bayesian probability, chaitin descriptions, and evolution

It matters whether B(our current state)"" is DEVELOPABLE (in the mathmatical sense) from e,h or e,h,d between the time you should have elapsed between your first post AND nnNot making the second. I have no idea if "things like intelligence" is not simply a SQL hook for a bot or not. e=environment, h=heritability, d=development. The differences of Haldane,Fisher and Wright can stack brains differntly but first I must address LAM who seemed to NOT want the "slack' of not involving my own ideas and to whom I dont know if he is ONLY interested in Criticism or is going to try to find out more about such possible envelopments.

If we take an unbiased source of random binary digits and record the first n digits it produces, the probability of getting any specific sequence is 2^-n.This is true regardless of the length of the shortest description of the sequence we get (and that must be true since there are 2^n possible sequences, each can be described in n bits or fewer and the probabilities must add up to 1).Do you accept this and understand the implications for your argument ?

No, I define P(Y) as the chance of me winning the lottery BY FIXING IT. P(Y) is going to be some large probability near 1.0.Yes, the chance of me winning becomes P(X|Y) (if i have the symbolism right).The chance of my winning the lottery is greater than the chance of my winning by blind chance OR by fixing it. That is the correct view of the blind chance or RM&NS giving raise to any particular advantageous form. As you agree with P(X|Y) as my chance of winning. Why is the P(X|Y) * P(Y) introduced? The absolute chance of me being in a position to fix the lottery has no bearing on it the relationship of the various probabilities. This is a red herring.

Your last statement is incorrect.
Pure chance means you go and pick one of the 1000 strings completely at random (e.g. using a random number generator, whatever). 10 of those strings are intelligent, so picking one at random you have 10/1000 probability (1%) chance of getting an intelligent string.What you have defined in your last sentence above is prob(Pi(X)|not Pn(X))"generated by pure chance" does not equate to "not generated by natural selection".We assume that even if a string was not generated by a natural selection procedure, it was generated by some method (i.e. program). Pure chance means "assuming we know nothing about the thing that generated X, what is the chance X is intelligent?".

No, prob(E) is *not* equal to 1.If you recall, E refers to L and M combined, that is the *actual mutations* that occured and any additional laws governing the natural selection process. E outputs B, our current biological state.A *huge* percentage of E is those mutations. The prior probability of that specific sequence occurring is *not* 1.In any case, you mangled the formula I actually gave. We're not interested in the probability of some specific value of E, but rather the probability that E has some property, e.g. Pn(E). The *actual* formula I gave (numerous times) was:
prob(Pi(B)) >= prob(Pi(B)|Pn(E))* prob(Pn(E)).The initial statement you made above about "natural selection being necessary" is a little vague, and requires some analysis.As stated repeatedly B refers to an ending biological state, and can also be imagined as a binary string. I have implicitly referred to B as our current biological state, but imagine for the moment it representing any possible biological state. Thus B might have to represent anything from a world of only a few single-celled organisms to where we are today, or anything in between. A given state of the biological world B' would result in a new state B'' which would result in a new state B''' and so on. Thus for example you might have, 011110000100001 --> 1111011111111011111110 --> 101011010100000 and so on.Now there is nothing intrinsic in the number 01111000010001 that necessitates why it should yield the number 1111011111111011111110. There has to be some program, i.e. some set of laws that dictate how you get from one state of B to another (e.g. B' -> B''), and we refer to that program as L. L can be small or large, but it must exist. Furthermore, we know there is another factor causing changes in B, and that is M, the mutations. I referred previously to a specific value of L and a specific value of M collectively as the program E. B in effect resides in the memory utilized by E, but E is not the same as B. While E is running, B (the biological world) is changing states .e.g. B'->B''->B''', as dictated by E. The ending state is the final state of B.Now, as far as L, it could in fact be *very* simple For example, it could equate to a universal program U that just interprets B' as a URM program, executes B' and replaces B' with the output B''. (U would be a few hundred bytes long.) In that case L wouldn't be adding *anything* to the process that would favor intelligence, for example. So then the question remains, how did B get intelligence except through blind chance? We're not saying a mutation sequence couldn't happen resulting in intelligence, but mutations are random, after all.However, whatever L is, (even if it favors intelligence) we know that prob(Pi(B)) > prob(Pi(B)|L)*prob(L).Furthermore (and this is something I haven't stated explicitly before):Suppose E' is some arbitrary set of laws and mutations. (E' can be *ANYTHING*.) Suppose B' is some arbitrary biological configuration. (B' can be *ANYTHING*.) E' and B' need not be related in any way (that is E' may output something other than B').THE CHANCE THAT E' OUTPUTS A STRING THAT CONTAINS INTELLIGENCE IS EQUAL TO THAT CHANCE THAT B' CONTAINS INTELLIGENCE.(I will provide a proof for this if compelled to.)If the laws L in our universe can detect intelligence and favor it, that cannot just be brushed aside as irrelevant. It has to be explained.For any specific value of E and B, if E outputs B, then E is a description of B and cannot be smaller than the smallest description of B. E and B equate to each other in a meaningful sense. For B to exist requires that some process E that equates to it predate it. This will apply as far back as you recede in a backward chain of causation until you hit something that has always existed.[This message has been edited by sid, 04-26-2004]

No, the last statement is entirely correct. There are 900 strings generated by pure chance and one of them is intelligent. So the probability of pure chance generating intelligence is 1/900.
And yes it IS Prob(Pi(X)|~Pn(X)) - because that IS the correct probability - as I said. All you've done is confirm that you made exactly the mistake I indicated - and therefore credited the successes of natural selection to pure chance. And your argument relies on just that error.You have to distinguish your selection from the actual *generation* of intelligence. That after all is the point you are supposedly trying to refute - that natural selection has a higher probability of PRODUCING intelligence than pure chance. So you can't select a string that happens to have been produced by natural selection and attribute it to pure chance.And no you CAN'T equate "generated by an unknown process" to "generated by chance". The unknown process could have significant statistical variations from a pure chance process - as natural selection does.

This is superficially in the area of my own professional expertise... formal logic.In response to sid's persistent assumption that the rest of the world is just too stupid to follow his argument, I shall return arrogance for arrogance and in this case I'm pretty sure I have a more solid basis for being arrogant.I have a PhD in formal logic; and sid has written what is mostly mathematical gibberish; a thin veneer of formal notation over a mishmash of poorly defined and improperly applied concepts. The problem is not that I fail to understand the various fields of maths to which sid appeals. I do understand them just fine; and sid's post is still gibberish. The use of formal notation obscures the poor definition of terms. The use of "for example" is confusing; following text suggests this qualifier should be omitted. I'll assume a domain of some kind, and that Pi and Pn denote subsets of the domain, informally representing "intelligent" items and items "containing natural selection laws". This makes sense. Effectively, we are assuming a mapping between strings, which represents the result of computing a string.I'll let "Comp" denote the mapping strings as input-less programs to strings as output. That is, "Comp(E) = B". Despite sid saying that E and B are "specific" strings; I think he really means "arbitrary strings", so that he can use symbols B and E to denote arbitrary strings related by the Comp function. That is, B and E are placeholders, or variables; not one specific string. That is a trivial error; not a consequence of Bayes theorem. By definition of conditional probability: Thus, as Ned correctly points out, the conclusion of your "if" expression is a vacuous truth. You don't need any initial assumption.A persistent problem for sid is the misuse of "B" and "E" as free variables. I'll show how to fix this.Are Pi, Pn, B and E specific predicates and strings; or not? If they are specific terms in this argument, then what does "prob(Pi(B))" even mean? On the other hand, if B and E are placeholders, we can give a more formally accurate exposition by using the Comp mapping directly.Here is my best attempt to rework the above into something approaching formal clarity.

• Let "U" denote the domain of discourse. We can think of elements of U as strings. Formally speaking, it is just a set.
• Let "Comp : U --> U" be a total function. We can think of Comp as mapping a string to the output produced when the given string is executed as an input-less program. As is common in set theory, I will actually apply the function Comp to sets of strings, under the natural generalization of function image. That is, Comp(X) is the set of output strings obtained by executing programs in the set X.
• Let "InvComp" be the inverse mapping. That is, InvComp(X) is the set of all strings E such that Comp(E) is in X.
• For example, "InvComp(Pi)" denotes the set of strings which, when evaluated as programs, return a string that is in Pi. I'll use this one below.
• Let "Pi" and "Pn" be subsets of "U". We can think of them as the set of "intelligent strings" and the set of "natural selection containing strings", whatever that means.
• Let "prob : pow(U) --> [0..1]" be a total function from subsets of U to the real interval [0..1]. It is assumed to satisfy the axioms for a probability distribution on strings.
• In the usual way, let prob(X|Y) denote the binary function for conditional probability, defined by prob(X|Y) = prob(X intersect Y) / prob(Y)
• The term "prob(Pi(B)|Pn(E))" is, I suspect, intended to denote the probability that a string B satisfies Pi, given that B = Comp(E) and E satisfies Pn. The notation here is poor, because the scope of the variables B and E is not defined; they appear as free variables in the term. The intended meaning of sid is almost certainly written more correctly as "prob(InvComp(Pi) | Pn)". We can read this informally as the probability that a randomly selected string is evaluated to give an "intelligent" result, given that the string "contains natural selection"

This correction helps resolve a persistent problem in discussion in which "B" and "E" are being taken as specific strings. The cause of this confusion is sid's poor use of formal notation.For convenience, let Pc = InvComp(Pi). The application of Bayes theorem is thus The expression given by sid above is his purported application of Bayes theorem is vacuous. There are many confusions in the above. For example, "natural selection" in this case has only been described as a predicate on strings. I do understand it. It's wrong. If you were one of my students in a class on formal logic, this paper would fail.Your argument is essentially that the probability that a randomly chosen string shows intelligence is greater than the probability it shows intelligence and is generated by natural selection.This is vacuous; it would be true no matter what sets you identify as "intelligent" and "generated by natural selection"; and this says nothing useful.The rest gets no better; and makes some trivial errors in application of the Chaitin's theory of algorithmic complexity for strings.You can see the thread where sid tried to fly this in talkorigins in the Google archive. The responses do not fit sid's description.Cheers -- Sylas

You said: Let me restate that correctly:
(Actually, I've edited this several times trying to get it correct, I apologize: Note:
"The chance of winning by not fixing it"
*DOES NOT EQUATE TO*
"The chance of winning by blind chance"The correct statement of all this (according to elementary probability and using *my* version of Y) is:(1) prob(X) = prob(X|Y)*prob(Y) + prob(X|not Y)*prob(not Y)BTW, the above is where I got the following:(2) prob(X) >= prob(X|Y)*prob(Y),by just dropping the second half of the formula.I have stated elsewhere in this thread that (2) equates to,(3) prob(X) >= prob(X and Y).But if (1) is true, then so is(4) prob(X) >= prob(X |not Y)*prob( not Y),In any case, prob(X) is what I call *by blind chance*, which is the chance of you winning the lottery, assuming we don't know anything about you.Suppose you hadn't fixed the machine. That doesn't mean there isn't some other method Z you could have concievably employed to increase your odds. But once again, the probability of Z occuring would have to be factored in. That's why we don't just call the negation of Y "blind chance".This is more difficult to explain than I imagined. One thing I know for sure: No mathematician is reading this thread or they would back me up. (You're making the same error PaulK is.)[This message has been edited by sid, 04-26-2004]

Sylas,I haven't had time to read your post, but I will deal with it later.All I can say is, it is VERY VERY STRANGE, that not a SINGLE PERSON has read this thread, and said, "Yes sid I understand you, I agree your points have validity, at least in this conext" or WHATEVER, because I KNOW what I have written is valid and relevant.And as I have said Sylas, I will deal with your post later.And if you are a real mathematician, logician or whatever, then I ask you PROVE IT by backing me up in points to Nosey Ned and PaulK in this thread.Regards

It is not strange at all. What you KNOW just ain't so. I do understand what you are saying, and your points do not have validity. The isolated cases where you happen to write some correct arithmetic and probability formulae don't change that, because your application remains incorrect.Drop the arrogant tone, and I will return courtesy with courtesy. I will cease to make comments about you as an individual, and will confine myself to the substantive material and the maths.Continue trying to make a presumption of engagement that you are correct and anyone who fails to recognize that must not know maths, and I will continue to tell you that you are full of it.Deal? I am absolutely a bona fide mathematician with a PhD in formal logic. I have taught formal logic on a number of occasions. You are wrong. Nosy's corrections are spot on. PaulK, on the other hand, has made some errors, and your response to him in Message 19 is correct.A major source of confusion is your use of "B" and "E" as free variables. I've shown how you can fix this.The centerpiece of your argument is the formula However, you have never actually applied any putative properties of the predicate Pn. The same argument you give works just as well for the predicates Pn "involves natural selection", Pd "involves intelligent design" and Pm "does not involve natural selection".That is, you could reword your argument so that any conclusions now you make about "natural selection", will apply without change for "not natural selection".Your argument fails as a criticism of ANY method by which "intelligent" strings are formed; and Nosy's criticism goes to this aspect of the nonsense.Sylas

Poilkinhorne just finished lectureing at Cornell. I can say uncategorically the level of scholarship available on this board is ABOVE what one can experience At CORNELL. So before I answer in thread head terms I would like to ask (by the way P dissed Gould's magestirea but retained by implication Eldgridge's use ofMIVART saying that ID is nothing new) are Pd and Pn different or the same OR am I going to finish reading these posts with the "multiple universe" view ofphysical reality as the conclusion?I specifically asked if he had everheard of Glaydshev or macrothermodynamics he had not. (as an aside towards the evolution part of this thread I did better appreciate how he UNDERSTOOD anthopic principally by science of carbon. Thatwas lost on nonbelievers in the audience.<Polkinghorne>[This message has been edited by Brad McFall, 04-26-2004]

I'm curious how you distinguish PaulK's argument from Nosey Ned's, as I see them saying essentially the same thing:PaulK equates anything that isn't natural selection to "blind chance".
NoseyNed equates anything that isn't "fixing the machine" to "blind chance"Those are both obvious fallacies.In addition, Nosey Ned says:"The chance of my winning the lottery is greater than the chance of my winning by blind chance OR by fixing it."However you parse this vague sentence its not correct, and I would think you would know this. The relevant aspect of Pn(E) is that we assert thatprob(Pi(B)|Pn(E)) > prob(Pi(B))IOW, we assume that Pn(E) increases the liklihood of intelligence occuring. With that assumption *we don't care* what Pn(E) represents it could be *anything*, "e.g. E contains natural selection." The point is, evolutionists propose some aspect of E that they say *increases* the liklihood of intelligence over blind chance. What exactly that is, I don't care.Furthermore,
if
prob(Pi(B)|Pn(E)) > prob(Pi(B))
then
prob(Pi(B)|not Pn(E)) < prob(Pi(B))Thus, *we don't care* if the argument applies to not Pn(E) as well,prob(Pi(B)) >= prob(Pi(B) and not Pn(E)),because we would *assume* that, given that the probability of getting intelligence are *less* given not Pn(E) than with blind chance.I would appreciate it if you can admit you understand my point here, as I think it should be clear.I still haven't finished your first post, yet.

I don't really see anything substantive here I need to address. If I had used notation with the sort of rigor and completeness you demand, there would be no chance whatsover of my posts being understood. (In all honesty, I probably could learn some things by going over all this, however, and I probably will.)I have addressed a substantive point of yours from post #25 above (in post #27).Its related to this assertion: If there's anything else here I need to address someone let me know.
(Actually, I'm still going through it all.)[This message has been edited by sid, 04-26-2004]

PaulK treats "blind chance" as a predicate on strings, as if one can look at an individual string and identify it as being chosen by blind chance or not. Nosy refers to "blind chance" as a property of algorithms for approaching a lottery. This is a subtle but meaningful distinction. Stop introducing as a presumption into this debate that I would have to "know" you are correct. Incomprehensible as it may seem ... my impression is that you are not particularly good at maths. However, I will abstain from saying that out loud if you will stop being stop introducing into the thread these allusions to how you just know you are correct and that anyone who knows mathematics would agree with you.Deal?Ned's meaning is clear in context; though expressed informally. I have used parentheses to bracket clauses that denote calculated probabilities, which may help you parse it better. Ned's meaning is The way Ned is using the word "or" is a bit confusing, but it has precedent in English, and a bit of thought should have been enough to parse his meaning. Ned's text treats "fixing the lottery" as another event. It is important to note the difference between "probability of winning the lottery by fixing it" and "probability of winning the lottery given that I have fixed it".This meta-discussion is pointless. I understand what Ned is getting at, and he is correct. No-one here has written their posts with total clarity and lack of ambiguity, me included. So I am not going to try to argue that Ned's text is unambiguous, or further defend him.Let us confine ourselves to the substance. It you are going to try and use mathematical notations, you should use them correctly. The use of "B" and "E" as free variables makes your formulae incorrect, and obscures your meaning.The formula "prob(Pi(B)|Pn(E)) > prob(Pi(B))" contains the following free variables: The variable "prob" denotes the probability function. The variables "Pi" and "Pn" denote specific predicates on the universe of discourse. However, "B" and "E" do not denote specific strings, but act as place holders that range over the space of strings. This is a problem in the formal maths, and I recommend you fix it.My proposal is to introduce another variable "Pc", to denote a specific predicate, defined as follows.Pc(E) is true for a string E if and only if Pi(Comp(E)). That is, Pc is true for strings which when "computed" will give an "intelligent" result.The expression "prob(Pi(B))" is not sensible; it would be rejected by a simple type check. The expression Pi(B) is either true or false, depending on the value of B, and you can't make sense of "prob(true)" or "prob(false)". The proper use of the "prob" function is to apply it to an event, or subset, or predicate, not to an evaluated predicate. Hence, for example, "prob(Pi)" is sensible... it is the probability that a chosen string will be intelligent.By this convention, your formula "prob(Pi(B)|Pn(E)) > prob(Pi(B))" is written more precisely as follows: The intuitive meaning is that strings satisfying Pn are more likely give an "intelligent" result when evaluated, than strings taken over the whole domain of discourse.Note that none of the above correction to the use of variables changes or refutes your argument. It just tries to express the argument with meaningful mathematics.Now for the comment on the argument itself... you never actually apply this assumption; and the same assumption applies equally for other plausible methods of forming strings, be they "goddidit", or "selectiondidit", or "designdidit". Shrug. Try the other example I gave. Let Pd be the predicate which is true of methods of forming strings that incorporate intelligent design, rather than natural selection.Just as for with natural selection, we assume that intelligent design is more likely to give an intelligent result.That is, prob(Pc | Pn) > prob(Pc), and also prob(Pc | Pd) > prob(Pc)In so far as your argument says anything useful about natural selection, it says the same thing exactly about intelligent design. You are still suffering the same failure of understanding. Your point is vacuous, and does not constitute any kind of meaningful statement about natural selection. The presumption that natural selection makes "intelligent results" more probable is fine, but your argument does not use that assumption to discredit selection.My extract you quoted in message 28 stands precisely as given. In so far as your argument makes sense, it applies equally to "natural selection", "intelligent design", "god" and "random choice" as ways of forming so called "intelligent" strings. The plain fact is that the content of the argument is vacuous, and the implication that it constitutes an argument against of any of these ways of forming strings is erroneous.Cheers -- Sylas

This is going to sound rather off the wall, and not really related to anything else in this thread.But I felt compelled to give my own personal ruminations about origins, etc. ( I may even contradict things I have said in this thread.)As I've stated repeatedly, there's no reason not to assume that God didn't use some finite intermediary mechanism to create man. For many, (in both evolution and ID camps) theistic evolution is some sort of worthless compromise position, but to some extent I disagree. There may be problems with evolution being the mechanism of choice, because the extreme gradualism doesn't fit the fossil record, or whatever. But even for a Bible believing Christian, the most reasonable view I think is that God must have used some intermediary mechanism or a chain of mechanisms to create the biological world. IOW, if not evolution, then I do think there is some mechanism out there we haven't found yet, that on its own could account for life. Now this mechanism might require as much information in it as the biological world but it would still be a mechanism.There are many reasons I say this. For example, Does any bible-believer think the following: One day there was an empty grass plain in Africa, and then poof! - instantaneously there was a herd of wildebeest that materialized out of thin air, thundering across the plain? Was there an empty ocean, and an instant later, it was teeming with life? Where do we see God working like that anywhere in the natural world? Just as one example, a woman doesn't get pregnant and then give birth an instant later to a fully developed baby. Rather, the baby goes through gradual stages of development. You may disagree with me, but in that one example, I see a model that one might reasonably assume was mirrored in the creation of life on this planet as well. If a baby take eight months to born, was all of life as we know it created in six literal days? Actually, now that I think of it, the amount of time it took for all humans that have ever lived to be created was approx. 10,000,000,000*8 months which is *several billion* woman-years, I guess.Another factor: When I look at the cosmos and consider the unimaginable amount of stellar energy it contains, I think, did God create all that energy for no reason? What if all that energy was somehow harnessed in the creation of life? What if when we look out into the cosmos we are beholding the cosmic mother of life on this earth? The bible says "we are fearfully and wonderfully made". If all those stars were somehow a necessary energy source in our creation, it is an awe inspriring thought. Our own sun literally sustains life on this planet. What if stars were intrinsically tied to our very origin? (And I feel I may getting perilously close to idolatry and "worshipping the creature rather than the creator" or worshipping stars or something.) In any case, I don't have a particular mechanism in mind. There may even be some stochastic attributes to our creation, where God literally created the entire cosmos just so he would have the probabilistic resources for life to emerge over in an insignificant corner of it by "chance", I don't know.Now, in the Genesis account there are some interesting things. For example, the Bible says that the serpent was condemned to crawl on its belly, and it originally walked on legs. Could not this be a microcosm of sorts implying the extent of morphological change that has occured throughout the animal kingdom over time? As far as common descent, who actually believes that each species of snake for example was created seperately, and so on? Furthermore, the Bible says that Adam was created out of the dust of the earth. What if dust doesn't mean dirt, but rather a virtual sea of primordial microorganism's from which all of life emerged. One thing I want to be clear on, though. That is, the Bible says that Man was created last after all the other animals. I would take that to imply that Man was created on a seperate track from the rest on the animal kingdom. Interestingly, there is a cryptic reference elsewhere in the Old Testament (in one of the poetic books) to the "primal dust of the earth". It is very interesting, and if I weren't so lazy I would go get a Bible now and quote it directly. Finally, concerning the creation of the world in a literal week. The Bible uses time symbolically more than any other concept. Look at the "70 weeks of Daniel" that really means 490 years. In II Peter it says that to God a day is as a thousand years and a thousand years is as a day". Over and over and over again we see this sort of thing.The Proverbs say, "It is the glory of God to conceal a matter, the glory of kings to search a matter out". The knowledge that man amasses about the workings of nature is part of the task he was assigned by his creator. Which of the myriad branches of science was derived directly from the Bible? The Bible's overriding concern is with things that man *cannot* discover on his own, i.e. his eternal destiny.Well, I'll just end abruptly. I haven't really lurked long enough in this forum to know how all this will be received. I don't know whether most people here think the Bible is an irrelevant joke (which I definitely do not) or whether most think the world was created in 6 literal days. In any case, just my own personal reflections.[This message has been edited by sid, 04-27-2004]