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# Gregory Chaitin on true randomness

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How would Darwinism fare according to his attempt to define true randomness via algorithmic information theory?

Chaitin (right) found that concepts from computer programming worked well because, if the data is not random, the program should be smaller than the data:

Gregory Chaitin: I didn’t like that definition so I wanted a definition of lack of structure. You see, with the normal coin tosses, actually every possible finite sequence of heads and tails in a sense is equally random, because they were all generated by tossing a fair coin. But some of them, all heads has a lot of structure, all tails have a lot of structure, alternating heads and tails have a lot of structure. I was looking at something that ignored how the sequence is generated and just looked at it and said, is there structure here or isn’t there?

Now, the reason for doing this is because you can think of a physical theory to explain a phenomenon as a program — software that can calculate the predictions. If the program is short, then you have a very comprehensible theory and a lot of structure. But if the program is the same size in bits as the number of bits of experimental data, then that’s not much of an explanation. It’s not much of a theory because there always is a program the same size in bits as the bits of data.

Why? Because it just puts the data into the program directly and prints it out. That can always be done. But the smaller the program is, compared in size in bits to the number of bits of data that you’re trying to explain — and I’m talking about an explanation that gives no noise — it’s not a statistical theory. It has to give every bit of the data correctly. If that’s a small program, then you have a good theory. If you have two theories and one of them is a smaller program than the other, the smaller program is a better theory if the two of them calculate the exact sequence of your experimental data. It’s sort of a model of the scientific method.

News, “Chaitin’s discovery of a way of describing true randomness” at Mind Matters News

Darwinism seems so full of exceptions now that it would be a very long program indeed.

Here are the stories, with links, to the earlier podcast discussion with Gregory Chaitin last week:

Gregory Chaitin’s “almost” meeting with Kurt Gödel. This hard-to-find anecdote gives some sense of the encouraging but eccentric math genius. Chaitin recalls, based on this and other episodes, “There was a surreal quality to Gödel and to communicating with Gödel.”

Gregory Chaitin on the great mathematicians, East and West: Himself a “game-changer” in mathematics, Chaitin muses on what made the great thinkers stand out. Chaitin discusses the almost supernatural awareness some mathematicians have had of the foundations of our shared reality in the mathematics of the universe.

and

How Kurt Gödel destroyed a popular form of atheism. We don’t hear much about logical positivism now but it was very fashionable in the early twentieth century. Gödel’s incompleteness theorems showed that we cannot devise a complete set of axioms that accounts for all of reality — bad news for positivist atheism.

You may also wish to read: Things exist that are unknowable: A tutorial on Chaitin’s number (Robert J. Marks)

and

Five surprising facts about famous scientists we bet you never knew: How about juggling, riding a unicycle, and playing bongo? Or catching criminals or cracking safes? Or believing devoutly in God… (Robert J. Marks)

Perhaps the the most clear example of how the Christian founders of modern science themselves viewed any mathematics that might describe this universe is the following quote that Kepler made shortly after he discovered the laws of planetary motion,
"O, Almighty God, I am thinking Thy thoughts after Thee!" - Johannes Kepler - In book five of The Harmonies of the World (1619)
And it is not as if Kepler's belief is some antiquated and superstitious belief that is left over from medieval Christian Europe. Eugene Wigner, (who's insights into quantum mechanics continue to drive breakthroughs in quantum mechanics; A. Zeilinger), and Albert Einstein, who formulated General Relativity, are both on record as to regarding it as a 'miracle' that mathematics should even be applicable to the universe in the first place.
The Unreasonable Effectiveness of Mathematics in the Natural Sciences - Eugene Wigner - 1960 ?Excerpt: ,,certainly it is hard to believe that our reasoning power was brought, by Darwin's process of natural selection, to the perfection which it seems to possess.,,,?It is difficult to avoid the impression that a miracle confronts us here, quite comparable in its striking nature to the miracle that the human mind can string a thousand arguments together without getting itself into contradictions, or to the two miracles of the existence of laws of nature and of the human mind's capacity to divine them.,,,?The miracle of the appropriateness of the language of mathematics for the formulation of the laws of physics is a wonderful gift which we neither understand nor deserve. We should be grateful for it and hope that it will remain valid in future research and that it will extend, for better or for worse, to our pleasure, even though perhaps also to our bafflement, to wide branches of learning. ?http://www.dartmouth.edu/~matc/MathDrama/reading/Wigner.html On the Rational Order of the World: a Letter to Maurice Solovine – Albert Einstein – March 30, 1952 Excerpt: “You find it strange that I consider the comprehensibility of the world (to the extent that we are authorized to speak of such a comprehensibility) as a miracle or as an eternal mystery. Well, a priori, one should expect a chaotic world, which cannot be grasped by the mind in any way .. the kind of order created by Newton’s theory of gravitation, for example, is wholly different. Even if a man proposes the axioms of the theory, the success of such a project presupposes a high degree of ordering of the objective world, and this could not be expected a priori. That is the ‘miracle’ which is constantly reinforced as our knowledge expands. There lies the weakness of positivists and professional atheists who are elated because they feel that they have not only successfully rid the world of gods but “bared the miracles.” -Albert Einstein http://inters.org/Einstein-Letter-Solovine
Moreover, although atheists have been, basically, fruitlessly banging their heads on the wall for several decades trying to find a single overarching mathematical 'theory of everything' that will successfully unify Quantum Mechanics with General Relativity, on the other hand, Christians, (who believe that any mathematics that might describe this universe are the product of God's thoughts), find a ready solution for the much sought after 'theory of everything. Namely, allowing the Agent causality of God ‘back’ into physics, as the Christian founders of modern science originally envisioned,,,, (Isaac Newton, Michael Faraday, James Clerk Maxwell, and Max Planck, to name a few of the Christian founders),,, and as quantum mechanics itself now empirically demands (with the closing of the free will loophole by Anton Zeilinger and company), rightly allowing the Agent causality of God ‘back’ into physics provides us with a very plausible resolution for the much sought after ‘theory of everything’ in that Christ’s resurrection from the dead provides an empirically backed reconciliation, via the Shroud of Turin, between quantum mechanics and general relativity into the much sought after ‘Theory of Everything”. Here is a video where I defend my claim that Jesus Christ's resurrection from the dead provides a much better resolution to the 'theory of everything' than string theory does.
Jesus Christ as the correct "Theory of Everything" - video https://youtu.be/Vpn2Vu8--eE
When I first presented the preceding video on UD in January, one commenter called the video 'borderline retarded'. I asked him for his specific reasons for thinking that. He gave no reasons. He just offered his personal opinion with no explanation as to why he thought so. Regardless of his personal opinion for which he offered no defense, IMHO, Jesus Christ's resurrection from the dead 'fits just a little too perfectly' with the scientific evidence and is indeed the correct solution for the much sought after 'theory of everything'. I can simply find no holes in this Christian 'theory of everything' that would render it untenable as a viable scientific theory theory and, indeed, I find much that renders the 'Christian theory' very plausible as the being the correct 'theory of everything' Verse:
Colossians 1:15-20 The Son is the image of the invisible God, the firstborn over all creation. For in him all things were created: things in heaven and on earth, visible and invisible, whether thrones or powers or rulers or authorities; all things have been created through him and for him. He is before all things, and in him all things hold together. And he is the head of the body, the church; he is the beginning and the firstborn from among the dead, so that in everything he might have the supremacy. For God was pleased to have all his fullness dwell in him, and through him to reconcile to himself all things, whether things on earth or things in heaven, by making peace through his blood, shed on the cross.
Of supplemental note:
January 2021 Whereas atheists have no observational evidence that the Multiverses that they postulated to ‘explain. away’ the fine tuning of the universe are real, nor do Atheists have any evidence that the ‘parallel universes’ that they postulated to ‘explain away’ quantum wave collapse are real, Christians, on the other hand, can appeal directly to Special Relativity, General Relativity, and Quantum Mechanics, (i.e. our most precisely tested theories ever in the history of science), to support their belief that God really does uphold this universe in its continual existence, as well as to support their belief in the reality of a heavenly dimension and in a hellish dimension.” https://uncommondescent.com/intelligent-design/closer-to-truth-are-there-really-extra-dimensions/#comment-722947
In further note, and in regards to the infinite mathematical divide that exists between General Relativity and Quantum mechanics, here is an interesting quote that just came to mind,
“Einstein’s equation predicts that, as the astronaut reaches the singularity (of the black-hole), the tidal forces grow infinitely strong, and their chaotic oscillations become infinitely rapid. The astronaut dies and the atoms which his body is made become infinitely and chaotically distorted and mixed-and then, at the moment when everything becomes infinite (the tidal strengths, the oscillation frequencies, the distortions, and the mixing), spacetime ceases to exist.” Kip S. Thorne – “Black Holes and Time Warps: Einstein’s Outrageous Legacy” pg. 476
i.e. Black Holes are found to be ‘timeless’ singularities of destruction and disorder rather than singularities of creation and order, such as the extreme order we see at the creation event of the Big Bang. Needless to say, the implications of this ‘eternity of destruction’ should be fairly disturbing for those of us who are of the ‘spiritually minded’ persuasion! Luke 16: 24-26
So he cried out, ‘Father Abraham, have mercy on me and send Lazarus to dip the tip of his finger in water and cool my tongue. For I am in agony in this fire.’ But Abraham answered, ‘Child, remember that during your lifetime you received your good things, while Lazarus received bad things. But now he is comforted here, while you are in agony. And besides all this, a great chasm has been fixed between us and you, so that even those who wish cannot cross from here to you, nor can anyone cross from there to us.’
bornagain77
March 14, 2021
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Querius, thanks for drawing attention to Seversky statement. I missed it the first time. Here is Seversky's full statement in context.
If anything, Godel’s incompleteness theorem could arguably apply something like the Christian concept of God. If we cannot devise a complete set of axioms that accounts for all reality then that must include the reality of God which is bad news for Christianity.
First off, it is interesting to note that, as a Darwinist, Seversky himself simply does not believe in 'bad news' for his own theory. As Dr.Cornelius Hunter noted, "Being an evolutionist means there is no bad news",,,
"Being an evolutionist means there is no bad news. If new species appear abruptly in the fossil record, that just means evolution operates in spurts. If species then persist for eons with little modification, that just means evolution takes long breaks. If clever mechanisms are discovered in biology, that just means evolution is smarter than we imagined. If strikingly similar designs are found in distant species, that just means evolution repeats itself. If significant differences are found in allied species, that just means evolution sometimes introduces new designs rapidly. If no likely mechanism can be found for the large-scale change evolution requires, that just means evolution is mysterious. If adaptation responds to environmental signals, that just means evolution has more foresight than was thought. If major predictions of evolution are found to be false, that just means evolution is more complex than we thought." ~ Cornelius Hunter
It might greatly behoove Seversky to first be able to recognize what is 'bad news' for his own theory before he decides what might, or might not, be 'bad news' for Christianity. Secondly, Godel's incompleteness can be succinctly stated as such, “Anything you can draw a circle around cannot explain itself without referring to something outside the circle—something you have to assume but cannot prove”.
Gödel's incompleteness theorem (1931), proves that there are limits to what can be ascertained by mathematics. Kurt Gödel halted the achievement of a unifying all-encompassing theory of everything in his theorem that: “Anything you can draw a circle around cannot explain itself without referring to something outside the circle—something you have to assume but cannot prove”. Stephen Hawking & Leonard Miodinow, The Grand Design (2010)
Thus, despite whatever Seversky tries to believe in his fevered imagination, Godel's incompleteness is certainly NOT 'bad news' for God and/or Christianity, but is instead VERY 'bad news' towards those who would try to dispense with God in their mathematical descriptions of the universe.
THE GOD OF THE MATHEMATICIANS - DAVID P. GOLDMAN - August 2010 Excerpt: we cannot construct an ontology that makes God dispensable. Secularists can dismiss this as a mere exercise within predefined rules of the game of mathematical logic, but that is sour grapes, for it was the secular side that hoped to substitute logic for God in the first place. Gödel's critique of the continuum hypothesis has the same implication as his incompleteness theorems: Mathematics never will create the sort of closed system that sorts reality into neat boxes. http://www.firstthings.com/article/2010/08/the-god-of-the-mathematicians
Thirdly, in regards to Seversky's comment on, "a complete set of axioms that accounts for all reality". Axioms are a matter of choice, and are therefore, necessarily, the product of the free will of an immaterial mind. In fact, as Douglas S. Robertson stated, "the famous “Turing test” for artificial intelligence could be defeated by simply asking for a new axiom in mathematics. Human mathematicians are able to create axioms, but a computer program cannot do this without violating information conservation. Creating new axioms and free will are shown to be different aspects of the same phenomena: the creation of new information."
Algorithmic Information Theory, Free Will and the Turing Test - Douglas S. Robertson? Excerpt: Chaitin’s Algorithmic Information Theory shows that information is conserved under formal mathematical operations and, equivalently, under computer operations. This conservation law puts a new perspective on many familiar problems related to artificial intelligence. For example, the famous “Turing test” for artificial intelligence could be defeated by simply asking for a new axiom in mathematics. Human mathematicians are able to create axioms, but a computer program cannot do this without violating information conservation. Creating new axioms and free will are shown to be different aspects of the same phenomena: the creation of new information.?http://cires.colorado.edu/~doug/philosophy/info8.pdf?
Moreover, as Gregory Chaitin himself has shown, "an infinite number of true mathematical theorems exist that cannot be proved from any finite system of axioms."
The Limits Of Reason – Gregory Chaitin – 2006 Excerpt: Unlike Gödel’s approach, mine is based on measuring information and showing that some mathematical facts cannot be compressed into a theory because they are too complicated. This new approach suggests that what Gödel discovered was just the tip of the iceberg: an infinite number of true mathematical theorems exist that cannot be proved from any finite system of axioms. http://www.umcs.maine.edu/~chaitin/sciamer3.pdf
Having an infinite set of mathematical theorems that cannot be derived from a finite system of axioms presents an irresolvable dilemma for atheists. As Steven Weinberg, who is an atheist himself, succinctly noted, "I don't think one should underestimate the fix we are in. That in the end we will not be able to explain the world. That we will have some set of laws of nature (that) we will not be able to derive them on the grounds simply of mathematical consistency. Because we can already think of mathematically consistent laws that don't describe the world as we know it. And we will always be left with a question 'why are the laws nature what they are rather than some other laws?'. And I don't see any way out of that."
"I don't think one should underestimate the fix we are in. That in the end we will not be able to explain the world. That we will have some set of laws of nature (that) we will not be able to derive them on the grounds simply of mathematical consistency. Because we can already think of mathematically consistent laws that don't describe the world as we know it. And we will always be left with a question 'why are the laws nature what they are rather than some other laws?'. And I don't see any way out of that. The fact that the constants of nature are suitable for life, which is clearly true, we observe,,," (Weinberg then comments on the multiverse conjecture of atheists) "No one has constructed a theory in which that is true. I mean,, the (multiverse) theory would be speculative, but we don't even have a theory in which that speculation is mathematically realized. But it is a possibility." Steven Weinberg – as stated to Richard Dawkins at the 8:15 minute mark of the following video Leonard Susskind – Richard Dawkins and Steven Weinberg – 1 in 10^120 Cosmological Constant points to intelligent design – video https://youtu.be/z4E_bT4ecgk?t=495
On the other hand, for the Christian this in no problem at all. As Dr. Bruce Gordon noted, "the transcendent reality on which our universe depends must be something that can exhibit agency – a mind that can choose among the infinite variety of mathematical descriptions and bring into existence a reality that corresponds to a consistent subset of them."
BRUCE GORDON: Hawking’s irrational arguments – October 2010 Excerpt: ,,,The physical universe is causally incomplete and therefore neither self-originating nor self-sustaining. The world of space, time, matter and energy is dependent on a reality that transcends space, time, matter and energy. This transcendent reality cannot merely be a Platonic realm of mathematical descriptions, for such things are causally inert abstract entities that do not affect the material world,,,?Rather, the transcendent reality on which our universe depends must be something that can exhibit agency – a mind that can choose among the infinite variety of mathematical descriptions and bring into existence a reality that corresponds to a consistent subset of them. This is what “breathes fire into the equations and makes a universe for them to describe.” Anything else invokes random miracles as an explanatory principle and spells the end of scientific rationality. http://www.washingtontimes.com/news/2010/oct/1/hawking-irrational-arguments/
Moreover, for atheists to presuppose that the universe is a necessary form of existence that is based on some mathematical 'finite system of axioms', rather than the universe being a contingent form of existence that is dependent upon there Mind of God, is for them, philosophically speaking, to take a major step backwards. It is precisely this necessitarian view of the universe that present day physicists presuppose in their quest for a purely mathematical 'theory of everything' that prevented the rise of modern science in the Ancient Greek cultures in the first place. As the following article notes, it was only with the quote/unquote "outlawing the deterministic and necessitarian views of creation" that modern science was finally able to gain a foothold and eventually flourish in medieval Christian Europe. As the following article goes on to note, modern science was born out of the belief that this universe is, "contingent in its nature and so God was free to create this particular form of world among an infinity of other possibilities. Thus the cosmos cannot be a necessary form of existence; and so it has to be approached by a posteriori investigation."
The War against the War Between Science and Faith Revisited - July 2010 Excerpt: … If science suffered only stillbirths in ancient cultures, how did it come to its unique viable birth? The beginning of science as a fully fledged enterprise took place in relation to two important definitions of the Magisterium of the Church. The first was the definition at the Fourth Lateran Council in the year 1215, that the universe was created out of nothing at the beginning of time. The second magisterial statement was at the local level, enunciated by Bishop Stephen Tempier of Paris who, on March 7, 1277, condemned 219 Aristotelian propositions, so outlawing the deterministic and necessitarian views of creation. These statements of the teaching authority of the Church expressed an atmosphere in which faith in God had penetrated the medieval culture and given rise to philosophical consequences. The cosmos was seen as contingent in its existence and thus dependent on a divine choice which called it into being; the universe is also contingent in its nature and so God was free to create this particular form of world among an infinity of other possibilities. Thus the cosmos cannot be a necessary form of existence; and so it has to be approached by a posteriori investigation. The universe is also rational and so a coherent discourse can be made about it. Indeed the contingency and rationality of the cosmos are like two pillars supporting the Christian vision of the cosmos.?http://www.scifiwright.com/2010/08/the-war-against-the-war-between-science-and-faith-revisited/
It is also interesting to note that long before Godel's incompleteness came along, the Christian founders of modern science also correctly held that mathematics, especially any mathematics that might describe this universe, were the 'thoughts of God' and that mathematics is not a 'rival to God' as present day physicists are prone to believe. As Paul Davies noted, "Christians envisage God as upholding the natural order from beyond the universe, while physicists think of their laws as inhabiting an abstract transcendent realm of perfect mathematical relationships."
Taking Science on Faith – By PAUL DAVIES – NOV. 24, 2007 Excerpt: All science proceeds on the assumption that nature is ordered in a rational and intelligible way. You couldn’t be a scientist if you thought the universe was a meaningless jumble of odds and ends haphazardly juxtaposed. ,,, the very notion of physical law is a theological one in the first place, a fact that makes many scientists squirm. Isaac Newton first got the idea of absolute, universal, perfect, immutable laws from the Christian doctrine that God created the world and ordered it in a rational way. Christians envisage God as upholding the natural order from beyond the universe, while physicists think of their laws as inhabiting an abstract transcendent realm of perfect mathematical relationships. http://www.nytimes.com/2007/11/24/opinion/24davies.html
And as Edward Feser noted, Mathematical truths exhibit infinity, necessity, eternity, immutability, perfection, and immateriality because they are God’s thoughts, and they have such explanatory power in scientific theorizing because they are part of the blueprint implemented by God in creating the world. For some thinkers in this tradition, mathematics thus provides the starting point for an argument for the existence of God qua supreme intellect. There is also a very different answer, in which the mathematical realm is a rival to God rather than a path to him. According to this view, mathematical objects such as numbers and geometrical figures exist not only independently of the ­material world, but also independently of any mind, including the divine mind.,,,"
KEEP IT SIMPLE - by Edward Feser - April 2020 Excerpt: Mathematics appears to describe a realm of entities with quasi-­divine attributes. The series of natural numbers is infinite. That one and one equal two and two and two equal four could not have been otherwise. Such mathematical truths never begin being true or cease being true; they hold eternally and immutably. The lines, planes, and figures studied by the geometer have a kind of perfection that the objects of our ­experience lack. Mathematical objects seem immaterial and known by pure reason rather than through the senses. Given the centrality of mathematics to scientific explanation, it seems in some way to be a cause of the natural world and its order. How can the mathematical realm be so apparently godlike? The traditional answer, originating in Neoplatonic philosophy and Augustinian theology, is that our knowledge of the mathematical realm is precisely knowledge, albeit inchoate, of the divine mind. Mathematical truths exhibit infinity, necessity, eternity, immutability, perfection, and immateriality because they are God’s thoughts, and they have such explanatory power in scientific theorizing because they are part of the blueprint implemented by God in creating the world. For some thinkers in this tradition, mathematics thus provides the starting point for an argument for the existence of God qua supreme intellect. There is also a very different answer, in which the mathematical realm is a rival to God rather than a path to him. According to this view, mathematical objects such as numbers and geometrical figures exist not only independently of the ­material world, but also independently of any mind, including the divine mind. They occupy a “third realm” of their own, the realm famously described in Plato’s Theory of Forms. God used this third realm as a blueprint when creating the physical world, but he did not create the realm itself and it exists outside of him. This position is usually called Platonism since it is commonly thought to have been ­Plato’s own view, as distinct from that of his Neoplatonic followers who relocated mathematical objects and other Forms into the divine mind. (I put to one side for present purposes the question of how historically accurate this standard narrative is.) https://www.firstthings.com/article/2020/04/keep-it-simple
bornagain77
March 14, 2021
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If we cannot devise a complete set of axioms that accounts for all reality then that must include the reality of God which is bad news for Christianity.
Has this been done? If it hasn't, then science currently must support the paradigm of an intelligent designer. To find evidence that the universe wasn't created, then scientists must demonstrate how space-time, mass-energy, the laws of physics (including gravity), the physical constants, and possibly dark energy and dark matter emerges out of Nothing. Pleading a hypothetical multiverse doesn't help, because that also needs to emerge from Nothing. Some people suggest that "Multiverse" is the name that atheists use for God. Pleading infinite space-time doesn't help either because it results in more problems and paradoxes than it solves including infinite red shift and infinite entropy. -QQuerius
March 13, 2021
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> If we cannot devise a complete set of axioms that accounts for all reality then that must include the reality of God which is bad news for Christianity. An interesting line of thought. If we could not devise a set that accounts for all reality, then A) Perhaps reality is not such that any fixed, finite axiom set could describe/predict it; B) Perhaps God's reality is not among the aspects that can be axiomatically described; C) Perhaps God's reality lies in the "incomplete" part of Godel. I'm not seeing a clincher argument against God here.EDTA
March 13, 2021
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Nothing really new about parsimony, even when measured as bits. There are a couple of wild cards in this realm. 1. A fair coin, or a Zener noise source, will always produce noticeable stretches of patterns. If you want to apply random stimuli to a human for perception testing, or use random to control a gradual process of approximation, you need to filter out those patterns. You need to load the coin so it looks more random. The patterns will pull the brain in the direction of the pattern, which pulls away from the desired end approximation. 2. The simplest formula (least bits) usually isn't the best solution for a real engineering problem. The real solution is often an unsolvable analog interaction of all the pieces of the machine or the sections of concrete or the zones of soil. The simplest way to solve this is with a true analog computer (unmeasurable in bits), but highly complex software can reach usable approximations.polistra
March 13, 2021
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As to:
,,, "you can think of a physical theory to explain a phenomenon as a program — software that can calculate the predictions. If the program is short, then you have a very comprehensible theory and a lot of structure. But if the program is the same size in bits as the number of bits of experimental data, then that’s not much of an explanation. It’s not much of a theory because there always is a program the same size in bits as the bits of data."
And as to:
"Darwinism seems so full of exceptions now that it would be a very long program indeed."
Well actually, one of the main and primary reasons why Darwinian evolution would be a very long program is due to 'conservation of information'. As Dembski, Marks, (and Ewert, etc..) have established, no evolutionary algorithm will ever successfully find information unless that information for a successful search is already programmed into the computer program.
Main Publications - Evolutionary Informatics http://evoinfo.org/publications/ Here is the search for a search paper: The Search for a Search: Measuring the Information Cost of Higher Level Search William A. Dembski and Robert J. Marks II Abstract: Needle-in-the-haystack problems look for small targets in large spaces. In such cases, blind search stands no hope of success. Conservation of information dictates any search technique will work, on average, as well as blind search. Success requires an assisted search. But whence the assistance required for a search to be successful? To pose the question this way suggests that successful searches do not emerge spontaneously but need themselves to be discovered via a search. The question then naturally arises whether such a higher-level “search for a search” is any easier than the original search. We prove two results: (1) The Horizontal No Free Lunch Theorem, which shows that average relative performance of searches never exceeds unassisted or blind searches, and (2) The Vertical No Free Lunch Theorem, which shows that the difficulty of searching for a successful search increases exponentially with respect to the minimum allowable active information being sought. http://evoinfo.org/publications/search-for-a-search/
And as Dr. Marks commented in the following article, "Those hoping to establish Darwinian evolution as a hard science with a model have either failed or inadvertently cheated. These models contain guidance mechanisms to land the airplane squarely on the target runway despite stochastic wind gusts. Not only can the guiding assistance be specifically identified in each proposed evolution model, its contribution to the success can be measured, in bits, as active information.,,,”,
Top Ten Questions and Objections to ‘Introduction to Evolutionary Informatics’ – Robert J. Marks II – June 12, 2017 Excerpt: “There exists no model successfully describing undirected Darwinian evolution. Hard sciences are built on foundations of mathematics or definitive simulations. Examples include electromagnetics, Newtonian mechanics, geophysics, relativity, thermodynamics, quantum mechanics, optics, and many areas in biology. Those hoping to establish Darwinian evolution as a hard science with a model have either failed or inadvertently cheated. These models contain guidance mechanisms to land the airplane squarely on the target runway despite stochastic wind gusts. Not only can the guiding assistance be specifically identified in each proposed evolution model, its contribution to the success can be measured, in bits, as active information.,,,”,,, “there exists no model successfully describing undirected Darwinian evolution. According to our current understanding, there never will be.,,,” https://evolutionnews.org/2017/06/top-ten-questions-and-objections-to-introduction-to-evolutionary-informatics/
And, due to 'Conservation of Information', the amount of preexisting information in the computer program that is necessary to find a target in an evolutionary algorithm is always equal to, or greater than, the information that is generated by the evolutionary algorithm. In short, there is no computer algorithm that will ever generate the complete works of Shakespeare unless that computer algorithm already has the complete works of Shakespeare programmed within itself. i.e. the evolutionary algorithm will always be the same, or greater, size as the 'experimental data' that needs to be explained. And therefore, via Chaitin, Darwinism is "not much of an explanation",,, (i.e. not much of a scientific theory),,,
if the program is the same size in bits as the number of bits of experimental data, then that’s not much of an explanation. It’s not much of a theory because there always is a program the same size in bits as the bits of data."
bornagain77
March 13, 2021
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It sounds like Chaitin is talking about something very similar to data compression theory. For the most efficient compression routine, the amount of information is equal to the data compressed plus the compression routine itself. For highly structured data, there is a ton of compression so the overall size is small. For highly random data the amount of compressed data plus compression routine can be greater than just the size of the random data itself. Not an exact corollary I know, but related I think.drc466
March 13, 2021
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Seversky: A Darwinist is someone who, once everything is boiled down to the very basics, denies intelligence had any involvement in the creation of the universe and beyond. Did the laws of physics happen randomly or is their intelligence that led to their creation? If the laws are random, how did energy come about, since it cannot be created or destroyed? Darwinists cannot accept that any intelligence exists anywhere in the universe, which is very unlike what Einstein believed. Einstein did not humanize God, but believed God to be the most logical explanation for the order he saw in the universe.BobRyan
March 12, 2021
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Darwinism seems so full of exceptions now that it would be a very long program indeed.Darwinism seems so full of exceptions now that it would be a very long program indeed.
"Darwinism", as used on this site, seems to be a label for a grab bag of metaphysical or epistemological or theological ideas, concepts or "worldviews" that the opponent finds objectionable in some way. This seems to include a panadaptationist position on the theory of evolution or, indeed, any interpretation which is regarded as undermining the need to posit a "Creator" or naturalism/materialism/atheism/agnosticism/socialism/communism/progressivism or any combination thereof. More specifically, "random" refers to the position that mutations in the genome, while caused, do not appear to be directed towards enhancing the survival prospects of the animal in which they occur. They are random only in that respect. Godel did not destroy atheism or logical positivism. Atheism is the position of a lack of belief on the existence of gods and the logical positivist program was regarded as being fatally undermined by self-contradictions of which both the positivists and their critics became aware. If anything, Godel's incompleteness theorem could arguably apply something like the Christian concept of God. If we cannot devise a complete set of axioms that accounts for all reality then that must include the reality of God which is bad news for Christianity.
Five surprising facts about famous scientists we bet you never knew: How about juggling, riding a unicycle, and playing bongo? Or catching criminals or cracking safes? Or believing devoutly in God… (Robert J. Marks)
Why should we find that surprising? Why shouldn't scientists display the same range of idiosyncratic behaviors as any other population of human beings like mathematicians or Christians?Seversky
March 12, 2021
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