Uncommon Descent Serving The Intelligent Design Community

Siding with Mathgrrl on a point, and offering an alternative to CSI v2.0

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There are two versions of the metric for Bill Dembski’s CSI. One version can be traced to his book No Free Lunch published in 2002. Let us call that “CSI v1.0”.

Then in 2005 Bill published Specification the Pattern that Signifies Intelligence where he includes the identifier “v1.22”, but perhaps it would be better to call the concepts in that paper CSI v2.0 since, like windows 8, it has some radical differences from its predecessor and will come up with different results. Some end users of the concept of CSI prefer CSI v1.0 over v2.0.

It was very easy to estimate CSI numbers in version 1.0 and then argue later whether the subjective patterns used to deduce CSI were independent and not postdictive. Trying to calculate the CSI in v2.0 is cumbersome, and I don’t even try anymore. And as a matter of practicality, when discussing origin-of-life or biological evolution, ID-sympathetic arguments are framed in terms of improbability not CSI v2.0. In contrast, calculating CSI v1.0 is a very transparent transformation going from improbability to taking the negative logarithm of probability.

I = -log2(P)

In that respect, I think MathGrrl (who’s real identity he revealed here) has scored a point with respect to questioning the ability to calculate CSI v2.0, especially when it would have been a piece of cake in CSI v1.0.

For example, take 500 coins, and suppose they are all heads. The CSI v1.0 score is 500 bits. The calculation is transparent and easy, and accords with how we calculate improbability. Try doing that with CSI v2.0 and justifying the calculation.

Similarly, with pre-specifications (specifications already known to humans like the Champernowne Sequences), if we found 500 coins in sequence that matched a Champernowne Sequence, we could argue the CSI score is 500 bits as well. But try doing that calculation in CSI v2.0. For more complex situations, one might get different answers depending on who you are talking to because CSI v2.0 depends on the UPB and things like the number possible primitive subjective concepts in a person’s mind.

The motivation for CSI v2.0 was to try account for the possibility of slapping on a pattern after the fact and calling something “designed”. v2.0 was crafted to try to account for the possibility that someone might see a sequence of physical objects (like coins) and argue that the patterns in evidence were designed because he sees some pattern in the coins somewhat familiar to him but no one else. The problem is everyone has different life experiences and they will project their own subjective view of what constitutes a pattern. v2.0 tried to use some mathematics to create at threshold whereby one could infer, even if the recognized pattern was subjective and unique to the observer of a design, that chance would not be a likely explanation for this coincidence.

For example, if we saw a stream of bits which some claims is generated by coin flips, but the bit stream corresponds to the Chapernowne sequence, some will recognize the stream as designed and others will not. How then, given the subjective perceptions that each observer has, can the problem be resolved? There are methods suggested in v2.0, which in and of themselves would not be inherently objectionable, but then v2.0 tries to quantify how likely the subjective perception can arise out of chance and then it convolves this calculation with the probability of the objects emerging by chance. Hence we mix the probability of an observer concocting a pattern in his head by chance and then mixing it with the probability an event or object happens by chance, and after some gyrations out pops a CSI v2.0 score. v1.0 does not involve such heavy calculations regarding the random chance an observer formulates a pattern in his head, and thus is more tractable. So why the move from v1.0 to v2.0? The v1.0 approach has limitations witch v2.0 does not. However, I recommend, that when v1.0 is available to use, use v1.0!

The question of post diction is an important one, but if I may offer an opinion — many designs in biology don’t require exhaustive rigor as attempted in v2.0 to try to determine if our design inferences are postdictive (the result of our imagination) or whether the designed artifacts themselves are inherently evidence against a chance hypothesis. This can be done using simpler mathematical arguments.

For example, consider if we saw 500 fair coins all heads, do we actually have to consider human subjectivity when looking at the pattern and concluding it is designed? No. Why? We can make an alternative mathematical argument that says if coins are all heads they are sufficiently inconsistent with the Binomial Distribution for randomly tossed coins, hence we can reject the chance hypothesis. Since the physics of fair coins rules out physics as being the cause of the configuration, we can then infer design. There is no need in this case to delve into the question of subjective human specification to make the design inference in that case. CSI v2.0 is not needed to make the design inference, and CSI v1.0, which says we have 500 bits of CSI, is sufficient in this case.

Where this method (v1.0 plus pure statistics) fails is in questions of recognizing design in a sequence of coin flips that follow something like the Champernowne sequence. Here the question of how likely it is for humans to make the Champernowne sequence special in their minds becomes a serious question, and it is difficult to calculate that probability. I suppose that is what motivated Jason Rosenhouse to argue that the sort of specifications used by ID proponents aren’t useful for biology. But that is not completely true if the specifications used by ID proponents can be formulated without subjectivity (as I did in the example with the coins) 🙂

The downside of the alternative approach (using CSI v1.0 and pure statistics) is that it does not include the use of otherwise legitimate human subjective constructs (like the notion of motor) in making design arguments. Some, like Michael Shermer or my friend Allen MacNeill, might argue that we are merely projecting our notions of design by saying something looks like a motor or a communication system or a computer, but the perception of design is owing more to our projection than to an inherent design. But the alternative approach I suggest is immune from this objection, even though it is far more limited in scope.

Of course I believe something is designed if it looks like a motor (flagellum), a telescope (the eye), a microphone (the ear), a speaker (some species of bird can imitate an incredible range of sounds), a sonar system (bat and whale sonar), a electric field sensor (sharks), a magnetic field navigation system (monarch butterflies), etc. The alternative method I suggest will not directly detect design in these objects quite so easily, since the pure statistics are hard pressed to describe the improbability of such features in biology even though it is so apparent these features of biology are designed. CSI v2.0 was an ambitious attempt to cover these cases, but it came with substantial computational challenges to arrive at information estimates. I leave it to others to calculate CSI v2.0 for these cases.

Here is an example of using v1.0 in biology regarding homochirality. Amino acids can be left or right handed. Physics and chemistry dictate that left-handed and right-handed amino acids arise mostly (not always) in equal amounts unless there is a specialized process (like living cells) that creates them. Stanley Miller’s amino acid soup experiments created mixtures of left and right handed amino acids, a mixture we would call racemic (a mix of right and left-handed amino acids) versus the homochiral variety (only left-handed) we find in biology.

Worse for the proponents of mindless oirgins of life, even homochiral amino acids will racemize spontaneously over time (some half lives are on the order of hundreds of years), and they will deanimate. Further, when Sidney tried to polymerize homochiral amino acids into protoproteins, they racemized due to the extreme heat and created many non-chains, and the chains he did create had few if any alpha peptide bonds. And then in the unlikely event the amino acids polymerize, in a soup, the amino acids can undergo hydrolysis. These considerations are consistent with the familiar observation that when something is dead, it tends to remain dead and moves farther away from any chance of resuscitation over time.

I could go on and on, but the point being is we can provisionally say the binomial distribution I used for coins also applies to the homochirality in living creatures, and hence we can make the design inference and assert a biopolymer has at least -log2(1/2^N) = N bits of CSI v1.0 based on N stereoisomer residues. One might try to calculate CSI v2.0 for this case, but me being lazy will stick to the CSI v1.0 calculation. Easier is sometimes better.

So how can the alternative approach (CSI v1.0 and pure statistics) detect design of something like the flagellum or DNA encoding and decoding system? It cannot do so as comprehensively as CSI v2.0, but v1.0 can argue for design in the components. As I argued qualitatively in the article Coordinated Complexity – the key to refuting postdiction and single target objections one can formulate observer independent specification (such as I did with the 500 coins being all heads) by appeal to pure statistics. I gave the example of how the FBI convicted cheaters of using false shuffles even though no formal specifications for design were asserted. They merely had to use common sense (which can be described mathematically as cross or auto correlation) to detect the cheating.

Here is what I wrote:

The opponents of ID argue something along the lines: “take a deck of cards, randomly shuffle it, the probability of any given sequence occurring is 1 out of 52 factorial or about 8×10^67 — Improbable things happen all the time, it doesn’t imply intelligent design.”

In fact, I found one such Darwinist screed here:

Creationists and “Intelligent Design” theorists claim that the odds of life having evolved as it has on earth is so great that it could not possibly be random. Yes, the odds are astronomical, but only if you were trying to PREDICT IN ADVANCE how life would evolve.

http://answers.yahoo.com/question/index?qid=20071207060800AAqO3j2

Ah, but what if cards dealt from one random shuffle are repeated by another shuffle, would you suspect Intelligent Design? A case involving this is reported in the FBI website: House of Cards

In this case, a team of cheaters bribed a casino dealer to deal cards and then reshuffle them in same order that they were previously dealt out (no easy shuffling feat!). They would arrive at the casino, play cards which the dealer dealt and secretly record the sequence of cards dealt out. Thus when the dealer re-shuffled the cards and dealt out the cards in the exact same sequence as the previous shuffle, the team of cheaters would be able to play knowing what cards they would be dealt, thus giving them substantial advantage. Not an easy scam to pull off, but they got away with it for a long time.

The evidence of cheating was confirmed by videotape surveillance because the first random shuffle provided a specification to detect intelligent design of the next shuffle. The next shuffle was intelligently designed to preserve the order of the prior shuffle.

Biology is rich with self-specifying systems like the auto correlatable sequence of cards in the example above. The simplest example is life’s ability to make copies of itself through a process akin to Quine Computing. Physics and chemistry makes Quine systems possible, but simultaneously improbable. Computers, as a matter of principle, cannot exist if they have no degrees of freedom which permit high improbability in some of its constituent systems (like computer memory banks).

We can see the correlation between a parent organism and its offspring not being the result of chance, and thus we can reject the chance hypothesis for that correlation. One might argue that though the offspring (copy) is not the product of chance, the process of copying is the product of a mindless copy machine. True, but we can further then estimate the probability of randomly implementing particular Quine computing algorithms (that makes it possible for life to act like computerized copy machines). The act of a system making copies is not in-and-of-itself spectacular (salt crystals do that), but the act of making improbable copies via an improbable copying machine? That is what is spectacular.

I further pointed out that biology is rich with systems that can be likened to login/password or lock-and-key systems. That is, the architecture of the system is such that the components are constrained to obey a certain pattern or else the system will fail. In that sense, the targets for individual components can be shown to be specified without having to calculate the chances the observer is randomly formulating subjective patterns onto the presumably designed object.

lock and key

That is to say, even though there are infinite ways to make lock-and-key combinations, that does not imply that emergence of a lock-and-key system is probable! Unfortunately, Darwinists will implicitly say, “there are infinite number of ways to make life, therefore we can’t use probability arguments”, but they fail to see the errors in their reasoning as demonstrated with the lock-and-key analogy.

This simplified methodology using v1.0, though not capable of saying “the flagellum is a motor and therefore is designed”, is capable of asserting “individual components (like the flagellum assembly instructions) are improbable hence the flagellum is designed.”

But I will admit, the step of invoking the login/password or lock-and-key metaphor is a step outside of pure statistics, and making the argument for design in the case of login/password and lock-and-key metaphors more rigorous is a project of future study.

Acknowledgments:
Mathgrrl, though we’re opponents in this debate, he strikes me a decent guy

NOTES:
The fact that life makes copies motivated Nobel Laureate Eugene Wigner to hypothesize a biotonic law in physics. That was ultimately refuted. Life does copy via a biotonic law but through computation (and the emergence of computation is not attributable to physical law in principle just like software cannot be explained by hardware alone).

Comments
RE: #26 if that's the case we can calculate the number of ways to succeed as C(n,k) where n is the number of trials and k is the number of tosses coming up tails. C(n,k) = n! / k!(n-k)! It's pretty simple then: Bits = -log2[C(n,k)/n] I think that's correct but my brain is beginning to rebel now.Chance Ratcliff
May 18, 2013
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Sal, I think I understand you better in #21 now. We could use -log2(P) where P is "the number of ways to succeed" divided by the total search space. Is that correct? I get just over 491 bits using that form for 1 tails and 499 heads.Chance Ratcliff
May 18, 2013
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Here is an example of an statistically constructed specification that has no subjective component. Pure statistics would reject the chance hypothesis. It deals with the convergence of patterning between rat and mouse genomes that can't be attributed to common descent. It has huge correlations across huge data samples. See the graph "The Mystery Signal" at the bottom of Sternberg's article: http://www.evolutionnews.org/2010/03/signs_in_the_genome_part_2032961.html There are tons of these cross correlating features in biology that scream out "STEGANOGRAPHY". CSI v1.0 and statistics are good for identifying these as designs, but really, practically speaking you don't need to go that far, your eyes will tell you there is design such as found merely by looking in Sternberg's graph. Obscure data, yes. But hey, that's why you need to read Uncommon Descent to uncover gems that few are privy to. :-) Salscordova
May 18, 2013
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Sal @21, you are correct, and I understand the simplification. But I couldn't use the simplification for what I was doing. It may have been wholly inappropriate for me to apply it the way I did, because in truth a biased coin that comes up tails 1 out of 500 tosses is not exactly the same as a sequence of 500 coins with exactly 1 tails. Yet the similarity in outcomes between my method and yours is striking, imo (except for the mystery 1.5 bits). So that more complete form was necessary to calculate a biased coin, which was the model I applied. Thanks much for helping me with this and for spending the time. :)Chance Ratcliff
May 18, 2013
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The “specification” part of CSI is quite often not subject to calculation. At least not with the Shannon bit-calculation approach.
CSI v1.0 can be amenable to Shannon bit-calculations for specification in some cases. CSI v2.0 is not If you can't describe number of bits in the specification for v1.0, it is harder to make the design inference formally. Some constructs are really difficult to analyze, like say, how improbable is assembly of a house of cards. Formalisms work only well for tractable examples, things like 747s? Forget it. But the nice thing is that for such complex systems, do you really have to make the calculations? For Darwinists, no number of probability will ever satisfy them, so it won't matter in their case anyway. Some of the more trivial cases (like homochirality and the computers in life) are sufficient for me at a personal level. I have no ambition to persuade anyone or any group of people that are commited to some mindless account. No amount of numbers will ever be persuasive to them. These considerations are for people like myself who are skeptical but sympathetic. These exercises are helpful to me to reassure me that the Darwinists have only assertions, nothing even attempting the rigor the ID side provides. The calculations for some of the specifications described by Chance Ratcliff are under the assumption of v1.0.scordova
May 18, 2013
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RE: #20, in the first case of 500 heads, there is zero uncertainty, and 500 bits of info. In the second case, there is 1 tails and 499 heads, with a delta of 9 bits more uncertainty, and so 491 bits of information, as Sal calculated it. (My method at #3 produces 492.5 bits, 1.5 bits higher.) So Eric, you are correct this is not the same as CSI, but I thought it was interesting nonetheless.Chance Ratcliff
May 18, 2013
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Chance, There is something with respect to caculating Shannon Entropy: U = I = -p(x0)log2(p(x0)) - p(x1)log2(p(x1)) - p(x2)log2(p(x2)).....p(xn)log2(p(xn)) each xi is a microstate, and there are 2^500 microstates or way that 500 coins can be configured. So, it's rather painful to use this form of Shannon entropy where n = 2^N and N = 500! Shannon included it to be complete, but if you have the assumption that every microstate (a complete collection of 500 coins) is equally probable, you can simplify the above torturous equation to U = I = N bits = 500 bits where N is the number of coins, in this case 500. Alternatively we can simply take the number of possible microstates and take the logarithm of them. The number of microstates is 2^500, so U = I = log2(2^500) = 500 bits or alternatively we can take the probability of any specific outcome, in this case 1/2^500 and then take the alternative formula frequently used in Bill's writings: I = -log2(P) = -log2(1/2^500) = 500 bits I saw you tried to make a variation of the more tortured form in your calculations. Maybe that will help you connect the dots. The reason various forms are used is sometimes the bits can more easily be calculated using probability, at other times it is easier to count microstates. The torturous version is the most comprehensive, but if there are special conditions (like fair coins), the calcutions can be simplified to the forms I was using. The torturous version of the Shannon entropy is frequently used to calculate bandwidth in communication systems with an analog connection such as in fiber optic or wireless communication, but for nice digital bitwise communication, the simpler formulations will suffice.scordova
May 18, 2013
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Eric, would you agree that 500 heads out of 500 trials is an objective specification having 500 bits of information? If so, could "1 tails and 499 heads" also be an objective specification with 500 sequences matching the specification? In the latter case, the uncertainty is higher, and I was toying with the idea that we might quantify this with Shannon entropy.Chance Ratcliff
May 18, 2013
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I presume we are all keeping in mind that measuring so-called Shannon information is not measuring CSI. It is only measuring the complexity (improbability, surprise factor, however else you want to describe it). The "specification" part of CSI is quite often not subject to calculation. At least not with the Shannon bit-calculation approach.Eric Anderson
May 18, 2013
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OK, now that I'm using the binomial calculator correctly: Trials = 100, 1 tails 99 heads Binomial method: 93.4 bits My method: 94.8 bits Difference: 1.4 bits Trials = 500, 1 tails 499 heads Binomial method: 491.0 bits My Method: 492.5 bits Difference: 1.5 bits Trials = 1000, 1 tails 999 heads Binomial method: 990.0 bits My Method: 991.5 bits Difference: 1.5 bits In each case the difference is small but constant. Huh. Well at least I wasn't far off the mark, but I'd sure like to understand why the delta hovers at 1.5 bits.Chance Ratcliff
May 18, 2013
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Sal @14, yes that makes sense.Chance Ratcliff
May 18, 2013
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I was thinking that this could be viewed through the lens of Shannon entropy.
Any time we talk bits we are talking shannon entropy. I know get flak about this, but shannon entropy is a measure of uncertainty, not disorder. A 500 meg disk has 500 megs of shannon entropy (or shannon information). Information and uncertainty are different sides of the same coin (pun intended).scordova
May 18, 2013
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If our sequence specification is 500 heads, then there is zero uncertainty per bit
My understanding is there is the specification and then there is the outcome. The uncertainty for the outcome of 500 fair coins is always 500 bits.
Yes, I believe that is correct. If the coin is not fair though, that number will go down. You can plug in the numbers for say, 1/4 probability of tails and 3/4 heads into that simple entropy equation and you'll get ~0.811 bits per toss. WRT specification, we could specify "1 tails and 499 heads" if we wanted, and that specification would include some uncertainty, so there would be 500 cases where we could get that same outcome. I was thinking that this could be viewed through the lens of Shannon entropy. Perhaps it can. In that case the uncertainty is present in our specification, which could be satisfied by multiple outcomes.Chance Ratcliff
May 18, 2013
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However with 499 heads and 1 tails, there is some uncertainty introduced, in that heads could come up in any one of 500 positions. We still know that we’ll get 499 heads, but we lose some certainty about each individual toss.
Another way of saying is that if we know for sure that we'll get 1 (and only 1 tail) the question is which of the above enumerated subspecifications will emerge. The probability that any one of the 500 specification will emerge is: P(a specific 1 tail, 499 head configuration) = 1/500 which translates to -log2(P) = -log2(1/500) = 9 bits notice that I calculated the specification for 1 tail as 491 bits Take the above result of 9 bits and look at this: 500 - 9 = 491 If I were the observer, and said, "Chance Ratcliff, there is 1 tail and 499 heads" I would have reduced your uncertainty in what the outcome of the experiment was by 491 bits, or equivalently I have communicated to you 491 bits of information. The only thing you wouldn't know at that point is where the tail coin is located. You still have 9 bits of uncertainty. When I tell you the postion, I've reduced your uncertainty about the coins another 9 bits (or equivalently increased your information by 9 bits), hence I then have communicated a total of 491 + 9 = 500 bits of information about the outcome of the experiment. Once you have 500 bits of information, your knowledge of the outcome is complete.scordova
May 18, 2013
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By the way, the reduction in uncertainty does make some intuitive sense. For 500 heads, there is no uncertainty as to the value of each toss, it will always be heads. However with 499 heads and 1 tails, there is some uncertainty introduced, in that heads could come up in any one of 500 positions. We still know that we'll get 499 heads, but we lose some certainty about each individual toss.Chance Ratcliff
May 18, 2013
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The difference between what I proposed in #3 and what you're suggesting in #9 is that my calculation for 1 tails out of 500 tosses is the same as presuming an unfair coin that comes up tails only 1 out of 500 throws, which is very low uncertainty per toss, or 0.021. Contrast this with a fair coin which is exactly 1 bit. Fair coin: U = -[0.5*log2(0.5) + 0.5*log2(0.5)] = [0.5 + 0.5] = 1 bit per toss, or maximum uncertainty. As the coin becomes more biased, the measurement gets smaller and uncertainty (entropy) is reduced. I thought that this would make sense when applied to the bit measurement for N throws, but I'm not so sure at this point. Anyway, thanks for indulging me Sal. It was fun. :)Chance Ratcliff
May 18, 2013
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so perhaps there is something wrong with my approach at #3. Wouldn’t be the first time.
Well, there are many Darwinists claiming superior intellect over we humble idists. I'm waiting for them to give us free-of-charge peer review and fix any mistakes we made. They always seem eager to "fix" our misunderstandings, so I eagerly await to hear from them.scordova
May 18, 2013
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Well I tested the numbers for 100 tails out of 1000 tosses with the binomial calculator you provided, and the numbers are not converging, so perhaps there is something wrong with my approach at #3. Wouldn't be the first time. ;)Chance Ratcliff
May 18, 2013
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If our sequence specification is 500 heads, then there is zero uncertainty per bit
My understanding is there is the specification and then there is the outcome. The uncertainty for the outcome of 500 fair coins is always 500 bits. It's a little hard to say there is uncertainty in ANY specification since the specification is precisely defined, but we can say a given 500-bit specification has 500-bits of information. A 499-bit specification has 499-bits of information, etc. How can a specifation be less than 500 bits if the number of coins is 500? This happens if a specification is actually composed of subspecifications. The measure of information is the measure of the reduction of uncertainty. When 500 coins are flipped we have reduced 500 bits of uncertainty because we now know what the outcome is and thus we have 500 bits of information whereas before the flipping we had 500 bits of uncertainty. So you can see uncertainty and information mirror each. We have the rather counter intuitive result if we lump several sub-specifications together where each is 500 bits, the composite probability of hitting one of those specification isn't 500bits + 500bits + 500 bits .... it is (gosh I hope I don't mess this up): -log2( 1/2^500 + 1/2^500 ...) bits Hence when we have 1 coin tails and 499 coins heads we have the following 500 possiblities (sub-specifications if you will): 1. T H H ......H or 2. H T H ......H or 3. H H T ......H ..... .... 498. H H H .... T H H 499. H H H...... H T H or 500. H H H......H H T That tallies to 500 different possible outcomes where one of the coins is tails. That is to say when we have 1 coin tails and 499 heads, there are actually 500 ways this can be achieved with 500 coins. The specification that there are "1 tail and 499 heads" is actually 500 sub-specifications as enumerated above. One can extend the previous calculation to tally these 500 cases: -log2( 1/2^500 + 1/2^500.....) = -log2(500/2^500) = 491 bits which was the same result using the binomial probability. The specification of 1 coin tails and 499 heads is a single specification of 491 bits composed of 500 separate specifications where each sub-specification has 500 bits. You can see the counter intuitive result is that by adding five-hundred 500-bit specifications, you get one 491-bit specification! That is the way I understand things anyway.scordova
May 18, 2013
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As a footnote, dealing with specificity from an uncertainty perspective does require a slightly different way of looking at the sequence. When considering 1 tails and 499 heads, instead of insisting upon exactly 1 tails in a string of 500 coins, we consider each coin to have an entropy relating to the probability of 1/500. This is a Shannon information perspective. U = -[p1*log2(p1) + p2*log2(p2)] = -[1/500*log2(1/500) + 499/500*log2(499/500)] = -[0.002*log2(0.002) + 0.998*log2(0.998)] = ~[0.0179 + 0.0029] = ~0.021 bits of entropy per coin Then U can be used in the specificity equation: S = N - U*N, where N is the number of coin tosses. S = 500 - 0.021*500 = 489.5 bits (specified, but not above the UPB) I'm guessing that this value converges on the true probability with large N. I can't say whether this method is better overall than the binomial approach, but it appears less cumbersome.Chance Ratcliff
May 18, 2013
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Sal, thanks for your response. Using the uncertainty/specificity formula at #3, here's what I get: 2 tails, 498 heads: ~481 bits 1/3 tails, 2/3 heads: ~41 bits The numbers certainly aren't exactly the same as yours, but the numbers get closer together when uncertainty is low, as in the 2 tails case. So perhaps they converge for large values of N. Just to note, with 1000 tosses, 100 tails and 900 heads still comes in above 500 bits. There certainly appears to be some sort of objective specificity in those ratios. In any case, it appears that cases with 1 heads, or 2, and so on, could still be considered complex and specified for larger values of N.Chance Ratcliff
May 18, 2013
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For the example with a single tails and 499 heads: S = 500 – 0.021*500 = 489.5 bits of specificity
My calculation yielded 491 bits. The way I got it was going to http://stattrek.com/online-calculator/binomial.aspx Then enetering the following parameters: Probability of success on a single trial : .5 Number of tirals : 500 Number of successes: 1 Then press calculate and it does that cumbersome binomial probability via this formula: P(1) = P(499) = [500!/ ( 1! (500-1)!)] .5^1 (1 - .5)^(500-1) = This will yield a probability of 1.527 x 10^-148 which can be expressed in bits by -log2(1.527 x 10^-148) = 491 bitsscordova
May 18, 2013
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Chance, With 498 coins heads, and 2 coins tails, would we say that this is obviously designed? There are many possibilities to achieve this with 500 coins. Some examples TT.....HHHHHHHH or HHHH.....TT.....HHHH or HHHHHHH........THTH We would have to count how many of these exist and that will yield a certain probability for hitting one of those configurations. I'd probably use something like the binomial distribution to calculate the improbability in this case, and that will yield the bit number. The same sort of approach would work for 2 heads and 1 tail ratios. I'm open to differing opinions, but the point is, whatever the number of CSI bits, we have methods outside CSI to tell us something is improbable. I haven't examined your calculations in detail. Neil Riekert is the mathematician among us and so is DiEb, DiEb especially seems quite eager to offer critiques. :-) But I'll take a stab: P(498 heads,2 tails) = P(2) = [500!/ ( 2! (500-2)!)] .5^2 (1 - .5)^(500-2) = 3.811 x 10^-146 = 483 bits I used this website: http://stattrek.com/online-calculator/binomial.aspx to calculated the binomial probability For 2 heads and 1 tail ratio P(500/3 tails) = P(166 tails) = 45 bitsscordova
May 18, 2013
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Nice post, Sal! In my opinion, the ideal way to determine CSI would be a two-pronged approach that utilizes the -log2(P) to determine Shannon information coupled with some sort of database that could a sequence could be compared with to determine specification.Optimus
May 18, 2013
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Sal, interesting and thought-provoking post, thanks. I wonder. Your coin example calls out an objective sequence for a design inference: 500 heads out of 500 coins. However, might it be possible to say something similar about sequences with only 1 coin tails, or 2, and so on? Consider this in terms of uncertainty. If our sequence specification is 500 heads, then there is zero uncertainty per bit: for any coin in the sequence, the probability that it will be heads is 1 and the probability of tails is 0. Now consider sequences with exactly 1 tails among 499 heads. In this case we've increased uncertainty from zero to around 0.021 bits of informational entropy. For two tails and 498 heads, we end up with around 0.038 bits. These numbers come from this formula for entropy: U = -[p0*log2(p0) + p1*log2(p1)], where p0 is the probability of tails and p1 is the probability of heads for each coin. Constructing a case where zero uncertainty translates to maximum specificity, and complete uncertainty yields minimum specificity: S = N - U*N, where N is the number of coins and U is the informational entropy per coin. Plugging in the case with 500 heads, which would equate to maximum specificity and minimum uncertainty: S = 500 - 0*500 = 500 bits of specificity For minimum specificity and maximum uncertainty: S = 500 - 1*500 = 0 bits of specificity That would be the case where each coin had an equal probability of being heads or tails. If at maximum specificity we have all heads, we still have 500 bits of specificity. For the example with a single tails and 499 heads: S = 500 - 0.021*500 = 489.5 bits of specificity I think this is interesting. At maximum specificity, the sequence of all heads yields 500 bits, which is 3.27E150, breaking the universal probability bound. At 489.5 bits of specificity, which is exactly one tails, we get 2.26E147, which is shy of the UPB. Of course as we increase the string length, that is, the number of coins in the sequence, we would find cases where one, two, or any number of tails would still yield results above the UPB. It seems to me that if this is reasonable, then it may provide objective criteria for more than just the extreme case of all heads or all tails in a sequence. We can actually apply uncertainty to determining the specification content. Hopefully my reasoning is sound and I haven't made any significant errors.Chance Ratcliff
May 18, 2013
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The problem is there isn't a 1.0 nor 2.0. The 2005 paper refined his earlier works, it didn't replace them. For example, now he admits that a universal UPB of 10^150 was too high and that some scenarios could have a much lower UPB- the UPB is now dynamic as opposed to static.Joe
May 18, 2013
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First and foremost, I apologize to you if I hurt your feelings in your last post Sal.,,, It's a delicate balance to walk above the fray without getting personal and I stumble much more than I would like from that delicate mark. ,,,This recent article by Dr. Dembski may be of some interest to your post if you, or some reader, has not seen it yet: Before They've Even Seen Stephen Meyer's New Book, Darwinists Waste No Time in Criticizing Darwin's Doubt - William A. Dembski - April 4, 2013 Excerpt: In the newer approach to conservation of information, the focus is not on drawing design inferences but on understanding search in general and how information facilitates successful search. The focus is therefore not so much on individual probabilities as on probability distributions and how they change as searches incorporate information. My universal probability bound of 1 in 10^150 (a perennial sticking point for Shallit and Felsenstein) therefore becomes irrelevant in the new form of conservation of information whereas in the earlier it was essential because there a certain probability threshold had to be attained before conservation of information could be said to apply. The new form is more powerful and conceptually elegant. Rather than lead to a design inference, it shows that accounting for the information required for successful search leads to a regress that only intensifies as one backtracks. It therefore suggests an ultimate source of information, which it can reasonably be argued is a designer. I explain all this in a nontechnical way in an article I posted at ENV a few months back titled "Conservation of Information Made Simple" (go here). ,,, ,,, Here are the two seminal papers on conservation of information that I've written with Robert Marks: "The Search for a Search: Measuring the Information Cost of Higher-Level Search," Journal of Advanced Computational Intelligence and Intelligent Informatics 14(5) (2010): 475-486 "Conservation of Information in Search: Measuring the Cost of Success," IEEE Transactions on Systems, Man and Cybernetics A, Systems & Humans, 5(5) (September 2009): 1051-1061 For other papers that Marks, his students, and I have done to extend the results in these papers, visit the publications page at www.evoinfo.org http://www.evolutionnews.org/2013/04/before_theyve_e070821.htmlbornagain77
May 18, 2013
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