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).
(As an aside) yes, I tried the <sup> markup too and it doesn’t work. I was too chicken to try up-arrows. Once on Panda’s Thumb I wrote 10^40 and it came out as 1040. Even though I in a later comment, and the admin of PT editing my post at my request, both corrected it quickly, people kept writing comments for days afterward saying “hey, you made a mistake, it’s not 1040!” I kept having to correct it and correct it to calm them down. I’m relieved to see that the up-arrow would work here, and that I don’t need to keep saying 10-to-the-150th-power.
These are highly pertinent points IMO, junkdnaforlife, with regard to the practical utility of CSI as a measure.
Firstly, “compressibility” in the strict Kolmogorov sense, is useless as a post-hoc specification, precisely because, of course, the most compressible yet complex sequences are the most banal, and can (and are) readily observable in the inorganic world, where nobody (that I know of) tries to claim intervention from a Designer. My favorite example is Chesil Beach on the south coast of the UK, an 18 mile tombola in which the pebbles are exquisitely sorted from pea size at the west end to fist size (and beyond) at the east. There are billions of pebbles, so the theoretical ways of sorting them is truly vast, and the number of sorted ways are a tiny subset of that. Yet it’s all done by a simple natural “sorting algorithm”.
Secondly, as I pointed out, if we apply Dembski’s principle to, say, a DNA sequence, we don’t observe the simplest sortings at all (which presumable be something like all the guanines-cytosines, then cytosine-guanines, then all the adenine-thymines then all the thymine-adenines. In fact, of course, what we are interested, which would be a tiny subset of the theoretically possible arrangements. In fact, of course, what we are interested in is the fact that out of the vast number of theoretically possible arrangements, what we observe are the tiny subset that code for organisms that thrive in some environment containing hazards and resources.
In my little virtual world that’s what I did – I started with “virtual organisms” that had to thrive in a virtual environment in which they competed for resources with genomes that coded for a phenotype that output products of runs-of-heads. The larger that product, the better their access to resources (an analog to bigger teeth, if you like). So we should not be surprised (and we are not) that in that virtual environment, my virtual organisms evolve genomes that code for “bigger teeth” (bigger products of runs-of-heads). It’s no different in principle from basing a CSI calculation of a real organism on a sequence that codes for some set of important proteins that promote the organism’s reproductive chances
So I don’t agree with you when you say:
In my virtual system “k” is the number of arrangements that code for high-product-of-runs-of-heads. I don’t see why that is in principle different from “k” as the number of base-pair sequences that code for “useful proteins”. My system has a different code of course. Instead of triplets of four possible base-pairs coding for an amino acid, with sequences limited by start and stop codons, and the output being a protein, my system has zeros serving to demarcate divisions between what would be codons in DNA, and are runs-of-heads in my sequences, and instead of coding for strings of amino acids, my series of runs-of-heads code for integers that are then multiplied together to output not a protein but a product. But in both cases, output (protein or product) serves to increase the phenotype’s chances of reproductive success. Sure, my system is absurdly simple, but then Dembski gives examples that are just as simple, and presumably finds them valid.
The fundamental problem with Dembski’s approach, of course, is that he infers Design from a pattern that exhibits some rare but specifiable property, but rejects the idea that such a pattern could have been generated by a system that tends to “select” for just that property, on the grounds (in his NFL arguments that is) that those systems “smuggle” in the specification.
No “smuggling” is required, as Chesil Beach demonstrates. A sorting system will sort. Sorting systems occur. And the result of such sorting systems are sorted patterns that are vastly unlikely to occur in the absence of such a sorting system, but will readily occur in its presence.
What we call natural selection is a sorting system. So it is no surprise that what emerges from it are the very patterns for which it selects! Namely, patterns that promote its own perpetuation.
There may be good arguments for ID, although I have not seen one. Behe’s is potentially better, as, even, is Meyer’s – both propose natural selection works (actually, even Dembski does, except when he doesn’t….) but that some features, crucial to further evolution are “unevolvable”. For Meyer it’s the ribosome. For Behe the poster children are the bacterial flagellum and chloroquine resisance in the malaria parasite.
My point here is that Dembski’s argument fails. If we take his compressibility criteria literally, he has to explain Chesil Beach. If we take a more functional approach to complexity (as Hazen et al do, and as I have done here), NS does the job.
Exactly. “pi” is not a “compression” of pi to N digits. An algorithm that output pi to N digits would be. But it would be longer than “pi”.
I’m now up to 1.7050e+59.
I’m reluctant to stop it and peek, because it seems to edging asymptotically towards my jackpot!
Which has more CSI, an onion, a cheetah, a blueberry, a mushroom, a human, a lobster, a lichen, a crinoid, or a halibut?
And which has more CSI, a western fence lizard or a garter snake?
Well said.
I hope you have a suitable fanfare programmed in – cream buns all round, too! Make mine a coffee puff.
Do you run all of your whacked assertions by Dembski before you blurt them out?
If you and Dembski are such close buddies, why don’t you ask him to come here and defend his claims?
In the paper he is talking about singular events- and just because you say the paper is incompotently written that does not make it so.
So have a great time with your strawman and your ignorance…
OK Liz- I am telling the UD folk of your folly…..
I didn’t say it was. I don’t think it is. That’s why I think it stands on its own, and can be critiqued as a coherent whole.
Joe, this kind of comment would normally lead me to send it to guano, but I tend to give extra leeway if the comment is directed at me. Please read the site rules, and try to stick with them. If you can’t, I will simply re-open one of your old posts, and let you post there without moderation and nowhere else, and people can engage with you or not, as they please. You will not be censored, but I am not going to spend time I could better spend elsewhere vetting all your comments for rule violations. This site has a specific purpose and that purpose is respectful dialogue. Please try to be respectful if you want to participate in the dialogue.
Elizabeth,
Matbat-
Outputting a random string and representing the set with a symbol would not describe the set. Give the symbol to someone else and see if they can recover the set, as they would be able to if you tell them, “every third coin is H,” or Pi such as, “the ratio of the circumference of a circle to its diameter”.
Specified relates to (proteins) by the specific arrangements that execute function / all possible arrangements. A protein sequence is specified for a
particular function. Random coin flips have no function to obsererve, therefore compressibility is measured. Another way to explain the simply describable/compressibility relationship between a binary population {H,T} and dna sequences is- a protien-coding dna sequence that can be simply describable as,”interacts with the glucocorticoid receptor,” such that the number of simply describable protien-coding dna sequences / all possible dna sequences, shares a relationship with, the number of simply describable {H,T} patterns / the number of all possible {H,T} patterns.
//”every forth coin is tails”
//”interacts with the glucocorticoid receptor,”
These both refer to specific patterns. The protien function was there when we looked, it was not added after we looked.
Liz-
Chesil Beach is the product of erosion in which the set of possible microstates of elements in the source population caught in the water, wind, ice, soil creep etc, were not in a state of equilibrium, or maximum uncertainty. Any sorting was certainly law like, whereas based on the source population in a state of erosion, the exact opposite arrangment of rocks was not as equally probable as the current arrangment of rocks.
This coin flip thing is not CSI. Selecting heads from a string, taking the top 50 clusters puts a ? on the complexity, which on top of the simply describable issue would be 0/2.
Please do. And please invite them to come over and discuss it directly if they would like.
I will do my best to ensure that they are treated with respect.
Oh, it’d be fun if kairosfocus showed up here. He is a chatty fellow.
Well, I would agree, junkdnaforlife, but I don’t see what is any less “law-like” about the sorting system that is evolutionary processes, namely heritable variance in reproductive success. As I am busy demonstrating, if I set up a system whereby a large product of runs-of-heads promotes reproductive success, then in a “law-like” manner, I will end up with a population whose genomes generate a large product of runs-of-heads. That is precisely the nature of the rebuttal to Dembski’s claim: that there can exist “law-like” sorting systems that generate CSI, with no intentional intelligence involved (except insofar as you might like to invoke a creative Intelligence behind the laws of our universe or existence itself).
And to go back to your earlier point, about which I have been thinking further: If my evolving population does succeed in producing a genome that produces the maximum possible product-of-runs-of-heads (a repeating sequence of HHHHT), then I will have generated a very compressible genome in the strict sense (a very short program is need to produce a regularly recurring short pattern), but, interestingly, not by selecting for that pattern itself, as in Weasel, but the property of a set of patterns of which that pattern happens to have the highest possible value. So I have not started by giving the system an information as to the form of the optimal solution, but simply the problem that it has to solve. I could much more easily generate a repeating string of HHHHTs using a Weasel algorithm, but it would be very boring. The Weasel equivalent of what I have done here would be to select letter strings not on how closely they resemble the target phrase, but on how closely they, for example, convey that meaning that the speaker considers that a certain cloud formation resembles a small mustelid, with the possible additional caveat that it must use Shakespearean vocabulary.
I don’t understand what you are saying here – could you rephrase? I just can’t parse it (possibly owing to caffeine depletion).
He did, in fact, but unfortunately his comment got stuck in an extra spam trap I hadn’t known about, and I only recently released it. Unfortunately I don’t know which post it was to, and I can’t find it.
I am not surprised. It was probably 10,000 characters long and contained 8 bazillion links to his web site.
It was quite short, but it might have been links that did it.
I’ve upped the link limit.
We’ll see. Joe has advertised this thread all over Uncommon Descent. (Hi Barry!)
It’s going to be a long slog to the target space. At this point, your sequences are short strings of H separated by single Ts. The trick is to move the Ts so that they become equally spaced, with 4 Hs between them. Single-point mutations are rather ineffective at this task: they mostly add a new T and sometimes remove it. Both types of changes knock the fitness down.
Adding mutations that exchange two adjacent bits (e.g., HT to TH) will get you there in no time. That would be cheating of course.
I have a c++ code that got me to 4×10^58 in less than a minute with point mutations only. Haven’t run it overnight.
Yes, I was thinking that. I had originally thought of using insertions and deletions and duplications, but they would alter the genome length, and make the CSI more difficult to compute.
It’s not very well-connected space up at the top end 🙂
Although the cool part is that if I get there, it’s going to be via IC pathways. Heh.
It would be good if gpuccio looked in. We could perhaps try to apply his metric.
Cool. My MatLab code is very clunky but at least I understand it 🙂
My code probably differs slightly from yours. It sorts the sequences by fitness and replaces the bottom half with exact copies of the top half. Then all of them undergo point mutations with a rate of the order p = 1/1000 or less. This does not guarantee that the fitness always marches upward. If the mutation rate is too high then it reaches an equilibrium and fluctuates there.
i haven’t read your algorithm, but let’s see if I understand it.
You started with a series of 100 coin tosses. From that you replicated them with mutations. From the population of children you select some to become the parents of the next generation. The fitness function counts the sequences of all heads. Is this right so far?
Some questions:
1. What is the mutation rate?
2. What is the population size? Do you have more than one parent per generation?
3. Your fitness function seems similar to that of my word generator, except I count substrings that appear in words. I do not look for a specific word or specific substring, so my target can wander. I made fitness dictionaries for six different languages, so I can see what happens as a result of fitness landscapes that have different degrees of connectedness.
Olegt:
Nah – just introducing a little biological realism! The organisms that have the most ‘complexity’ are sexual ones, or the descendants of sexual ones that have committed to never-ending diploidy (their complexity is inherited and frozen). Inversions, duplications et al. are most frequently caused by meiosis, not mitosis or repair. I suspect that adding recombinant sex to the mix (if I understand correctly, it is absent), with one or two methods that replicate meiotic chromosome alignment issues, would get you there in a jiffy.
Aside from trying to mimic biological mutations, the only cheat would be to have mutations that have knowledge of the fitness function.
Yes, and totals the number of heads in each run of heads. Then finds the product of all those totals.
Some questions:
1. What is the mutation rate?
In the version that is running right now it is quite low: .001, i.e. there is a .001 probability that any given location will flip.
Population size is 100 and is maintained at 100. Organisms in top half of the distribution survive into the next generation, and produce one offspring, subject to mutation. So out of each generation of 100, fifty survive and become parents of one child, bringing the population back up to 100.
Nice. I made one of those, once, where “pronouncability” was one fitness criteria, and “makes word in a dictionary” was another, and “noun-verb-noun” or “article noun” or “adjective-noun” combos were another. I got some quite cute little sentences out of it. The thread I was participating in was with a creationist who kept on changing the requirements, including what I started with. At one point, he challenged me to start with an already sensible sentence, and evolve another (cf “dogs into cats”). So he specified that I start with: The quick brown fox jumps over the lazy dog. I was thrilled to find that one of my winning outputs from that run was: “The quick brown fox jumps over the crazy dogma.
Or, arguably, a fitness function that is identical with the optimum solution (as in Weasel). This is not true in my set up – the fitness function does not specify the optimum solution, which I need not know in advance, and I do not know, in fact, what the near-optimal solutions are.
1.8186e+59
I just ran another version with a higher mutation rate, and got it to halt the loop when a genome hit 10^58.
The lineage is represented here (ancestor at the top), white is “Heads”, black is “Tails”:
And the fitness history is here:
The offspring that made it over the line had five simultaneous point mutations. Note that these were preceded by a number of deleterious mutations, so the thing is “IC”.
If you assign fitness according to how often substrings appears in words, pronounceability is automatic I do have one cheat, shich I don’t consider a cheat. To add to fitness, the substrings must be in the same position as they occur in words. I’m sure your function isn’t positional.
My reasoning is that I’m modelling a space in which a certain low percentage of strings are functional. That seems to me to have something in common with protein coding sequences. Presumably most are unknown, but they are not arbitrary. Chemistry provides the dictionary.
I don’t care which of this subset I reach, but I need to have a fitness gradient. From where I stand it appears that the only possible argument against evolution would be to assert that fitness gradients don’t exist. That seems to be gpuccio’s argument.
Congrats on reaching 59. Have you derived a power function that would predict how long it will take to reach 60?
clear% sets parameters
Ncritters=100; % population size
GenomeLength=500; % length of genome
MutationProp=.01; % probability that a point mutation will take place
% creates starting population in a structure called Pop
for ii=1:Ncritters
Genome=zeros(1,GenomeLength);
Rand=rand(1,GenomeLength);
Index=Rand>.5;
Genome(Index)=1;
Pop(ii).Genomes=Genome;
Pop(ii).Phenotype(1).Gen=[];
Pop(ii).Product=[];
end
% Initialises variables
jj=0;
MaxProducts=0;
% Loops generations, and continues to iterate until threshold Product is
% reached
while MaxProducts<1.00e+58
jj=jj+1 %increments while loop counter
Products=zeros(Ncritters,2); %preallocates memory
for ii=1:Ncritters
Pop(ii).Phenotype(jj).Gen=[];% creates field for storing phenotype data
CountOnes=0; %Initialises Heads counter
% loop counts runs of Heads (ones) in each critters genome to make
% "Phenotype".
for kk=1:GenomeLength
if Pop(ii).Genomes(jj,kk)==1
CountOnes=CountOnes+1;
else
if CountOnes>0
Pop(ii).Phenotype(jj).Gen(end+1)=CountOnes;
CountOnes=0;
end
end
end
% Computes the products of the runs, and stores them in the Pop structure
Products(ii,1)=ii;
Products(ii,2)=prod(Pop(ii).Phenotype(jj).Gen);
Pop(ii).Product(jj,1)=prod(Pop(ii).Phenotype(jj).Gen);
end
% Culls the least fit half of the population
Products=sortrows(Products,2);
MaxProducts=max(Products(:,2));
WinningCritters=Products(Ncritters/2+1:end,1);
WinningCritters=sortrows(WinningCritters,1);
Pop=Pop(WinningCritters);
% Generates offspring from each surviving organism, with mutated genomes
for mm=1:Ncritters/2
Pop(mm+Ncritters/2)=Pop(mm);
NewGenome=Pop(mm).Genomes(jj,:);
Pop(mm+Ncritters/2)=Pop(mm);
Pop(mm).Genomes(jj+1,:)=NewGenome;
PointMutations=rand(size(NewGenome));
PointMutationsIndex=PointMutations
That’s weird, the edit window has code tags but they don’t work.
Oh well.
No, but I reached 60 last Thursday 🙂 Took me about 60 years.
Got my Seniors Railcard to prove it.
Do furniture assembly instructions pertain to the origin of life?
Do you have copies of the assembly instructions, written by ‘the designer’, of any organism or anything else in nature to post here?
Computer programs, furniture assembly instructions, and encyclopedia articles are designed and produced by humans. What do they have to do with the origin of life?
Slightly off-topic, but …
Compression, as in those programs that you use on your computer to compress files, work by replacing a long sequence of symbols by a short sequence of symbols. When we replace an infinite decimal expansion by \pi (with latex, I would use
, but it prints as one Greek letter), then we could be said to be doing extreme compression. Examples such as this are why I am skeptical of the usefulness of Kolmogorov complexity.
Actually I work for a furniture manufacturer (doing IT) and I have produced instruction manuals. It would be news to me if the images couldn’t be algorithmically compressed to jpeg files and if the final document couldn’t be algorithmically compressed to a zip file.
I have no idea how compression relates to evolution. What evolution requires is that instruction sequences can be accumulated. If there is, in fact, no incremental path to currently functional sequences, then maybe goddidit. My understanding of the relevant research (Thornton and others) is that function is not isolated like cipher keys or lock combinations.
All 5 or 6 of them?
The fitness trajectory on a log scale:
My other run is at 1.9399e+58
I wish I’d made the mutation rate bigger.
Ok let’s see if this works:
No Free lunch pages 148-49
The next section is titled “The Origin of Complex Specified Information”.
In the paper Elizabeth is referring to Dembski has an addendum- Addendum 1: Note to Readers or TDI & NFL, in which he states
IOW it does not replace “No Free Lunch”, it is an extention of PART of it.
Taking only runs of length 3 just misses the aim of 10^60. Nevertheless, one can combine runs of length 3 and runs of length 4 – and throw in the odd 2, 5 or 6 to use the whole 500 places. E.g., 4 runs of length 3 combined with 97 runs of length 4 result in 2.034*10^60 (my optimum 🙂
The greatest number of 3-runs allowed in this system is 69 (combined wiht 45 4-runs). Not for all numbers of 3-runs smaller than 69 can the cut be made – there are 18 exceptions…
Nevertheless, such combinations add 9.1*10^34 elements to the target space (which is still miniscule).
Well, Joe, if “biological specificity always refers to function” according to Dembski, I am entitled to specify by function, which I do. That would seem to take care of junkdnaforlife’s point.
I’m specifying a tiny island of extremely high function: products that exceed 10^60.
I’m getting there, and I suspect that the shores I’ve already reached are beyond the probabilistic resources of the universe.
There a couple of really nice papers here and here by Olle Haggstrom, responding to Dembski.
Haggstrom’s point is that Dembski’s thesis boils down to the claim that the fact that in some landscapes, targetted search strategies work better than random search indicates that the world is non-uniform, and that that, in itself, indicates a Designer.
So he ask: in that case, why pick on biology? Why not point to any non-uniformity in the world as evidence of a designer? Because in any world in which non-uniform distributions occur, targetted search algorithms will work better that random search. Clearly biology is such a domain (as Haggstrom says, if it were not, there’d be an infinitesimal chances that any baby would resemble a baby, or even be viable), but so is physics and chemistry and cosmology.
So if you want to conclude an Intelligent Designer from the fact that the universe is non-uniform (lacks entropy, essentially) – fine. But in such a universe, evolutionary processes will be perfectly capable of creating CSI. And, more to the point, living things.
Less than an order of magnitude to go….
1- Your example has nothing to do with biology nor biological function
2- Nice of you to ignore the rest of my post which tells you that CSI pertains to its origins
3- The design inference has always extended beyond biology- read or watch “The Privileged planet”
4- Again with the equivocation pertaining to evolutionary processes
There is a rather interesting analog to this little exercise, and it comes from the world of physics.
If a set of external constraints are put on a system that require the system to adjust to these constraints, then either energy must be released from the system or energy must flow into the system so that the system can have whatever potential and kinetic energies are consistent with those constraints.
If energy is released, it flows out of the system at some temperature that is greater than the surroundings (otherwise it wouldn’t flow out). This means the entropy of the system decreases as the system “relaxes” into its new constraints.
On the other hand, a system can be “pumped” into a higher energy state that will allow it to adjust to new constraints by being in an energy cascade in which it can take in the energy needed. Many complex molecular systems are constructed this way. In this case, the entropy of the system can increase even as the system becomes more ordered (order has nothing to do with entropy).
Your little demonstration is an example of the latter. Your system can represent the building of an ordered structure in an energy cascade. And we have also noted the Shannon entropy goes to a maximum given the constraints. Multiply that by Boltzmann’s constant and you have the thermodynamic entropy.
What we don’t see in this example, however, is what the energy input is and what happens to the temperature of the system. What might correspond to the energy being put into the system? I would suggest that it is proportional to the products of the number of heads.
If that is the case, then I think we can calculate the change in entropy divided by the corresponding change in energy and get the reciprocal temperature of the system.
If I can find some free time in the next couple of days, I may take a look at it.
Your example could be a model for the formation of molecules in abiogenesis. Man, Dembski et.al are gonna hate this!
I look forward to it, Mike 🙂
Well, yes it has, because it evolves in exactly analogous fashion to the way functions are posited to evolve in biology.
And I’ve labeled the analogs clearly – it has a genome, a phenotype, a function, and a landscape in which it must survive and reproduce.
Well, so you keep saying, but when pressed, all you said was that it pertained to the origin of CSI. And I’m demonstrating the origin of CSI. My little algorithm is generating so much of it it’s already beyond Dembski’s threshold.
On the other hand, if all you are saying is that a world in which CSI is capable of being generated, must have been designed, fine. I’m just demonstrating that within a world in which as Haggstrom has it, like things cause like things, CSI can be readily generated by non-intelligent processes.
Yes, I know. But it seems weird to me to focus on biology when any snowflake would make the same point.
I’m not equivocating at all. I’ve set up a model of exactly the evolutionary processes that evolutionary scientists propose.
1- You need to explain how necessity and chance produced the original biological function or reproduction- you have not done so- you have just granted the very thing that needs explaining.
2- You may generate some specification but you have not generated CSI especially when you start with reproducing entities-
3- You only think we focus on biology
4-You are equivocating because you are assuming that evolutionary processes are not design processes.
As I have told you, and supported, ID is not anti-evolution. When a GA solves the problem it was designed to solve, that is ID, not the blind watchmaker.