>

I did not claim it was invented by geneticists. The facts are that until

> 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

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.

> additively.

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