Orgel and 500 Coins

_{Barry Arrington

November 25, 2014

Intelligent Design}

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In his 1973 book The Origins of Life Leslie Orgel wrote: “Living organisms are distinguished by their specified complexity. Crystals such as granite fail to qualify as living because they lack complexity; mixtures of random polymers fail to qualify because they lack specificity.” (189).

In my post On “Specified Complexity,” Orgel and Dembski I demonstrated that in this passage Orgel was getting at the exact same concept that Dembski calls “specified complexity.” In a comment to that post “Robb” asks:

500 coins, all heads, and therefore a highly ordered pattern.
What would Orgel say — complex or not?

Orgel said that crystals, even though they display highly ordered patterns, lack complexity. Would he also say that the highly ordered pattern of “500 coins; all heads” lacks complexity?

In a complexity analysis, the issue is not whether the patterns are “highly ordered.” The issue is how the patterns came to be highly ordered. If a pattern came to be highly ordered as a result of natural processes (e.g., the lawlike processes that result in crystal formation), it is not complex. If a pattern came to be highly ordered in the very teeth of what we would expect from natural processes (we can be certain that natural chance/law processes did not create the 500 coin pattern), the pattern is complex.

Complexity turns on contingency. The pattern of a granite crystal is not contingent. Therefore, it is not complex. The “500 coins; all heads” pattern is highly contingent. Therefore, it is complex.

What would Orgel say? We cannot know what Orgel would say. We can say that if he viewed the “500 coins; all heads” pattern at a very superficial level (it is just an ordered pattern), he might say it lacks complexity, in which case he would have been wrong. If he viewed the “500 coin; all heads” pattern in terms of the extreme level of contingency displayed in the pattern, he would have said the pattern is complex, and he would have been right.

About one thing we can be absolutely certain. Orgel would have known without the slightest doubt that the “500 coin; all heads” pattern was far beyond the ability of chance/law forces, and he would therefore have made a design inference.

Comments

Mark, thank you for the link to the wikipedia article. According to it and the way Aleta phrased the question, the answer is indeed 1/2.Orloog_{November 28, 2014
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Mark Frank:
(I just missed the deadline for deleting my comment!)
Don't delete comments! That way lies chaos. Just think of the 20-minute window as an opportunity to correct typos and add additional comments prefaced by "ETA"="edited to add". (I speak from experience. Internet discussions can become chaotic if people start deleting comments.) Even worse is when people delete entire threads.keith s_{November 28, 2014
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#127 This inspired me to look at the wikipedia article on the paradox. Apparently it is more complex and debateable than I thought. (I just missed the deadline for deleting my comment!)Mark Frank_{November 28, 2014
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Keith S, Orloog Aleta is right - the probability is 1/3 not 1/2. It is a well-known paradox. Prior to seeing the boy at the window the four possibilities: BB, GB, BG and GG are all equally probable. Observing the boy eliminates GG but does not change the relative probability of the other three possibilities. I am interested to know how you did your simulation Orloog. You can be pretty certain there is something wrong with it as the maths is bomb proof as far as I know.Mark Frank_{November 28, 2014
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Thank you, R0bb: I even run a simulation, as I didn't trust my calculations any longer, the result was 1/2...Orloog_{November 28, 2014
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R0bb:
Not to be contrarian, but I’m going to have to disagree with those who gave an answer of 1/3 to Aleta’s riddle. The solution in #112 assumes that BB, BG, and GB are all equally likely. But given that we’ve seen a boy, BB is actually twice as likely as each of the others. So the answer is in fact 1/2.
Interesting! I think I understand your logic, and I think I can show where it goes wrong, but let me think about it some more and reply later. In the meantime, I have some other comments to write. :-)keith s_{November 27, 2014
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Not to be contrarian, but I'm going to have to disagree with those who gave an answer of 1/3 to Aleta's riddle. The solution in #112 assumes that BB, BG, and GB are all equally likely. But given that we've seen a boy, BB is actually twice as likely as each of the others. So the answer is in fact 1/2.R0bb_{November 27, 2014
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Eric, After you've answered R0bb, a challenge awaits on your own thread.keith s_{November 27, 2014
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Mung @ 54:
Well there I went again. But this time it wasn’t Orgel using the word “information” but Kolmogorov. Can’t wait to see your snide remark about this one.
You've pointed out that Orgel, Kolmogorov, and Dembski all use the word "information". I'll gladly respond when you tell me what conclusion you draw from this.R0bb_{November 27, 2014
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Eric @ 119: Just to be clear, the dispute in this thread is over the claim that Orgel and Dembski mean the same thing when they say "complexity". Setting aside issues like origins, design, and the quality of Orgel's work, what is your take on this claim?R0bb_{November 27, 2014
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Eric, Orgel was talking about Kolmogorov complexity in the quote you gave us:
One can see intuitively that many instructions are needed to specify a complex structure. On the other hand a simple repeating structure can be specified in rather few instructions.
Does that mean that he wasn't interested in probability? Of course not. You can't do OOL work without taking probability into account. Orgel was smart enough to keep complexity separate from improbability. Dembski conflated the two.keith s_{November 27, 2014
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keith @29:
Orgel is talking about Kolmogorov complexity while Dembski is talking about improbability.
It is a simple question I am asking: Is Orgel in his book really focused on Kolmogorov complexity rather than improbability? Did Orgel say he was talking about Kolmogorov complexity in the context of the origin of specified complexity? That is the question. If he did, then he was off base. If not, then you have gotten us off track.Eric Anderson_{November 27, 2014
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Eric Anderson:
keith @29 commented that Orgel was interested in Kolmogorov complexity, not probability.
No, I didn't. Please read more carefully, Eric. Orgel was interested in both complexity and improbability, but unlike Dembski, he didn't conflate the two.keith s_{November 27, 2014
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Regarding Kolmogorov complexity, I've always been of the view (though I am certainly open to being corrected) that Kolmogorov complexity has little to do with what we are interested in for design purposes. keith @29 commented that Orgel was interested in Kolmogorov complexity, not probability. Much of the back and forth on this thread depends on whether that is in fact the case. Does anyone have a clear statement from Orgel that he was primarily interested in Kolmogorov complexity and not probability? After all, he wrote a book about the origins of life, so presumably he was interested -- one would think -- in the origin and source of the specified complexity he observed in living organisms, not so much on the compressibility of that complexity for modern information systems purposes. It seems strange that Orgel would be focusing only on Kolmogorov complexity and not on the probabilities that relate to the origin of such specified complexity. I'm wondering if the whole discussion has been taken down the garden path by comment #29. Again, however, while it may not have much relevance to the design inference I'd nevertheless be curious to know whether Orgel was in fact only discussing algorithmic compressibility as opposed to probability in his book on the origins of life. If so, then it seems he may have been off on the wrong track.Eric Anderson_{November 27, 2014
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Thanks, Aleta @112. Good explanation. Orloog, taken together, Aleta's riddle and mine make a great example of how information helps narrow the range of possibilities. In other words, an infusion of information helps narrow the search space. Very simple example, but quite clear. Indeed, one possible way of defining information is "the elimination of possibilities."Eric Anderson_{November 27, 2014
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Hi Orloog. See my explanation at #112 and see if that makes sense to you, and then see how my problem differs from Eric's, for which your reasoning applies.Aleta_{November 27, 2014
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keiths:
I’m curious. What do you think of Barry’s behavior?
Let's say Barry posted something and then realized he disagreed with what he wrote and so deleted it. So what? Every user has the opportunity to do just that. What do folks think of keiths's behavior? Should he maybe use that feature and delete most of his posts after submitting them?Mung_{November 27, 2014
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in 104, I wrote,
to Joe: consider a “coin” that is weighted so it comes up heads 99% of the time, and throw 20 of these coins. These would come up all heads about 82% of the time, which is a pretty high probability. However, 20 heads would have low Kolmogorov complexity because a simple rule could describe them. This is a case where Kolmogorov complexity and probability do not go hand in hand.
Joe replied,
There isn’t any complexity in your example. The high probability matches the simple rule.
This doesn't make sense. First consider what Wikipedia says (and I'm sure other sources would confirm this.)
The Kolmogorov complexity ... of an object, such as a piece of text, is a measure of the computability resources needed to specify the object. For example, consider the following two strings of 32 lowercase letters and digits: abababababababababababababababab and 4c1j5b2p0cv4w1x8rx2y39umgw5q85s7 The first string has a short English-language description, namely "ab 16 times", which consists of 11 characters. The second one has no obvious simple description (using the same character set) other than writing down the string itself, which has 32 characters. More formally, the complexity of a string is the length of the shortest possible description of the string in some fixed universal description language. It can be shown that the Kolmogorov complexity of any string cannot be more than a few bytes larger than the length of the string itself. Strings, like the abab example above, whose Kolmogorov complexity is small relative to the string's size are not considered to be complex.
So all strings have some measure of Kolmogorov complexity. You can't say that "there isn't any complexity" in a string. Consider this. As above, the string HHHHHHHHHH has a probability of 0.99^10 = 82%. The string TTTTTTTTT has a probability or 0.01 ^ 10 = 10^-20, which is extremely small. HHHHHHHHHH is quite probable, and TTTTTTTTTT is extremely improbable, but both have the same Kolmogorov complexity: both can be described with the same "computability resources", one as "10 heads" and one as "10 tails" Thus Kolmogorov complexity and improbability do not "go hand in hand."Aleta_{November 27, 2014
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Re: 110 1/2. Others might like an explanation The difference is between knowing that one of the children is a boy and knowing that a particular child (the oldest) is a boy. There are four possibilities, and assume the first in each pair is the oldest. BB BG GB GG In problem #1, at 64, knowing that we saw a boy eliminates the GG possibility. Of the remaining three possibilities, if we saw a boy, only one of the three has another boy, so the probability the other child is a boy is 1/3. In Eric's problem we are told the first child is a boy, which eliminates both GG and GB. Of the remaining two possibilities, one has the youngest child a boy, so the probability is 1/2.Aleta_{November 27, 2014
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Keith S, Aleta:
Aleta:
Fun with probability – maybe you guys know this one: A family moves into a house across the street. You know they have two children, but you know nothing about their gender. One day you see a boy in the window. Assuming equal probabilities for boys and girls, what is the probability the other child is also a boy?
I was waiting to see if any of the IDers would tackle this, but since they haven’t, I will. The probability that the other child is a boy is 1/3.
Sorry, I don't get it. For me, the probability that the other child is a boy is still 1/2 - isn't that independent from the sex of the child at the window? I painted trees, diagrams, filled out charts, but the result is always the same - unless you claim that boys are domineering windows...Orloog_{November 27, 2014
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Aleta @64: Good Punnett Square riddle! And a good example of how information can be used to help narrow a search space. Here is the follow up riddle: The neighbor walks across the street with the boy and says: "I'd like you to meet my son. He is our oldest." Now, what is the probability that the younger child is a boy? :)Eric Anderson_{November 27, 2014
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R0bb @36:
The probability of a string depends on the process (or hypothesized process) that produced it. Kolmogorov complexity does not.
Was Orgel's discussion related to the question of the process that produced such features, that is to say, in the origin of such features? His book, I believe, was called "The Origins of Life"?Eric Anderson_{November 27, 2014
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R0bb: WRT Shallit and randomness, you have to understand Shallit’s approach to ID discussions.
You have got it backwards. We don't have to understand Jeffrey Shallit, it's exactly the other way around. And J.S. fails miserably. Since it was Jeffrey Shallit who commented on an article by Barry. A quick summary of the article: Barry offered two strings of text. String #1 was created by Barry haphazardly running his hands across his computer keyboard. String #2 was the first 12 lines of Hamlet’s soliloquy. Now what should be obvious - in the context of an ID-debate - to anyone with half a brain is that string #1 is obviously random and string #2 is obviously DESIGNED (the opposite of random). So what does Jeffrey Shallit do? He entered the ID-debate but does he understand what it is all about? No, he hasn't got a clue. So, Jeffrey Shallit runs both strings through a stupid compression algorithm and states that a shakespearean sonnet is “more random” than keyboard pounding, thereby 'proving' that Barry is wrong. Talk about missing the point ....Box_{November 27, 2014
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Joe:
If there aren’t any cases in which something complex also has a high probability of occurring then it is clear the Kolmogorov complexity and probability go hand in hand.
First of all, non sequitur. Even if everything that's complex is also improbable, it could still be the case that some things that are improbable are not complex. And actually, there are both types of mismatches. To get something that's complex but highly probable, consider applying a ROT13 to a very complex string. With a probability of 1 you'll get a particular new string, and that string will be complex. And for an improbable outcome that isn't complex, consider the string in #36.R0bb_{November 27, 2014
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to Joe: consider a “coin” that is weighted so it comes up heads 99% of the time, and throw 20 of these coins. These would come up all heads about 82% of the time, which is a pretty high probability. However, 20 heads would have low Kolmogorov complexity because a simple rule could describe them. This is a case where Kolmogorov complexity and probability do not go hand in hand.
There isn't any complexity in your example. The high probability matches the simple rule.Joe_{November 27, 2014
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Box @ 103, Barry appealed to Shallit in Barry's now-disappeared post. Keith was responding to that post. WRT Shallit and randomness, you have to understand Shallit's approach to ID discussions. His usage of terms is always technical and rigorous, and he assumes (or pretends) that IDists are using the terms likewise. So when IDists talk about information, randomness, or even specified complexity, Shallit responds as if the IDists have the formal definitions of those terms in mind. One could argue that he's paying IDists a compliment. Most people have an informal understanding of the term "random", which they associate with non-determinism or arbitrariness. But in formal randomness measures, a highly random string may be produced by a deterministic process, or by deliberate design. What matters is the string itself, not the process that produced it. So while it may seem that the product of arbitrary tapping on the keyboard must be more random than an intentionally crafted sonnet, such is not necessarily the case for formal definitions of "random".R0bb_{November 27, 2014
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to Joe: consider a "coin" that is weighted so it comes up heads 99% of the time, and throw 20 of these coins. These would come up all heads about 82% of the time, which is a pretty high probability. However, 20 heads would have low Kolmogorov complexity because a simple rule could describe them. This is a case where Kolmogorov complexity and probability do not go hand in hand.Aleta_{November 27, 2014
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Keith:
Keith #101: Barry is the one who brought Shallit up in support of his argument, not me.
Now I'm confused ... if you did not bring Jeffrey Shallit up, then who is the guy - by the name of Jeffrey Shallit - that you quote extensively in your post #81?? So, here is my question again: are we talking about the same ‘barking mad’ Jeffrey Shallit who claims that a shakespearean sonnet is “more random” than keyboard pounding? And if so, wouldn't you agree that Jeffrey Shallit is a fine one to talk about “spouting nonsense”?Box_{November 27, 2014
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It is worth saying it again: If there aren’t any cases in which something complex also has a high probability of occurring then it is clear the Kolmogorov complexity and probability go hand in hand.Joe_{November 27, 2014
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Box, Barry is the one who brought Shallit up in support of his argument, not me. Take a look at the vanishing OP. I'm curious. What do you think of Barry's behavior?keith s_{November 27, 2014
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