“Conservation of Information Made Simple” at ENV

_{William Dembski

August 28, 2012

Informatics, Intelligent Design}

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Evolution News & Views just posted a long article I wrote on conservation of information.

EXCERPT: “In this article, I’m going to follow the example of these books, laying out as simply and clearly as I can what conservation of information is and why it poses a challenge to conventional evolutionary thinking. I’ll break this concept down so that it seems natural and straightforward. Right now, it’s too easy for critics of intelligent design to say, ‘Oh, that conservation of information stuff is just mumbo-jumbo. It’s part of the ID agenda to make a gullible public think there’s some science backing ID when it’s really all smoke and mirrors.’ Conservation of information is not a difficult concept and once it is understood, it becomes clear that evolutionary processes cannot create the information required to power biological evolution.” MORE

TEASER: The article quotes some interesting email correspondence that I had with Richard Dawkins and with Simon Conway Morris, now going back about a decade, but still highly relevant.

Comments

#44 “As for including numbers 7 – infinity (by which I assume you mean all integers greater than 6, none of which is actually infinity), is there any reason not to do so, other than inconvenience?”
Yes, if you include them then you could never figure out the odds of rolling a "6" with a fair die. As I said you appear not to know anything about the topic that you are trying to discuss. But seeing that you are anonymous you don't care that you look foolish.Joe_{September 5, 2012
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Okay, in #120 I told you, in set notation, what I think the definition of ? is in that example. Can you tell me, in set notation, what you’re claiming the definition of ? is?
I told you- • A is the uniform distribution over the rightmost four squares in the search space. • B is the uniform distribution over the bottom twelve squares in the search space. That you refuse to understand that exposes your agenda and your lack of integrity.Joe_{September 5, 2012
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Marks offers an example of searching for an good boiled egg recipe, given 66 possibilities.
Blah, blah, blah- It has already been proven that your intent is just to purposely mess up whatever Marks or Dembski says. So why should anyone try to respond to you?Joe_{September 5, 2012
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Given the following: - Set A has 4 elements - Set B has 12 elements - 3 of the elements in A are also in B - ? = A?B What is |?|? If we label the squares in the grid from the example as follows: 1.1 1.2 1.3 1.4 2.1 2.2 2.3 2.4 3.1 3.2 3.3 3.4 4.1 4.2 4.3 4.4 I claim that in the example we’re discussing, ? = {1.1, 1.2, 1.3, 1.4, 2.1, 2.2, 2.3, 2.4, 3.1, 3.2, 3.3, 3.4, 4.1, 4.2, 4.3, 4.4}.
You can claim that all you want. It proves my point that you are wasting my time. What the ACTUAL example says:
• A is the uniform distribution over the rightmost four squares in the search space. • B is the uniform distribution over the bottom twelve squares in the search space.
R0bb's example doesn't look like the actual example.Joe_{September 5, 2012
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What equation are you talking about?
The equation that goes with the figure/ exampe. As I said you are wasting my time.
What if I defined ? for a die as {even numbers, odd numbers}. Is that improperly defined?
Yes, it is as 8 is an even number that is not on the die. And BTW R0bb, throwing te die an having to have it land on a certain number is a measure of the physical difficulty of doing so.Joe_{September 5, 2012
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Joe:
We always exclude zero-probabilty outcomes. That you think we don’t or shouldn’t tells me that you aren’t interested in having a serious discussion.
Marks offers an example of searching for an good boiled egg recipe, given 66 possibilities. Knowledge of chemistry reduces the number of possibilities to 44. I claim that Marks would say that there are about .6 bits of active information in this knowledge of chemistry. According to your position, how many bits of active information are in this knowledge of chemistry? Dembski often uses an example in which a treasure map reduces the number of possible burial sites to one. According to your position, how much active information is in the map?
We have been over this alrewady and you pointed to an example that excluded 3 blocks that had a zero probability as if they were included.
Okay, in #120 I told you, in set notation, what I think the definition of Ω is in that example. Can you tell me, in set notation, what you're claiming the definition of Ω is?R0bb_{September 4, 2012
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Joe:
Which sets were improperly defined, and what was improper about them?
They look as if a 3 year old defined them. Other than that, nice job for a 3 year old. For example:
But we could, instead, define ? as {1, higher than 1}
Yes, you could so define the set, if you want to be a jerk or if you are a 3 year old.
What if I defined Ω for a die as {even numbers, odd numbers}. Is that improperly defined? What if we were talking about poker hands and I defined Ω as {royal flush, everything else}. Is that improperly defined?R0bb_{September 4, 2012
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But 3 of the squares in A are also in B.
And you’re just realizing that now?
Of course not. What makes you think that?
Did you not read the equatuation and discussion or did you jusrt decide to post without understanding it?
What equation are you talking about? Given the following: - Set A has 4 elements - Set B has 12 elements - 3 of the elements in A are also in B - Ω = A∪B What is |Ω|? If we label the squares in the grid from the example as follows: 1.1 1.2 1.3 1.4 2.1 2.2 2.3 2.4 3.1 3.2 3.3 3.4 4.1 4.2 4.3 4.4 I claim that in the example we're discussing, Ω = {1.1, 1.2, 1.3, 1.4, 2.1, 2.2, 2.3, 2.4, 3.1, 3.2, 3.3, 3.4, 4.1, 4.2, 4.3, 4.4}. According to you, what is Ω? Can you answer the questions in bold above?R0bb_{September 4, 2012
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Does evolutionism apply to the real world? If yes, in what way?Joe_{September 4, 2012
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R0bb- We always exclude zero-probabilty outcomes. That you think we don't or shouldn't tells me that you aren't interested in having a serious discussion. We have been over this alrewady and you pointed to an example that excluded 3 blocks that had a zero probability as if they were included.Joe_{September 4, 2012
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R0bb:
Which sets were improperly defined, and what was improper about them?
They look as if a 3 year old defined them. Other than that, nice job for a 3 year old. For example:
But we could, instead, define Ω as {1, higher than 1}
Yes, you could so define the set, if you want to be a jerk or if you are a 3 year old. You choose...Joe_{September 4, 2012
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R0bb:
But 3 of the squares in A are also in B.
And you're just realizing that now? Did you not read the equatuation and discussion or did you jusrt decide to post without understanding it?
As has been pointed out by Dieb and others, the probability is the same whether you search for the 6 by rolling the die directly or search for the 6 indirectly via the machines. Are you under the impression that when Dembski says “difficulty”, he’s referring to something more than just improbability?
The probability includes the probability of locating te machines, ie the difficulty.
But I didn’t say “without any prior knowledge of where the needle is located”. I said “without any prior knowledge”.
As I tried to tell, THAT doesn't even make any sense.Joe_{September 4, 2012
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R0bb, thanks, appreciated. "But I disagree with Chance’s statement that the scenario is perfectly clear." I'll revise my statement to say that it was perfectly clear to me. "Why does he say “the probability of finding item 6 using this machine, once we factor in the probabilistic cost of securing the machine”, rather than simply saying “the probability of finding this machine AND finding item 6 with it”?" Perhaps he thought his intended audience would understand his meaning. I certainly did. "Why not just state the LCI as “P(A&B) ? P(B)” and call it good?" Yes, that's exactly the implication. I can only imagine that he wanted to be clear to his audience, that given circumstances of a search for a shortcut, one might actually do definitively worse, and he wanted to show why this might be the case. I found the example straightforward enough. DiEb @93, I didn't see your comment previously. I didn't intend to ignore. "1) Do you agree that the probability to find the target “6? using the two-layered system of at first choosing a machine at random and then let the machine choose the target is 1/6 ?" I said as much in #87, and provided an example at #97, agreeing that the total probabiliity comes out to 1/6, but disagreeing that it was relevant to Dembski's example of an intersection of events. "2) W. Dembski says: “So our attempt to increase the probability of finding item 6 by locating a more effective search for that item has actually backfired, making it in the end even more improbable that we’ll find item 6.” How do you square this with your answer to 1) ?" If the machine is chosen specifically for its property of increasing the probability of securing item 6, then it comes with a 1/6 cost. If one cares not which machine one obtains, then there is no intersection to account for, and the total probability applies. Dembski was clear that the incurred cost may negatively affect the outcome, not that it certainly would. By that qualification, it may or may not come with a cost:
Conservation of information says that this is always a danger when we try to increase the probability of success of a search -- that the search, instead of becoming easier, remains as difficult as before or may even, as in this example, become more difficult once additional underlying information costs, associated with improving the search and often hidden, as in this case by finding a suitable machine, are factored in.
Those comments are very much in context to the example provided. That example was merely to demonstrate what might constitute a "cost" by necessitating the securing of the 'six' machine. onlooker @104, my #97 illustrates what I see as the difference. Glad to hear that you enjoyed your weekend. :-)Chance Ratcliff_{September 4, 2012
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Tangents, tangents . . .kairosfocus_{September 4, 2012
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Which sets were improperly defined, and what was improper about them?
They were set in jello?Mung_{September 4, 2012
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Ok R0bb- your math is invalid because your your sets were imporperly defined.
Which sets were improperly defined, and what was improper about them?R0bb_{September 4, 2012
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Joe:
R0bb? Is that it then?
That depends. Do you plan on answering the following questions that I've asked? #31 "Have you read the examples and proofs in Dembski's work?" #43 "As I pointed out in #31, endogenous probability is defined as |T|/|Ω|, not |T|/(number of choices). Do you agree that this is how it's defined?" #43 "You might be of the opinion that Ω is supposed to be defined such that |Ω| = number of choices, and therefore endogenous probability = |T|/|Ω| = |T|/(number of choices). Is that your position?" #43 "If that is your position, do you believe that Dembski and Marks always define Ω such that |Ω| = number of choices?" #43 "If that is not your position, why do you think that the endogenous probability is |T|/(number of choices)?" #43 "Consider the concept of "Brillouin active information" ... Why would Dembski and Marks define a measure that's always zero?" #44 "Pardon my thick skull, but are you referring to my random walk example? If so, what aspect of the random walk are you describing as a roll of the die? Or are you talking about the die example in my second post at TSZ?" #44 "No, it means that if we always exclude zero-probability outcomes from Ω, then in some cases active information will decrease when a search improves. Do you agree?" #44 "As for including numbers 7 - infinity (by which I assume you mean all integers greater than 6, none of which is actually infinity), is there any reason not to do so, other than inconvenience?" #45 "Can you provide definitions for your terms 'muddled' and 'properly defined'? A distribution is muddled iff __________________________. A distribution is properly defined iff __________________________." #57 "Where exactly did I mangle what Dembski said?" #57 "Consider some of their other examples of active information, like Marks' example of finding a good recipe for boiling an egg. ... Do you think Marks would agree that the active info is zero?" #57 "Also consider Dembski's oft-used example of a treasure map. Them map eliminates all outcomes except for one. Does the map have zero active information?" #68 "In #53 you said that my examples were mathematically valid. Have you changed your mind?" #69 "And BTW, how does Dembski's example apply to the real world?" #69 "How do his three CoI theorems apply to the real world?" #69 "If any of Dembski's examples or theorems don't apply to the real world, is he being uncivil by bringing them up?" And a question that I've asked three times: "If the LCI fails in mathematically valid cases, is it a true law?" And the most important questions, from #58: "1. Are you interested in doing the work it takes for us to understand each other?" "2. Are you interested in having a civil discussion, free of taunts?"R0bb_{September 4, 2012
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Dieb, Chance, and others: I agree with Chance, in that I think Dembski's intent is to say that the probability of A AND B is 1/12. I think this because he is more explicit about it in the section "The LCI Regress" on page 25 of this paper. The LCI Regress amounts to nothing more than the fact that hitting two targets is less likely than hitting just one. But I disagree with Chance's statement that the scenario is perfectly clear. I think Dembski could have easily made it more clear. Why does he say "the probability of finding item 6 using this machine, once we factor in the probabilistic cost of securing the machine", rather than simply saying "the probability of finding this machine AND finding item 6 with it"? Why speak sometimes in terms of "cost" and other times in terms of "probability", sometimes in the same sentence, when all he's talking about is probability? (For that matter, why does he use words like "complexity", "information", or "difficulty" when he means improbability? Some readers, including some IDists, take "complex" to mean complicated, "information" to mean symbols that convey meaning, and Joe thinks that Dembksi is referring, at least in part, to physical difficulty.) Why not just state the LCI as "P(A&B) ≤ P(B)" and call it good?R0bb_{September 4, 2012
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Joe:
A different 16. A 16 that does NOT include those 3: - A is the uniform distribution over the rightmost four squares in the search space. - B is the uniform distribution over the bottom twelve squares in the search space.
But 3 of the squares in A are also in B. If you're correct that Ω = A∪B, then |Ω| = 13, not 16. (Unless you're thinking that Ω is a multiset, but you realize that a sample space can't be a multiset, right?)
Is it easier to roll a die to get your 6, a 1/6 probability than it is to also have to search for a machine that will allow you to find your 6 by say flipping a coin? And if there are 6 machines out there that will help you find your 6, but only one is the 50/50, is that less or more difficult than just rolling a die?
As has been pointed out by Dieb and others, the probability is the same whether you search for the 6 by rolling the die directly or search for the 6 indirectly via the machines. Are you under the impression that when Dembski says "difficulty", he's referring to something more than just improbability?
Nope. My point was that someone without any prior knowledge of where the needle is located can use a metal detector to enhance his/ her chances of having a successful search- ie making it a much better chance of success than a blind search.
(Emphasis mine.) But I didn't say "without any prior knowledge of where the needle is located". I said "without any prior knowledge". To only consider prior knowledge of where the needle is located, and ignore the prior knowledge used to build a metal detector, is an example what Dembski and Marks call a "familiarity zone".R0bb_{September 4, 2012
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Ok R0bb- your math is invalid because your your sets were imporperly defined. That is why we don't leave math up to people intent on messing it up.Joe_{September 4, 2012
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Joe:
It is mathematically valid to say that 2 unicorns plus 2 unicorns = 4 unicorns. However in the real world there aren't any unicorns.
The only non-mathematical objects I've used in my examples are dice, boxes, and coins, which do exist in the real world. But that's beside the point. The point is that it's easy to show mathematical counterexamples to Dembski's mathematical "law". You said that my examples were mathematically valid, but when I asked "If the LCI fails in mathematically valid cases, is it a true law?", you said, "Can something be mathematically valid when applied to something that is invalid, such as your mangled sets?" So which is it -- are the counterexamples mathematically valid or not? Your follow-up questions were, "If so then how does it apply to the real world? And if it doesn't apply then why even bring it up unless you are not interested in a civil discussion?" My examples server the same purpose as Dembski and Marks' examples, namely to illustrate the math. They are not intended to show a useful application of the math to the real world. As I asked before, how does Dembski's dice-and-machines example apply to the real world?R0bb_{September 4, 2012
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onlooker, Which of your links contains evidence that blind and undirected processes can produce CSI? And if none of them do then what is the refutation, exactly?Joe_{September 4, 2012
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onlooker, R0bb smooched the pooch- notice that he hasn't returned once his folly was exposed.Joe_{September 4, 2012
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Chance, Sorry for the delay in replying. I was enjoying the long weekend and, when I finally got around to writing a response, got distracted by some additional reading on Dembski's "Law of Conservation of Information". More on that below.
Either Dembski is talking about the probability of finding the target after the right machine is found, a true conditional probability, in which case the answer is .5 or he is talking about the “final cost”, which is the total probability of the two step process of choosing a machine and then asking it for a value, in which case the answer is 1/6.
Or he is talking about the probability of both finding the correct machine (1/6) and finding the correct item after finding the correct machine (1/2), which actually what he said.
I agree that is what he said. My claim is that is exactly his error. By ignoring the fact that the other machines can produce the target, Dembski changes the definition of the problem midstream. The change in odds he calculates isn't due to the actual probability distribution but to an arbitrary choice to ignore possible solutions. That makes his "cost" incorrectly high. I suspect that we're doing the equivalent of arguing about angels dancing on pins, though. As I mentioned, while writing this response to you, I read through Dembski's LCI paper and discussions of it available online. I found several quite thorough refutations of it, including these: http://www.talkorigins.org/faqs/information/dembski.html#Conservation_of_Information http://scienceblogs.com/goodmath/2009/05/07/so-william-dembski-the/ http://scienceblogs.com/goodmath/2008/12/19/fitness-landscapes-evolution-a/ http://mfinmoderation.wordpress.com/2010/08/21/comments-on-the-law-of-conservation-of-information/ http://www.sciencemeetsreligion.org/evolution/information-theory.php http://mfinmoderation.wordpress.com/2010/08/21/comments-on-the-law-of-conservation-of-information/ The last one listed contains links to additional discussion of the issue. Have you read any of these? If so, I'd be interested in hearing your thoughts. Some of the points raised in those reviews are echoed by R0b in three posts at The Skeptical Zone. While I mostly lurk there, I'm sure your participation would be welcome.onlooker_{September 4, 2012
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Ah, yup, something like" "the cost of the search for a [good] search."kairosfocus_{September 3, 2012
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Kairosfocus- They can't even address the fact that their distraction point also demonstrates it is easier to role a die than it is to search for and locate the machines- just as Dembski said. However if you are giving points for being belligerent they are racking up the points. Bless their pointy little headsJoe_{September 3, 2012
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F/N: this is evidently yet another case of a red herring distractor led off to a strawman side issue. Notice, just how little of the above actually addresses the main point. KFkairosfocus_{September 2, 2012
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Chance- I am just saying it could be clearer and not lend any ammunition for any distractions from the point. Right now there is too much of one (distraction) and not enough of the other (discussion). It is bad enough that our opponents focus on the hand and finger that are doing the pointing and not the idea/ concept that is being pointed out. To just feed them stuff they can use to take other people's focus off the point is just poor planning. Unless, of course it was part of the plan so you could gather data studying those type of people-> people forced to dstract from the point by arguing the irrelevant minutia. Just sayin'... ¥Joe_{September 2, 2012
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Joe, I believe the scenario is perfectly clear, and I've nothing to add that hasn't been said already. If Dr. Dembski believes clarification or qualification is required, perhaps he'll offer it here. I'll check back later. Peace.Chance Ratcliff_{September 2, 2012
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Chance, In Dembski's scenario we can get the final target of a 6 without securing the "6" machine. And we would never know if the 6 we got was from the "6" machine or any of the other 5 machines. And if you can't tell the machines apart- isomorphic/ the principle of indifference- then the ONLY thing you will know is if your search was successful or not. You will never know why. That said the rest of what you said is correct given a specific scenario- that being the search can only continue IFF the "six" machine is chosen at the first level or the other machines do not offer a chance at the target 6.Joe_{September 2, 2012
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