Does gpuccio’s argument that 500 bits of Functional Information implies Design work?

On Uncommon Descent, poster gpuccio has been discussing “functional information”. Most of gpuccio’s argument is a conventional “islands of function” argument. Not being very knowledgeable about biochemistry, I’ll happily leave that argument to others.

But I have been intrigued by gpuccio’s use of Functional Information, in particular gpuccio’s assertion that if we observe 500 bits of it, that this is a reliable indicator of Design, as here, about at the 11th sentence of point (a):

… the idea is that if we observe any object that exhibits complex functional information (for example, more than 500 bits of functional information ) for an explicitly defined function (whatever it is) we can safely infer design.

I wonder how this general method works. As far as I can see, it doesn’t work. There would be seem to be three possible ways of arguing for it, and in the end; two don’t work and one is just plain silly. Which of these is the basis for gpuccio’s statement? Let’s investigate …

A quick summary

Let me list the three ways, briefly.

(1) The first is the argument using William Dembski’s (2002) Law of Conservation of Complex Specified Information. I have argued (2007) that this is formulated in such a way as to compare apples to oranges, and thus is not able to reject normal evolutionary processes as explanations for the “complex” functional information.  In any case, I see little sign that gpuccio is using the LCCSI.

(2) The second is the argument that the functional information indicates that only an extremely small fraction of genotypes have the desired function, and the rest are all alike in totally lacking any of this function.  This would prevent natural selection from following any path of increasing fitness to the function, and the rareness of the genotypes that have nonzero function would prevent mutational processes from finding them. This is, as far as I can tell, gpuccio’s islands-of-function argument. If such cases can be found, then explaining them by natural evolutionary processes would indeed be difficult. That is gpuccio’s main argument, and I leave it to others to argue with its application in the cases where gpuccio uses it. I am concerned here, not with the islands-of-function argument itself, but with whether the design inference from 500 bits of functional information is generally valid.

We are asking here whether, in general, observation of more than 500 bits of functional information is “a reliable indicator of design”. And gpuccio’s definition of functional information is not confined to cases of islands of function, but also includes cases where there would be a path to along which function increases. In such cases, seeing 500 bits of functional information, we cannot conclude from this that it is extremely unlikely to have arisen by normal evolutionary processes. So the general rule that gpuccio gives fails, as it is not reliable.

(3) The third possibility is an additional condition that is added to the design inference. It simply declares that unless the set of genotypes is effectively unreachable by normal evolutionary processes, we don’t call the pattern “complex functional information”. It does not simply define “complex functional information” as a case where we can define a level of function that makes probability of the set less than 2^{-500}.  That additional condition allows us to safely conclude that normal evolutionary forces can be dismissed — by definition. But it leaves the reader to do the heavy lifting, as the reader has to determine that the set of genotypes has an extremely low probability of being reached. And once they have done that, they will find that the additional step of concluding that the genotypes have “complex functional information” adds nothing to our knowledge. CFI becomes a useless add-on that sounds deep and mysterious but actually tells you nothing except what you already know. So CFI becomes useless. And there seems to be some indication that gpuccio does use this additional condition.

Let us go over these three possibilities in some detail. First, what is the connection of gpuccio’s “functional information” to Jack Szostak’s quantity of the same name?

Is gpuccio’s Functional Information the same as Szostak’s Functional Information?

gpuccio acknowledges that gpuccio’s definition of Functional Information is closely connected to Jack Szostak’s definition of it. gpuccio notes here:

Please, not[e] the definition of functional information as:

“the fraction of all possible configurations of the system that possess a degree of function >=
Ex.”

which is identical to my definition, in particular my definition of functional information as the
upper tail of the observed function, that was so much criticized by DNA_Jock.

(I have corrected gpuccio’s typo of “not” to “note”, JF)

We shall see later that there may be some ways in which gpuccio’s definition
is modified from Szostak’s. Jack Szostak and his co-authors never attempted any use of his definition to infer Design. Nor did Leslie Orgel, whose Specified Information (in his 1973 book The Origins of Life) preceded Szostak’s. So the part about design inference must come from somewhere else.

gpuccio seems to be making one of three possible arguments;

Possibility #1 That there is some mathematical theorem that proves that ordinary evolutionary processes cannot result in an adaptation that has 500 bits of Functional Information.

Use of such a theorem was attempted by William Dembski, his Law of Conservation of Complex Specified Information, explained in Dembski’s book No Free Lunch: Why Specified Complexity Cannot Be Purchased without Intelligence (2001). But Dembski’s LCCSI theorem did not do what Dembski needed it to do. I have explained why in my own article on Dembski’s arguments (here). Dembski’s LCCSI changed the specification before and after evolutionary processes, and so he was comparing apples to oranges.

In any case, as far as I can see gpuccio has not attempted to derive gpuccio’s argument from Dembski’s, and gpuccio has not directly invoked the LCCSI, or provided a theorem to replace it.  gpuccio said in a response to a comment of mine at TSZ,

Look, I will not enter the specifics of your criticism to Dembski. I agre with Dembski in most things, but not in all, and my arguments are however more focused on empirical science and in particular biology.

While thus disclaiming that the argument is Dembski’s, on the other hand gpuccio does associate the argument with Dembski here by saying that

Of course, Dembski, Abel, Durston and many others are the absolute references for any discussion about functional information. I think and hope that my ideas are absolutely derived from theirs. My only purpose is to detail some aspects of the problem.

and by saying elsewhere that

No generation of more than 500 bits has ever been observed to arise in a non design system (as you know, this is the fundamental idea in ID).

That figure being Dembski’s, this leaves it unclear whether gpuccio is or is not basing the argument on Dembski’s. But gpuccio does not directly invoke the LCCSI, or try to come up with some mathematical theorem that replaces it.

So possibility #1 can be safely ruled out.

Possibility #2. That the target region in the computation of Functional Information consists of all of the sequences that have nonzero function, while all other sequences have zero function. As there is no function elsewhere, natural selection for this function then cannot favor sequences closer and closer to the target region.

Such cases are possible, and usually gpuccio is talking about cases like this. But gpuccio does not require them in order to have Functional Information. gpuccio does not rule out that the region could be defined by a high level of function, with lower levels of function in sequences outside of the region, so that there could be paths allowing evolution to reach the target region of sequences.

An example in which gpuccio recognizes that lower levels of function can exist outside the target region is found here, where gpuccio is discussing natural and artificial selection:

Then you can ask: why have I spent a lot of time discussing how NS (and AS) can in some cases add some functional information to a sequence (see my posts #284, #285 and #287)

There is a very good reason for that, IMO.

I am arguing that:

1) It is possible for NS to add some functional information to a sequence, in a few very specific cases, but:

2) Those cases are extremely rare exceptions, with very specific features, and:

3) If we understand well what are the feature that allow, in those exceptional cases, those limited “successes” of NS, we can easily demonstrate that:

4) Because of those same features that allow the intervention of NS, those scenarios can never, never be steps to complex functional information.

Jack Szostak defined functional information by having us define a cutoff level of function to define a set of sequences that had function greater than that, without any condition that the other sequences had zero function. Neither did Durston. And as we’ve seen gpuccio associates his argument with theirs.

So this second possibility could not be the source of gpuccio’s general assertion about 500 bits of functional information being a reliable indicator of design, however much gpuccio concentrates on such cases.

Possibility #3. That there is an additional condition in gpuccio’s Functional Information, one that does not allow us to declare it to be present if there is a way for evolutionary processes to achieve that high a level of function. In short, if we see 500 bits of Szostak’s functional information, and if it can be put into the genome by natural evolutionary processes such as natural selection then for that reason we declare that it is not really Functional Information. If gpuccio is doing this, then gpuccio’s Functional Information is really a very different animal than Szostak’s functional information.

Is gpuccio doing that? gpuccio does associate his argument with William Dembski’s, at least in some of his statements.  And William Dembski has defined his Complex Specified Information in this way, adding the condition that it is not really CSI unless it is sufficiently improbable that it be achieved by natural evolutionary forces (see my discussion of this here in the section on “Dembski’s revised CSI argument” that refer to Dembski’s statements here). And Dembski’s added condition renders use of his CSI a useless afterthought to the design inference.

gpuccio does seem to be making a similar condition. Dembski’s added condition comes in via the calculation of the “probability” of each genotype. In Szostak’s definition, the probabilities of sequences are simply their frequencies among all possible sequences, with each being counted equally. In Dembski’s CSI calculation, we are instead supposed to compute the probability of the sequence given all evolutionary processes, including natural selection.

gpuccio has a similar condition in the requirements for concluding that complex
functional information is present:  We can see it at step (6) here:

If our conclusion is yes, we must still do one thing. We observe carefully the object and what we know of the system, and we ask if there is any known and credible algorithmic explanation of the sequence in that system. Usually, that is easily done by excluding regularity, which is easily done for functional specification. However, as in the particular case of functional proteins a special algorithm has been proposed, neo darwininism, which is intended to explain non regular functional sequences by a mix of chance and regularity, for this special case we must show that such an explanation is not credible, and that it is not supported by facts. That is a part which I have not yet discussed in detail here. The necessity part of the algorithm (NS) is not analyzed by dFSCI alone, but by other approaches and considerations. dFSCI is essential to evaluate the random part of the algorithm (RV). However, the short conclusion is that neo darwinism is not a known and credible algorithm which can explain the origin of even one protein superfamily. It is neither known nor credible. And I am not aware of any other algorithm ever proposed to explain (without design) the origin of functional, non regular sequences.

In other words, you, the user of the concept, are on your own. You have to rule out that natural selection (and other evolutionary processes) could reach the target sequences. And once you have ruled it out, you have no real need for the declaration that complex functional information is present.

I have gone on long enough. I conclude that the rule that observation of 500 bits of functional information is present allows us to conclude in favor of Design (or at any rate, to rule out normal evolutionary processes as the source of the adaptation) is simply nonexistent. Or if it does exist, it is as a useless add-on to an argument that draws that conclusion for some other reason, leaving the really hard work to the user.

Let’s end by asking gpuccio some questions:
1. Is your “functional information” the same as Szostak’s?
2. Or does it add the requirement that there be no function in sequences that
are outside of the target set?
3. Does it also require us to compute the probability that the sequence arises as a result of normal evolutionary processes?

1,971 thoughts on “Does gpuccio’s argument that 500 bits of Functional Information implies Design work?

  1. colewd,

    The scenario where all sequences are non-functional is merely a special case of situation where all sequences have the same level of function. Joe’s point holds in the more general case, so that is what he has described. The reader is expected to be able to figure out that if all sequences have zero function, then all sequences have the same function.
    The argument is that, in these situations, all sequences have zero FI.

    Mung has been equivocating between the sequence space (all possible sequences) and some extant population of sequences (a subset of all possible sequences).
    For a while.

  2. DNA_Jock,

    Joe’s point holds in the more general case, so that is what he has described.

    So can you describe a case where a sequence of all leucine AA’s are functional?

  3. OMagain,

    Noted you don’t dispute the idea you can get from that sentence to “to be or not to be” with a random mutation. Pathetic.

    We can also get there from a repair mechanism yet repair mechanisms don’t generate FI.

  4. colewd,

    Sure.
    The function is “has peptide bonds” or, if you insist that the function be adaptive, alternatively “serves as a low osmolarity reservoir of amino acids”.
    Length = N.
    All sequences in the sequence space (including [Leucine]N) have activity level N. Therefore the FI of all sequences is zero.

  5. colewd: So can you describe a case where a sequence of all leucine AA’s are functional?

    Why would he need to? I don’t see anyone having stated anything from which it is required that a sequence of only leucines would be functional.

  6. colewd: We can also get there from a repair mechanism yet repair mechanisms don’t generate FI.

    Why not?
    If the sequence meets the E(min) after having errors corrected (and did not before), why has no FI been created?

  7. Rumraket,

    If the sequence meets the E(min) after having errors corrected (and did not before), why has no FI been created?

    The correction required the pre existence of the FI. If it did not then James Shapiro”s NGE would be the new standard.

  8. colewd: The correction required the pre existence of the FI.

    So, a “target” then?

    colewd: If it did not then James Shapiro”s NGE would be the new standard.

    Well, and so what? At least I can go read about that. Whereas all literally you can say regarding the origin of FI is that “it was designed”. How very boring and unimaginative.

    You know how it did not come about, but cannot say anything at all about how it did. And yet you believe the latter. Double standard much?

  9. Joe Felsenstein: Logic having been contradicted, most likely the universe would instantly disappear.

    I see logic contradicted all the time, and yet the universe persists.

  10. Rumraket: He just told you that all sequences have the same level of function.

    Read with context. He was talking about sequences in a population., which of course is what I was also referring to.

    If he meant all possible sequences he should retract what he said at first. 🙂

  11. DNA_Jock: Mung has been equivocating between the sequence space (all possible sequences) and some extant population of sequences (a subset of all possible sequences).
    For a while.

    Aw shucks. Really? How hypocritical of me, after complaining about other people doing that very thing and insisting that to calculate FI they have to consider all possible sequences.

    So if we are considering all possible sequences, under what scenarios does the FI increase?

    Is it when we take one of those possible sequences and mutate it so it is just like one of the other possible sequences? Now we have one more sequence than we had before and one less possible sequence. FI increased!

    When’s the last time you had your sarcasm meter calibrated?

  12. Mung: Read with context. He was talking about sequences in a population., which of course is what I was also referring to.

    If he meant all possible sequences he should retract what he said at first.

    No, I’m afraid that I still think I’m correct in my understanding of what Joe wrote.
    It seems to me it is you who has misunderstood what he wrote.

    It would simply not make sense for Joe to state that it would not be possible to increase FI for a case where all sequences in a population had the same level of function, as for that to be the case then mutation would have to be impossible.

    Yet immediately before that (the actual context) Joe was trying to explain to Bill Cole that mutation could in principle turn a sequence with errors into a sequence without errors.

    If Joe had meant to imply that mutation was impossible, then your response to Joe would make even less sense, given that in your response you refer to the case where mutation changes one of the sequences in the population into one that meets an E(min) set above the level of function of all sequences in the population before that mutation happens.

  13. OMagain,

    Well, and so what? At least I can go read about that. Whereas all literally you can say regarding the origin of FI is that “it was designed”. How very boring and unimaginative.

    We know empirically that a conscious mind can generate FI. DNA repair cannot. Empirically supported inferences can be boring 🙂

  14. colewd: We know empirically that a conscious mind can generate FI. DNA repair cannot.

    Sorry but no we don’t know that DNA repair cannot. DNA repair can be the cause of mutations, and those mutations can result in increased levels of function or even entirely new functions.

  15. Rumraket,

    Sorry but no we don’t know that DNA repair cannot. DNA repair can be the cause of mutations, and those mutations can result in increased levels of function or even entirely new functions.

    I thought its function was to fix mutations 🙂

  16. Rumraket,

    Yet immediately before that (the actual context) Joe was trying to explain to Bill Cole that mutation could in principle turn a sequence with errors into a sequence without errors.

    Not without the pre existence of the FI with “errors”.

  17. Rumraket: Yet immediately before that (the actual context) Joe was trying to explain to Bill Cole that mutation could in principle turn a sequence with errors into a sequence without errors.

    And that’s just nonsense. You don’t know what is there due to “error” and what is not there due to “error.” They are all errors given evolutionary thinking. Just some errors are more useful then other errors. If it’s not there due to error it’s there by design.

  18. Rumraket: …as for that to be the case then mutation would have to be impossible.

    Repeat after me. Mutation is irrelevant. It’s a red herring.

  19. colewd: I thought its function was to fix mutations

    No it’s function is to repair broken DNA. You are confusing proofreading mechanisms, with repair mechanisms. Proofreading corrects mismatches (but even that can be a cause of mutations), repair fixes actual damage as in broken chemical bonds.

  20. Mung: So if all the sequences have the same level of function, and we set our threshold level of function just above that, and one of those sequences changes to now meet or exceed that threshold, that would not be an “increase” in FI?

    ROTFLMFAO! Mung, that was hilarious. oh my…

  21. Rumraket,

    No it’s function is to repair broken DNA. You are confusing proofreading mechanisms, with repair mechanisms. Proofreading corrects mismatches (but even that can be a cause of mutations), repair fixes actual damage as in broken chemical bonds.

    Or really? What does MMR stand for 🙂

  22. Mung: Read with context. He was talking about sequences in a population., which of course is what I was also referring to.

    If he meant all possible sequences he should retract what he said at first.

    I meant all possible sequences. I should have used the word “possible” to clarify that (it didn’t occur to me as FI is calculated with reference to all possible sequences).

  23. Mung: And that’s just nonsense.

    Not at all. It really is the case that mutation can cause a change of a sequence with an error in it, into one without.

    You don’t know what is there due to “error” and what is not there due to “error.” They are all errors given evolutionary thinking.

    Ahh so your objection isn’t that mutation can’t correct them, it’s that… what exactly? You’re just making some semantical distinction.

    Just some errors are more useful then other errors. If it’s not there due to error it’s there by design.

    Yeah yeah bla bla, call it what you want it’s completely irrelevant to the subject matter. The point is of course that any mutation is in principle reversible, so when Bill Cole claims three is no way for an evolutionary process to generate “any amount” of FI he’s just flat out incorrect.

    You can go blather about how changing a nucleotide that got there due to an error, back to the previous nucleotide is also a change due to an error until your face is purple.

  24. Mung: Repeat after me. Mutation is irrelevant. It’s a red herring.

    Irrelevant to what?

  25. Mung: So if we are considering all possible sequences, under what scenarios does the FI increase?

    Is it when we take one of those possible sequences and mutate it so it is just like one of the other possible sequences? Now we have one more sequence than we had before and one less possible sequence. FI increased!

    Eh? … so you were talking about a population that contains all possible sequences? I think a population like that would collapse into a small planet. Real-world biological populations contain only a small subset of the collection of all conceivable biopolymer sequences.

    For a given function (say the capability to convert pyruvate into lactate), the FI associated with a population increases whenever the frequency of sequences displaying a comparatively high degree of function increases. A Designer working her magic can do that, but so can mutation, drift, migration and natural selection. I don’t see what’s so hard about that.

  26. colewd: Not without the pre existence of the FI with “errors”.

    So what about changing Dave to Dale and vice versa (substrate switching)? Although he worked very hard to downplay that example, even gpuccio was forced to admit that some FI was introduced. Will you keep insisting that mutations cannot “generate” FI of any amount?

  27. I’m sorry to dip in without having closely followed the whole discussion but I feel the irresistible urge to point one thing out to colewd.

    One essential plank in gpuccio’s argument is the non-disprovable assumption that unknown proteins that have any function in any possible scenario are rare. I assert the contrary is true (see JNA_Jock on polyleucine. And what about polyphenylalanine?! 😉 ). Most proteins, in some scenario, will have at least some function. Prove me wrong!

    I’m also wondering about non-functional DNA. Presumably, by the same token, Bill and Guiseppe think non-functional DNA really is all junk.

  28. Rumraket: The point is of course that any mutation is in principle reversible…

    No, that isn’t the point, as the remainder of your sentence demonstrates. Whetehr or not mutations can revert a previous change is irrelevant. It’s a red herring

    … so when Bill Cole claims three is no way for an evolutionary process to generate “any amount” of FI he’s just flat out incorrect.

    Mutations don’t generate FI. You and Joe are both wrong and I have explained why and you’re just not listening.

    When calculating FI you have to consider all possible sequences, which means that any change to a base is already accounted for.

    Rumraket: Rofl how the hell are you calculating FI?

    It’s -log2(n/a^L)

    And now you are saying that is not how you calculate FI.

    a^L is all possible sequence of length L. So Joe’s proposed mutation has already been accounted for. It doesn’t introduce a new sequence, it doesn’t introduce any more FI, it’s irrelevant to the calculation.

  29. Corneel: Real-world biological populations contain only a small subset of the collection of all conceivable biopolymer sequences.

    So? Does that mean you disagree with Rimraket’s way of calculating FI?

    It’s -log2(n/a^L)

    What is a^L?

    And Joe agrees with me that it is all possible sequences.

    Joe Felsenstein: I should have used the word “possible” to clarify that (it didn’t occur to me as FI is calculated with reference to all possible sequences).

    So are you, Corneel, proposing that we calculate FI without reference to all possible sequences, replacing a^L with only actual sequences?

  30. Joe Felsenstein: I meant all possible sequences. I should have used the word “possible” to clarify that (it didn’t occur to me as FI is calculated with reference to all possible sequences).

    So then do you agree that both “to be or not to be” and “to bf or not to be” are already accounted for and the fact that you can change one letter in the latter sequence and make it the same as the former sequence is utterly irrelevant for calculating FI?

  31. Alan Fox: Most proteins, in some scenario, will have at least some function. Prove me wrong!

    Are you aware of any protein that doesn’t have some function in some scenario? What a silly challenge Alan.

  32. Mung: Are you aware of any protein that doesn’t have some function in some scenario? What a silly challenge Alan.

    But can you refute my claim with evidence? It is no sillier than to assert that functional proteins are rare in sequence space. There is no way that I am aware of currently to predict what function might exist among proteins not found in biological systems or not yet synthesized.

  33. Corneel,

    Will you keep insisting that mutations cannot “generate” FI of any amount?

    I agree with Mung that once we define a function the FI is already accounted for. Mutation cannot create FI it can only through serendipity stumble on to the FI that exists in sequence space for the specifically defined function.

  34. Alan Fox,

    But can you refute my claim with evidence?

    Given your claim how would you build a structure that powered a cell sufficiently to keep it alive?

    After your first protein in this structure was randomly generated then you need protein two to bind with it and the following proteins to not only bind to the others but to collectively catalyze reactions to mass produce energy molecules.

    You may not have sequence restriction on protein one but after that you are very functionally constrained. The “any sequence will do” canard is a non starter.

  35. Alan Fox: But can you refute my claim with evidence?

    Your claim doesn’t make any sense Alan. It’s safe to assume, don’t you think, that proteins have functions? Do you know of any that don’t?

    Do you mean AA sequences?

  36. Mung: When calculating FI you have to consider all possible sequences, which means that any change to a base is already accounted for.

    Here we see Mung’s confusion re FI in its most distilled form.

    Mung: And Joe agrees with me that it is all possible sequences.

    Joe Felsenstein: I should have used the word “possible” to clarify that (it didn’t occur to me as FI is calculated with reference to all possible sequences).

    You missed the import of the “with reference to”.
    FI is simply a transformation applied to an input level of activity, calculated with reference to the set of all possible sequences of length L.
    FI is -log2(1- the percentrank of the level of activity)
    In order to figure out the percentrank for any level of activity X, you need to know how many members of {the set of all possible sequences} has an activity level greater than or equal to X.
    THAT is where the {the set of all possible sequences} comes in. Any actual FI value depends on the level of activity; every individual member has an activity (it could be zero) and therefore has a FI value (it will be zero if you are the worst, or worst-equal).
    Obviously, different sequences can have different activity levels and therefore different levels of FI. Mutations can change FI.
    Joe assumed that you understood this much, so he moved on to talking about populations of sequences, and what happens to the average FI of a collection of sequences when frequencies change. Evidently this confused you.
    Imagine the set of all possible (5 card draw) poker hands: some are better than others. If you define a metric of hand strength say ‘two pair beats pair, etc.’, then you can calculate the FI of any given hand. Your objection is equivalent to claiming that filling an inside straight does not change the FI of your hand, since “any change in cards is already accounted for”.
    Nope, that is not how FI works.

  37. DNA_Jock,

    Your objection is equivalent to claiming that filling an inside straight does not change the FI of your hand, since “any change in cards is already accounted for”.
    Nope, that is not how FI works.

    I think Mung’s point is that filling an inside straight does not change the FI inside that deck of cards. That possible sequence always exists in the deck as does 4 of a kind or a straight flush.

    The challenge is getting one of these rare hands by chance. With a conscious mind you can deal a straight flush every time. With the ID mechanism chance is no longer a problem as long as the sequence exists in the system.

  38. colewd: I think Mung’s point is that filling an inside straight does not change the FI inside that deck of cards. That possible sequence always exists in the deck as does 4 of a kind or a straight flush.

    The challenge is getting one of these rare hands by chance. With a conscious mind you can deal a straight flush every time. With the ID mechanism chance is no longer a problem as long as the sequence exists in the system.

    There is no ID mechanism unless you know how something was designed and created, two questions that are forbidden to ask.

  39. newton,

    There is no ID mechanism unless you know how something was designed and created, two questions that are forbidden to ask.

    I am pointing to a mechanism that we know from analogy that can create FI.

  40. DNA_Jock: Any actual FI value depends on the level of activity; every individual member has an activity (it could be zero) and therefore has a FI value (it will be zero if you are the worst, or worst-equal).

    We’ve been over this. From the fact that every individual member has an activity it does not follow that every individual member has a FI value. That is simply a non-sequitur.

    And if every single member has an activity, that includes all possible sequences. Every possible sequence has an activity. Every possible sequence includes these imaginary mutations, so they are utterly superfluous. They don’t change the FI. They are already accounted for.

    To put it another way, every sequence that you assign to n can be found in the set a^L. You really ought to think of it as a sampling exercise.

    DNA_Jock: Mutations can change FI.

    A meaningless statement.

  41. colewd: The challenge is getting one of these rare hands by chance.

    The challenge is to get any one of them to show how they are calculating FI in actual practice for any of their examples.

  42. DNA_Jock: Your objection is equivalent to claiming that filling an inside straight does not change the FI of your hand, since “any change in cards is already accounted for”.

    I have no idea what you are talking about. Change has nothing to do with it. Nor does the supposed FI of any individual hand.

    In my opinion, being dealt a hand of poker, being able to toss away some cards you don’t like and drawing replacement cards that may or may not improve your hand is bound to be a flawed analogy for how to calculate FI.

  43. colewd: I think Mung’s point is that filling an inside straight does not change the FI inside that deck of cards. That possible sequence always exists in the deck as does 4 of a kind or a straight flush.

    Which is why we don’t just calculate the FI for a whole set of all possible sequences. That is not interesting.

    We calculate it for a given threshold of “function”. And the point of doing that is that some sequence has a level of function, and if we choose that level, we are calculating the FI for that sequence. The FI for an individual sequence is -\log_2(P), where P is the fraction of all possible sequences whose function is greater than, or equal to, the function of that particular sequence.

    So yes, all possible sequences are included … in the denominator of P. In its numerator is a number n that varies depending on the function level we choose, and I argue that we typically are interested in levels set by the function of a sequence, where our underlying interest is in how far out that sequence is in the tail of the distribution of values of function.

  44. colewd:
    Alan Fox,

    Given your claim how would you build a structure that powered a cell sufficiently to keep it alive?

    Evolution does it.

    After your first protein in this structure was randomly generated then you need protein two to bind with it and the following proteins to not only bind to the others but to collectively catalyze reactions to mass produce energy molecules.

    Seems to me you are talking about “origin of life” here.Evolution starts with the simplest self-sustaining self-replicators.

    You may not have sequence restriction on protein one but after that you are very functionally constrained.The “any sequence will do” canard is a non starter.

    Who said “any squence will do”? I’m refuting the “tiny-islands-in-a-vast-sea-of-non-functionality” claim which is gpuccio’s unsupported assertion (and your’s apparently).

  45. Mung: The challenge is to get any one of them to show how they are calculating FI in actual practice for any of their examples.

    I will surely link to this on UD the next time one of the FIASCO metrics comes up.

  46. Mung: Your claim doesn’t make any sense Alan. It’s safe to assume, don’t you think, that proteins have functions? Do you know of any that don’t?

    Do you mean AA sequences?

    I don’t know of any proteins that aren’t amino-acid sequences. What is your point?

  47. Mung: We’ve been over this. From the fact that every individual member has an activity it does not follow that every individual member has a FI value. That is simply a non-sequitur.

    Yes, we have been over this. Pay attention:
    Within the context of a given sequence space (a^L) and a definition of “function”, then Functional Information is a function of the level of activity that a member displays, and not it’s sequence.
    We map from sequence to level of activity (Ex), and then from level of activity (across the space, [M(Ex) ) to FI value.
    Hazen 2007 defines FI as
    I(Ex) = – log2[M(Ex)/26n].
    Since M(Ex) cannot be zero or negative, thus, logically, if every member has an activity, then every member has an FI.
    You still don’t understand FI.

  48. Joe Felsenstein: Which is why we don’t just calculate the FI for a whole set of all possible sequences.

    We don’t need to calculate FI for any of the sequences. What matters for any individual sequence is its degree of function.

    I gave Rumraket an example where I calculated FI. I didn’t need to calculate the FI for any specific sequence to do that. All I needed to know was whether its level of function was at or above the threshold.

  49. Alan Fox,

    Evolution does it.

    Your faith is to be admired 🙂

    Seems to me you are talking about “origin of life” here.Evolution starts with the simplest self-sustaining self-replicators.

    Are you claiming that energy mass production came before the first replicators?

    Who said “any squence will do”? I’m refuting the “tiny-islands-in-a-vast-sea-of-non-functionality” claim which is gpuccio’s unsupported assertion (and your’s apparently).

    Gpuccio has supported it well with his empirical evidence including a number of highly preserved sequences over deep time. We see lots of sequences at local optimums where many AA substitutions lead to purifying selection.

    You are asserting that the tiny islands don’t ever exist. Any support here or should we duly note your assertion?

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