Uncommon Descent Contest Question 10: Provide the Code for Dawkins’ WEASEL Program
| August 26, 2009 | Posted by O'Leary under Darwinism |
Special invitation for Richard Dawkins – but any civil person is entitled to enter.
There’s been some discussion here and elsewhere whether the the recent IEEE article by Dembski and Marks correctly characterizes Richard Dawkins’ famous METHINKS IT IS LIKE A WEASEL program.
Does the program ratchet correct letters or does it let them vary? One is a partitioned or stair-step search, the other a more realistic evolutionary search. From The Blind Watchmaker, where Dawkins describes the program, its performance suggests that it could be either of these options (though he doesn’t say).
On the other hand, from a (video-run of the program , go to 6:15), it seems to be the latter.
It’s easy enough to settle this question: Make the code for the program public. Perhaps Richard Dawkins himself or his friends at RichardDawkins.net can finally provide this code (apparently a program written in BASIC).
The prize is a copy of either Stephen Meyer’s new Signature in the Cell or Richard Dawkins’ soon-to-be-out The Greatest Show on Earth.
Should the winner choose the latter, I will ask Dawkins’s publicist to mail the copy. Given that at his site, he calls himself “the most formidable intellect in public discourse,” I would assume that if he signs the copy, it will be worth millions.
But wait. Let’s see that code first.
377 Responses to Uncommon Descent Contest Question 10: Provide the Code for Dawkins’ WEASEL Program
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India, or Nepal once they get rid of the communists. And thank you for asking, tribune7.
India, or Nepal once they get rid of the communists.
You mean India with the legal system based on English Common Law which at the time of its application to India was (and remains) firmly established on Christian values, right?
With regard to Nepal, why are you confident that they will replace the communist with a pro-freedom, pro-scientific inquiry government of light and tolerance, assuming they do replace them?
Mr DNA_jock,
Onlookers will notice that kf fails to respond to a very simple request : “Just some numerical values”‘.
You might start with a simpler query to KF-san, such as “Have you ever been wrong? Ever mismatched your socks or ended a sentence in a preposition?” Work up to mathematical issues slowly.
Trib and Clive:
Thanks.
GEM of TKI
Footnotes:
1] Re Sev, 356: you persist in the flawed argumentum ad nauseum ad Lewontin – who neither speaks for the whole of science nor, as far as I am aware, claims such . . .
In fact, Seversky here is wrong.
For, in the original remarks in my Section E the always linked, in the initial brief mentions (through links to Section E) and most recently in the expansion at 347 supra I point out the way that the US National Academy of Sciences [NAS] bases its current definition and interpretation of “Science,” AND in its interventions in Kansas c 2005 [and I gather 2001]. Moreover, this is the same position that appears in say the ACLU advice to Judge Jones, which he reproduced practically verbatim as his decision at Dover c 2005 — his much celebrated decision. (All that stuff about centuries-old rules of science.)
So, Sev knows, or should know, that the Lewontinian a priori materialism — whether explicitly metaphysical or implicitly so through the term “methodological naturalism” — is not an easily dismissible idiosyncrasy of one man but a widespread, entrenched, instituionalised problem. Precisely what my reference to a nneo-magisterium issuing ideological evolutionary materialist edicts in the name of science (metaphorically, while wearing lab coats) is highlighting and correcting.
2] Quote of Cromwell, 356: I beseech you, in the bowels of Christ, think it possible you may be mistaken.
Observe, Mr Cromwell (no mean sinner himself) spoke correctively, and in Sev’s opinion, correctly. So, fallible and fallen sinners can be right, even when they speak correctively; some of the time at least. Therefore, we need to focus on the merits of any given case, rather than distractive, mischaracterising or dismissive side issues such as the above Darwinist pattern shows.
Yes, I openly admit that like the old Protector, I am finite, fallible, and indeed fallen and under reconstruction through gospel ethics. And I have made and corrected acknowledged mistakes [e.g. my initial interpretation of Q]; including in the general context of this discussion for coming on a year now. (And Nakashima-San, you should know that before hinting as you do above.)
Indeed, on a point from DNA-J I will do so again below.
However, it is also objectively true that on many core matters relating to Weasel I have been correct; i.e. even fallible humans sometimes succeed in being correct after all.
For instance, Weasel is admitted by Mr Dawkins to be targetted, artificially selected search on mere proximity to target that rewards the smallest increments in proximity for NONSENSE — non-functional — phrases. That is why Weasel is fundamentally misleading entirely apart form the credibly observed phenomenon of latching and ratcheting in the showcased runs c 1986.
Across these months, here are some points where I have been bitterly opposed by Darwinist critics and have proved objectively correct:
a –> That the Weasel c 1986 runs show samples of 300+ letters in which in over 200 cases — every case where a letter goes correct and could revert — once a letter goes correct in a sample generation champion, it never is seen to revert. This, in a context where it is easy to see incorrect letter values persisting for decades of generations.
b –> That this is reflective of the import of he law of large numbers, and so it is reasonable on the observations and Mr Dawkins’ effusive remarks on the power of “cumulative selection” on the plain meaning of terms, to conclude that for the showcased runs, latching and ratcheting of correct letters in generational champions is real.
c –> That this evidence c 1986 can be accounted for on two major mechanisms, explicit and implicit latching-ratcheting ones.
d –> That, on subsequent testimony from CRD as reported indirectly, implicit latching best accounts for the evidence in hand from 1986. Though — and thus the focus of this prize thread — only credible code will prove actually decisive. (From recent remarks from CRD, it seems this will not be forthcoming, but he says that the general pattern of Weasel recreations out there is sufficiently good of a representation.)
e –> That implicit latching, quasi-latching and non-latching based on runs with parameter settings that facilitate such behaviour has been DEMONSTRATED here at UD [from here on] by the undersigned on Atom’s Weasel implementation at EIL, hosted by Marks and Dembski. Ever since April 9th inst.
f –> That the analysis on p. 1055 of the IEEE paper by M & D hinges on the observation of latching as a part of ratcheting, and enfolds in it the issue of whatever mutation rates and pop sizes may lead to implicitly latched runs. So, whatever issues may be taken with the M & D analysis or mine, latching behaviour is observable, and controls onward discussion on the point.
3] DNA-J, 361: kf fails to respond to a very simple request : “Just some numerical values”‘.
At 348 above, my response was:
In short, my observationally and dynamically based point is that where we deal with an implicitly latched case [which we can demonstrate to be real], mut rate per letter, is enfolded with pop per gen and filter characteristics [which may yield implicit or explicit latching . . . i.e a mask register or the like is effectively part of a filter] and issues in the OBSERVED latching.
Citing M & D:
________________
>>Assuming uniformity, the probability of successfully identi-
fying a speci?ed letter with sample replacement at least once in
Q queries [in the context of a ratcheting, partitioned search] is 1 – (1 – 1/N)^Q [NB: Cf below, this DOES imply the 100% mutation rate per letter], and the probability of identifying all L characters in Q queries is
q = 1 ? (1 – (1/N))^Q)^L (22)
[NB: Q -- number of mutants to date; N -- number of characters in the "alphabet", L -- length of target phrase]
For the alternate search using purely random queries of the entire phrase, a sequence of L letters is chosen. The result is either a success and matches the target phrase, or does not. If there is no match, a completely new sequence of letters
is chosen . . . >>
_____________
So, the issue is to be addressed in a context of observed latching.
4] So equation 22 is correct, whatever the mutation rate is? What happens to the number of queries needed to reach the target as the mutation rate approaches zero?
Eqn 22 would be correct on the premise that latching behaviour is OBSERVED, and the particular features of the M & D illustrative model (i.e. the context for their discussion) are followed. Latching, in turn depends on a matching of mutation rate per letter to pop size and to filter characteristics.
This is pivotal.
Mut rate –> 0 or –> 100% are cases where diverse effects will happen depending on pop size and filter characteristics. One of these will be that under certain circumstances latching will be lost one way or another.
(For instance if pop per generation size = 1 [to make the point obvious to all] or only a few, with a low but non-zero mutation rate, reversions will predictably appear — so latching will vanish — as there will be insufficient population per generation at the mut rate to reasonably assure observability of no-change cases. It is the highly reliable presence of the no-change cases that acts with the filter to lock in [ = latch] progress to date. The presence of a sufficiently — but not “too-” — high mut rate is required to get single-step progress to target. With a too-high mut rate, multiple letter effects such as substitutions will occur, leading to reversions and parallel advances, again destroying latching. In short, the issue is that the analysis is on the premise that latching must be observed and to be observed must be based on certain dynamics, whatever errors may or may not be present otherwise in the M & D analysis. [Yes, M & D use a simplistic illustration of what partitioning means, and do so in a way that invites dismissal of what they analysed. Yes, they look at a case where for illustration, every letter is changing in the envisioned generation champions, and this produces obviously implausible single generation advances -- 5 letters -- in their constructed example. Yes, one can construct a strawman algorithm from this which will not resemble Dawkins' "algorithm"; howbeit M & D also host a recreation of a wide range of possible Weasel algorithms and display their comparative effects, indeed going on to analyse some to these in later sections. And, Mr Dawkins has not provided actual code or a technical summary of his algorithm[s] so various possibilities are credible or at least legitimate on the relevant evidence.])
5] eqn 22 does not take the mutation rate into account (he [KF] may or may not realize that it actually sets it at 100%) and that eqn 22 CANNOT take the generation number into account, because it cannot describe a search that uses generational champions.
I have shown that generation number for a proximity reward search case — which under certain conditions will implicitly latch — can be accounted for on simply reckoning that Q comes in generational lumps of size S. In G generations, of size S, Q = G * S. (And so, on any given mut per letter rate etc, there will be Q queries at any given time, but say it will jump in lots of 50. And if in any given lot of 50 the correct phrase appears, the Weasel will of course pick it up. And if any advance appears, it will be recognised.)
Now, you make an intersting point, that in the model in Eqn 22, the implied per letter mut rate on unlatched letters is 100%, which is of course the pattern they illustrate with their example.
Now, since I have focussed hitherto on the empirical data and dynamics of variable mut rates and the appearance of latching as a control, I have based my view of what was going on on this; which is an objective external control above and beyond the mathematics involved. (Such a control, BTW, limits the effect of errors one may make in a logical analysis. that is why the Galilean principle is correct and helpful: ideas must be subject to empirical tests. And, that is why even though his explanation of tides etc was rather plainly wrong, we today reckon that Galileo had the better of the case on balance regarding whether the Copernican scheme was more or less correct.)
In a 100% mutation per letter rate situation of course, implicit latching will be practically impossible — especially with a pop size of one per gen. So, the didactic model would at once fall apart if it were to be attempted practically. [That means, practically, it CANNOT be a real world case on proximity reward search. I do believe it would in general work on explicit latching, though getting a five letter increment in proximity to target on a single member generation model is rather unlikely adn would not be typical behaviour. M & D are most likely giving a didactic illustration, not a credible actual run.]
Where I went wrong.
Now, let’s look at the probability on a particular letter position going correct that M & D use: {1 – (1 – 1/N)^Q}. The second component is that odds of not being correct are (1 – 1/N)^Q, i.e. Q independent tries on (1 – 1/N). This last is odds on not being correct on a uniform distribution on N states. And you are correct, this is indeed implying 100% odds of change on the letter per generation-member.
I stand corrected on this.
And, the case will not be observable on a proximity reward case without explicit latching, as a 100% mut rate will impose in praxis non-latched non-ratcheting behaviour. Implicit latching and ratcheting are are observable, but not credibly on the terms discussed on p. 1055.
However, using odds of selection for mutation per letter, s, brings to bear the analysis in App 7 point 18 on, e.g.:
In short, the M & D model in part E of the paper is correctable in principle.
The analysis in part F of that paper points the way [I forget who said that, he is correct], with the proviso that population size and mutation rate actually need to be matched, as beyond a certain limit, substitution effects etc. will tend strongly to do away with latched, ratcheting behaviour also. (Also, demonstrated.)
6] Nakashima-San, 3564: “Have you ever been wrong? Ever mismatched your socks or ended a sentence in a preposition?” Work up to mathematical issues slowly.
You have a point, given what I have acknowledged above; on taking a closer look at the model M & D presented in Eqn 22.
I do not and have not claimed infallibility, however I do maintain that empirical controls do limit error, as I also highlighted. (And in that context, I think it is also fair comment that there are several specific points [cf. above] where — despite rather strident criticism — I have been right. Right in ways that strongly limit the impact of limitations of Eqn 22. And, the pattern of destructive rhetoric I have spent much of this thread addressing is real and needs to be corrected.)
7] On Judaeo-Christian heritage.
I think many of us have been indoctrinated into thinking that does not accurately or fairly reflect the actual balance or key foundational role of the historical contribution of the Judaeo-Christian frame to our civlisation, not only on law and morality and liberty etc, but on even the rise of science. (Cf Peterson’s introductory discussion in the context of the ID debate, here.)
___________
So, the above includes not only points where I think I am right, but a key point where I have been wrong and set out on correcting that error.
GEM of TKI
Following up:
Let’s see what an adjusted form of the M & D analysis could look like; again in the context of OBSERVED latching.
1] Each letter has N states, which we may take the “odds” — I am using this loosely for probability — of being selected on any try as s. If so, on a default, uniform distribution, odds of being selected and going correct on any mutant phrase would be:
s* (1/N) = s/N
[For s =1, s/N --> 1/N, the case that M & D seem to have analysed]
2] Complementing, the odds of not being selected and/or not going correct would be
1 – s/N
3] With Q independent tries,the extended complement becomes odds of not being selected and/or not going correct after Q tries:
(1 – s/N)^Q
4] So odds that somewhere in the Q choices a letter will be selected and will go correct are the second tier complement:
[1 - (1 - s/N)^Q]
5] For L independent letters, this extends:
[1 - (1 - s/N)^Q]^L
6] Now, to get to “catch and keep,” we first allow Q to increment by generations of size z, so in G generations, we see Q = G*z
7] Then, the odds of L letters going correct in G generations would seem to be (under “catch and keep” constraints to be discussed following):
q ~ [1 - (1 - s/N)^{G*z}]^L
8] Obvious limitation — need to catch and keep. That is, this extension of the M & D analysis implies that if a letter goes correct it must be caught and kept, i.e. there is a generational sparseness but observability of go-correct mutations such that no more than one letter changes to go correct per mutant as a rule, and that the pop is of scope that once one correct mutation appears, it will be captured. In the meanwhile, the pop should be of sufficient size for the rate — which needs to be small enough too — that no-change cases are overwhelmingly likely to be present. that way, we don’t have a holed keep-net.)
9] This boils down to saying that the already identified plausible and empirically observed conditions for implicit latching must be met if this simple extension to M & D is to work. [Note that approximation rule: ~ not =.]
10] under such circumstances it seems likely enough that we will see cases of implicit latching of the generational champions, and that selection of such to showcaswe will be a feasible action, especially iof per Weasel 1986, one is looking for “good” examples of “cumulative selection.” Where, “cumulative” normally means: Increasing or enlarging by successive addition.
11] Which was what was to be explained, per showcased run excerpts circa 1986.
_______________
So, let’s see what others have to say . . .
GEM of TKI
kairosfocus, it’s gratifying to see that some progress is being made in this debate — a rather rare occurrence on this forum. But issues still remain.
From what I can tell, each of the points in your list has either not been disputed, or is in fact incorrect. We can go through each point individually if you’d like.
Of course Eq. 22 is correct given the particular features of M&D’s model, since eq. 22 is derived from those features, which include explicit latching. Explicit latching clearly does not depend on a matching of mutation rate to pop size, as it includes an added mechanism that shields correct letters from mutation.
Nor does implicit latching depend on a matching of mutation rate to pop size. The higher the pop size, the lower the probability of losing a correct letter. And the lower the mutation rate, the lower the probability of losing a correct letter. No matching is necessary. If you don’t believe it, we can work through the math. If you’re claiming that latching will be lost as the mutation rate goes to zero, you’re wrong.
The algorithm described textually and mathematically in section III.E of M&D’s paper clearly contradicts both the description of WEASEL and the results thereof reported in TBW. The strawman algorithm is of M&D’s making. If you think that someone here has strawmanned M&D’s strawman algorithm, then tell us how.
The algorithm described by M&D in section III.E is not a possibility, as it contradicts Dawkins’ description and reported results.
Your position has been shown to be false by both the mathematics and the empirical results, so the above statement rings rather hollow.
I’ll comment on your extension of M&D’s math later.
kairosfocus:
Couple of problems I see here.
Big problem: The probability of a given letter going correct on any mutant phrase is 1/N only if you assume a 100% mutation rate. But that assumption would contradict your assumptions in #8.
Not-as-big problem: P(A&B)=P(A)*P(B) only if the two events are independent. Obviously, getting selected is not independent of the given letter going correct. This can be remedied by defining s as “the probability of this sequence being selected given that the letter in question went correct”.
But s is also dependent on whether other letters in the sequence went correct, and also on whether letters in other sequences went correct. The upshot is that I see no way to define s such that all of the steps in your derivation are true. Maybe you can see a way.
Setting aside the problems in the derivation, we can easily see that your conclusion is not true. Consider that we can make the mutation rate arbitrarily low and still meet the conditions stated in your #8. Your conclusion says that q should remain constant as the mutation rate drops ridiculously close to zero, but we know that q would, in fact, also decrease.
If there’s anything wrong with my take on your math, I’m open to correction.
KF-san,
Sir, I honor you. Keep up the good work.
–kf
In #123 you stated:
In #222 you described a proximity reward search with a population of 500 and a mutation probability µ of .04 as implicitly latched.
So, according to you, eq. 22 should apply. I just ask you to do the actual math, and to calculate the values. This should not be that complicated, should it?
Could you do the math, please, with S=500, and µ=.04?
P.S.: I’d take it as a personal favour if you could start your answer with the sentence: Yes, the value is … and No, I couldn’t calculate the value. After this, feel free to elaborate.
Okay:
After an 8-hr power cut last night since before midnight and dodgy net connexions since [hope this is not a hint from "someone" on the likely prospects of the new Govt . . . "Mons'rat lack arf" is not a joke if/when it moves from song to reality!], a few footnotes:
1] Rob: Nor does implicit latching depend on a matching of mutation rate to pop size. The higher the pop size, the lower the probability of losing a correct letter.
This underscores the importance of a dynamical-empirical view rather than a principally mathematical one.
Once pop size goes up enough, implicit latching is lost the other way: far tail effects such as substitutions [one reverts, another advances] — also demonstrated [cf line 25] — show up.
Hence too the importance of the law of large numbers here in making relatively improbable “far tail” or “black swan” events observable as sample size goes up.
2] The algorithm described textually and mathematically in section III.E of M&D’s paper clearly contradicts both the description of WEASEL and the results thereof reported in TBW.
M & D do not describe an algorithm, they give an unrealistic illustration. It seems that given the rhetorical environment it would have been better to have given an actual run showing implicit latching and ratcheting.
Recall, such exist and have been demonstrated, since April.
3] Your position has been shown to be false by both the mathematics and the empirical results
In fact implicit latching has been empirically demonstrated, ever since April 9th, as has repeatedly been underscored [and as was just linked]; whatever debates may be had over mathematical models and errors regarding thereof; the dynamical-empirical framework is valid.
And, once implicit latching has been shown, it is a credible explanation of the showcased runs of Weasel 1986.
Also, on the mathematical side my issue was that I misread a term in an equation. (BTW, it seems that you, too, seem to have done so; cf. below.)
Once I saw that I did, I acknowledged that and provided an alternative that fits with the relevant regime. I see you challenge it, so I comment:
4] The probability of a given letter going correct on any mutant phrase is 1/N only if you assume a 100% mutation rate. But that assumption would contradict your assumptions in #8.
N states for the L relevant characters, prob of being selected for mut s; on flat random model, odds go to essentially s/N.
(Independence is effectively true: each letter is picked in succession, and once it is in the hopper the s-odds die is thrown; deciding whether or not to let it take up any of the N available values at random. then, next letter. With odds of say 4% or so, typically one letter per 28-letter phrase will be varied, and 1 in 27 times it will repeat itself. And with a big enough but not too big pop, there will be to high odds no-change cases or at lest no distance to target change cases, and when a change occurs that goes closer home, it is likely to win. If pop is too big, multiple mutaiton effects will be more likely to pop up, and when a correct letter reverts while another advances in the same pop member, then this may crop up in the gen champs line, which would break the latching effect. Such substitutions were also demonstrated, as can be seen here in line 25.)
note again: I have also in effect inferred that we look at any given letter, say: l; then roll the dice to see if it will be permitted to mutate to one of 27 states, with s being odds that the given letter will mutate.
Then the next letter is fed in etc.
5] Consider that we can make the mutation rate arbitrarily low and still meet the conditions stated in your #8. Your conclusion says that q should remain constant as the mutation rate drops ridiculously close to zero, but we know that q would, in fact, also decrease.
Where did this come from?
In the analysis above, at 367, I am using q analogous to M & D for their s = 100% case. [I have already noted that s = 100% is not a practically feasible case to have implicit latching. I note that due to the required matching to get implicit latching, which was demonstrated, s is indeed factored in once we see latching. I simply misread the full import of M & D's 1/N; this I have adjusted on seeing it, for he relevant implicit latching and ratcheting to target case: catch and keep in effect all cases where letters go correctt he first time. ]
That is q is NOT a constant but the odds of going correct after G generations of size z. Thus, since s is a variable which will affect a rather large exponentiation, s will affect its value as it falls.
Indeed at s = 0, q will be zero independent of G; save for the trivial case where the initial string is the target. As s –> 0, q for a given G will fall towards zero, and that will be in the context of a probably large Q = G* z.
Which is what the intuitive expectation is too.
(And I think this all shows just how hard it is to “read” these eqns right, on all sides.)
6] Nakashima-san:
Appreciated.
I guess I need to go off and do 500 lines of serious derivation as due penance to the gods of mathematics . . .
However, the dynamical-empirical fundamentals of Weasel and why implicit latching is a credible account for the showcased runs c 1986 remain the same. (And that is why I rely on and prioritise dynamical-empirical methods.)
GEM of TKI
PS: I may need clarify what I mean by no-change cases: members of a pop of mutants that are equal to the seed for the generation. With pops of reasonable size and low enough mut rates per letter, they are very likely to be present. So they are the latching backstop: another mutant is likely to be chosen by the gen champ selecting filter only if they preserve the existing letters AND add a new one. Failing such, the no-change case passes through to be the next gen champ. And in fact the two 1986 showcased runs hit target in 40+ [with 3 initially correct letters] and 60+ gens, indicating that about 1/2 the time no-change members won the contest to be seed for the next gen. [This is of course discussed in my App 7 the always linked. (I confess I get the distinct feeling that a lot of critiques are in a context of having never read what I actually have to say step by step on the matter.)]
PPS: For a more technically sophisticated version:
1] Bayes Th:
p(A|B) = p(A AND B) / p(B)
2] Here, what I have given as probability of going correct is actually in context prob of going correct on being selected:
p(K|S) = 1/N,
–> where N alternative values for a given character are possible (here, 27) and there is no reason to prefer any one value relative to the rest
–> of these N values, one is correct
–> in the case of potential implicit latching, each letter in turn for a member of a pop is subject to selection and if chosen, will take up one of N values at random, one of these being correct relative to the “distant” target. [This is of course at he heart of the dis-analogy between Weasel and real life as CRD acknowledged in BW.]
3] We are interested in the probability of being selected AND being correct:
p(K AND s) = p(K|S) * p(S)
–> Where p(S) = s, by definition, i.e. the per letter mut rate.
–> And we see already that p (K|S) = 1/N
4] So, substituting and rearranging:
p(K AND S) = (1/N) * s = s/N
–> this is the result presented more loosely above.
–> And, it is why I said the probs are ‘effectively” independent. (I am aware that conditional probability and Bayes th etc are even harder to think through. Cf my discussion in App 6 on Caputo et al . . .)
PPPS: And of course weirdly enough for s = 1, it turns out that we see 1/N. (But the case is artificial, as an implicitly latched version would be practically — with probability, almost anything is logically possible but some things are practically impossible — impossible and an explicitly latched version would be utterly unlikely to run as illustrated. That is the M & D example is most credibly by way of illustration, not a credible actual run. And of course we should reckon with the implications of the multiple algors at EIL. There is no THE M & D algorithm to be contrasted to a “THE” Dawkins algor. [Indeed, it is now quite clear that here will be no fortcoming c 1986 Weasel code; absent such code, we do not know the actual state of the algors c 1987 beyond all reasonable dispute; so various interpretations of Weasel c 1986 have a certain degree of legitimacy, and indeed that is so despite statements and declarations made in subsequent years. A declaration is not a demonstration, especially when it is made after the fact of a debate challenge and the decisive evidence is not forthcoming.])
Utterly unlikely? I don’t think so! And if you asked W. Dembski and R. Marks, I’m sure they’ll tell you that the example wasn’t constructed, but an actual run of some program. Of course, they may have discarded some runs without any (new) correct letters in the first two generation (the most probable events) – but their example is more probable than getting firstly a queen and secondly a black two from a deck of card.
But I suppose you’ll tell me that drawing the queen of hearts and then the two of spades is utterly unlikely and not a credible actual run of the game of drawing two cards.
This is fun.
This has to be the slowest derailment I have ever watched.
kairosfocus at post 66
kairosfocus at post 372
Expedient, but wrong. You were correct at post 66, but since then you have had to concede that the partitioned search they ‘described, exemplified, and analyzed’ is quite different from TBW Weasel. Hence the evasion.
So now, according to kf, there is no “THE” M&D algorithm in Section E, just an unrealistic illustration – Huh? So what are they calculating the active information for?
As the train ever so slowly comes off the rails, kf has learnt that eqn 22 can be simply modified to take into account mutation rates other than 100%. Now would be a good time to re-read posts 34, 114, 164, and the first half of 305.
With s/N replacing 1/N in eqn22, do some exploring. You still cannot get a partitioned search that looks like the TBW run.
kairosfocus at post 375
That’s not really “weird“, it is the starting point, and the algorithm that M&D explicitly describe. With Math. And it CANNOT be Weasel.
More importantly, equation 22 cannot be modified to take generational champions into account. When DiEb asks you to “just show me some values”, he is gently trying to show you that your Q = GenSize x Gen# approximation leads to results that are waaaay off. I can help you here: You have showcased a run of 21 generations, where Q = 999 x 21 = 20,979, with a mutation rate of 8% (your run D). According to your math (post 367)
the probability that this search is not finished within the first 11 generations is 1 in 5 million million. Try it at home:
My computer returns zero if I try to put a number >12 into this equation….