Using Math to Obscure Bad Arguments

Using Math to Obscure Bad Arguments December 5, 2014

Some might think, given the headline, that this post would be about Richard Carrier. But mythicists aren’t the first or the only fringe stance to try to use math to obscure the weakness of their arguments. P.Z. Myers drew attention to a response to Michael Behe that Ken Miller posted online. You can read it here. PZ writes:

I recall sitting in a creationist lecture in the 1980s, and the guy leading us through his ‘mathematical’ disproof of evolution. You see, there are 20 possible amino acids in each position in a protein. So the probability that the first amino acid, for example, is lysine is 0.05. Then the probability of the second amino acid being arginine is also 0.05, which means that the probability of a specific two amino acid peptide being lys-arg is (0.05 * 0.05), or (0.05)2. Which means that the probability of a 1000-amino acid protein existing is (0.05)1000, or effectively zero, therefore impossible.

It’s exactly the same game Behe is playing. It was crude, stupid, and ridiculous when J. Random Creationist was doing it, and it’s even worse when a guy with a Ph.D. in biochemistry, who ought to know better, panders to the mob of creationists who don’t even grasp middle school mathematics by using fallacious operations in probability.

Couching dubious arguments in math may impress some, but sooner or later, someone with the patience to engage the math as well as the substance of the arguments will come along to address it.

The problem is that people whose math was weak enough to be fooled by the initial claim, will also be open to being fooled into believing that the response is unpersuasive.

Here’s what Miller wrote by way of introduction to the piece on his website:

Suppose you published a book making a set of very specific claims. Then, after highly critical reviews of your book are published in major scientific journals, an international research team publishes a detailed study in the Proceedings of the National Academy (PNAS) on the very system that was the focus of your book. Great news?  Well, maybe, except for one little problem. That research paper shows, in great detail, why the claims at the heart of your book were wrong. Do you walk away quietly, hoping no one notices?

chloroquine resistance

Figure 1: Masthead of the paper on the evolution of chloroquine resistance. (Summers et al, 2014. PNAS 111: E1759-E1767)

(Click for link to the article)

Not if you’re Michael Behe. Instead, you declare victory, tell everyone who will listen that the research actually vindicates you, and then get your friends at the Discovery Institute to demand apologies from those who had criticized your book. In the strange world of “intelligent design” (ID), that’s how things seem to work. When new scientific findings support evolution, the ID crowd tries to spin things around by pretending they actually contradict it. They’ve done this before, and they’ll probably do it again.

And here’s another sample from later in the article:

Interestingly, Behe’s kind of math would apply only in one very special situation, and that would be if both drugs were applied in similar doses at exactly the same time, so that the emergence of resistance to one would be useless without the simultaneous appearance of resistance to the other. That, in fact, is the reason that multiple drug therapy can be effective against HIV and other diseases. By manipulating the doses of several anti-viral drugs at once, it’s possible to prevent the emergence of resistant strains of the virus. But this situation only prevails under carefully designed therapeutic conditions. You might say, ironically, that it takes “intelligent design” to produce conditions favoring the long odds he demands, conditions that don’t exist in nature.

Click through to read the entire thing. See too Larry Moran’s response to another Intelligent Design proponent.

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  • Just Sayin

    And we can be confident in the atheist use of math, because they would never seek to mislead.

  • arcseconds

    The basic error that Behe makes seems somewhat easy to describe, and seems worth so describing.

    He ends up assuming that the two mutations that make for cholorquine resistance have to occur together in the same individual, which is overwhelmingly unlikely.

    But there’s no reason to suppose that the mutations do have to occur in the same individual. One could occur first, and get established in the population (perhaps simply by genetic drift, i.e. by chance) and the other occur later.

    More detail:

    He claims that the chance of a particular mutation occurrng in Plasmodium is around 10^-20, a figure which the mainstream biologists do not dispute (at least they’re prepared to accept it for the sake of the argument), but at this rate we’d expect this mutation to occur from time to time (there being many billions of Plasmodium individuals and the lifecycle being short).

    However, the chloroquine resistance resulted from two mutations, neither being sufficient on its own to confer resistance. Behe says the chances of this is (10^-20)^2, or 10^-40, which is a vastly smaller number that we would never expect to see.

    But that is assuming that both mutations have to occur in the same individual.

  • arcseconds

    It also sounds kind of like Behe is assuming that what does occur is what must occur. That it was inevitable that Plasmodium developed chloroquine resistance by this method, or it was inevitable that humans ended up with the genome as it is now.

    Modern biology entails that any particular genetic sequence or protein structure is highly unlikely, and Behe takes that to conflict with the fact that a particular genetic sequence has the sequence it has.

    If humans as we know them today were inevitable, and the chances of them arising exactly as they know them today according to modern biology are infinitesimally remote, then there is indeed a problem and we need something else to force evolution to produce the inevitable human beings.

    But this is opening doors to smuggle in a designer twice: once to have a plan for there to be human beings, and secondly to miracle evolution along to produce the planned human beings.

    EDIT: And I wonder whether Behe might be tempted to do this because he’s already inclined to see humans and organisms more generally as being deliberate inventions, and therefore not contingent.

    (leaving aside the possibility that humans were inevitable yet biology can’t explain this for boring reasons: if the universe is deterministic then they were inevitable giving the starting conditions, and the reason modern biology can’t show us that is merely understandable ignorance of every single event that happens in the universe. )