Do the ID interpretations of NFL theorems imply the creationist Genetic Entropy hypothesis?

@Joe:

Just because someone can fabricate an alleged bijective function doesn’t mean it is right.

What do you mean by "right"? Is the function f(x)=a "right" or "wrong"?

How can one set contain all of the elements of another set and have members the other does not and still have the same cardinality?

I told you the condition for two sets having the same cardinality. What exactly do you not understand? Are you by any chance confusing cardinality with JOEC (your invention)? JWTruthInLove

JW, if you aren't going to read my responses then just leave it be. Just because someone can fabricate an alleged bijective function doesn’t mean it is right. And I do mean fabricate- as in it is just a figment of one’s imagination. and How can one set contain all of the elements of another set and have members the other does not and still have the same cardinality? It’s as if you believe infinity is some sort of magical equalizer. It isn’t… Deal with that or don't bother because all you are doing is repeating what I am disputing. And just repeating that says you have no clue. Joe

We might have a communication problem.

And what makes your math book correct?

What do you mean by "correct"? What are you testing it against?? JWTruthInLove

@Joe

How can one set contain all of the elements of another set and have members the other does not and still have the same cardinality?

Wiki provides you with an answer, as does any math book:

Two sets A and B have the same cardinality if there exists a bijection, that is, an injective and surjective function, from A to B. Such sets are said to be equipotent, equipollent, or equinumerous. (Wiki)

My math book actually explicitly states that if A is a proper subset of B, then the cardinality of A can be equal to cardinality of B. JWTruthInLove

And what makes your math book correct? Why is it that you are not dealing with what I said? How can one set contain all of the elements of another set and have members the other does not and still have the same cardinality? It's as if you believe infinity is some sort of magical equalizer. It isn't... Joe

My math book provides an equivalent definition. So Wiki seems to be correct. Do you have any evidence that cardinality is defined differently in literature? JWTruthInLove

JW what makes wiki correct? Just because someone can fabricate an alleged bijective function doesn't mean it is right. And I do mean fabricate- as in it is just a figment of one's imagination. Joe

@Joe: A has cardinality strictly greater than the cardinality of B if there is an injective function, but no bijective function, from B to A. (Wiki) You ve claimed theres an error. Where is the error? JWTruthInLove

JW, it's like this: Given two sets, A & B, such that set A has all the members of set B PLUS has members set B does not, set A's cardinality has to be greater than set B's. That is unless you think that infinity is some sort of magical equalizer. Joe

@Joe: Do you have a link to the specific post? JWTruthInLove

On my blog JW. Joe

I disagree with Cantor and I have explained why he is wrong.

Where did you explain that? JWTruthInLove

You are my tag line DiEB. You and all the moronic evoTARDs. And mathematicians don't seem to be able to appraise what i have said. They are all just stuck on Cantor and the think just repeating his tripe will convince me. What's up with that? Why is it that not one mathematician can tell us the utility of saying all countable and infinite sets have the same cardinality. Look, you chumps can continue to believe that infinity is some sort of magical equalizer. That reflects on you, not me. Joe

natural scientists DiEb

I disagree with Cantor and I have explained why he is wrong. Joe, could you please make this your tag line? It would save mathematicians and natural so much time when they have to appraise a point you make... DiEb

LoL! Just say that you can't do it, DiEB. So infinity only exists in our minds. It is a mental construct only. Joe

Joe: "Can you show me infinity in the real world, DiEB? Are there an infinite number of atoms in the universe? Are there an infinite number of events in the universe?"

When we model the world, we make some assumptions: one of the most important is that we often assume that things are continuous or even smooth - think of Newtonian mechanics. Why? Because it works! So, in modeling the world we introduce analysis, a branch of mathematics loaded with all kinds of infinite things.... DiEb

DiEB spews:

More precisely: you struggle with Cantor’s concept, but you don’t have any problems with your concept.

Nice spewage. I disagree with Cantor and I have explained why he is wrong. Just because you morons are too stupid to grasp that you have to lie about me. And I am making OBSERVATIONS not invectives. Joe

Joe: "I don’t have any struggles with infinity, you do." More precisely: you struggle with Cantor's concept, but you don't have any problems with your concept. For mathematicians in general it's the other way around. BTW: what is it with all these invectives? I never thought that insults would be helpful when discussing mathematics! DiEb

DiEB:

I’m speaking about infinity in a purely mathematical sense without any atheistic or religious implications: for those, you should look for Nikolaus von Kues…

You speak of infinity yet you cannot demonstrate its existence outside of our minds. Infinity is a mental construct only. It does not exist in biology. It does not exist as a search space. And DiEB's cowardly refusal to answer my questions proves that he is not interested in any discussion. Joe

Earth to the lying keiths- I don't have any struggles with infinity, you do. But now I see your desperation has you lying through your teeeth, as usual. Joe

DiEB:

I don’t see how any discussion of the mathematical theory of the No Free Lunch theorems can be carried out with you on such premises.

LoL! Cantor's thouhts have nothing to do with NFL. Nothing at all. That you would even drag him into it shows your desperation. Joe

Hmm, seems that our Darwinian faithful want to claim ‘infinity’ as a concept that belongs in their atheistic province.

I'm speaking about infinity in a purely mathematical sense without any atheistic or religious implications: for those, you should look for Nikolaus von Kues... DiEb

As for the other topic here, it seems pretty obvious to me that the "search space" in biology is not one of potentially infinite functions on a set of elements. The actual "space" being "searched" is just the physically realizable configurations of biological creatures. Only actual concrete organisms are "selected," not abstract functions about those organisms. I also don't see how, even in a hypothetical search of an infinite space, it wouldn't still hold that an evolutionary algorithm doesn't outperform chance in arriving at particular goals without being given any information about the those goals, which is the part of the NFL theorems that the ID folks use in their argumentation. Deuce

Hmm, seems that our Darwinian faithful want to claim 'infinity' as a concept that belongs in their atheistic province. I really don't think they want to go down that route: This following video on 'infinity' is very interesting for revealing how difficult it was for mathematicians to actually 'prove' that mathematics was even true in the first place:

Georg Cantor - The Mathematics Of Infinity - video http://www.metacafe.com/watch/4572335 entire video: BBC-Dangerous Knowledge - Part 1 https://vimeo.com/30482156 Part 2 https://vimeo.com/30641992

Kurt Godel's part in bringing the incompleteness theorem to fruition can be picked up here

Kurt Gödel - Incompleteness Theorem - video http://www.metacafe.com/w/8462821

As you can see, somewhat from the preceding 'Dangerous Knowledge' video, mathematics cannot be held to be 'true' unless an assumption for a highest transcendent infinity is held to be true. A highest transcendent infinity which Godel, and even Cantor, held to be God.

Taking God Out of the Equation - Biblical Worldview - by Ron Tagliapietra - January 1, 2012 Excerpt: Kurt Gödel (1906–1978) proved that no logical systems (if they include the counting numbers) can have all three of the following properties. 1. Validity . . . all conclusions are reached by valid reasoning. 2. Consistency . . . no conclusions contradict any other conclusions. 3. Completeness . . . all statements made in the system are either true or false. The details filled a book, but the basic concept was simple and elegant. He summed it up this way: “Anything you can draw a circle around cannot explain itself without referring to something outside the circle—something you have to assume but cannot prove.” For this reason, his proof is also called the Incompleteness Theorem. Kurt Gödel had dropped a bomb on the foundations of mathematics. Math could not play the role of God as infinite and autonomous. It was shocking, though, that logic could prove that mathematics could not be its own ultimate foundation. Christians should not have been surprised. The first two conditions are true about math: it is valid and consistent. But only God fulfills the third condition. Only He is complete and therefore self-dependent (autonomous). God alone is “all in all” (1 Corinthians 15:28), “the beginning and the end” (Revelation 22:13). God is the ultimate authority (Hebrews 6:13), and in Christ are hidden all the treasures of wisdom and knowledge (Colossians 2:3). http://www.answersingenesis.org/articles/am/v7/n1/equation# The God of the Mathematicians - Goldman Excerpt: As Gödel told Hao Wang, “Einstein’s religion [was] more abstract, like Spinoza and Indian philosophy. Spinoza’s god is less than a person; mine is more than a person; because God can play the role of a person.” - Kurt Gödel - (Gödel is considered one of the greatest logicians who ever existed) http://www.firstthings.com/article/2010/07/the-god-of-the-mathematicians

bornagain77

Hi Sal: I think if random chance tends to degrade and eliminate biological complexity, and if the No Free Lunch implies Darwinian evolution will do no better than random chance, then the ID interpretation of the No Free Lunch theorem mandates the Genetic Entropy thesis. It wouldn't be biological complexity per se that would be expected to go down or stay the same, right, but rather specified complexity in particular? That seems like the right prediction, but I think it would be tough to measure. Deuce

DiEb, For more on Joe's struggles with infinity, see this thread. keiths

Not only that but followers of Cantor don’t seem to be able to deal with infinite sets. I don't see how any discussion of the mathematical theory of the No Free Lunch theorems can be carried out with you on such premises. DiEb

The ID interpretation of No Free Lunch theorems argues that Darwinian processes on average will not do better than chance processes for the emergence of biological complexity.

On explanation for why "Darwinian processes" do not perform any better than a blind search is that "Darwinian processes" are in fact blind searches. Not just a blind watchmaker. No watchmaker at all. Mung

Can you show me infinity in the real world, DiEB? Are there an infinite number of atoms in the universe? Are there an infinite number of events in the universe? What part of taht quote refutes what I said? Joe

Search spaces whose elements are themselves searches may be thought of as consisting of probability measures or fitness landscapes or other functions on the original search space. Spaces of functions on an original space are always richer than the original space and, in case the original space is finite, grow exponentially or even super-exponentially in cardinality. Spaces of probability measures, for instance, are always infinite.

Footnote 18 from Dembski's, Ewert's, and Marks's article "A General Theory of Information Cost Incurred by Successful Search" DiEb

DiEB:

Unfortunately, the issue which I raised cannot be discussed without at least the most modest understanding of probability theory not only on finite but on infinite sets.

LoL! Your position doesn't deserve a seat at probility discussions and infinite sets do not exist in the real world of biology- infinity only exists in our minds. Not only that but followers of Cantor don't seem to be able to deal with infinite sets. And you don't seem to be capable of ideas. BTW evolutionary algorithms are design mechanisms... Joe

Thanks Dieb, I have nothing much to add, it's not my field of expertise, and hence I posted to solicit more expert discussion. At issue is what we should actually see in the field. I think deterioration is the correct prediction. Sal scordova

@Joe, it is very nice of you that you try to contribute. Unfortunately, the issue which I raised cannot be discussed without at least the most modest understanding of probability theory not only on finite but on infinite sets. Our little exchange of ideas let me to the conclusion that you are lacking the basic skills to follow this discussion on an advanced high-school or even undergraduate niveau. So, while I acknowledge your taking notice, it is of little consequence for any of the ideas involved, I'm afraid. DiEb

Anyone what? Anyone notice that DiEB did NOT post any evidence that demonstrates darwinian processes can actually do something more than just eliminate the defincient and defective? That anyone? OK, I have noticed. Satisfied? Joe

Anyone? DiEb

My 2¢: In all these optimization problems, you try to find the extremum of a function f taken from a set of functions F by evaluating f at various points. The NFLT hold when F has a certain kind of symmetry: it has to be closed under permutation. This is trivially given when you look at the characteristic functions of elements of a search space - the favorite example of Robert Marks and William Dembski. But when the functions get less simple, this closedness of F is rarely given: I haven't seen a real world example where the functions take more than two values and F is closed under permutation - other than F being the set of all possible functions. In fact, F seems to be very "asymmetric" in general - think of TSP as an example. Evolutionary algorithms aren't clever or elegant. They tend to be wasteful - and if you have an "intelligent" solution for a problem, this is to be preferred. But they are easily programmable and often work on the sets F we find as problems taken from reality. I don't think that the proponents of ID will find a striking argument for ID by looking at the NFLT - and I'm generally not happy by the way they try to exploit them: see my e-mail to Dembski, Ewert & Marks about BI:NP - A General Theory of Information Cost Incurred by Successful Search . DiEb