Category Archives: Mathematics

Evo-Info sidebar: Conservation of performance in search

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Introduction to Evolutionary Informatics, by Robert J. Marks II, the “Charles Darwin of Intelligent Design”; William A. Dembski, the “Isaac Newton of Information Theory”; and Winston Ewert, the “Charles Ingram of Active Information.” World Scientific, 332 pages.
Classification: Engineering mathematics. Engineering analysis. (TA347)
Subjects: Evolutionary computation. Information technology–Mathematics.

Denyse O’Leary, an advocacy journalist employed by one of the principals of the Center for Evolutionary Informatics, reports that I have essentially retracted the first of my papers on the “no free lunch” theorems for search (1996). What I actually have done in my online copy of the paper, marked “emended and amplified,” is to correct an expository error that Dembski and Marks elevated to “English’s Principle of Conservation of Information” in the first of their publications, “Conservation of Information in Search: Measuring the Cost of Success.” Marks, Dembski, and Ewert have responded, in their new book, by deleting me from the history of “no free lunch.” And the consequence is rather amusing. For now, when explaining conservation of information in terms of no free lunch, they refer over and over to performance.1 It doesn’t take a computer scientist, or even a rocket scientist, to see that they are describing conservation of performance, and calling it conservation of information.

The mathematical results of my paper are correct, though poorly argued. In fact, the theorem I provide is more general than the main theorem of Wolpert and Macready, which was published the following year.2 If you’re going to refer to one of the two theorems as the No Free Lunch Theorem, then it really should be mine. Where I go awry is in the exposition of my results. I mistake a lemma as indicating that conservation of performance in search is due ultimately to conservation of information in search.
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Evolution and Functional Information

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Here, one of my brilliant MD PhD students and I study one of the “information” arguments against evolution. What do you think of our study?

I recently put this preprint in biorxiv. To be clear, this study is not yet peer-reviewed, and I do not want anyone to miss this point. This is an “experiment” too. I’m curious to see if these types of studies are publishable. If they are, you might see more from me. Currently it is under review at a very good journal. So it might actually turn the corner and get out there. An a parallel question: do you think this type of work should be published?

 

I’m curious what the community thinks. I hope it is clear enough for non-experts to follow too. We went to great lengths to make the source code for the simulations available in an easy to read and annotated format. My hope is that a college level student could follow the details. And even if you can’t, you can weigh in on if the scientific community should publish this type of work.

Functional Information and Evolution

http://www.biorxiv.org/content/early/2017/03/06/114132

“Functional Information”—estimated from the mutual information of protein sequence alignments—has been proposed as a reliable way of estimating the number of proteins with a specified function and the consequent difficulty of evolving a new function. The fantastic rarity of functional proteins computed by this approach emboldens some to argue that evolution is impossible. Random searches, it seems, would have no hope of finding new functions. Here, we use simulations to demonstrate that sequence alignments are a poor estimate of functional information. The mutual information of sequence alignments fantastically underestimates of the true number of functional proteins. In addition to functional constraints, mutual information is also strongly influenced by a family’s history, mutational bias, and selection. Regardless, even if functional information could be reliably calculated, it tells us nothing about the difficulty of evolving new functions, because it does not estimate the distance between a new function and existing functions. Moreover, the pervasive observation of multifunctional proteins suggests that functions are actually very close to one another and abundant. Multifunctional proteins would be impossible if the FI argument against evolution were true.

Dice Entropy – A Programming Challenge

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Given the importance of information theory to some intelligent design arguments I thought it might be nice to have a toolkit of some basic functions related to the sorts of calculations associated with information theory, regardless of which side of the debate one is on.

What would those functions consist of?

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Thorp, Shannon: Inspiration for Alternative Perspectives on the ID vs. Naturalism Debate

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The writings and life work of Ed Thorp, professor at MIT, influenced many of my notions of ID (though Thorp and Shannon are not ID proponents). I happened upon a forgotten mathematical paper by Ed Thorp in 1961 in the Proceedings of the National Academy of Sciences that launched his stellar career into Wall Street. If the TSZ regulars are tired of talking and arguing ID, then I offer a link to Thorp’s landmark paper. That 1961 PNAS article consists of a mere three pages. It is terse, and almost shocking in its economy of words and straightforward English. The paper can be downloaded from:

A Favorable Strategy for Twenty One, Proceedings National Academy of Sciences.

Thorp was a colleague of Claude Shannon (founder of information theory, and inventor of the notion of “bit”) at MIT. Thorp managed to publish his theory about blackjack through the sponsorship of Shannon. He was able to scientifically prove his theories in the casinos and Wall Street and went on to make hundreds of millions of dollars through his scientific approach to estimating and profiting from expected value. Thorp was the central figure in the real life stories featured in the book
Fortune’s Formula: The Untold Story of the Scientific Betting System that Beat the Casino’s and Wall Street by William Poundstone.
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Wistar Day

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Koprowski and I, the only biologists present, were confronted by a rather weird discussion between four mathematicians – Eden, Schutzenberger, Weisskopf, and Ulam – on mathematical doubts concerning the Darwinian theory of evolution. At the end of several hours of heated debate, the biological contingent proposed that a symposium be arranged to consider the points of dispute more systematically, and with a more powerful array of biologists who could function adequately in the universe of discourse inhabited by mathematicians.

– Martin Kaplan

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A Beautiful Question

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I’ve just completed the book A Beautiful Question: Finding Nature’s Deep Design by Nobel Prize winning physicist Frank Wilczek.

This book is a long meditation on a single question:

Does the world embody beautiful ideas?

Our Question may seem like a strange thing to ask. Ideas are one thing, physical bodies are quite another. What does it mean to “embody” an “idea”?

Embodying ideas is what artists do. Starting from visionary conceptions, artists produce physical objects (or quasi-physical products, like musical scores that unfold into sound). Our Beautiful Question then is close to this one:

Is the world a work of art?

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Wright, Fisher, and the Weasel

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Richard Dawkins’s computer simulation algorithm explores how long it takes a 28-letter-long phrase to evolve to become the phrase “Methinks it is like a weasel”. The Weasel program has a single example of the phrase which produces a number of offspring, with each letter subject to mutation, where there are 27 possible letters, the 26 letters A-Z and a space. The offspring that is closest to that target replaces the single parent. The purpose of the program is to show that creationist orators who argue that evolutionary biology explains adaptations by “chance” are misleading their audiences. Pure random mutation without any selection would lead to a random sequence of 28-letter phrases. There are 27^{28} possible 28-letter phrases, so it should take about 10^{40} different phrases before we found the target. That is without arranging that the phrase that replaces the parent is the one closest to the target. Once that highly nonrandom condition is imposed, the number of generations to success drops dramatically, from 10^{40} to mere thousands.

Although Dawkins’s Weasel algorithm is a dramatic success at making clear the difference between pure “chance” and selection, it differs from standard evolutionary models. It has only one haploid adult in each generation, and since the offspring that is most fit is always chosen, the strength of selection is in effect infinite. How does this compare to the standard Wright-Fisher model of theoretical population genetics? Continue reading →

Philosophy and Complexity of Rube Goldberg Machines

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Michael Behe is best known for coining the phrase Irreducible Complexity, but I think his likening of biological systems to Rube Goldberg machines is a better way to frame the problem of evolving the black boxes and the other extravagances of the biological world.
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Chargaff Parity Rule 2, Biased/Non-Random Mutations

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There is an approximate 8% excess of Adenine and Thymine above random in the DNA of humans. This suggests mutational bias and/or non-random mutation. If 3 billion coins were found to be 58% heads vs. 42% tails, then the chance hypothesis of a random unbiased coin flip would be easily rejected. The odds of such an event happening are astronomical according to the binomial distribution.

But such an imbalance is reflected in the human genome where:
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The Reasonableness of Atheism and Black Swans

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As an ID proponent and creationist, the irony is that at the time in my life where I have the greatest level of faith in ID and creation, it is also the time in my life at some level I wish it were not true. I have concluded if the Christian God is the Intelligent Designer then he also makes the world a miserable place by design, that He has cursed this world because of Adam’s sin. See Malicious Intelligent Design.
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Math Genome Fun 2, UPB and beyond?

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This is a follow-on from the original “Math Genome Fun” thread here

I think it’s time to test out GAs on a bigger problem, the old one was at the boundary of home computation for an exhaustive search (OMD I said “search!” get on that Mung) – but I’m going to propose a *much* bigger search / smaller target.

Friends, you target is Pi

I’ve chosen Pi because of its qualities, being irrational and transcendental you cannot describe it in an equation, only approximate it.

Our target is the first 150 digits of Pi.

Our vocabulary is the same numbers and operators as before: [1,2,3,4,5,6,7,8,9,+,-,*,/], but this time they can all be used as often as required and the genome can be anywhere from 1 to 1000 characters in length.

The design approximation is now harder due to the decimal place and the absence of zeros in our vocabulary (but there’s quite a few in Pi).

I’ve done no computation on this myself, can a GA find that proverbial needle in a haystack?

 

Those Weasely IDCists!

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A couple recent comments here at TSZ by Patrick caught my eye.

First was the claim that arguments for the existence of God had been refuted.

I don’t agree that heaping a bunch of poor and refuted arguments together results in a strong argument.

here

Second was the claim that IDCists do not understand cumulative selection and Dawkins’ Weasel program.

The first time I think I was expecting more confusion on Ewert’s part about the power of cumulative selection (most IDCists still don’t understand Dawkin’s Weasel).

here

In this OP I’d like to concentrate on the second of these claims.

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The Myth of Biosemiotics

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I recently came across this book:

Biosemiotics: Information, Codes and Signs in Living Systems

This new book presents contexts and associations of the semiotic view in biology, by making a short review of the history of the trends and ideas of biosemiotics, or semiotic biology, in parallel with theoretical biology. Biosemiotics can be defined as the science of signs in living systems. A principal and distinctive characteristic of semiotic biology lies in the understanding that in living, entities do not interact like mechanical bodies, but rather as messages, the pieces of text. This means that the whole determinism is of another type.

Pardon my skepticism, but

  1. There is no information in living systems.
  2. There are no codes in living systems.
  3. There are no signs in living systems.

Biosemiotics is the study of things that just don’t exist. Theology for biologists.

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What A Code Is – Code Denialism Part 3

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My intent here in these recent posts on the genetic code has been to expose the absurdity of Code Denialism. The intent has not been to make the case for intelligent design based upon the existence of biological codes. I know some people find that disconcerting but that would be putting the cart before the horse. No one is going to accept a conclusion when they deny the premise. And please forgive me if I choose not to play the game of “let’s pretend it really is a code” while you continue to deny that it actually is a code.

First I’d like to thank you. It’s actually been pretty neat looking up and reading many of these resources in my attempt to see whether I could defend the thesis that the genetic code is a real code. I admit it’s also been much too much fun digging up all the reasons why code denialism is just plain silly (and irrational).

That the genetic code is a code is common usage and if “meaning is use” that alone ought to settle the matter. But this is “The Skeptical Zone” and Code Denialism is strong here. But I’m not just claiming that it’s a code because we say it’s a code in common usage. I’m claiming it is a code because it meets the definition of a code. The reason we say it is a code is because it is in fact a code.

My first two posts have been on some of the major players and how they understood they were dealing with a code and how that guided their research. I’ll have more to say on that in the future as it’s a fascinating story. But for now …

What A Code Is

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Dictionary halting problem makes A=A fallible

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It would seem superficially this is correct

A=A, necessarily and infallibly true

but it is false for non-trivial A and where the EQUAL SIGN means equal in essence, not just equal in description. This is a consequence of the dictionary and halting problem that has been well demonstrated by first rate mathematical logicians and computer scientists (like Alonzo Church who was a devout Christian) who actually work with formal languages vs. people clinging to antiquated and non-rigorous theological notions.
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What is obvious to Granville Sewell

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Granville Sewell, who needs no introduction here, is at it again. In a post at Uncommon Descent he imagines a case where a mathematician finds that looking at his problem from a different angle shows that his theorem must be wrong. Then he imagines talking to a biologist who thinks that an Intelligent Design argument is wrong. He then says to the biologist:

“So you believe that four fundamental, unintelligent forces of physics alone can rearrange the fundamental particles of physics into Apple iPhones and nuclear power plants?” I asked. “Well, I guess so, what’s your point?” he replied. “When you look at things from that point of view, it’s pretty obvious there must be an error somewhere in your theory, don’t you think?” I said.

As he usually does, Sewell seems to have forgotten to turn comments on for his post at UD. Is it “obvious” that life cannot originate? That it cannot evolve descendants, some of which are intelligent? That these descendants cannot then build Apple iPhones and nuclear power plants?

As long as we’re talking about whether some things are self-evident, we can also discuss whether this is “pretty obvious”. Discuss it here, if not at UD. Sewell is of course welcome to join in.

A question for Winston Ewert

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Added June 17, 2015: Jump in with whatever comments you like, folks. Dr. Ewert has responded nebulously at Uncommon Descent. I’d have worked with him to get his meaning straight. I’m not going to spend my time on deconstruction. However, I will take quick shots at some easy targets, mainly to show appreciation to Lizzie for featuring this post as long as she has. Here, again, is what I put to Dr. Ewert:

Your “search” process decides when to stop and produce an outcome in the “search space.” A model may do this, but biological evolution does not. How do you measure active information on the biological process itself? Do you not reify a model?

Dr. Ewert seemingly forgets that to measure active information on a biological process is to produce a specific quantity, e.g., 109 bits.

One approach is to take the search space not to be the individual organisms, but rather the entire population of organisms currently alive on earth. Or one could go further, and take it to be the history of organisms during the whole of biological evolution. One could also take it to be possible spacetime histories. The target can then be taken to be spacetimes, histories, or populations that contain an individual organism type such as birds.

These “search spaces” roll off the tongue. But no one knows, or ever will know, what they actually contain. Even if we did know, no one would know the probabilities required for calculation of the active information for a given target. And even if we did know the probability of a given “target” for a given “search,” we would not be able to justify designating a particular probability distribution on the search space as the “natural” baseline. By the way, Dr. Ewert should not be alluding to infinite sets, as his current model of search applies only to finite sets.

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