[extropy-chat] damien's psi book

[spike]

This is a math related post, so those who do not
like this sorta thing, please delete immediately.

Damien posted recently about psi in lottery results.

He supplied lotto data which has had me thinking the past
few weeks, struggling to recall lessons from a college
class from so verrry many years ago (we were programming in
Fortran for evolutions sake).

The lectures were about using the powerful Monte Carlo
techniques for modeling physical systems.  The exercise 
was to write down a number of random decimal digits.  
Then we were to generate a number of random numbers
using the keypad along the top of the keyboard, then
do the same using the ten key pad.  Then we applied
a number of tests of randomness to the number sets.
You already know what happened: the human-generated
number sets nearly all failed one or more criteria for 
randomness.  The test that nearly all the human-generated 
lists failed was the one that requires taking the 
difference between adjacent numbers: humans think 
that random means spread out.  {8-]

The next assignment was to write a program to
generate random decimal digits.  I came up with
an algorithm which relied on prime numbers, for
everyone knows there are no consistent patterns
in the primes, other than their density goes as
n/ln(n).  My program was slow and complicated, 
but at least it didn't work right.  {8^D

If we look at the ones column in the primes, we
see only ones, threes, sevens and nines, clearly
not random.  But what about the tens column: are
the tens column of the primes evenly distributed 
enough over all ten digits to pass the traditional
tests for randomness?  How do you prove it?

All these years later, and just this week I
discovered the answer to that interesting question,
which I will share here if I hear any echoes to
the sonar pings.  Speculation welcome.

spike