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## [evol-psych] Iq genetic or environmental?

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• ... I did not claim it was invented by geneticists. The facts are that until the advent of electronic digital computers multiplication was a hard problem. Even
Message 1 of 1 , Dec 4, 1999
Peter Kabai wrote:
>
> Hi, let me briefly respond to M. Hubey and Irwin Silverman.
>
> Peter Kabai:
> This basic model is additive, because variances are additive. Quite simple.
>
> M. Hubey's response:
> THis is backwards. The variances are additive because the model is additive.
>
> It might be backwards, depending from where one looks at it. However, the basic
> model, analysis of variance was not invented by geneticists. It was just applied

I did not claim it was invented by geneticists. The facts are that until
the advent of electronic digital computers multiplication was a hard
problem. Even in the 1950s in places like engineering schools at Yale
they were using mechanical multipliers. AT the turn of the century, most
of these calculations would have been done by hand. So the simplest linear
models were chosen.

> to a very simplistic model: a number of independent factors affect the trait

that again is the wrong model. Suppose there are n genes affecting intelligence.
To make it simple, suppose we know what these genes are and by how much each
affects IQ. We use normalized variables (and again keep it a simple Boolean
model). Then "normal Iq",m Nq is given by

Nq= g1*g2*g3*....*gn.

If g1=g2=g3=....=gn=1, then Nq=1. That means that the person has normal Iq.
But if any of the g's are zero. Then Nq=0, meaning that the person will
not have normal IQ.

This will work for any n. If you made it additive you'd have

Nq=1 + 1 + 1 + ...+ 0 + 1 + 1 = 1

Now if you do not use Boolean (logical) values, then you'd get

Nq=1 + 1 + 1 + ...+ 0 + 1 + 1 = n-1

For every problem of this type you'd get a different number. And normality
would be n (again a different number for every n). YOu could never combine
them (different types of behavio-genetic phenotypes) in any meaningful
equation.

Now if we made it more sophisticated and allow the variables to take
on values between 0 and 1 (as in probability theory and fuzzy logic),
then for normal Iq if all the genes are OK, you'd get the same answer as
above which is fine. But if one of the genes was not OK, say the gene
for Down's syndrome, and we know from empirical evidence that this gives
the person 0.83 of normal intelligence then we'd simply write

Nq= g1*g2*g3*....*gn = 1*1*...0.83*1*1..*1= 0.83

exactly as expected. Furthermore of two genes cause problems again
multiplication solves that problem if the effect is accumulative.

Obviously, this would also work if we reasoned probabilistically,
meaning that, say the expected number of people to have the Down's
syndrome gene is p, then the expected IQ (average) of the population
(assuming that the other genes are expected to be normal) is again
as above. Furthermore if we know what the probabilities are for the
rest of the genes, say p1, p2, p3....pn, then again

Iq= p1*p2*p3*....*pn

The reason all this comes out perfectly is because there is very
fundamental effect that has been forgotten for a 100 years. The
multiplication, as is well known corresponds to AND in probability
theory (with independence and all that), and it also corresponds
to AND in logic. And when we talk about debilitating effects of
genes, we are talking about AND. In order for a person to have
normal intelligence, gene 1 has to be ok, AND gene 2 has to be ok,
AND gene 3.....

Notice it is not OR. In fact we all know it has to be AND.

Why then does everyone use OR in their equations? This must be
one of the greatest mysteries of this century.

--
Sincerely,
M. Hubey
Dept of Computer Science, Montclair State University
hubeyh@... http://www.csam.montclair.edu/~hubey
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