Gpuccio has made a series of comments at Uncommon Descent and I thought they could form the basis of an opening post. The comments following were copied and pasted from Gpuccio’s comments starting here
To onlooker and to all those who have followed thi discussion:
I will try to express again the procedure to evaluate dFSCI and infer design, referring specifically to Lizzies “experiment”. I will try also to clarify, while I do that, some side aspects that are probably not obvious to all.
Moreover, I will do that a step at a time, in as many posts as nevessary.
So, let’s start with Lizzie’s “experiment”:
Creating CSI with NS
Posted on March 14, 2012 by Elizabeth
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)
Now, some premises:
a) dFSI is a very clear concept, but it can be expressed in two different ways: as a numeric value (the ratio between target space and search space, expressed in bits a la Shannon; let’s call that simply dFSI; or as a cathegorical value (present or absent), derived by comparing the value obtained that way with some pre define threshold; let’s call that simply dFSCI. I will be specially careful to use the correct acronyms in the following discussion, to avoid confusion.
b) To be able to discuss Lizzie’s example, let’s suppose that we know the ratio of the target space to the search space in this case, and let’s say that the ratio is 2^-180, and therefore the functional complexity for the string as it is would be 180 bits.
c) Let’s say that an algorithm exists that can compute a string whose product exceeds 10^60 in a reasonable time.
If these premises are clear, we can go on.
Now, a very important point. To go on with a realistic process of design inference based on the concept of functionally specified information, we need a few things clearly definied in any particulare example:
1) The System
This is very important. We must clearly define the system for which we are making the evaluation. There are different kinds of systems. The whole universe. Our planet. A lb flask. They are different, and we must tailor our reasoning to the system we are considering.
For Lizzie’s experiment, I propose to define the system as a computer or informational system of any kind that can produce random 500 bits strings at a certain rate. For the experiment to be valid to test a design inference, some further properties are needes:
1a) The starting system must be completely “blind” to the specific experiment we will make. IOWs, we must be sure that no added information is present in the system in relation to the specific experiment. That is easily realized by having the system assembled by someone who does not know what kind of experiment we are going to make. IOWs, the programmer of the informational system just needs to know that we need random 500 bits string, but he must be completely blind to why we need them. So, we are sure that the system generates truly random outputs.
1b) Obviously, an operator must be able to interact with the system, and must be able to do two different things:
– To input his personal solution, derived from his presonal intelligent computations, so that it appears to us observers exactly like any other string randomly generated by the system.
– To input in the system any string that works as an executable program, whose existence will not be known to us observers.
OK?
2) The Time Span:
That is very important too. There are different Time Spans in different contexts. The whole life of the universe. The life of our planet. The years in Lenski’s experiment.
I will define the Time Span very simply, as the time from Time 0, which is when the System comes into existence, to Time X, which is the time at which we observe for the first time the candidate designed object.
For Lizzie’s experiment, it is the time from Time 0 when the specific informational system is assembled, or started, to time X, when it outputs a valid solution. Let’s say, for instance, that it is 10 days.
OK?
3) The specified function
That is easy. It can be any function objectively defined, and objectively assessable in a digital string. For Lizzies, experiment, the specified function will be:
Any string of 500 bits where the product calculated as described exceeds 10^60
OK?
4) The target space / search space ratio, expressed in bits a la Shannon. Here, the search space is 500 bits. I have no idea how big the target space is, and apparently neither does Elizabeth. But we both have faith that a good mathemathician can compute it. In the meantime, I am assuming, just for discussion, that the target space if 320 bits big, so that the ratio is 180 bits, as proposed in the premises.
Be careful: this is not yet the final dFSI for the observed string, but it is a first evaluation of its higher threshold. Indeed, a purely random System can generate such a specified string with a probability of 1:2^180. Other considerations can certainly lower that value, but not increase it. IOWs, a string with that specification cannot have more than 180 bits of functional complexity.
OK?
5) The Observed Object, candidate for a design inference
We must observe, in the System, an Object at time X that was not present, at least in its present arrangement, at time 0.
The Observed Object must comply with the Specified Function. In our experiment, it will be a string with the defined property, that is outputted by the System at time X.
Therefore, we have already assessed that the Observed Object is specified for the function we defined.
OK?
6) The Appropiate Threshold
That is necesary to transorm our numeric measure of dFSI into a cathegorical value (present / absent) of dFSCI.
In what sense the threshold has to be “appropriate”? That will be clear, if we consider the purpose of dFSCI, which is to reject the null hypothesis if a random generation of the Oberved Object in the System.
As a preliminary, we have to evaluate the Probabilistic Resources of the system, which can be easily defined as the number of random states generated by the System in the Time Span. So, if our System generates 10^20 randoms trings per day, in 10 days it will generate 10^21 random strings, that is about 70 bits.
The Threshold, to be appropiate, must be of many orders of magnitude higher than the probabilistic resources of the System, so that the null hypothesis may be safely rejected. In this particular case, let’s go on with a threshold of 150 bits, certainly too big, just to be on the safe side.
7) The evaluation of known deterministic explanations
That is where most people (on the other side, at TSZ) seem to become “confused”.
First of all, let’s clarify that we have the duty to evaluate any possible deterministic mechanism that is known or proposed.
As a first hypothesis, let’s consider the case in which the mechanism is part of the System, from the start. IOWs the mechanism must be in the System at time 0. If it comes into existence after that time because of the deterministic evolution of the system itself, then we can treat the whole process as a deterministic mechanism present in the System at time 0, and nothing changes.
I will treat separately the case where the mechanism appears in the system as a random result in the System itself.
Now, first of all, have we any reason here to think that a deterministic explanation of the Observed Object can exist? Yes, we have indeed, because the nature itself of the specified function is mathemathical and algorithmic (the product of the sequences of heads must exceed 10^60). That is exactly the kind of result that can usually be obtained by a deterministic computation.
But, as we said, our System at time 0 was completely blind to the specific problem and definition posed by Lizzie. Therefore, we can be safely certain that the system in itself contains not special algorithm to compute that specific solution. Arguing that the solution could be generated by the basic laws physics is not a valid alternative (I know, some darwinist at TSZ will probably argue exactly that, but out of respect for my intelligence I will not discuss that possibility).
So, we can more than reasonably exclude a deterministic explanation of that kind for our Observed Object in our System.
7) The evaluation of known deterministic explanations (part two)
But there is another possibility that we have the duty to evaluate. What if a very simple algorithm arose in the System by random variation)? What if that very simple algorithm can output the correct solution deterministically?
That is a possibility, although a very ulikely one. So, let’s consider it.
First of all, let’s find some real algorithm that can compute a solution in reasonable time (let’s say less than the Time Span).
I don’t know if such an algorithm exists. Im my premise c) at post #682 I assumed that it exists. Therefore, let’s imagine that we have the algorithm, and that we have done our best to ensure that it is the simplest algorithm that can do the job (it is not important to prove that mathemathically: it’s enough that it is the best result of the work of all our mathemathician friends or enemies; IOWs, the best empirically known algorithm at present).
Now we have the algorithm, and the algorithm must obviously be in the form of a string of bits that, if present in the System, wil compute the solution. IOWs, it must be the string corresponding to an executable program appropriate for the System, and that does the job.
We can obviously compute the dFSI for that string. Why do we do that?
It’s simple. We have now two different scanrios where the Observed Object could have been generated by RV:
7a) The Observed Object was generated by the random variation in the System directly.
7b) The Observed Object was computed deterministically by the algorithm, which was generated by the random variation in the System.
We have no idea of which of the two is true, just as we have no idea if the string was designed. But we can compute probabilities.
So, we compute the dFSI of the algorithm string. Now there are two possibilities:
– The dFSI for the algorithm string is higher than the tentative dFSI we already computed for the solution string (higher than 180 bits). That is by far the most likely scenarion, probably the only possible one. In this case, the tentative value of dFSI for the solution string, 180 bits, is also the final dFSI for it. As our threshold is 150 bits, we infer design for the string.
– The dFSI for the algorithm string is lower than the tentative dFSI we already computed for the solution string (lower than 180 bits). There are again two possibilities. If it is however higher than 150 bits, we infer design just the same. If it is lower than 150 bits, we state that it is not possible to infer design for the solution string.
Why? Because a purely random pathway exists (through the random generation of the algorithm) that will lead deterministically to the generation of the solution string, with a total probability of the whole process which is higher than our threshold (lower than 150 bits).
OK?
8) Final considerations
So, some simple answers to possible questions:
8a) Was the string designed?
A: We infer design for it, or we infer it not. In science, we never know the final truth.
8b) What if the operator inputted the string directly?
A: Then the string is designed by definition (a conscious intelligent being produced it). If we inferred design, our inference is a true positive. If we did not infer design, our inference is a false negative.
8c) What if the operator inputted the algorithm string, and not the solution string?
A: Nothing changes. The string is designed however, because it is the result of the input of a conscious intelligetn operator, although an indirect input. Again, if we inferred design, our inference is a true positive. If we did not infer design, our inference is a false negative. IOWs, our inference is completely independent from how the designer designed the string (directly or indirectly)
8d: What if we do not realize that an algorithm exists, and the algorithm exists and is less complex than the string, and less complex than the threshold?
A: As alreday said, we would infer design, at least until we are made aware of the existence of such an algorithm. If the string really originated randomly througha random emergence of the algorithm, that would be a false positive.
But, for that to really happen, many things must become true, and not only “possible”:
a) We must not recognize the obvious algorithmic nature of that particular specified function.
b) An algorithm must really exist that computes the solution and that, when expressed as an executable program for the System, has a complexity lower than 150 bits.
I an absolutely confident that such a scenario can never be real, ans so I believe that our empirical specificity of 100% will be always confirmed.
Anyways, the moment that anyone shows tha algorithm with those properties, the deign inference for that Object is falsified, and we have to assert that we cannot infer design for it. This new assertion can be either a false negative or a true negative, depending on wheterh the solution string was really designed (directly or indirectly) or not (randomly generated).
That’s all, for the moment.
AF adds “This was done in haste. Any comments regarding errors and ommissions will be appreciated.”
Favorite Pet?
I entirely agree. It’s tempting to fight snark with snark, but there is a genuine profundity (IMO) at the heart of the ‘minimal’ GA, where there is only replication of replication: inevitable fixation of ancestry. (The reasons why this is ‘profound’ may not be immediately clear!)
The null is a very useful starting point, one all budding designers of organisms (in whose shoes you can put yourself, as God-of-the-GA) should be aware of. It’s hard to spot the null in ‘real’ organisms, because the little bastards keep on hopping about all over the place.
“Favorite Pet?”
LOL, yes, but I wouldn’t recommend it to fish lovers!
Hi Zachriel
Not sure what the problem is. In Lizzie’s absence, I’ve reinstated them. Any member can start a post thread and has some moderation control over those threads. I don’t have the time to monitor more than once every day or so.
Where’s Lizzie!
Your link has an extra quote at the end, leading to a 404.
https://gist.github.com/3837791
The code is indeed atrocious and unlike anything that’s been discussed before.
olegt,
From an earlier comment:
Mung’s comment reported above suggests that he WOULD have “problems” with things that DON’T “smack of teleology”
It seems to me to be an odd thing to have said, and quite revealing of a way of thinking that is not the most fruitful.
The teleology would have to be of a pretty extreme nature, in the case of recombination. How do you actively get two combinationally useful genetic segments together, while still allowing their bearers free will? Unless randomisation is part of the design, for its novelty-generating capacity. In which case, blind and undirected processes can …
olegt,
And there should be a mutation rate parameter that is independently applied to each bit. Currently, every call to mutate() sets exactly one bit in a genome, never more or less.
The corrected fitness function should work like this:
1. If the genome is all 0’s, return a fitness of 0.
2. Otherwise, initialize the fitness to 1.
3. Scan the genome for contiguous runs of 1’s.
4. For each run, let fitness = fitness * length of run.
5. Return fitness.
Mung has shared only the class definition, so I can’t comment on what changes are needed in the rest of his code.
How’d you guess our PIN?
To make a child, you need to take each bit, one by one. Compute a random number between zero and one. If the mutation rate exceeds this random number you apply the mutation.
To apply the mutation, compute a random integer between zero and one and this becomes the new bit. It may be the same as the old bit.
Petrushka, I agree with your first paragraph, but not with the second:
I think it’s better to always flip the bit when you apply the mutation. Otherwise it’s not a mutation at all, and the true mutation rate is lower than the parameter indicates.
On the other hand, you might argue that by sometimes leaving the bit unchanged, you are modeling neutral mutations. Even if that is your intent, however, the approach is still flawed because it fixes the ratio of neutral to non-neutral mutations at 1:1. Better to either make that ratio adjustable, or not to bother modeling neutral mutations at all.
What Mung has there is a 735-bit individual from Lizzie’s digital binary menagerie (assuming his program generates all possibilities from the ASCII set, including control characters).
There are 2^735 such creatures. They can simply be regarded as all the 735-bit binary numbers from all-zeroes to all-1’s. If you generate one at random, it may help to view it as actually picking the ordinal position of the string in that set, as much as the string itself. No position in the set is more ‘privileged’ that any other. You can easily map other base-n systems (eg DNA) onto this assumed underlying ‘binary’ set. Inside your computer, that’s pretty much what they all are anyway.
That’s the digital genotype. It’s what would be inherited, if you copied it. Whether it has ‘CSI’ or not depends entirely on how strings are evaluated – upon phenotype. This is related to the fitness function, but is not quite the same.
If your phenotype involves slicing it into 7-bit chunks and generating a unique bitmap corresponding to the ASCII character set, and the evaluation further depends upon a human operator recognising it as meaningful text, then obviously this would not stand out. If CSI depended upon the string looking like a bit of Bill Gates’s horse in photoshop, however, it could have CSI in one system but not the other. And if you sliced it another way and turned it into a segment of RNA with added promoters, it might become a useful fragment of protein.
The point is, that each of those evaluation methods gives a completely different structure to the distribution of ‘well-formed strings’ in the space. ‘CSI’ is context-dependent. And whatever it is, you can potentially generate strings with more of it by selection, mutation and recombination among strings with less.
If function was defined as everything with a zero in it, almost the entire space would have it. If it was defined by a run of 200 consecutive 0’s, there would be much less. But you can’t take a space evaluated under one rule (eg meaningful English) and assume that all spaces of the same size (eg protein or RNA) will be structured in the same way with regards to the distribution of ‘surprise’, or its navigability.
Nope. A blind mutation can result in no change. What you are suggesting is not conceptually different from latching. It requires the mutation process to have some knowledge of the current state, which is forbidden.
Assuming that “mutation rate” means an observed rate of actual change, the only “fair” way to define it it is to define the rate of mutation events to take the “no change” case into account.
Now, I could be wrong about how typical GAs work. I took my definition from Elsberry’s version of weasel. From my understanding, it is important for the mutation event not to know anything.
Petrushka,
A mutation is by definition a change in the genome. No change means no mutation. If it were otherwise, then every moment that a gene remained stable would count as a mutation, and the mutation rate would be astronomical.
It’s the antithesis of latching. Any bit in any genome can change in any generation. Values are never locked in.
I think this may be the source of your confusion: in real life, we identify mutations after the fact by observing that the genome has changed. A mutational process doesn’t “know” the content of the genome before or after the change. It doesn’t even know that the genome has changed. It doesn’t possess the “forbidden knowledge” to which you refer.
By counting the number of genomic changes that we observe after a given period, we can estimate the mutation rate by dividing the number of changes by the time elapsed. (If we’re really anal, we can factor in the probability of mutations happening and then being reversed, but this can be neglected if the mutation rate per locus is sufficiently low).
In a model or a GA, things work backwards. We don’t identify mutations after the fact. Using the mutation rate, we decide beforehand whether a mutation should happen right now. If the answer is yes, then we change the genome. If we didn’t change the genome, it wouldn’t be a mutation — by definition.
In order to change the genome in the model, we have to know its current value. This isn’t “forbidden knowledge”. It’s essential knowledge, without which the model would be inaccurate.
The model is distinct from the thing being modeled. “Forbidden knowledge” in the real world is not the same as forbidden knowledge in the model. It’s okay to use real-world “forbidden knowledge” in order to make the model accurate. What’s not okay is to model the use of real-world “forbidden knowledge”.
Your analysis works on a binary code, but becomes more difficult as the number of possible values goes up. Is the mutation engine supposed to do a lookup to see what values are possible that will result in a change?
That seems not to model reality. It would seem more realistic simply to tweak the mutation rate so the change rate is what you want it to be.
Incidentally, I love being able to have a disagreement and discussion that isn’t stupid. What we have here is a dispute over arbitrary definitions.
In Weasel you have 26 possible values rather than two. That’s in the same ballpark as the number of amino acids. A mutation resulting from a quantum event has no way of knowing if it is making a change.
And the actual difference in effective rate is not that great.
I just think a blind event is conceptually cleaner, regardless of the numeric base.
Me too! It’s a real pleasure to disagree with an intelligent person who’s open to reasoned argumentation and actually tries to understand what I’m saying, and why.
I’ll respond to your other points later. Right now I’m out of time.
My two cents, you can’t go far wrong if you mirror biology. DNA polymerase makes a mistake once every 10^7 to 10^8 bits. That would equate to a RAND threshold examined for every bit but which only causes a flip once every 10^7 or so bits copied. Once your mutational threshold has been breached, you must mutate (flip) – that’s what the mutational error is.
Polymerase ‘knows’ what the bit is when it does its job properly. It’s not so much that the mutation process has knowledge of the current state, but that you are simulating the situation where the accurate-copying process (which must know the current state) gets it wrong.
There are other mutational processes with subtly different characteristics, more akin to a lump of radioactive material. Atoms either decay (flip) or they don’t. Bits stay stable most of the time, and the mutational process does not need to look at them to see if they can stay stable. Stochastically, with a mean of so many events per time t per genome, a stable bit ‘decays’ – the mutational process zooms in on a bit at random, and flips it.
So there are two possibilities with biological merit – check every bit but flip every nth (stochastically) or zoom in on a random bit in a time-dependent manner and flip it. The first can occur during replication, the second at any time.
The first could be coded a bit more efficiently than checking a RAND for every bit. You know you are replicating everything that goes into the copy method, which gives you N x L bits (organisms x genome length), of which you want a stochastic 1 in 10^7 (say) to be incorrect. So just flip them, at random. You should never need to look at a bit you aren’t going to flip, in short.
How important this is depends on the application, of course. No-one’s going to write a problem-solving GA worrying too much about biologically accurate mutation rates and methods.
158 Mung October 5, 2012 at 7:21 pm
There are some interesting reasons why you might want to add that kind of randomness. However, I don’t want to spoil the joy of learning, so for now I will refrain from explaining why you need it. Instead, I would like to encourage you to finish the program and send it on its merry way to the top of the fitness landscape. Go ahead, it’s going to be fun.
159 Mung October 5, 2012 at 8:08 pm
If I understand this correctly, your fitness function is the length of the longest string of ones in a given binary sequence. That does not match Lizzy’s fitness function.
Your program has not run yet. It did not produce digital organisms from a suitably small target space.
Why does that matter?
I don’t mean that in a “my favourite language is better than your favourite language” sort of way, I really mean that it doesn’t matter in any way.
Object oriented code was being written before C++ or SmallTalk or any other language that explicitly defined objects existed simply because experienced programmers started to use structures in that manner.
When I hear that code is in any way “better” because it explicitly uses formal classes, I cringe! 🙂
Any “runnable” code is not going to be easy for everyone to figure out if they are not familiar with the syntax and operators of that language.
If you use pseudocode instead, everyone no matter what their language of choice is can understand it.
That doesn’t run but gives an idea of what you want to do and allows everyone to give some constructive criticism without needing you to explain the nuances of Ruby.
Its even better to simply say in English what you want to do before coding and get feedback before you commit to anything.
It was obviously being written before you were born! 🙂
I’ve used structures in assembler to map both data and pointers to functions.
Sound familiar?
Yup, it’s an object definition!
Every time I need to instantiate an object, I just point at some memory and use the structure as a template for the object.
I don’t understand why your side is so emotional all the time! 🙂
I started working on C++ in 1988 and discovered an amazing thing.
This language that I thought would finally help bad programmers do a better job did exactly the opposite!
It gave them the ability to “virtually” hide mistakes that affected the whole system.
Mung, do you think pseudocode will compile? 🙂
Seriously though, there is a part of this sentence you don’t understand and I want to help.
“If you use pseudocode instead, everyone no matter what their language of choice is can understand it.”
Everyone, (that means “all people”), can understand, (that means they don’t have to keep asking “why”), no matter what their language of choice is, ( that means even if they use a computer language other than yours).
The side benefit of pseudocode is that it never fails to compile because its purpose is to illustrate concepts, not to generate code.
The fact that you expected an explanation for pseudocode amazes me.
Let me guess; you generate a “specification” for your code after the “functionality” has been observed.
I bet you have no bugs, just “features”! 🙂
At least you’re consistent with ID’s concept of “specified function” in that whatever you end up with must be what you wanted.
Bad engineering though as kairosfocus will agree with me.
Mung:
Toronto:
And me. If Mung spent just half as much energy learning as he does flaming people, he wouldn’t have to ask questions like that.
Petrushka,
It could, but it doesn’t have to. Here’s another way to do it: Suppose each locus contains one out of N symbols which are represented by the integers 0 through N-1. To mutate a locus, just generate a random number between 1 and N-1 (inclusive). Add the random number to the existing symbol, modulo N, and you have your new symbol for that locus.
Yes, in the sense that any definition is arbitrary. However, the terms in question have an established usage in biology. A mutation in biology, as the name implies, is a change in the genome. The mutation rate is the number of these changes divided by the elapsed time. I think we minimize confusion by using these established definitions when talking about our models.
You still seem uneasy about the idea of modeling a mutation by “reading” the current value at a locus and replacing it with a different value. Here’s a way to convince yourself that this is legitimate. Imagine we have a live organism alongside a model of that same organism. The model uses my proposed method of modeling mutations.
Both the organism and the model start out in the same state (let’s call it the “before” state). Now imagine that a mutation occurs in the organism, and a corresponding mutation occurs in the model. If the model did something illegitimate by looking at the “before” value at the locus, then the “after” states of the organism and the model should be different. But if you work it out, they’re not. The states remain exactly the same, and the model hasn’t gained any advantage over the real organism by looking at the “before” value of the locus in question.
If you’re still unpersuaded, please reread this earlier comment of mine.
Using your approach, the effective mutation rate is 50% lower than the programmed rate when the loci are bits, as in Lizzie’s program. That seems pretty significant to me.
How quickly distractive red herrings obscure the path of truth!
Joe F tries to illustrate an evolutionary principle to GP using a simplified GA, and many moons later we are discussing the relevance of pseudocode as a helpful intermediary on the requirements -> coding path, and the extent to which more ‘traditional’ structural elements map onto objects!
OK, I’ll join in – you’ll get more quickly and reliably to working code if you pseudocode it first, and desk-run it. And if you are speccing it up for someone else to evaluate or code, formalising the logic and structure removes some of the ambiguities of an English spec, while avoiding the excessive detail and technical arcanities of actual code. Just simple, almost-BASIC stuff – If-else-endif, For-each end-for, While end-while.
I’d agree – you are using a process that cannot make a mistake to simulate one that can. The randomness is in isolating the bit you are going to make your ‘accidentally-on-purpose’ mistake on. Once you have your bit, it must mutate. You can simply add 1 to it for binary flips, but even then, to do that the OS must ‘know’ what the bit is set to, even if you don’t check its value in your code.
For more bit-types, you could model a probability distribution for the various errors and ‘pick’ one based upon this. You can’t do transition-transversion bias, for example, without looking at bits.
Mung, you said: “Darwinian evolution does not need “the right fitness landscape” to work. (What would a “wrong” fitness landscape look like?)”
I replied: “Think about what a fitness landscape for a 64 bit encryption key would look like – you have 18,446,744,073,709,551,615 possible key values and only one of them is right.”
You said: “I’m sorry, but that question doesn’t even make sense to me. 64 bit encryption keys don’t exhibit differential reproduction, do they? In what sense is one 64 bit encryption key more fit than another 64 bit encryption key?”
Exactly – that is my point, that is what a “wrong” fitness landscape looks like. Perhaps I should walk you slowly through it again.
Mung, you said: “Darwinian evolution does not need “the right fitness landscape” to work. (What would a “wrong” fitness landscape look like?)”
A GA can be used to search any problem space for potential solutions. Your code example searches for the longest string of 1’s in a binary string, my example problem also involves a search for binary string. In your system there is a proportional relationship between the bit string and the result of fitness evaluation, in my example there is a binary relationship between the bit string and the fitness evaluation when we use a GA to search for the key.
This demonstrates why some problem spaces, and their resulting fitness landscapes (or if you prefer, error landscapes) are not amenable to an evolutionary search.
Mung: “Why are you calling it a fitness landscape? Fitness is a measure of differential reproduction. So, context.”
It is called a fitness landscape when a GA is used as the search algorithm. We are discussing GA’s and you had asked “What would a “wrong” fitness landscape look like?” I gave an example of the fitness landscape you get when applying a GA to a problem for which it is unsuitable.
Or to put it another way – If you apply a GA to some problems, like finding an encryption key, you don’t get differential reproduction (and it should be obvious why when you look at the fitness landscape that the GA has to navigate)
Just been reading a series of posts from Mung:
keiths:
Mung:
keiths:
Mung:
There’s absolutely nothing to prevent fitness being defined in that way. But it becomes trivial – it is pretty clear, without even running the thing, that a program that
1) rewards the longest string of H’s and
2) makes T’s mutatable but not H’s
is going to throw up a string of all-H’s in pretty short order.
The second is the problem; it’s biologically unrealistic, and was the criticism levelled at Weasel.
So just allow a more realistic mutation function, knocking genomes downhill as well as up (which is not actually always a bad thing, and is why more rugged and dynamic landscapes are more interesting) and apply the ‘product-of-runs-of-heads’ fitness criterion. You wonder if anyone but you understands Lizzie’s algorithm, but you seem curiously unwilling to even replicate it, in order to see the relevance of the various subroutines. Just follow the spec! (That has a familiar ring).
You’re not actually bouncing cosmic rays into the electronic memory, but modeling, in the abstract, biological mutation. In this case, we would want our results to match the definition of biological mutation, which is the change in a base.
Ironically, in Word Mutagenation, we didn’t bother as it wasn’t worth the trouble with 26 letters, as it didn’t affect the results significantly. With binary, it would slow the effective mutation rate by half.
Better yet, change them one at a time. Mutation first. See what impact this has with a fitness function that relies on uninterrupted stretches of sequence where every bit counts. Which is also biologically unrealistic, but less importantly so for GA searching.
163 Mung October 5, 2012 at 9:25 pm
Just trying to understand what your program is supposed to do, Mung. I was under the mistaken impression that it was similar to Lizzy’s. Now I see that it is not.
A small nit to pick. A fitness function does not maximize something. It is merely a quantitative measure. A selection procedure could maximize a fitness function. I might comment on your program later (have errands to run), but I largely agree with Allan Miller above.
You have a large enough search space (500 bits) and a small enough target space (a sequence of all ones). Your organisms are guaranteed to get there as the fitness landscape is smooth all the way up. Your algorithm will get there in a few thousand steps, doing much better than a blind search, which will take forever to find the sequence of all ones.
Does this produce CSI? Certainly the S and the I. Your friends at UD will complain that the C is missing: we know the solution in advance and there is nothing complex about that. More on that later.
Any number of random strings meet the description. While the complexity is high, the specification is low based on that description.
Good! But there’s a point there. By your description, the sequence has no specificity. But by our description, it’s unique, and therefore is high in specified complexity.
Of course, what are the chances you guessed our PIN? This is an example of what Dembski would call a post-specification. Nevertheless, it shows how the calculation of specified complexity changes depending on our understanding.
The program code says it’s random, so you would actually have a conundrum. It could just as easily be a programming error, such as not resetting the randomizer seed.
That’s right. In this case, all sequences have fitness at the floor, except for one.
Yes, depending on the definition of complexity. It is very easy, especially on very simple landscapes. Your landscape, as we understand it, is a simple hill. Evolutionary algorithms quickly climb hills. All roads lead to the top.
But this also shows the problematic nature of specified complexity. If we define the specificity as the highest possible fitness, there is only one sequence that qualifies, and that makes it highly improbable in the Dembskian sense. On the other hand, if we define fitness as 90% of the highest possible fitness, then the specified complexity is much less.
Yes. Like any simulation.
Yes, that is what it represents. We could imagine a library which has the relative fitness of every possible genome, though due to technological limitations, we either substitute a smaller library (a landscape map), or utilize an abstraction.
It certainly can be, as has been experimentally demonstrated. However, as far as specified complexity is concerned, that’s unimportant.
olegt:
That’s because Mung said it was:
I’d go for a more definitive ‘no’. Breaking proteins (rendering them nonfunctional in engineering or chemical terms), can increase reproductive rate. One imagines the fitness landscape of a particular peptide sequence as being the set of all sequences of that length, each sitting on a contour which represents the fitness of that sequence in an assumed static context. ‘Function’ would require a different mapping – colour, for example, with shading to represent yet another dimension – the degree of that activity. Colour and shading would not necessarily align with the rise and fall of the landscape.
Mung,
We’re still waiting for you to modify your program to address your own challenge, and to explain why you think the challenge is relevant.
Ouch! That doesn’t sound right.
And in the next comment, Mung ads more nonsense:
She didn’t of course. These were generated as random sequences.
Again, the initial sequences were random. Any sequence will do. Mung can supply his own initial sequences if he wants to. The program will run in the same way, unless he supplies one of the solutions, of course.
And the probability of that would be one in 10 to the power of 150 or something like that. So what?
Sorry, Mung, but from this it is safe to conclude that you don’t understand what Lizzie did. At least not when you wrote that. Maybe you do now, but I have seen no evidence of that.
I can dig out my own code that I wrote when we were discussing Lizzie’s program. There should be no difference whatsoever even if one starts with all zeroes. The landscape is pretty smooth at the bottom.
Well, synonymous is too strong a word, as you point out, but the contours are often isomorphic within the domain of interest.
Don’t bother. Everyone but Mung understands that there won’t be any significant difference.
He needs to do the experiment himself in order for the lesson to sink in.
Here is a program I’ve written. It follows the pseudocode as far as possible, as far as I understand it.
http://complexspecifiedinformation.appspot.com/
unoptimised atm, and likely to run out of resources, but it’s late.
Enjoy. Suggestions on a atbc thread which I can monitor. That’s here:
http://www.antievolution.org/cgi-bin/ikonboard/ikonboard.cgi?s=5070c55b20f20f9b;act=ST;f=14;t=7414
Funny! 🙂
If anyone wants to know why ID/creationists can’t understand genetic algorithms, here are all the reasons (and emotions) in this recent ID/creationist video in which numerous concepts are conflated and mangled beyond recognition.
Compare this with Thomas Kindell’s sneering presentation; or with Werner Gitt’s “In the Beginning was Information.”
This is why Salvador T. Cordova – one of their own, no less – was so brutally rebuffed over at UD when he had the temerity to suggest that Sewell was wrong.
Toronto:
He’s unusually quiet today. The weather must be crappy in
Mung World
I’m not following this. I don’t know which pseudocode you are referring to or what the program is attempting to do.
181 Mung October 7, 2012 at 1:13 pm
As I have already said, the target of your program is a sequence of all ones. My suggestion would be to ask your friends at UD whether it qualifies as complex. My hunch is that they might not agree.
In contrast, Lizzie’s target space features sequences that are more complex. She did not know in advance what they would be, although with some effort one can figure that out.
In any event, complexity is in the eye of the beholder. By some measures (e.g., Kolmogorov’s), your sequence is quite simple: it can be concisely described as “500 ones in a row.” I don’t think a typical solution from Lizzie’s target space can be described in a similarly concise way. On the other hand, your UD friends may not find these solutions particularly complex. If that happens, we get evidence that complexity (and thus CSI) has a subjective component.
One could make increasing Kolmogorov, or Shannon, information the fitness function. Whether that landscape is searchable by a GA, I don’t know, but it would be of interest.