kairosfocus at post 66

23 –> however, on p. 1055, they simply describe, exemplify and analyse a partitioned search.

kairosfocus at post 372

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
[Emphasis DNAJ's]

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

PPPS: And of course weirdly enough for s = 1, it turns out that we see 1/N.

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)

q ~ [1 - (1 - s/N)^{G*z}]^L

the probability that this search is not finished within the first 11 generations is 1 in 5 million million. Try it at home:

q ~ [1 - (1 - 0.08/27)^(999*11)]^28

My computer returns zero if I try to put a number >12 into this equation….

[ .. ] 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.

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.

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 . . .)

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

As you know, Eqn 22 on p 1055 of the IEEE paper is about the effect of latched search, with the probability of capturing a correct letter built in already in the parameters.

In #123 you stated:

Again, once the run of generational champions takes on the cumulative progress, ratcheting-latching pattern [and cf the showcased runs of 1986 on that], it makes but little difference whether it is produced explicitly or implicitly.

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.

Sir, I honor you. Keep up the good work.

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

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.

Across these months, here are some points where I have been bitterly opposed by Darwinist critics and have proved objectively correct:

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.

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.

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.

Yes, one can construct a strawman algorithm from this which will not resemble Dawkins’ “algorithm”

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.

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.])

The algorithm described by M&D in section III.E is not a possibility, as it contradicts Dawkins’ description and reported results.

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.

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.