Imagine a coin-tossing game. On each turn, players toss a fair coin 500 times. As they do so, they record all runs of heads, so that if they toss H T T H H H T H T T H H H H T T T, they will record: 1, 3, 1, 4, representing the number of heads in each run.
At the end of each round, each player computes the product of their runs-of-heads. The person with the highest product wins.
In addition, there is a House jackpot. Any person whose product exceeds 1060 wins the House jackpot.
There are 2500 possible runs of coin-tosses. However, I’m not sure exactly how many of that vast number of possible series would give a product exceeding 1060. However, if some bright mathematician can work it out for me, we can work out whether a series whose product exceeds 1060 has CSI. My ballpark estimate says it has.
That means, clearly, that if we randomly generate many series of 500 coin-tosses, it is exceedingly unlikely, in the history of the universe, that we will get a product that exceeds 1060.
However, starting with a randomly generated population of, say 100 series, I propose to subject them to random point mutations and natural selection, whereby I will cull the 50 series with the lowest products, and produce “offspring”, with random point mutations from each of the survivors, and repeat this over many generations.
I’ve already reliably got to products exceeding 1058, but it’s possible that I may have got stuck in a local maximum.
However, before I go further: would an ID proponent like to tell me whether, if I succeed in hitting the jackpot, I have satisfactorily refuted Dembski’s case? And would a mathematician like to check the jackpot?
I’ve done it in MatLab, and will post the script below. Sorry I don’t speak anything more geek-friendly than MatLab (well, a little Java, but MatLab is way easier for this).
Might I point out that you can’t calculate the improbability of a sequence unless you know at least something about the history of the sequence.
What Dembsky seems to be doing is making a Bayesian inference and simultaneously denying having to know anything about the likely actors that could have produced the string. I believe Dembski denies that applicability of Bayes unless it is convenient, as in calculating the probability that an election has been rigged.
It has always seemed odd to me that when deciding which of two agents is responsible for the history of a gene sequence, that the agent that has no physical presence and has never been observed is preferred to an agent that is observable and which has been the subject of a century and a half of active research. I suppose that’s why Dembski avoids discussing Bayes.
The other thing being done here is the implied comparison of a gene sequence with the lock combination, the combination that has to be perfect in all 400 digits in order to have any function at all.
This is demonstrably not the way genetic sequences behave.
I admit I don’t understand why microbes are less specified than birds. Or why they are less evolved. I’m not going to be convinced that they are even less complex without some operational definition of complexity.
Seriously, for all I know the Designer specified a biosphere composed entirely of bacteria (and viruses preying on them), in which case He got it ALMOST right, but not quite, and these bigger critters are errors, noise in the system, outcomes that fail to meet the specification.
So maybe it would reflect my confusion most accurately to say that I am NOT seeing any useful, quantified, operational definitions of complexity, specification, OR information. And if NONE of the terms in CSI are defined in some operational way that they can be measured (to everyone’s agreement) and compared, we’re either discussing how many blurks it takes to gronch, or else we’re using purely post hoc definitions based on gut hunches. And THESE are quite clearly based on theological preconceptions.
And btw, here is my “semiotic agent’s” description of the specified subset:
Sequences of 500 coin-tosses in which the product of the sums of runs-of-heads exceed [Jackpot].
That’s the problem!
I am looking at this from the “functional” point of view of an n bit window of “information”, as Dembski does, not “survivability” of the entire object.
As an example, the odds of me growing instead of fingernails, razor blades complete with the brand name “Wilkinson Sword” written on them, would exhibit loads of CSI according to Dembski, but might prove fatal to me! 🙂
Well, that’s not Dembski’s definition.His is the opposite.He uses compressibility as a measure of specification.From Dembski’s paper:
All I’m demonstrating is that Dembski is incorrect.
Again apples and oranges- you really need to read “No Free Lunch” – really
Umm you cannot falsify Dembski until you address his argument, which you haven’t.
I agree.
You would think that the ID side would have a whole list of worked out examples, clearly showing their work, but they don’t.
I see CSI as ID’s way of tying evolution to the toss of dice.
I assume that Dembski intended that paper to be internally coherent. Moreover, he actually says it supecedes his previous treatments of CSI. And how can “algorithmically incompressible” not mean the opposite of “algorithmically compressible”?!
And I’ve read his NFL papers. They don’t help his case. I’ve just demonstrated that for this landscape evolutionary search is way more efficient than random search.
I’ll say it’s “apples and oranges”!
I’ve addressed it head on. I’ve used his exact formula to calculate an exactly equivalent scenario to his own examples (coin-tosses), and demonstrated that I can get a sequence with chi>1 from evolutionary processes only (random point mutations and natural selection).
It’s a direct falsification.
Mike, I’m recording the lineages of the genomes, so provided the thing doesn’t crash overnight, I’ll post the lineage of the winner tomorrow.
I would seriously suggest that you have not read it yourself. You don’t appear to have the ability.
So if you are going to continue to snark at and taunt people, you should at least demonstrate that you can understand some math.
Elizabeth is giving a pretty clear demonstration here, and you don’t even know what is happening.
Cool! 🙂
Elizabeth,
I suggest you are being disingenuous, but maybe that’s just my ignorant impression. What you pretend not to deal with is Dembski’s underlying argument, which is (of course) that goddidit. If using his methods you can show that Dembski’s God is not necessary, you are doing it wrong. Even if you can successful show that Dembski’s god can be factored out of any possible coherent interpretation of his formulation, then you are REALLY doing it wrong. Surely you’re aware that Dembski’s entire purpose, from day 1, has been to “find” his God lurking behind biololgical processes which are exasperatingly easy to understand without Him.
I think at some point in the past you attempted, and subsequently gave up trying, to get any ID proponent to produce a single actual CSI calculation for any biological entity. So as I read it, you are attempting to find ever-simpler implementations of Dembski’s ideas, all of which make no use of Dembski’s God. And no matter how simple you make it, if your example works “you haven’t addressed his arguments”.
And you haven’t! At least, you are superficially addressing what he SAYS, but not what he MEANT. He MEANT that goddidit. You know that, the ID proponents know that, we all know that. Dembski’s rationalizations and circumlocutions and mathematical language can be directly refuted, as you keep doing. But his Faith, his rejection of natural processes producing natural results, can’t be refuted by the misguided expedient of addressing his words. And that’s why you’re racing around playing whack-a-mole with Joe G and William Murray. You are unwilling to address a spiritual issue on spiritual terms.
Liz, a computer program is CSI. Furniture assembly instructions are CSI. Encyclopedia articles are CSI. Not one of those can be algorithmically compressed.
Dembski says:
A collection of non-random sequences.
And guess what? If you don’t get it right the first time, it doesn’t get to reproduce with variation.
But yeah if any ole nucleotide sequence could just start reproducing with variation- that means functional variation- then Dembski would be falsified.
Ya see that random coin toss would equal the sequence you need to match to get replication with variation. If you don’t get it you have to start over.
Joe G, I do suggest you read Dembski’s paper (the one linked to in the other thread) carefully. I am solely dealing with the point Dembski makes in that paper which is that patterns that have a chi>1 signify Design. He shows us how to calculate it, and even uses coin-tosses as an example.
What I am saying is that a system of self-replicators that reproduce with heritable variance in reproductive success can also produce patterns with chi>1.
Yes, you have first to have the system of self-replicators, reproducing with heritable variance in reproductive success, and if Dembski’s argument was that only a Designer could produce a self-replicator that replicates with heritable variation in reproductive success, that would be be quite different. But Dembski, specifically, says that Darwinian processes cannot create chi>1.
I have just demonstrated that they can. They can increase it from levels well below threshold to well above.
I’d be more than willing to address the spiritual issue on spiritual terms, and indeed, have occasionally done so on UD – I have grave theological issues with ID as well.
But the argument that Dembski presents in that paper is a simple mathematical one, and it is simply and demonstrably false.
As my computer is busy demonstrating (not that it has not been done before, many times, but this script has the bonus of taking a scenario directly related to the examples in Dembski’s paper, namely specified subsets of sequences of coin-tosses, and we can calculate the CSI quite precisely (well, someone might have to help in getting an exact value for that N, but I’ve ballparked it safely enough).
What about crystals? Are they CSI?
I must say, I’d find Joe G’s and William’s objections more persuasive if either of them would provide a ballpark calculation for the CSI of the various examples that they’ve referred to.
And Joe, you need to read at least the section of Dembski’s paper on compressibility. You often accuse me of not understanding ID, but I seem to understand that paper considerably better than you do!
The paper refers to specification only.
No- they are not complex- this is in “No Free Lunch” and Orgel says it too- Meyer goes over it in several of hiis writings also.
Umm Darwinian processes have not produced any self-replicators with variation.
As I said:
But yeah if any ole nucleotide sequence could just start reproducing with variation- that means functional variation- then Dembski would be falsified.
You can’t even get started with Darwinian processes.
If you plot the curve of x^(1/(x+1)), you will see a very broad peak. Your program may find lots of stuff in the range of 10^58, but there is no strong “pull” toward the absolute peak.
So in a world in which coin toss results could be reproduced with random variation, some specification may eventually be produced.
I doubt Dembski will be impressed…
No, it does not. He’s changed his terminology somewhat since CSI, and in this paper (which he clearly states supercedes earlier treatments) he says that “specification” refers to patterns that exhibit both “pattern simplicity (i.e., easy description of pattern) and event-complexity (i.e., difficulty of reproducing the corresponding event by chance)”.
If you read the paper you will see that “pattern simplicity” is also referred to as “compressibility” and “event-complexity” is his old “complexity”: essentially Shannon Entropy * string length.
That combination is what he calls “specification” and also “specified complexity”, which he quantifies as “chi”. When the value of chi exceeds 1, he claims that we must reject non-Design.
My Darwinian algorithm, however, produces patterns in which chi exceeds 1. Ergo, Darwinian processes, as well as Design processes, can produce “specified complexity” >1.
Well, he should be. The “some specification” my system produces exceeds his very stringent threshold of 1.
Yes, I thought that might be the case. Certainly the rate of increase is now very slow. But still going! I’m at 9.4720e+58 as I go to bed 🙂
No, you can’t get started with Darwinian processes. Darwin himself, famously said that.
But that’s not what Dembski is saying. You may be, but he isn’t.
And we don’t yet know what the simplest possible Darwinian-capable self-replicator is so we can’t compute its CSI. But if it’s <1, then it can happen by chance.
ETA: and it doesn't even have to. It could also happen by chemistry.
Yes, it was simple, And your demonstration is simple. And the argument is simply false. Great. And NOW, why do you suppose Joe G and William Murray can’t see that? Do you propose they are stupid? Your same arguments have been presented (repeatedly) to Dembski. He ignores them. Do you suppose he is also stupid? You have presented analogous (and equally well-supported) arguments on UD, and met with universal rejection. Are they ALL stupid? What could possibly explain such a thumpingly consistent unwillingness to accept what is so simple and obvious?
Sigh. The argument Dembski is making is NOT mathematical, despite careful construction to create that appearance. It is a spiritual argument dressed up in mathematical terms. You can easily refute the math, missing the point in the process. Joe G and William Murray haven’t (and couldn’t) do any of the math; they wouldn’t know a distributive property from eggnog. But they KNOW you are wrong. How do you suppose they know this?
The size of the target space can be estimated as follows.
As has been already pointed out, the best solutions are the two periodic sequences in which four Hs are followed by one T: (HHHHT)(HHHHT)…(HHHHT) and (THHHH)(THHHH)…(THHHH). Both yield the fitness equal to 4100 = 1.61 ×1060. These sequences can viewed as Ts forming a crystal: the distance between adjacent Ts is always 4.
Other solutions from the target space can be obtained by slightly changing these “ground states.”
One type of a perturbation shifts one of the Ts by one position, so we get THHHTHHHHHT with 3 and 5 Hs. The fitness goes down by a factor (3×5)/(4×4) to 1.51×1060, so we are well within the target space.
Let’s count these sequences. In Liz’s notation, we convert one of the 4s in {4,4…4} to a 3 and another to a 5. These do not have to be adjacent. There are 400×399=159600 possible ways to choose which 4s to convert. Multiply that by 2 (to account for 2 initial, perfectly periodic states) to get 319200 states in the target space.
(contd)
Liz, You don’t have any idea what Dembski is saying- and getting started is what Dembski is talking about
some points-
1- self-replicators with variation is not a living organism
2- you need self-replicators with complexity-increasing-variation, and not just any complexity will do
3- a self-replicator may not have to have CSI- again if any sequence will do then there isn’t any specification
4- A self-replicator with SI that can evolve via Darwinian mechanisms into a replicator with CSI would put a huge whole into CSI = design
5- Self-replicators are imaginary as even RNA replication takes TWO- one RNA for a template and one RNA for the catalyst
6- The evidence now says that the RNA world couldn’t exist without proteins, meaning there wasn’t a RNA world
7- A ribonulceoprotein world is the new RNA world
Your system has nothing to do with his claims.
In the case of a maximally uncertain binary population, the set would need be simply describable such as “every fourth coin is tails”, or “heads and tails alternating,” or the first 100,000 is heads and rest is tails” etc. I would say any description under about 1000 characters would be considered simply describable. unless I’m misunderstanding, taking repeats as sets and adding them up is not simply describable
Yes, I do have an idea of what he is saying, Joe, because I have read his paper very carefully, something it appears you have not done, as you have made several blatant errors, like getting the compressibility thing diametrically wrong, and failing to note that his definition of “specification” incorporates both complexity and compressibility. And is also referred to as Specified Complexity. And is Information. And that he regards it as his most up-to-date treatment of CSI.
I’m off to bed now, so I won’t be able to release any more of your comments from the holding tank for a few hours. If you can go for a week without inducing me to send any to guano, I might release you into the wild.
Sleep well 🙂
Liz- I am starting to not care- if you think you can read that one paper- in isolation- and know what Dembski is saying, without running it by him, I say you are just whacked.
(contd)
OK, the <sup>n</sup> trick for superscripts did not work. Too bad.
We can convert more 4s into 3s and 5s. With four conversions, the fitness is still an acceptable 1.41×10^60. There are 2×(400×399×398×397)/(2×2) = 1.26×10^10 such configurations. That’s way more than the number of ground states.
We can convert up to fourteen 4s into 3s and 5s with the fitness staying above 10^60. The number of these configurations is 2×400!/(386!×7!×7!) = 1.67×10^29. I think these sequences represent the bulk of the target space.
There is, as people have noted here, no particular reason why natural selection should generally tend to increase complexity of the organism. That means that NS is not a good explanation for increased complexity if that complexity does not increase fitness. When there is increased “complexity” which increases fitness, then that is what we need to explain, and fortunately NS is then relevant to explaning it.
Dembski just says, in effect, to use some relevant scale. I try to use a scale related directly to fitness, to avoid getting tangled in these issues. We are, after all, basically talking about how adaptation can be explained. Even though at certain points Dembski talks of using compressibility of the description of the phenotype as the criterion, I think that this runs into the problem that it is unrelated to adaptation. A perfect sphere is then more Complex Specified than is an actual organism.
Using fitness itself is better, and lets us move on to the more real issue, of whether Dembski’s conservation laws work and are relevant.
(contd)
There are other ways to introduce defects into the “ground states” consisting of all 4s, but they probably contribute less to the target space than the above describe sequences.
For example, we can remove one T somewhere in the middle converting 4 and 4 Ts into 9. This reduces the fitness by a factor 9/(4×4) thus making it less than 10^60. It looks like this won’t help.
However, we can move one of the Ts between the 9 Hs and an adjacent 4 Hs so that {…9,4…} becomes {…8,5…} or, even better, {…7,6…}. Then the fitness goes down by (7×6)/(4×4×4) and that keeps the new sequence in the target space, barely so. The number of these sequences is only 641600, which does not add up much to the previously identified ones.
It’s a lot more describable than a DNA sequence coding for a protein 🙂
Yes, it’s simply describable, and in any case, Dembski’s condition is that the subset should consist of patterns that are as simply, or more simply describable than the observed pattern.
My patterns are describable as: sequences of 500 coin tosses where the product of the lengths of runs-of-heads is greater than [threshold].
I guess you have a point though, in that I should also include even easier-to-describe patterns in my N. I think that’s a problem for Dembski, though, because he doesn’t operationalise his “compressibility” thing at all well, and I can’t think of a way of operationalising it that would make a DNA sequence for a protein one of a really rather large subset of sequences that could be “compressed” by a “semiotic agent” with sufficient ingenuity!
The fact remains though that NS (as exemplified in my little script) can find a member of a vary rare subset of patterns really quite rapidly, where without NS it would require more than the “probabilistic resources” of the universe (which wouldn’t of course mean that it couldn’t happen – improbable things do).
Dembski’s counter-argument would be, I think,that I have “smuggled” the specification into my fitness function. Well, it’s not smuggled – it’s there in plain sight. My counter-rebuttal is that the natural world presents any population of self-replicators with abundant fitness criteria, and those criteria will fairly reliably result in patterns that match the criteria, and enable the populations to thrive.
So it then makes to sense (IMO) to then say: hey, look! How improbable that this population should “by chance” have a genome that fits its phenotypes so well for this environment! Because what has happened, of course, is that the reason the genome fits its phenotype for its environment is precisely because the specification (fitness for environment) is right there in the environment!
Yes, indeed, which is why I keep bringing up Chesil Beach! Which is a dead simple ranked sorting of pebble sizes over 18 miles. Very compressible, very Complex, and achieved by means of a simple natural sorting algorithm.
I keep meaning to try to compute its CSI. I got started once.
I think I can understand what he is saying in that paper. And if that paper only makes sense if read in combination with some other paper, then it’s incompetently written.
But in fact it isn’t, and he specifically says that it supercedes his earlier treatments.
If I was a reviewer of that paper (and it’s got up like a peer-reviewed paper) I would point out that his case is flawed and he needs to tackle my objections before publication.
Many people have done this, in fact, but he hasn’t tackled them.
The biologists have generally had the better terminology because their definitions reflect what is based in observation and the laws of chemistry and physics.
There is nothing wrong with trying to find good mathematical ways of pulling out the patterns in the evolution of a system; but these methods had better be anchored back to observational evidence and physical laws.
Fitness makes more sense that some kind of “information” or “compressibility.” Some of the simplest organisms are quite robust while the more complex ones have more things that can go wrong.
Indeed. Consider a spherical cow.
Thanks Olegt:)
That seems to leave me some leeway.
(odd that the tags didn’t work for you. They do for me. hmmm.)
ETA I mean the [sup] tags (substitute <>) lol.
Yes; I have also been noticing that some of the tags I am used to don’t work.
Correction: 2×400!/(386!×7!×7!) = 6.48×10^31.
Elizabeth,
You say:
“sequences of 500 coin tosses where the product of the lengths of runs-of-heads is greater than [threshold].”
Your statement is not simply describable, this is:
“Alternating heads and tails”
Whereas the pattern is (ahem) described simply.
You say:
“It’s a lot more describable than a DNA sequence coding for a protein”
DNA sequences have a near optimal functioning sequence, k/n, whereas
k are arrangments that code for specific function, and n are all possible configurations. This is specification. If we are trying to demonstrate this by flipping coins, then the string must be simply describable. This is how specificity can be mapped with binary populations. Whereas k is the amount of simply describable patterns of {H,T}, and n is all possible patterns of {H,T}.
Joe F’s example of a sphere is dead on. I read that in his paper and thought is was a great example of CSI, such that an equiprobable population of {0,1,2,…,9} outputting {3.141592653589793238462643383279502884,…,n}, whereas n approaches infinity, that can then be compressed into a single character, or Pi, is the most elegant example of CSI.
One needn’t compare a functional sequence to all possible functional sequences. It’s only necessary to know if there’s a nearby functional sequence.
petrushka,
That does seem to be the core of the debate
I don’t understand. The DNA sequence is not required to be simply describable in order to be called *specified*, but the sequence of coin flips must be simply describable in order to be called *specific*?
Again, I don’t understand. In what sense is the character Pi a *compression*? It is simply a symbol that we use to signify a particular infinite sequence. Under that logic, it seems to me that I can assign a symbol to signify any particular sequence I wish and then call the sequence *compressible*.
Sorry, first sentence is supposed to read: The DNA sequence is not required to be simply describable in order to be called *specified*, but the sequence of coin flips must be simply describable in order to be called *specified*?