Mathematically Defining Functional Information In Biology

_{January 28, 2009

Intelligent Design}

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Lecture by Kirk Durston, Biophysics PhD candidate, University of Guelph

[youtube XWi9TMwPthE nolink]

Click here to read the Szostak paper referred to in the video.

HT to UD subscriber bornagain77 for the video and the link to the paper.

Comments

So professor , did you also learn that winning two 1000 to 1 lotteries is the same odds as winning 1 million to one lottery, thus Gils rightful stress that the odds get far worse! Please Tell me you aren't deliberately being deceptive (then again if you were deliberate would you tell me?), for my respect for you is plummeting the longer I see your misleading debating style. Slightly off topic video I just loaded: A Few Hundred Thousand Computers vs. A Single Protein Molecule http://www.youtube.com/watch?v=G-6mVr6vJJQbornagain77_{January 29, 2009
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GilDodgen[47], I learned last week that 1000 times 1000 equals a million.Prof_P.Olofsson_{January 29, 2009
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Gil: what math is that?Venus Mousetrap_{January 29, 2009
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Robbie[43], Thanks for your kind words! Thanks also for providing the link because it reminded me it needed updating.Prof_P.Olofsson_{January 29, 2009
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Darwinists insist that the obvious probabilistic barriers presented by living systems can be breached through incrementalism. But this is probabilistic nonsense on its face. When boiled down to the basic argument, the Darwinist thesis is: It might be highly unlikely that you will win the million-dollar lottery, so just win the thousand-dollar lottery a thousand times! Problem solved. Not! The problem becomes astronomically greater. Do the math. My conclusion is that Darwinist philosophers don't have a clue about basic mathematics like this, which I learned from my father when I was in grade school.GilDodgen_{January 29, 2009
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Now this is going to get very interesting!!!!bornagain77_{January 29, 2009
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Hello Kirk, Good to have you here to answer questions about your lecture!DaveScot_{January 29, 2009
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Re #35 I didn't pick up the assumption that P(data|ID) is one. This certainly makes a difference. Then for very small values of P(data|chance) and the assumption P(chance) = P(ID) = 0.5 then it is true that effectively P(chance|data) = P(data|chance). However, this is a hell of a set of assumptions. Consider P(ID) = 1 - P(chance). So in this case ID includes all possible hypotheses that involve intelligence. I am not sure that it possible to attach a meaning to that. But to then go on and assume that the observed data is certain given this megahypothesis! We are truly into la la land here. Actually we have no idea what the prior hypotheses: chance and design mean. They are just too vague. We have a very broad estimate of the probability of the outcome given one of the chance hypotheses. And no idea of the probability of the outcome given the meaningless set of design hypotheses. Given that, it is an error to confuse p(data|chance) with p(chance|data). Actually this is a minor error compared to some of the big ones.The real big one is the weird statement about the number of fits required for a fitness function. This is the only time he addresses natural selection but it is stated without proof or reference. In fact it is nonsense. I guess what he is trying to say is that given a target, what are the chances of creating a fitness function leading to that target. There may be some research that supports this. But evolution is not seeking a target so it doesn't need a fitness function that matches the target. Rather it reacts to whatever fitness functions happen to be out there and is lead by them. And we know there are highly complicated fitness functions out there - they are the environment.Mark Frank_{January 29, 2009
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Bayesian: Prof P., and all those that bring up Bayesian probability, you’re bluffing. Do the math, or shut up. You do know who Prof_P.Olofsson is, no? I may be going out on a limb here but I doubt 'doing the math' is his problem. Call me crazy... but, perhaps some respect is in order. Seeing as he's an expert in the field and is kind enough to contribute at all. Dr. Dembski rarely, if ever, contributes to the discussions and debates around here so I'm thankful for Prof. Olofsson's contributions on the topic of ID as it relates to mathematics. Regardless of his opinion of ID in general. Thanks, Professor Olofsson.Robbie_{January 29, 2009
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Hello folks. I've been away for 6 days and just got back last night. There is a backlog of work that has piled up, some of which is pressing, but I'll post a comment in the next day or so. The video you see is a portion of a lecture I gave to a general audience of students at the University of Edinburgh about a year ago, so it is quite simplified and there is very little technical detail. Those who are concerned about how I did the probabilities can relax; I'll post more about that when I get a little more time in a day or so. Also, I noticed that there are some who are assuming natural selection is relevant in assisting the search for folding functional proteins in sequence space. It isn't. Finding a folding functional sequence is not a hill-climbing problem. I'll look forward to posting a little more detail in a day or so. Cheers, KirkKD_{January 29, 2009
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bornagain[25], In fairness, you made the conditional statement
Do you want to argue that the Venter watermark was not intelligently designed? If so there is no point in trying to persuade you since you are unreasonable.
and as the answer is "no" I suppose I am still conditionally reasonble, please?Prof_P.Olofsson_{January 29, 2009
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Bayesian[21,35], Mark[32] Bayesian, Mark is right and you and I are both wrong. Your claims are wrong and I was wrong is assuming that you know how to do the calculations. If we have P(ID)=1/2 P(chance)=1/2 P(data given chance)=p P(data given ID)=1 then Bayes' rule gives P(chance given data)=p/(1+p) &nbsp and P(ID given data)=1/(1+p) so your claim in [21] is only true if p=0. In other words, Mark's comment [32] is correct.Prof_P.Olofsson_{January 29, 2009
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I think I want to stand in the dining room for the heat in the kitchen is getting intense,,LOL, but just a thought before I scamper off, given the infinite universe conjecture postulate by Koonin and others to evade the overwhelming evidence for design that is being found by all levels of science, what is the probability of a "infinitely powerful and transcendent being" "evolving" in one of this other infinite universes. I would say the probability is 1.bornagain77_{January 29, 2009
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Bayesian[36], I can stand the heat of a rational and respectful discussion. Claiming that I am bluffing respresents neither. But OK then, let's go personal: You are ugly and smell slightly of boiled potatoes! You obviously know how to do the calculations but I still agree with Bill Dembski; there is no way we can compute, or estimate, P(ID), P(chance), or P(data|ID). Sure, we can say that an intelligent designer would always get precisely the result we see and claim that P(data|ID)=1 but that's already a biased assumption. And even if we agree on it, if you choose the "unbiased" prior of 50-50, the entire setup is biased in favor of ID. If, in a court case, you replace "chance" by "innocent" and "ID" by "guilty, and consider some piece of circumstantial evidence such as a DNA or finger print match, you would always convict.Prof_P.Olofsson_{January 29, 2009
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Well, I can't seem to draw any conclusions from the discussion going on between all these people. It's interesting though, very interesting! :) PO, you should come back. How am I supposed to draw a conclusion without hearing more from both sides? While I very seriously hope that Durston is accurate in his calculations, I'm not going to jump the gun. Although, I will admit that I'm assuming that the case for ID is going to turn out much, much better than chance and/or natural selection.Domoman_{January 29, 2009
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Do what you must, PO. At the very least, you could give us a link. But if you can't stand the heat, you may as well get out of the kitchen.Bayesian_{January 29, 2009
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#32 (Mark) No. As a matter of fact a in Durstons calculations P(data|ID) =1 and P(data|chance) is the low non-zero probability he calculated. If you think I'm wrong, then please show me a different calculation. If I work out the math, and believe me, I'd love to, the critics will simply accuse me of demolishing a straw man and/or misapplying bayesian probabilities. So let the critics show us exactly how Bayesian probabilities nullify or weaken the probabilistic arguments and then we'll see if they are right. Otherwise, stop yelling "Bayes!" and engage the meat of the arguments.Bayesian_{January 29, 2009
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Bayesian and bornagain, Well then, as I have now been exposed as (a) bluffing and (b) unreasonable, I'd better stay away from the discussion to leave it to the honest and reasonable. Cheers, POProf_P.Olofsson_{January 29, 2009
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The -log2 arises because functional information is based on the Shannon notion of uncertainty, and indeed this is the problem I had with it. It is not a meaningful measure of information. Durston has an example with a dodgy safe, but I have a better one: keys. Suppose there exist a billion keys in the world, and you are testing them on their ability to open one specific lock. If it's such a badly made lock that all keys will open it, the functional information of the lock is -log2[one billion / one billion], which is zero bits. If half the keys will open it, the information is -log2[half a billion / one billion], which is one bit. If only one key will open it, the information is -log2[1 / one billion], which is about 30 bits. All these bits just tell you how much information you'd need to distinguish a functional entity from a non-functional one. That's why, when he does the calculation for Venter's watermark, he gets such high information; there is only one Venter's watermark out of quadrillions of possible sequences. That only happens because he knows there is only one. It's not a very interesting result. If you define a function as 'be this precise sequence of nucleotides', of course it has high information. Even a sequence of hundreds of G nucleotides has high information by that definition, yet you know it's not very complex. If we were getting messages sent to us in English in our DNA, then I'd be impressed, and I'd have to admit that some intelligence had put it there. But we're not, and falling back on functional information is less impressive when it's defined in terms of ability to perform functions - something that natural selection is known to effect.Venus Mousetrap_{January 29, 2009
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Re #21 But if we start as agnostics and assume that P(ID) = P(chance) = 0.5. and apply bayes rules, then we find P(data given ID) = P(ID given data) and P(data given chance) = P(chance given data). Surely this is only true if P(data|ID) = 1 - P(data|Chance)?Mark Frank_{January 29, 2009
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Bornagain77, thanks for the full link. Durkston's argument seems much more complete now. That said, I still detect a major flaw in his neo-darwinan case. Durkston argues that one can determine the necessasary information content of the fitness function must be equivelant to the amount of change that has taken place. He argues that there is a large, quantifiable amount of information change between a fish genome and an amphibian genome. Therefore there must be a fitness function that itself contains this amount of information. I think his logic is weak. Consider the amount of difference between the genome of the fish and the genome of the reptile. These genomes are more different than that of the fish and the amphibian. His logic suggests that the necessary fitness function now be greater than the fitness function required to get from fish to amphibian. I hold that two fitness functions, one with the information content to get from fish to amphibian and another with the information content to get from amphiban to reptile would be fully adequate for the job. So, if there are intermediate steps, each intermediate step requres a fitness function with sufficient info to get to that step. The total information of all of these fitness functions must be sufficent to get to the final step. However, no individual fitness function need have all of the information in it. Now, Darwinists know of only one fitness function. This fitness function, natural selection, has possibly 2 bits of information in it -- 4 states as rendered in any Darwinian conflit: 1 - Organism A is better suited for this specific environmmental event. 2 - Organism B is better suited. 3 - Both are adequately suited. 4 - Neither are adequately suited. That is the total information content of the known fitness function. However, the neo-Darwinists also propose a whole whap of intermediates. In fact, for each mutational event (could include: insertions, deletions, HGT etc., not just point mutations), the fitness function is applied. The fitness function, then, is applied at the level of a single bit of increased information (even a multi-nucleotide mutation, as a single mutational event only produces one bit of information -- "this organism is changed.") As such, the 2 bit fitness function is fully adequate to handle the single bit of new information that it is applied against. Now, each time natural selection is applied, it is applied under slightly different circomstances. As such, each time the function is applied, it adds its 2 bits to the total information content of the sum of the fitness functions. The number of bits of information in the sum of the fitness functions then equals the two times number of times the function has been applied in the transition between fish and amphibian. I therefore contend that Durkston's case is not by any means strong enough to defeat neo-Darwinism.bFast_{January 29, 2009
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Sorry, it is getting late here. 4^4=64 64/8=8 log2(8)=3 So in my example it would need 3 bits to specify the functional ones out of the entire lot.Alex73_{January 29, 2009
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bornagain77: Thanks for the video and the link to the article. The role of the log2 function is obvious: The information in the formula is measured in bits. The figure N/M(Ex) tells the ratio between all possible sequences and the ones with a function. log2(N/M(Ex)) tells you hoy many bits you need to specify a functional sequence out of all possible sequences. For example, if you have 4 nucleotids in your RNA, then you have 4^4=16 possible sequences. If 8 of these exhibit a function, then you need log2(16/8)=1 bit of functional information, which somehow relates to that half of the lot that exhibit the function. Am I right?Alex73_{January 29, 2009
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jerry[17], It wasn't clear to me what I said that you disagree with.Prof_P.Olofsson_{January 29, 2009
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bornagain[21], I have no problems with the equation, or the attempts to use information theory per se. In my post [7] I criticize his confusion of conditional probabilities. If there is a 1-in-a-million chance that something happens by chance versus some other explanation, you cannot say that "chance is a million times less likely." You'd put a lot of innocent people in jail with such a logic! I don't want to belabor this point further. I also don't want to brush aside his entire argument just because he misstates his conclusions; that would not be fair. Hopefully we will get to hear from Mr Durston himself at some point. As for the logarithm, the main reason for using it is to "turn multiplicatio into addition" by the logarithm law log(ab)=log(a)+log(b). It is easier mathematically to deal with additivity.Prof_P.Olofsson_{January 29, 2009
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tribune[13], Ever the nonsequiturian!Prof_P.Olofsson_{January 29, 2009
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bfast, Prof_P.Olofsson, I agree with Jerry. The equation is universal, as far as I know, and can be applied in forensics, archaeology, SETI and most intriguing with the Venter watermark: Do you want to argue that the Venter watermark was not intelligently designed? If so there is no point in trying to persuade you since you are unreasonable. As well this is not an argument from what we do not know, This is an argument from what we do know. I find his case for the functional information of the highly isolated islands of structural integrity for proteins, based on D. Axe's work and the universal protein's, to be especially compelling. Do you want to argue that proteins are not highly isolated in structural integrity or that universal proteins are not required in evolutionary theory? If so provide the empirical evidence to the contrary but do not hand wave as that line of reasoning is "not even wrong". Though I am not at all that well mathematically literate, the equation itself is, as far as I can tell, a brute force measure that will get us into the ballpark as to determining the probability that this functional information was implemented from the primary "transcendent information dimension" of reality. I am disappointed that no one here at UD has elucidated why the -log function was necessary. I am fascinated that this particular function is required. That some would suggest it is possible to divorce probability from a measure of functional information is a very unrealistic scenario for biology. To completely eliminate probability from any scientific measure of functional information in biology would require that we know every possible configuration of every possible protein that could ever possibly exist in this universe. This is, of course, so as to have complete knowledge of functional information possible in this universe! Do you claim to know every possible configuration of proteins that will produce any function being studied? Shoot, it takes a entire year for the Blue Gene supercomputer to figure out how one 300 amino acid protein will fold into its 3D structure. Thus it seems apparent to me, since we clearly are at such a disadvantage to obtaining complete knowledge of total functional information possible in this universe, then we are stuck with using the brute force measure illustrated in this equation. For we are indeed operating within what we do know as to the isolation of islands of functional information within protein structures and indeed within all evidence that is coming in for the complexity required for the first self replicating molecule. (in fact 382 genes is seen as generous by some, since even at that number robustness of adaptability and thus longevity is questioned) As well, Behe's work in "The Edge" supported Genetic Entropy, with no concrete exceptions to this foundational rule of decay that I could see save for the exception that was required for the HIV binding site. Yet even there the HIV deteriorated the complexity of its host in order to gain its trivial binding site of functional complexity. Why should we expect molecules to self organize into "islands of extreme functional irreducible complexity when all research thus far indicates that molecular degeneration is the overiding rule? Evolution absolutely requires the ability to randomly generate the functional complexity and yet no evidence exists that this ability is present in nature. as tribune7 stated; we won, now its time for someone to wake the evolutionists up and let them know they can stop dreaming evolutionary fairy tales to tell our children.bornagain77_{January 29, 2009
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Jerry (17 & 18) very well said.tribune7_{January 29, 2009
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Figures, I'm only an hour away from there. Didn't even know about it.IRQ Conflict_{January 29, 2009
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minor edit, in the second paragraph "then P(ID given chance) will be one." should obviously read "then P(chance given data) will be one." And in the second to last paragraph: "So if (chance given data) = 10^-80, it is now 10^71." should read: "So if P(data given chance) = 10^-80, then we now have P(chance given data) = 10^-71."Bayesian_{January 29, 2009
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