-- Bayesian Correlations

In my quest for an understanding of modular arithmetic, number and
group theory, and abstract algebra I have used my fascination with
cryptograms, FLT, and video encoders as ways to maintain progress, but
always there seems to be a special project.

Quasi and I have abandoned the Computability thread on FLT but this
remains unconsidered from that thread.

A black box accepts an input and provides an output. Its process is
unknown. Feed it (in this case) (x,y,z) and it says out ( 0, 1, 1, 0,
1, 0) or similar binary codes (five of 'em) that indicate in this case
the truth of logical propostions about whether (x,y,z) might be a
candidate for an FLT counterexample and in the general case any
testable thing; it could be a patient's HIV status....

The Bayeysian part of it is in figuring out, of course "What is in the
damn box".

What I am thinking is that with an integer input and two binary
outputs, we might see a pattern develop relating the two outputs.
We'll call them a and b. Like this

Input Output
5 1, 0
6 0, 1
7 1,0 ....

In this example, we see that a excludes b and vice versa, or at least
"tends to" in the cases we've tried.

So I am wondering about phase space, correlations, and Bayesian
stastics.

Try another example:

Box = Do you like to dance with a man or a woman?

Subject Answer
1 Y N
2 N Y
3 Y N
4 N Y
5 N N
6 Y Y

5 doesn't like to dance; 6 might be bisexual or just likes to dance a
lot! Can you imaging polling a huge population and getting the
Bayesian relations from the data? Was that what Bayes had in mind?

There are an infinite supply of triples (x,y,z) but only a finite
number of statements related to them; at least I can only come up with
finite number. So I am thinking of writing a sort of Bayesian Probe
into Z "spaceP and { (x,y,z) | x,y,z are in Z}, a larger "space" to
see if the space is heterogeneous, that is, to see if there are
correlations betwen the statements.

I do have my stats I text.

Doug Goncz
Replikon Research
Seven Corners, VA 22044-0394
.