**From:** Ben Goertzel (*ben@goertzel.org*)

**Date:** Tue Nov 08 2005 - 11:25:17 MST

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Eliezer,

Your story of trying to disprove Cantor's diagonalization argument, in your

youth, really resonated with me!

I was *not* as much of a prodigy as you were -- I was just a very bright

kid. I entered university at 15 and graduated at 18; I suppose I could have

entered uni at 12 had the opportunity arisen; but I couldn't have done

university material at 8 or 10, no way, my brain just wasn't there yet.

Anyway, I remember that at some point during my teens (late teens; I was

probably 19, in fact) I spent nearly a week convinced that I had proved

mathematics inconsistent! Or, more specifically, that I had proved the

Axiom of Infinity led to logical inconsistency within Zermelo-Frankel set

theory. That was an exhilarating week...

But unfortunately (and predictably), all I had discovered was yet another

(screwy and not so elegant, really) form of Godel's Incompleteness Theorem,

somewhat related to algorithmic information theory.

Perhaps this merely proves that I'm even crazier than you: You were just

trying to disprove aleph-one, but I was nuts enough to try and disprove

aleph-zero as well!

[I still am not comfortable with the notion of the infinite in mathematics,

and especially not with aleph-one and all those nasty random entities that

exist as a group yet can never be demonstrated on an individual basis. But

unfortunately the paradoxical nature of these things doesn't seem to take

the form of a real logical inconsistency, just an incompatibility between

the commonsense notion of "is" and the mathematical notion of "is".]

I knew a real child prodigy once, fairly well -- he was a classmate of my

son's, and at age 5 he was doing trigonometry and analytic geometry (while

my son, who was gifted in math but not a prodigy, was merely having fun with

simple binary arithmetic examples and very basic algebra... my son was by

far the *second* best kid in the class in math, but this prodigy kid blew

him away). Indeed, he did not seem generally more *intellectually mature*

than my son or other very bright kids, even though he had more capability to

absorb and manipulate technical ideas. In more respects his judgment was

still that of a young child.

As member of a math dept. hiring committee, in the early 90's I I once

interviewed an ex-prodigy for a professor position. He was clearly VERY

bright, and was unusual in having well-developed research careers in two

very different areas, set theory and mathematical physics. But we ended up

hiring someone else, a number theorist who had not been a prodigy but seemed

to have more creative and important research ideas. This encounter

reinforced what the literature shows: prodigies nearly always grow into very

gifted adults, but not necessarily more gifted than some others who were not

prodigies. Yet another aspect in which brain function and development are

very mysterious!

-- Ben G

**Next message:**Eliezer S. Yudkowsky: "Re: the ways of child prodigies"**Previous message:**Michael Vassar: "Re: the ways of child prodigies"**In reply to:**Michael Vassar: "Re: the ways of child prodigies"**Next in thread:**Eliezer S. Yudkowsky: "Re: the ways of child prodigies"**Messages sorted by:**[ date ] [ thread ] [ subject ] [ author ] [ attachment ]

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