"Uncommon Descent" and "The Skeptical Zone" in 2015

Since 2005, Uncommon Descent (UD) - founded by William Dembski - has been the place to discuss intelligent design. Unfortunately, the moderation policy has always been one-sided (and quite arbitrary at the same time!) Since 2011, the statement "You don't have to participate in UD" is not longer answered with gritted teeth only, but with a real alternative: Elizabeth Liddl's The Skeptical Zone (TSZ). So, how were these two sites doing in 2015?

Number of Comments 2005 - 2015

year	2005	2006	2007	2008	2009	2010	2011	2012	2013	2014	2015
UD	8,400	23,000	22,400	23,100	41,100	24,800	41,400	28,400	42,500	53,700	53,100
TSZ	-	-	-	-	-	-	2,200	15,100	16,900	20,400	45,200

In 2015, there were still 17% more comments at UD than at TSZ.

Uncommon Descent in Numbers - 2nd edition

Three years ago, I put up some pictures showing the number of comments and threads at Uncommon Descent. Now seems to be a good occasion to up-date some of this information.

1. Google Trends

Look for yourself: The phrase Uncommon Descent was most searched for in 2008. After that, everybody had bookmarked the site, so further googling became unnecessary. The same holds true for The Panda's Thumb - both sites are equally popular...

2. Threads per Month

The number of new threads per month peaked in 2011, but is still on a high level - though it seems to be decreasing. What makes all the difference is "News" - a.k.a. Denyse O'Leary - adding her news items. While in 2011/2012, those often were left uncommented, since 2013, they attract the attention of her fellow editors (though I got the impression that some commentators use them for their off-topic-remarks, while others just cannot let the copious factual inaccuracies stand uncommented.)

Questioning Information Cost - A reply to Winston Ewert

Over at Uncommon Descent, Winston Ewert (one of the three authors of the paper A General Theory of Information Cost Incurred by Successful Search) answers in the article "Questioning Information Cost to "a number of questions and objections to the paper" I raised. He states fives points, which I will address in this post. Obviously, I'll give my reply at Uncommon Descent, too, but their format doesn't allow for mathematical formulas, so it is easier to make a first draft here. I thank Winston Ewert for his answers, but I'd appreciate some further clarifications.

Firstly, Dieb objects that the quasi-Bayesian calculation on Page 56 is incorrect, although it obtains the correct result. However, the calculation is called a quasi-Bayesian calculation because it engages in hand-waving rather than presenting a rigorous proof. The text in question is shortly after a theorem and is intended to explicate the consequences of that theorem rather than rigorously prove its result. The calculation is not incorrect, but rather deliberately oversimplified.

Fair enough. So it's not a quasi-Bayesian calculation, but a Bayesian quasi-calculation. I will amend my post (Please show all your work for full credit...) by Winston Ewert's explanation.

Secondly, Dieb objects that many quite different searches can be constructed which are represented by the same probability measure. However, if searches were represented as a mapping from the previously visited points to a new point (as in Wolpert and Macready’s original formulation), algorithms which derive the same queries in different ways will be represented the same way. Giving multiple searches the same representation is neither avoidable nor inherently problematic.

The problem is that Dembski's, Ewert's and Marks's construction of the representation does not only depend on the discriminator (see the next point), but on the target, too. Take $\Omega = \{1,2,3,4\}$ and two searches with two steps:

• The first search consist just of two random guesses, i.e., at each step, one of the numbers is given with probability $1/4$.
• The second search has two guesses, too. But at the first step, $1$ is taken with probability $7/16$ and each other number with $3/16$, while at the second step, one is omitted from the guess and each other number it guessed with a probability of $1/3$.

These two searches are quite different: the first may produce a query $(1,1)$ with probability $1/16$, while the second never will. Now take a discriminator $\Delta$ which returns the target if it is in the query and otherwise another element in the query at random. Such a discriminator seems to be quite natural and it is certainly within the range of the definition on pages 35--36.
Now, the distribution which $\Delta$ infers on $\Omega$ depends on the target: if we are looking for $\{1\}$, we get:

• First search: $\mu_{\{1\}}^1$ given by $\mu_{\{1\}}^1(\{1\}) = 7/16$, $\mu_{\{1\}}^1(\{2\})= \mu_{\{1\}}^1(\{3\})= \mu_{\{1\}}^1(\{4\})=3/16$
• Second search: $\mu_{\{1\}}^2 = \mu_{\{1\}}^1$

These are two algorithms which don't derive the same queries albeit in different ways, but nonetheless they will be represented the same way!
In fact, if our target is $\{2\}$, we get other distributions:

• First search: $\mu_{\{2\}}^1$ given by $\mu_{\{2\}}^1(\{2\}) = 7/16$, $\mu_{\{2\}}^1(\{1\})= \mu_{\{2\}}^1(\{3\})= \mu_{\{2\}}^1(\{4\})=3/16$
• Second search: $\mu_{\{2\}}^2\{1\} = 14/96$, $\mu_{\{2\}}^2\{2\} = 44/96$, $\mu_{\{2\}}^2\{3\} = \mu_{\{2\}}^2\{4\}= 19/96$.

Frankly, this seems to be "inherently problematic".

Thirdly, Dieb objects that a search will be biased by the discriminator towards selecting elements in the target, not a uniform distribution. However, Dieb’s logic depends on assuming that we have a good discriminator. As the paper states, we do not assume this to be the case. If choosing a random search, we cannot assume that we have a good discriminator (or any other component). The search for the search assumes that we have no prior information, not even the ability to identify points in the target.

This seems to be a little absurd. Shouldn't your representation work for any discriminator - even a good one? If we are following Wolpert's and Macready's formulation, a blind search means that we try to maximize a characteristic function. So, the natural discriminator should return this maximum if it is found in a query. If it doesn't, we build a discriminator which does: we have the output of the inspector, so why not use it? If you are telling us that the output of the inspector may be false, then I'd use another inspector, one which gives us the output of the fitness function. If you say now that the output of the fitness function may be dubious, I'd say "tough luck: I maximize this function whether the function is right or wrong - what else is there to do?". These added layers of entities which have a hidden knowledge about the target which isn't inherent to the fitness function seem to be superfluous.

Fourthly, Dieb doesn’t see the point in the navigator’s output as it is can be seen as just the next element of the search path. However, the navigator produces information like a distance to the target. The distance will be helpful in determining where to query, but it does not determine the next element of the search path. So it cannot be seen as just the next element of the search path.

So, what is the difference between the inspector and the navigator? The navigator may take the output of the inspector into account, but nonetheless one could conflate both into a single pair of values - especially as you allow "different forms" for the inspector. So you could get rid of the third row of the search matrix.

Fifthly, Dieb objects that the inspector is treated inconsistently. However, the output of the inspector is not inconsistent but rather general. The information extracted by the inspector is the information relevant to whether or not a point is in the target. That information will take different forms depending on the search, it may be a fitness value, a probability, a yes/no answer, etc.

Sorry, I may have been confused by the phrase "The inspector $O_{\alpha}$ is an oracle that, in querying a search-space entry, extracts information bearing on its probability of belonging to the target $T$": if we look at the Dawkins's Weasel and take the Hamming-distance as the fitness function, each returned value other than $0$ tells us that the probability of belonging to the target $T$ for an element is zero itself, whether it is "METHINKS IT IS LIKE A WEASER" or "AAAAAAAAAAAAAAAAAAAAAAAAAAAA". I understand that you want to avoid the notion of proximity to a target, but your phrasing is misleading, too. Have you any example of a problem where the inspector returns a probability other than 0 or 1? In your examples, it seems to be always the output of a fitness function.

The authors of the paper conclude that Dieb’s objections derive from misunderstanding our paper. Despite five blog posts related to this paper, we find that Dieb has failed to raise any useful or interesting questions. Should Dieb be inclined to disagree with our assessment, we suggest that he organize his ideas and publish them as a journal article or in a similar venue.

It's always possible that I've misunderstood certain aspects of the paper. I would be grateful if you helped to clear up such misunderstanding. I hope that my comments above count as useful and at least a little bit interesting. I'm preparing an article, as I've promised earlier, but the work is quite tedious, and any clarification of the matters above. Furthermore, I'd like to know whether this "general framework" is still in use, or whether you have tried another way of representing searches as measures. Again, thank you Winston Ewert!

The Ithaca Papers

William A. Dembski announces in his CV/Resumé on his web site Design Inference - Education in Culture and Worldview some books which are still in preparation. Top of the list is

Biological Information: New Perspectives (co-edited with Robert J. Marks II, John Sanford, Michael Behe, and Bruce Gordon). Under contract with Springer Verlag.

Well, rejoice, the electronic version of this book has been published (and is free for download!), and the hard copy is announced for August 2013. Albeit the publisher switched from Springer to World Scientific, the announcement hasn't changed:

In the spring of 2011, a diverse group of scientists gathered at Cornell University to discuss their research into the nature and origin of biological information. This symposium brought together experts in information theory, computer science, numerical simulation, thermodynamics, evolutionary theory, whole organism biology, developmental biology, molecular biology, genetics, physics, biophysics, mathematics, and linguistics. This volume presents new research by those invited to speak at the conference.

While the publication of Stephen C. Meyer's new book Darwin's Doubt is hailed with great fanfare at the Discovery Institute's news-outlet Evolution News, the appearance of this volume hasn't made their news yet - though Dembski and Meyer are both fellows of the Discovery Institute's Center for Science and Culture (granted, Meyer is its director). Only at Dembski's (former) blog, Uncommon Descent, there are two posts about the book:

• Download the Cornell papers free here
• Download Cornell papers on origin of biological information free

Instantly, there arose a discussion about Denyse O'Leary's (commenting under the nom de guerre "News") choice of title, where the usual combatants switched sides: the evolutionists claimed the title was designed to mislead the average reader to think that the Cornell University was somewhat involved in the conference, the apologists of Intelligent Design argued that this was just chance. Unfortunately, no one answered to my comment:

In the interest of discussing the data and the evidence, could we have posts on various articles of the book? I’d be quite interested in a thread on Chapter 1.1.2 “A General Theory of Information Cost Incurred by Successful Search” by William A. Dembski, Winston Ewert and Robert J. Marks II.
I hope that the authors are still reading this blog: this way, we could have a productive discussion, and perhaps some questions could be answered by the people involved!
And for the sake of a swift exchange of ideas: could someone please release me from the moderation queue?

Maybe there is no interest in such a discussion at Uncommon Descent. Maybe no one read the comment - it was hold in the moderation queue for five days, and when it appeared, the article wasn't any longer at the front page. Therefore I'll start a number of posts on “A General Theory of Information Cost Incurred by Successful Search” here at my blog: I just can't believe that this peer-edited article would have been successfully peer-reviewed by Springer....

Again a proud number as a headline at Uncommon Descent: 10,000!

Again a proud number as a headline at Uncommon Descent: 10,000! The whole thing reads:

This is the 10,000th post at UD. We would like to thank all of our loyal readers, lurkers, commenters, writers, webmaster, contributors and all the others who have made this a wonderful run so far!

So congratulations! But I just have to pour some water in Barry Arrington's wine:

1) It comes actually a little bit late...

The last announcement of a milestone was the thread on Uncommon Descent's 9,000 post on May 14, 2012 - I commented on this event here. At this time, more than 200 threads were created per month, so the 10,000-ceiling should have been shattered in August 2012 (or September 2012) at the latest. What happened? Denise O'Leary - who put on thread after thread under the witty name "news" - left and took here energy over to The Best Schools' Blog, where she now baffles a non-existing audience (which isn't allowed to respond). I don't know why she did so, but it cut the number of threads per month by 75%.

2) The loyal commenters aren't that loyal any longer...

More than 3,300 editors have commented on Uncommon Descent. But over the last months, the number of unique editors per month is decreasing: in October, November and December 2012 it fell even below 100 - the smallest numbers since mid-2005!

3) But at least the number of comments is up - somewhat...

After a period of drought in the first half of the year 2012, the numbers have risen again. Most comments are made by the regulars, therefore the number of deleted comments became very small in November and December 2012. Not small enough though: a couple of my remarks never appeared...

Some Annotations to the Previous Post

1. Joe, at this point I'd advice students to draw a decision tree. Some would draw one with six nodes in the first layer, representing the machines $M_1, M_2, ... , M_6$ and then 36 nodes in the second layer, representing each of the possible outcomes from $1,2,...,6$ for each of the machines. At each of the branches, they put the possibility to get from one node to the next, and at the end of the the diagram they write down the 36 probabilities for the outcomes which they get by multiplying the probabilities on the branches which lead to the outcome. However, others would opt for a much easier design, summarizing the machines $M_2, M_3, ..., M_6$ as $\overline{M_1}$, and the non-desirable outcomes $\{1,2, ...,5\}$ as $\overline{6}$, which leads to the following graph:

Could you please correct your miscalculation, Dr. Dembski?

William A. Dembski wrote "a long article […] on conservation of information. " at Evolution News and Views (ENV), an outlet of the Discovery Institute. Others have commented on more sophisticated problems, either at Uncommon Descent or at The Skeptical Zone. Here I want just to correct some simple math which occurs in a toy example used in the article:

To see how this works, let's consider a toy problem. Imagine that your search space consists of only six items, labeled 1 through 6. Let's say your target is item 6 and that you're going to search this space by rolling a fair die once. If it lands on 6, your search is successful; otherwise, it's unsuccessful. So your probability of success is 1/6. Now let's say you want to increase the probability of success to 1/2. You therefore find a machine that flips a fair coin and delivers item 6 to you if it lands heads and delivers some other item in the search space if it land tails. What a great machine, you think. It significantly boosts the probability of obtaining item 6 (from 1/6 to 1/2).

9,000!

9,000! is the proud headline of a post by Barry Arrington at Uncommon Descent. The whole thing reads:

The post before this one was UD’s 9,000th. Thank you to all of our readers for your support as we celebrate this milestone.

So congratulations! But a comment by SCheesman pours a little water into the celebratory wine:

I wish I could celebrate, but I fear 9000 is a reflection of a vast inflation in the number rate of postings in the last year or two, with a corresponding decline in comments.
I owe a good deal of what I know today about ID from UD, both from a scientific and theological perspective, and used to enjoy the long threads and back-and-forth between proponents and opponents.
But now, many, if not most posts get nary a comment, and the ones engendering some debate often are lost in the crowd. Since the recent purge of participants who failed to pass what amounted to a purity test, it’s been pretty quiet here. The most lively recent discussion featured a debate between OEC’s and YEC’s. Now I enjoy that sort of thing (like on Sal Cordova’s old “Young Cosmos” blog), but it’s hardly what UD used to be known for.
Maybe the new format gets more visitors than it used to, but I’d be interested in seeing the stats, including comments per post, posts per month, unique visitors etc. over the last few years.
I miss the old days. I expect a lot of us do.

I'll try to satisfy the curiosity as good as I can.

Posts per month

Uncommon Descent in numbers

Uncommon Descent was started in April 2005 as the “Intelligend Design WebLog of William Dembski”. Since then some 200,000 comments (77 per day) were made to 8,600 (3.4 per day) posted articles.
That's not shabby: I don't think that Panda's thumb (including AtBC) or the discussion board at www.RichardDawkins.net are more busy, though PZ Myers would probably be disappointed by such a low turn out.

Horizontal No Free Lunch Theorem

In my previous post I criticized the Horizontal No Free Lunch theorem for searches consisting of at least two queries. But even in the case of a single assisted query, I can't get my head around it.

Dembski and Marks define an assisted query as any choice from Ω₁ that provides more information about the search environment or candidate solutions than a blind search. As an example, they give for instance, we might imagine an Easter egg hunt where one is told “warmer” if one is moving away from an egg and “colder” if one is moving toward it.

The ultimate assisted search is no search at all, the unveiled Easter egg. So, imagine a blind (A), a drunken (B), and a seeing, sober (C) chess-player, and ask them to locate the White Dame (♕) on a chess board. (A) will be find it with a probability of 1/64, (C) with a probability of 1, and lets assume for (B) a probability of 1/2.

Then (A) represents the blind search, (B) an assisted search and (C) what the authors call a perfect search on our search space Ω = {a1,a2,....,h8} (|Ω|=64).

Imagine that ♕ is positioned on a1, so T₁ = {a1}. Then we have three probability measures, α_a1, β_a1, and γ_a1 for each one of our players, which allow us to calculate the probability for each one to find T₁:

• α_a1(T₁)= 1/64


• β_a1(T₁) = 1/2


• γ_a1(T₁) = 1

And we can calculate - according to (3.1) (10) the active information of these measures for various sets and combinations, e.g.
I₊(β_a1|α_a1(T₁)){a1} = log₂1/2 - log₂1/64 = 5.

So, the drunken player has more active information on the whereabouts of ♕ than the blind one.

I₊(γ_a1|α_a1(T₁)){b1} = log₂0 - log₂1/64 = -∞

A more surprising result: if ♕ is on b1, but (C) sees it on a1, he is much less informed than (A).

But of course, γ_a1 isn't the right measure if ♕ is on b1, we would expect γ_b1: the idea of an assisted search seems to be that it assists to the right direction - for our Easter egg hunt: if your helper directs you always to the same place, whether there is an egg or not, he is no helper indeed, he's just a nuisance:

Trivially, a search helped in this way can't be differed from an unassisted search.

But I'm afraid that exactly what W. Dembski and R. Marks do in their Horizontal No Free Lunch Theorem: let's take the partition T~ = {{a1},{a2},...,{h8}} of our Ω₁ above. What does

Σ α_a1{T_i} × I₊(γ_a1|α_a1){T_i}

mean? Nothing else than that our seeing, sober man errs 63 times out of 64 when looking for ♕. That just doesn't make sense.

The meaningful expression would have been:

Σ α_Ti{T_i} × I₊(γ_Ti|α_Ti){T_i}

And while the first sum adds up to -∞ the latter one is not negative at all: it's just 6.

nota bene: I think this is the idea behind Rob's (R0b?) comment to my previous post. So, thanks Rob!

Search for Search Paper Finally Out

William A. Dembski informs us at Uncommon Descent that the paper A Search for a Search:Measuring the Information Cost of Higher Level Search (a collaboration with Robert Marks II) is finally published. To things are remarkable about his post:

• The comments are turned off
• It's so restrained - wasn't this paper once announced as a nail to the coffin of Darwinism?

One obvious flaw I found in an earlier draft of the paper is addressed: instead of talking about any searches, they are now talking about searches without repetition.

But I've still a(t least one) problem with this paper, which may be resolved by more careful reading over the next few days. As I wrote to Robert Marks:

I was a little bit irritated that the proof of the HNFLT still uses the
Kullback-Leibler distance, as I can't see how a non-trivial search-space
(i.e., a search spaces for a search existing from at least two queries)
can be exhaustively partitioned in a meaningful way.

Here's is an example I used earlier: Imagine a shell game with three shells where you are allowed to have two guesses. To put it more formally:

• The search space Ω₁ is {1,2,3}

In section 2.1. Blind and Assisted Queries and Searches, Dembski and Marks describe how such searches can be construed as a single query when the search space is appropriately defined. They introduce an augmented search space Ω_Q, existing from the sequences without repetition of length Q, i.e., the number of queries. In our case:

• The augmented search space Ω₂ is {(1,2),(1,3),(2,1),(2,3),(3,1),(3,2)}

Of course, the target has to be changed accordingly to T_Q, where T_Q ∈ [sic] Ω_Q consists of all the elements containing the original target.

So, if in the original game the shell with the pea was No. 1, in our new space, T₂ = {(1,2),(1,3),(2,1),(3,1)}. All of this seems to be sensible

Let's have a look at a search strategy, for instance:

• First, look under a random shell
• Second, look under another random shell

By such a strategy, a probability measure is introduced on Ω₂, and the probability of a successful search for T₂ can be seen immediately: it's |T₂|/|Ω₂| = 4/6 = 2/3. No surprise here.

In fact, any search strategy can be seen as a measure on Ω_Q - and that's what Dembski and Marks are doing in the following. My problem: not any subset of Ω_Q can be seen as a reasonable target for a search: The complement of T₂ doesn't represent any target in the original space Ω₁! And though this set can be measured by the measure introduced above (2/6), this measure doesn't make sense in the context of a search.

And that's what I don't understand about the Horizontal No Free Lunch Theorem (3.2). The first sentence is:

Let φ and ψ be arbitrary probability measures and let T~={T_i}_i=1^N be an exaustive partition of Ω all of whose partition elements have positive probability with respect to ψ

How can Ω₂ partitioned in a sensible way? And why should I try to compare two search strategies on sets which they will never look for?

The Original Weasels?

W. Dembski introduces two programs in his post The original weasels at his blog Uncommon Descent. These programs were sent to him by someone called Oxfordensis, and W. Dembski states

These are by far the best candidates [for being Dawkins's original program] we have received to date.

Let's have a short look:

Weasel 1

Here's how this program works for the target "METHINKS IT IS LIKE A WEASEL":

1. Chose random string
2. copy string 100 times, each time changing exactly one letter at random
3. select string with most correct letters in place
4. is the number of correct letters 28? Then STOP. Otherwise:
5. goto 2

The mutation procedure is interesting: While most programs I've seen mutate the parent string by changing each letter with a certain probability, here, exactly one letter is changed - but I've seen implementations of this version, too. The letter-based mutation seems to be more natural, while the other one has mathematical advantages: the neighbourhood of a string s, i.e., the strings s can mutate into, becomes small: it isn't the whole set of size 27²⁸ ≈ 1.20 * 10⁴⁰ anymore, but only of size 27 * 28 = 756...
Another advantage: you only have to call your random generator twice for each child, while a straight-forward implementation of the letter-mutating process take (1+μ)*28 of these costly calls per child - though this number can be reduced to (1+28*μ) calls per child....
So, one parameter less to tweak: though the number of children is set to 100 in this program, this can be changed easily.

But which value to chose for the remaining parameter - the size of the population? The bigger the size of the population, the less generations (black line) it takes to complete the search. So, make it big? No, not necessarily: commonly, you want your program to be fast. Therefore, you should try to reduce the number of queries (blue line), i.e, the number of mutated strings - which is the number of evaluations of the fitness function, too. Mutating at random, and calculating the fitness function, that's what's taking time.
I suppose if you fool around with the program for a while, you'll quickly find out that the optimal size of generations in the sense above is about 50 - and an exact calculation leads to an average of 3931 queries for a population size of 49 as an optimum (σ = 648.04).

Weasel 2

Well, this beast is boring. BORING. Look how it works for the target "METHINKS IT IS LIKE A WEASEL":

1. Chose random string
2. make new string by copying old string one time, changing exactly one letter at random
3. chose string from old and new string with most correct letters in place
4. is the number of correct letters 28? Then STOP. Otherwise:
5. goto 2

It's just a randomized version of the hangman game, taking 2969 steps on average (σ = 959.2). And it's what W. Dembski and R. Marks call Optimization by Mutation With Elitism in their current paper:

3) Optimization by Mutation With Elitism: Optimization by
mutation with elitism is the same as optimization by mutation
in Section III-F2 with the following change. One mutated
child is generated. If the child is better than the parent, it
replaces the parent. If not, the child dies, and the parent
tries again. Typically, this process gives birth to numerous
offspring, but we will focus attention on the case of a single
child. We will also assume that there is a single bit flip per
generation.

Conclusions

Could these be the programs used by R. Dawkins in his book The Blind Watchmaker? The first one would fit his algorithm, and with a population size, it would take 47.6 generations on average (σ= 11.7). And what's about the BBC video? If the second version was used for this, I'd regard it at best as a visual effect, as it doesn't match Dawkins's algorithm. And yes, it is (implicitly) latching :-)

Random Mutation

In their paper Conservation of Information in Search: Measuring the Cost of Success William Dembski and Robert Marks present an algorithm which resembles Dawkins's weasel (the algorithm I talked about before - at length :-)
It isn't the algorithm Partioned Search introduced on p. 1055, it's the algorithm Random Mutation on p. 1056. The differences

1. the alphabet consists of two letters, not 27.
2. the target length is 100, not 28
3. the size of a generation is quite low: it's two
4. the mutation probability per letter is very small: µ = 0.00005

Many programmers have implemented weasel-like programs, and the runs I've seen usually use a µ between 0.04 and 0.05, while the generation size is greater than 20.

So, why do W. Dembski and R. Marks use their values? Well, in the appendix of their paper, they calculated an approximation for the number of correct letters depending on the number of generations. This approximation discards terms quadratic in µ, so to use it, not only has µ << 1, but the size of a generation has to be small, too.

But should they use these values? I don't think so: As usual, I modeled their algorithm as a Markov chain and could calculate some exact values. The expected number of generations to get to the target for their choice of parameters is 55,500. (see pic 1)

Some fooling around with their program should have shown that this number can be reduced dramatically by using an more appropriate value for µ. The optimum lies near to µ ~ 0.0005, which takes only 10,600 generations.


And though their approximation doesn't work as fantastically as for the parameter ten times smaller, the numbers are not more than 2.5% off. (see pic 2)

A New Weasel

At Uncommon Descent, W. Dembski presents us with a new weasel: Someone with the name Oxfordensis programmed years ago two Pascal versions.
The interesting aspect: In contrast to the usual weasels - as discussed in the earlier posts - not every letter is changed with a certain probability in this program, but exactly one letter is changed in each child. Here, the word change is used loosely, as with a probability of 1/27, no letter is changed at all.
Mathematically, this is easier to handle: the transition matrix of the corresponding Markov process gets sparser...
And you have only one parameter which can be changed: the size of the generation.
If I had any reader he may ask himself: Does this algorithm latch? Well, the pic provides the answer: it depends :-)
And here are some values for the probability that the program will show a change to the worse during a run of the program, depending on the size of the population:

10. 99.999 %
20. 98.485 %
30. 83.879 %
40. 55.944 %
50. 30.008 %
60. 14.071 %
70. 6.168 %
80. 2.649 %
90. 1.137 %
100. 0.491 %
110. 0.214 %
120. 0.094 %

So, even with a generation size of one hundred children, one in two hundred runs will show that this algorithm doesn't latch - it's not what W. Dembski and R. Marks describe as a partitioned search.

"Your comment is awaiting moderation...."

Perhaps I should be grateful that I'm not blocked at Uncommon Descent. Update: Perhaps I should have been grateful that I was not blocked at Uncommon Descent.
But it's rather annoying to wait for a couple of hours to get your comment through moderation while a discussion is ongoing: my edit contributed at 2:52 am today (Aug 26, 2009) has still not appeared over six hours later, though there were fifteen other comments in the meantime. What is so hard in moderating the following?

I took the string
SCITAMROFN*IYRANOITULOVE*SAM
and calculated a next generation using Dawkins's algorithms with populations of 10,50 and 100 - and mutation rates of .04, .05 and .1. The tenth string in the list is the second generation given in the paper of Mark and Dembski. The differences with the first generation are in bold face:

1. SCITAMROFN*IYRANOIEULOVE*SAM
2. SCITAMROFN*IYRANOITULOGE*SAM
3. ECITAMRI*N*IYZANOITULOVE*SAM
4. SCITAMROFN*IYRANOITUL*VE*SAM
5. SCITAMROFN*IYRANOITULOVE*SEM
6. SCITAMOOLNOIYRAMOITULOVE*SEM
7. SCITANROFN*IYYANOITULOVE*SAM
8. SCITIMROFN*JYRANOITULOVE*SAM
9. SCITAMROFN*ICRHNOITSLOWE*SAV
10. OOT*DENGISEDESEHT*ERA*NETSIL

Can anyone spot a difference in the design of the strings? Anyone? KF? Anyone?

I'll stay tuned :-)

Update: Now I've two comments waiting in the queue:

232 - DiEb - 08/26/2009 - 9:39 am Your comment is awaiting moderation.
I try to get involved in the discussion, but my last edit (#213) is now in moderation for nearly seven hours…

Update: After eight hours, the comment got through. But I seem to be blocked from now on....