I thought that for a followup to yesterday’s repost of my takedown of Berlinksi, that today I’d show you a digested version of the debate that ensued when Berlinksi showed up to defend himself. You can see the original post and the subsequent discussion here.
It’s interesting, because it demonstrates the kinds of debating tactics that people like Berlinski use to avoid actually confronting the genuine issue of their dishonesty. The key thing to me about this is that Berlinski is a reasonably competent mathematician – but watch how he sidesteps to avoid discussing any of the actual mathematical issues.
Berlinksi first emailed his response to me rather than posting it in a comment. So I posted it, along with my response. As I said above, this is a digest of the discussion; if you want to see the original debate in all its gory detail, you can follow the link above.
The way the whole thing started was when Berlinski emailed me after my original post criticizing his sloppy math. He claimed that it was “impossible for him to post comments to my site”; although he never had a problem after I posted this. His email contained several points, written in Berlinski’s usual arrogant and incredibly verbose manner:
1. He didn’t make up the numbers; he’s quoting established literature: “As I have indicated on any number of occasions, the improbabilities that I cited are simply those that are cited in the literature”
2. His probability calculations were fine: “The combinatorial calculations I
made were both elementary and correct.”
3. Independence is a valid assumption in his calculations: “Given the chemical
structure of RNA, in which nucleotides are bound to a sugar phosphate backbone
but not to one another, independence with respect to template formation is not
only reasonable as an assumption, but inevitable.”
4. He never actually said there could be only one replicator: “There may be many sequences in the pre-biotic environment capable of carrying out various chemical activities.”
Of course, he was considerably more verbose than that.
This initial response is somewhat better at addressing arguments than the later ones. What makes that a really sad statement is that even this initial response doesn’t *really* address anything:
* He didn’t address the specific criticisms of his probability calculations, other than merely asserting that they were correct.
* He doesn’t address questions about the required sizes of replicating molecules, other than asserting that his minimum length is correct, and attributing the number to someone else. (While neglecting to mention that there are *numerous* predictions of minimum length, and the one he cited is the longest.)
* He doesn’t explain why, even though he doesn’t deny that there may have been many potential replicators, his probability calculation is based on the assumption that there is *exactly one*. As I said in my original response to him: In your space of 1060 alleged possibilities, there may be 1 replicator; there may be 1040. By not addressing that, you make your probability calculation utterly worthless.
* He doesn’t address his nonsensical requirement for a “template” for a replicator. The idea of the “template” is basically that for a replicator to copy itself, it needs to have a unique molecule called a “template” that it can copy itself onto. It can’t replicate onto anything *but* a template, and it can’t create the template itself. The “template” is a totally independent chemical, but there is only one possible template that a replicator can copy itself onto. He doesn’t address that point *at all* in his response.
* He doesn’t address the validity of his assumption that all nucleotide chains of the same length are equally likely.
Berlinksi responded, in absolutely classic style. On of the really noteworthy things about Berlinksi’s writing style is its incredible pomposity. This was no disappointment on that count; however, it was quite sad with respect to content. I have to quote the first several lines verbatim, to give you a sense of what I’m talking about when I say he’s pompous:
>6 April, 2006
>I have corrected a few trivial spelling errors in your original posting, and I
>have taken the liberty of numbering comments:
>I discuss these points seriatim:
You see, we *really* needed to know that he was in Paris. Crucially important to his arguments to make sure that we realize that! And I’m a bad speller, which is a very important issue in the discussed. And look, he can use latin words for absolutely no good reason!
He spends fifty lines of prose on the issue of whether or no 100 bases is the correct minimum possible length for a replicator. Those 50 lines come down to “I have one source that says that length, so nyah!” No acknowledgment that there are other sources; no reason for *why* this particular source must be correct. Just lots and lots of wordy prose.
He response to the question about the number of replicators by sidestepping. No math, no science; just evading the question:
>2a) On the contrary. Following Arrhenius, I entertain the possibility that
>sequence specificity may not, after all, be a necessary condition for
>demonstrable ligase activity — or any other biological function, for that
>matter. I observed — correctly, of course — that all out evidence is against
>it. All evidence – meaning laboratory evidence; all evidence – meaning our
>common experience with sequence specificity in linguistics or in any other
>field in which an alphabet of words gives rise to a very large sample space in
>which meaningful sequences are strongly non-generic – the space of all
>proteins, for example.
The template stuff? More sidestepping. He rambles a bit, cites several different sources, and asserts that he’s correct. The basic idea of his response is: the RNA-world hypothesis assumes Watson-Crick base pairing replication, which needs a template. And the reason that it needs to be Watson-Crick is because anything else is too slow and too error prone. But why does speed matter, if there’s no competition? And *of course* the very first replicator would be error prone! Error correction is not something that we would suppose would happen spontaneously and immediately as the first molecule started self-replicating. Error correction is something that would be *selected for* by evolution *after* replication and competition had been established.
Then he sidesteps some more, by playing linguistic games. I referred to the chemicals from which an initial self-replicator developed as “the precursors of a replicator”; he criticizes that phrasing. That’s his entire response.
And finally, we get to independence. It’s worth quoting him again, to show his tactics:
>There remains the issue of independence. Independence is, of course, the de
>facto hypothesis in probability calculations; and in the case of pre-biotic
>chemistry, strongly supported by the chemical facts. You are not apt to
>dismiss, I suppose, the hypothesis that if two coins are flipped the odds in
>favor if seeing two heads is one in four on the grounds that, who knows?, the
>coins might be biased. Who knows? They might be. But the burden of
>demonstrating this falls on you.
One other quote, to give you more of the flavor of a debate with Berlinski:
>5a) There are two issues here: The first is the provenance of my argument; the
>second, my endorsement of its validity. You have carelessly assumed that
>arguments I drew from the literature were my own invention. This is untrue. I
>expect you to correct this misunderstanding as a matter of scholarly probity.
>As for the second point, it goes without saying that I endorsed the arguments
>that I cited. Why on earth would I have cited them otherwise?
I really love that quote. Such delightful fake indignance; how *dare* I accuse him of fabricating arguments! Even though he *did* fabricate them. The fake anger allows him to avoid actually *discussing* his arguments.
After that, it descends into seeming endless repetition. It’s just more of the “nyah nyah I’m right” stuff, without actually addressing the criticism. There’s always a way to sidestep the real issue by either using excess wordiness to distract people, or fake indignance that anyone would dare to question anything so obvious!
My response to that is short enough that I’ll just quote it, rather than redigesting it:
>As I’ve said before, I think that there are a few kinds of fundamental errors
>that you make repeatedly; and I don’t think your comments really address them
>in a meaningful way. I’m going to keep this as short as I can; I don’t like
>wasting time rehashing the same points over and over again.
>With regard to the basic numbers that you use in your probability calculations:
>no probability calculation is any better than the quality of the numbers that
>get put into it. As you admit, no one knows the correct length of a minimum
>replicator. And you admit that no one has any idea how many replicators of
>minimum or close to minimum length there are – you make a non-mathematical
>argument that there can’t be many. But there’s no particular reason to believe
>that the actual number is anywhere close to one. A small number of the possible
>patterns of minimum length? No problem. *One*? No way, sorry. You need to make
>a better argument to support eliminating 10^60 – 1 values. (Pulling out my old
>favorite, recursive function theory: the set of valid turing machine programs
>is a space very similar to the set of valid RNA sequences; there are numerous
>equally valid and correct universal turing machine programs at or close to the
>minimum length. The majority of randomly generated programs – the *vast*
>majority of randomly generated programs – are invalid. But the number of valid
>ones is still quite large.)
>Your template argument is, to be blunt, silly. No, independence is not the de
>facto hypothesis, at least not in the sense that you’re claiming. You do not
>get to go into a probability calculation, say “I don’t know the details of how
>this works, and therefore I can assume these events are independent.” You need
>to eliminate dependence. In the case of some kind of “pool” of pre-biotic
>polymers and fragments (which is what I meant by precursors), the chemical
>reactions occuring are not occuring in isolation. There are numerous kinds of
>interactions going on in a chemically active environment. You don’t get to just
>assume that those chemical interactions have no effect. It’s entirely
>reasonable to believe that there is a relationship between the chains that form
>in such an environment; if there’s a chance of dependence, you cannot just
>assume independence. But again – you just cook the numbers and use the
>assumptions that suit the argument you want to make.
The rest of the debate was more repetition. Some selected bits:
>No matter how many times I offer a clear and well-supported answers to certain
>criticisms of my essays, those very same criticisms tend to reappear in this
>discussion, strong and vigorous as an octopus.
>1 No one knows the minimum ribozyme length for demonstrable replicator
>activity. The figure of the 100 base pairs required for what Arrhenius calls
>”demonstrable ligase activity,” is known. No conceivable purpose is gained from
>blurring this distinction.
>Does it follow, given a sample space containing 1060 polynucleotides of 100
>NT’s in length, that the odds in favor of finding any specific polynucleotide
>is one in 1060?
>Of course it does. It follows as simple mathematical fact, just as it follows
>as simple mathematical fact that the odds in favor of pulling any particular
>card from a deck of cards is one in fifty two.
>Is it possible that within a random ensemble of pre-biotic polynucleotides
>there may be more than one replicator?
>Of course it is possible. Whoever suggested the contrary?
This is a great example of Berlinksi’s argument style. Very arrogant argument by assertion, trying to throw as much text as possible at things in order to confuse them.
The issues we were allegedly “discussing” here was whether or not the space of nucleotide chains of a given length could be assumed to be perfectly uniform; and whether or not it made sense to assert that there was only *one* replicator in that space of 1060 possible chains.
As you can see, his response to the issue of distribution is basically shouting: “**Of course** it’s uniform, any moron can see that!”.
Except that it *isn’t* uniform. In fact, quite a number of chains of length 100 *are impossible*. It’s a matter of geometry: the different chains take different shapes depending on their constituents. Many of the possible chains are geometrically impossible in three dimensions. How many? No one is sure: protein folding is still a big problem: given our current level of knowledge, figuring out the shape of a protein that we *know* exists is still very difficult for us.
And his response to his claim that there is exactly one replicator in that space? To sidestep it by claiming that he never said that. Of course, he calculated his probability using that as an assumption, but he never explicitly *said* it.
His next response opened with a really wonderful example of his style: pure pedantry that avoids actually *discussing* the criticisms of his points.
>>The point is that we’re talking about some kind of pool of active chemicals
>>reacting with one another and forming chains ….
>What you are talking about is difficult to say. What molecular biologists are
>talking about is a) a random pool of beta D-nucleotides; and b) a random
>ensemble of polynucleotides. The polynucleotides form a random ensemble because
>chain polymerization is not sequence-specific.
>>The set of very long chains that form is probably not uniform ….
>Sets are neither uniform nor non-uniform. It is probability distributions that
>are uniform. Given a) and b) above, one has a classical sampling with
>replacement model in the theory of probability, and thus a uniform and discrete
Ok. Anyone out there who could read this argument, and *not* know what I was talking about when I said “some kind of pool of active chemicals reacting with one another and forming chains”?
How about anyone who thinks that my use of the word “set” in the quote above is the least bit unclear? Anyone who thinks that “the set of very long chains that form is probably not uniform” is the *least* bit ambiguous?
No, I thought not. The point, as usual, is to avoid actually *addressing* difficult arguments. So when confronted with something hard to answer, you look for a good distraction, like picking on grammar or word choice, so that you can pretend that the reason you can’t answer an argument is because the argument didn’t make sense. So he focuses on the fact that I didn’t use the word “set” in its strict mathematical sense, and then re-asserts his argument.
Another example. At one point in the argument, disputing his assertion of independent probabilities for his “template” and his “replicator”, I said the following:
>I’m *not* saying that in general, you can’t make assumptions of independence.
>What I’m saying is what *any* decent mathematician would say: to paraphrase my
>first semester probability book: “independence between two events is a valid
>assumption *if and only if* there is no known interaction between the events.”
>That is the *definition* of independence…
Berlinksi’s response? Again, pure distractive pedantry:
>If you are disposed to offer advice about mathematics, use the language, and
>employ the discipline, common to mathematics itself. What you have offered is
>an informal remark, and not a definition. The correct definition is as follows:
>Two events A and B are independent if P(AB) = P(A)P(B). As a methodological
>stricture, the remark you have offered is, moreover, absurd inasmuch as some
>interaction between events can never be ruled out a priori, at least in the
Does this address my criticism? No.
The Bayesian rules for combining probabilities say “If A and B are independent, then the probability of AB is the probability of A times the probability of B”. You *can* invert that definition, and use it to show that two events are independent, by showing that the probability of their occurring together is
the product of their individual probabilities. What he’s doing up there is a pedantic repetition of a textbook definition in the midst of some arrogant posturing. But since he’s claiming to be talking mathematically, let’s look at what he says *mathematically*. I’m asserting that you need to show that events are independent if you want to treat them as independent in a probability calculation. He responds by saying I’m not being mathematical; and spits out the textbook definition. So let’s put the two together, to see what Berlinksi is arguing mathematically:
>We can assume that the probability of two events, A and B are independent and
>can be computed using P(AB) = P(A)×P(B) if and only if the probability
>P(AB) = P(A)×P(B).
Not a very useful definition, eh?
And his response to my criticism of that?
>I am quite sure that I have outstayed my welcome. I’m more than happy to let
>you have the last words. Thank you for allowing me to post my own comments.
And that was the end of the debate.
Sad, isn’t it?