not recognize it unless we're actively looking for it. Hence, my suggestion to the informed readers at UD is to keep on the lookout. I espcially think we'll find a lot of IC richness in study of neuroscience. Mathematical physicist Roger Penrose seems to be of this opinion.... Biology might be teaching us where there are interesting IC phenomena in physics. We might not recognize these exploitable technologies if we are not actively looking for them too. We might actually learn physics by studying biology! And finally, if Chaitin is right about experimental math, biology might also clue us in on interesting areas of experimental math!!!! scordova
geoffrobinson: A mechanism for submitting stories would be great.
As a temporary solution, how about a thread at ARN maybe in their off topic forum???? Let's save further commentary on this idea for another 2 days, and then let's open discussion of this at the tail end. If it ends up being a substantial issue, I, or someone will open a thread on reader feedback. In the meantime, I have a few more comments... Sal scordova
If the base is random noise, why is everything up top so orderly? geoffrobinson
A mechanism for submitting stories would be great. geoffrobinson
"More is different," Philip W. Anderson Just as reductionism in physics doesn't seem to describe or accurately predict macro behavior. (The Heisenberg Uncertainty principle which is probably true at the quantum level would predict that lasers shouldn't lase, yet they do) So also reductionism in biology in no way predicts or explains life. Isn't the very foundation of IC buried right there in that concept? Latemarch
darth I did not find the Milan Journal of Mathematics in the ISI index of science journals. why not? You didn't find it because you're a lazy and not particularly bright troll who seldom if ever exercises any due diligence before writing. http://users.mat.unimi.it/users/smf/MJM.html It may not be listed in older indexes because for most of its 80 year history it was published under the name "Rendiconti". Or maybe you just can't read because it's right here under "M" in the ISI master journal list: http://scientific.thomson.com/isilinks/journals/m/ 1424-9286 MILAN JOURNAL OF MATHEMATICS Either way, you were warned and now you're out of here. DaveScot
I did not find the Milan Journal of Mathematics in the ISI index of science journals. why not? darth314
> If biological systems take advantage > of irreducible phenomena in physics > (for example, what if we discover > the brain uses irreducible physical > phenomena ) we will have a strong > proof by contradiction that there > are no Darwinian pathways for > biolgoical systems to incorporate > that phenomena. I don't see how that follows. Darwinian evolution says that organisms will evolve to utilise the physical environment they find themselves in. Whether that environment contains "irreducable phenomena" is irrelevant - it's equivalent to saying that animals which can't create crystals can't possibly metabolise salt. Phevans
TerryL - haha - too funny. Those darn math zealots! With their so called "calculus" books, protractors and bibles. Knocking on my doors asking me if I know algebra. Mathematics the new creationism lite. JGuy
Well, it's official! Mathematics is now a pseudoscience! You see? THIS is what's bad about creationist pretension! What's next? Oh, how Darwin must be rolling over in his grave! Er, if there WERE an afterlife, that is! TerryL
Before the existence of IC in mathematics, to say that “God plays dice in pure mathematics” may be misunderstanding. It would be better to say that in mathematics there are (apparently random) things that cannot be derived from laws simpler than themselves. But to say that means that such things are themselves laws. Instead to say that “God plays dice” may be understood as God is a passive testimony of dice throws and must accept their results. Of course this is a non sense because God is always active and moreover there aren’t “dices” external to God. What Chaitin calls “total lawlessness” in mathematics is therefore simply the existence of a-priori complex laws that seem random but that are very laws, wanted – as all things – by God. In other words, IC things in mathematics are to be considered as complex axioms that cannot be reduced to or derived from simpler rules. niwrad
[...] Irreducible Complexity in Mathematics, Physics and Biology [...] Darwiniana » Science and irreducible complexity
Let me add, I have a sneaking suspicion biology exploits emergent phenomena. If the next generation of novel discoveries in physics are not through reductionistic methods, then one source of discovering novel solid state principles is finding them when used in biology. Consider the hypothesis that the universe is optimized for scientific discovery. Why would we not extend that to the idea of life. There may be things about physics which we might not otherwise learn if we did not study life. This may seem radical, but that would seem a consistent extension of the Richards and Gonzalez notion of a Privileged Planet. scordova
Robo, Thank you for the info. I realize many visitors to our weblog would like to have certain topics discussed, and most times the only way I'm alerted is when readers simply post an idea and hope for the best. However, in the spirit of creating orderly discussion, if you can refrain from posting off topic ideas at least until the dicussion is beginning to wane, then that would be helpful. Some of the other authors might prefer otherwise, but if you post at the tail end, that's fine. Thanks, and good to hear from you. Sal scordova
OFF TOPIC... http://www.physorg.com/news89385584.html * Researchers at the University of Pennsylvania School of Medicine have discovered that microtubules -- components responsible for shape, movement, and replication within cells -- use proteins that act as molecular motors and brakes to organize into their correct structure. If microtubules are not formed properly such basic functions as cell division and transport can go wrong, which may have implications in such disease processes as cancer and dementia.* Robo

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