Sunday, September 28, 2014

Conservation of Information in Evolutionary Search - Talk by William Dembski - part 5

For an introduction to this post, take a look here. As I ended part 4 quite abruptly, this section starts in the middle of things....

Part 4: 45' 00" - 52' 50"

Topics: What is Conservation of Information? Example continued.

William Dembski: These tickets have probability 1/2, 1/2, 1/2, 1/2, and this one ticket has probability 1. If I happen to get this ticket, I have probability 1/2 of choosing curtain 1, but it is also probability 1/9 of getting that ticket. When you run the numbers, at the end of the day, by using these tickets, I'm not better of than I was originally. It is still only a probability of 1/3 of finding curtain 1, of finding the prize there. Once one factors in how did I limit myself to these tickets in the first place. Going from this whole space to this, that is information intensive. I have ruled out certain possibilities, that incurs an information cost. As I said, the cost is 5/9. It is really just an accounting thing. That is what conservation of information is. Once you factor in the information that it takes to get the search, get a search which has improved the probability for finding your original target, we haven't gained anything. It is called Conservation of Information, as the problem can even get worse. At this case, we have broken even, we are back to 1/3 for the probability of getting the prize, but let's say, you really want to improve the probability, you want to guarantee that you get that prize with this tickets. Well, then you have got only one ticket that will work for you.

Conservation of Information in Evolutionary Search - Talk by William Dembski - part 4

For an introduction to this post, take a look here.

Part 4: 31' 25" - 45' 00"

( I had to pause at 45', there is such an elementary mistake in Dembski's math, it was just to funny...)

Topics: What is Conservation of Information?

William Dembski: Now let us get to the heart of things "Conservation of Information". What is that conservation? Let me put on the next slide.

William Dembski: This is probably the most gem-packed slide in this talk. I want to make a distinction between -what I call - probable and improbable events, and probable and improbable searches. An improbable event is just something that is high in improbability: flip a coin a thousand times, get a thousand heads in a row. Highly improbable. It happens: if you believe in a multi-universe, then there is a universe where this is happening, where someone like me is speaking, my double-ganger flips a coin over the next hour and sees 1000 heads in a row. Probable and improbable search, that is where what is the probability that a search is successful. It is not so much asking whether it actually succeeds, it is not concerned with the result. It is concerned with the probability distribution associated with the search. This is an important distinction because so many intelligent design arguments look for a discontinuity in the evolutionary process. We look for highly improbable events. Such as the intelligent design people: you get for instance Thomas Nagel's "Mind and Cosmos". He is basically looking at probabilistic miracles. Think how the origin of life undercuts a materialistic understanding of biology. So he is looking into improbable events. That is what we do when we try to find evidence for a discontinuity. What I'm doing in this talk is saying, look, I'm going to give you evolution, give you common ancestry, all of that. That is no problem. What I'm interested though is the probability of success for a search.

member of the audience: What are we searching for?

William Dembski: It is whatever the target happens to be.

Saturday, September 27, 2014

Conservation of Information in Evolutionary Search - Talk by William Dembski - part 3

For an introduction to this post, take a look here. There is some interaction with the audience (15'30" - 18'00") which I wasn't able to understand fully. Any help is appreciated!

Part 3: 12' 45" - 31' 25"

Topics: What is an evolutionary search?

William Dembski: Now let's add this next term evolutionary. What does evolutionary - when we put it in front of search - add to the discussion? I think it changes one key aspect here. Whereas we were looking at some query feedback, now this query feedback takes the form of fitness: how good is it? Query feedback can be quite general. Maybe the query feedback is nothing, when we examine it. Or maybe the query feedback may just say "I'm in the target" or "I'm not in the target". That would be very simple. Fitness is going to give some sort of range of values that ideally identify how close am I to the target.

William Dembski: There are examples of evolutionary search. There is the Dawkins' weasel example from his book "The Blind Watchmaker", that is the one I'm going to focus on here. Then there are various - what I would regard as - embellishments of that, because I don't think that there is anything fundamentally new about them. There is MSU's Avida program, Tom Ray's Tierra, Schneider's ev. What is at the heart of these programs that these are computer programs which mimic - try to mimic - Darwinian evolutionary processes. What are they supposed to show? That is interesting. Look at the history of this field of evolutionary computing and there is a reason why people wanted to do evolution in the computer. That is because the computer would allow evolution to be done in real time, because we cannot really see it in real time in the wild.

Friday, September 26, 2014

Conservation of Information in Evolutionary Search - Talk by William Dembski - part 2

For an introduction to this post, take a look here. This is quite a short section, with some annotations from me.

Part 2: 09' 40" - 12' 45''

Topics: What is a search?

William Dembski: We talked about information. Let's now look at that second key term "Search". What is a search. There are seven key components in a search.

William Dembski: You have a search space, you have a target - we are looking for something in the search space. There is initialization - where do we start off? There is a query limit - how many things in the search space can we check out? There is query feedback - when we have checked out, when we have located some item - what is it telling us about itself in terms of how it relates to the target? There is an update rule - once we have queried something, what do we query next? And then finally a stop criterion - when do we stop? How do we know that we have done enough? This is very general.

Thursday, September 25, 2014

Conservation of Information in Evolutionary Search - Talk by William Dembski - part 1

For an introduction to this post, take a look here.

Part 1: 00' 00" - 09' 40''

Topics: Introduction, What is information?

Leo Kadanoff: [???] He went on to broader interests in subjects including information theory, philosophy and parts of biology. The best write-up I could find about him was the Discovery Institute's write-up on the web: "mathematician philosopher William A. Dembski is senior fellow with the Discovery Institute. He has taught at the Northwestern University, the University of Notre Dame, and the University of Dallas. He has done postdoctoral work in mathematics at MIT, in physics in Chicago, and in computer science at Princeton. He is a graduate of the University of Illinois, of the University of Chicago, and of Princeton.
His fields include mathematics, physics and philosophy, as well as theology. We probably hear only a fraction of those interests today in his talk about the "Creation of Information in Evolutionary Search".

William Dembski: Okay, well, Leo, it is a pleasure to be back here. Leo was my adviser back in 87/88, along with Patrick Billingsley and [???]. The topic is actually "Conservation of Information in Evolutionary Search. I want to speak about that

Leo Kadanoff: I said creation! [???]

William Dembski: I'm called a creationist enough, so I make that distinction when I can. What I will describe is the work that I have done with the Evolutionary Informatics Lab - this is their website.

William Dembski's talk at the University of Chicago

Invited by Leo Kadanoff, William Dembski spoke on Aug 15, 2014 at the University of Chicago's "Computations in Science" seminar. Jerry A. Coyne - a professor in the department of ecology and evolution at the same university - questioned the judgement of the seminar's organizers. Afterwards, the Discovery Institute was very pleased with its paladin William Dembski.
"The talk itself and the Q&A afterward, which were at a pretty high level, went very well."
, and they loved a concluding remark by Leo Kadanoff:
I think the ball is in the court of people who believe in evolution. They have to deal with these questions. ...Bill has made his case and we should all go home and think.
At William Dembski's former blog Uncommon Descent, a video of the talk-cum-questions was posted on Sep 14, 2014:

This video has gotten very little resonance. To make it easier to access, I have created a transcript, which I will publish on this blog in a short series of posts. Obviously, the usual caveats apply: I'm not a native speaker, but I tried my best to understand and reproduce the talk as truthfully as possible. I apologize in advance for my errors, which inevitably have occurred, and I'm grateful for any correction.

How "official" is the video?

The question arose: who actually taped the talk? Some student, who then put it up on youtube? I think that it is a work of members of the Discovery Institute:
  1. The youtube channel MissIngaNiball on which the video is presented seems to belong to Robert Marks (wikipedia, American Loons), or at least a member of his family (in which case a predilection for feeble puns would be hereditary).
  2. Two stills taken from the video are credited to Paul Nelson (wikipedia, American Loons)in the Discovery Institute's article.

Dembski's talk: Part 1 - 5

Sunday, July 14, 2013

Dembski's, Ewert's and Marks's Concept of a Search Applied to Exhaustive Searches

At Uncommon Descent, Winston Ewert, co-author of the paper A General Theory of Information Cost Incurred by Successful Search, writes:
"The search is defined to be a six-tuple consisting of the initiator, terminator, inspector, navigator, nominator, and discriminator. The paper studies the question of picking a search at random, and that would imply picking each of the six components at random. We did not consider it necessary to specifically state that each individual component was also selected at random. That would seem to be implied.
So, let $\Omega = \{\omega_1, \omega_2, \dots, \omega_N\}$ be our finite search space with $N$ elements. We are looking for a single element $\omega_k$, so we try to maximize the fitness function $f = \chi_{\omega_k}$. To keep everything finite, we don't allow repetitions, i.e., in our search each place can only be visited once. This is - as Macready and Wolpert observed - always possible by keeping a look-up table and thus doesn't change the set-up. Therefore, our search is completed in at most $N$ steps.
(BTW: The claim that "each of the six components [is picked] at random" seems not to apply to the inspector: this is a fixed function for a search - in our case, the inspector returns the value of the fitness function. Of course, you can say that we pick the inspector at random out of the set of the one possible inspector.)
Let's take a look at all the searches which are ended by their terminator only after the $N$-s step, i.e., the subset of all exhaustive searches. The price question: What is the probability to find the target in such an exhaustive search? Until now, everyone looking at such problems would have thought that this probability is one: we certainly visited $\omega_k$ and spotted that the function $f$ takes it maximum there. But in the world of Dembski, Ewert, and Marks it is not, as a random discriminator takes its toll - and discriminators aren't obliged to return the target if it was found and identified...
Counterintuitive? That is a flattering description: the discriminator's purpose seems to be to turn even a search which is successful by all human standards into a guess to fit the idée fixe that each search can be "represented" by a measure on the search space.
Addendum: We can drop the condition of not having repetitions in our searches and just look at those searches which are terminated only after the whole search space was visited: terminators with this property exist. Such searches may have length $N$, but can be much longer. The result is the same: the probability of finding the target during a complete enumeration of the search space is (much) less than one. I have to ask: What good is a model in which an exhaustive search doesn't fare much better than a single guess?