Kieth Devlin’s “The Math Gene”

People can count indefinitely because there is a conventional (cultural) pattern for forming big numbers. How many of us could count to 100 without a numeral scheme? How many Romans could count beyond 4000?

When Piaget asked “how many” he was making the hermeneutic error. The baby may have a well developed sense of number, yet not know what “how many” means. I like the explanation in the book. Piaget was not testing the baby, the baby was testing Piaget to find the meaning of “how many” and Piaget provided the wrong answer!

Devlin presumes that there were no steps between one level grammars and many level grammars. I wish it were so. I had to design programs once for a machine with one level of subroutine. Fortunately the machine was not built. I think that noun phrases (and other sorts) were enough like nouns that confusing the two became adaptive. There is experimental evidence that we have a depth limit of about 7 today.

Many Chinese ideographs arise from melding two others. Then it evolves so as to obscure its origin.

On page 221 Devlin uses the phrase “single female human ancestor” in conjunction with the genetics of mitochondria. He calls her Eve. I recall such suggestions from other authors. Balderdash—a simple logical error. “single matrilineal ancestor” yes; “single female ancestor” no! Three generations later a person might speak of his mother’s father’s mother, a female ancestor who need not be Eve. What the evidence indicates is that Eve is unique among matrilineal ancestors; Indeed we each have just one such per generation. We have, on the other hand, 2n−1 female ancestors going back n generations, not necessarily distinct. There is no reason to think that they were all Eve!

The only thing that you can say is that other female ancestors of her generation are connected to us thru a line of descendants with at least one male. Big deal! Mitochondrial Eve is important in understanding mitochondria, but what else? Even sex linked genes pass thru both sexes.

I think that I could prove the following with weak statistical assumptions:
If Z was an interbreeding contemporaneous set of humans, log(population) generations ago, then any female in Z that is an ancestor of any of us now, is almost certainly an ancestor of all of us.

The thing that I like best about the book is the common sense, yet novel idea, that smart is better than dumb and thus adaptive. That possibility was briefly mentioned in Miller’s “The Mating Mind” and dismissed for reasons that entirely escaped me.

I suspect something akin to Political Correctness among evolutionary biologists who divide the world into natural and artificial, as if rockets had nothing to do with biology. A smart biological creature built the rocket. That it was able to, has something to do with our big heads.

The “Big Bang” chapter of Pinker’s “The Language Instinct”, has a good discussion of these issues and the ideas of several other people.