[extropy-chat] damien's psi book

[spike]

> --- spike <spike66 at comcast.net> wrote:
> >
> > I generated all the primes less than a billion
> > to test the theory.  It works.
> >
> THis sounds really interesting, Spike. Have you used this theory to
> predict Mersenne primes?
> 
> =====
> Mike Lorrey


No, wouldn't work Mike.  The GIMPS project is searching up in
the 8 million decimal digit range.  The probability that
the leading digit of a prime that size is very nearly equal 
across the spectrum.  Take 9E8000000 over the natural 
log of 9E8000000, subtract 8E8000000 over ln(8E8000000), 
then divide by the difference of (2E8E6 over ln(2E8E6) minus
1E8E6 over ln(1E8E6)), you will see that the excess probability
of the leading digit being 9 versus a 1 is about one
part in 50 million.  For the next digit over, the excess
probability is about one part in about 500 million.

That example I gave before of about an 11 percent greater
chance of a leading digit 9 than leading digit 1 is for
numbers of magnitude around 10 million, such as one might
see in a lottery.

Consider this: suppose someone had a clear plastic globe
filled with numbered ping pong balls, like they use in 
the lottery, except that instead of the customary 49 numbered
balls, the globe contains a billion balls.  (This plastic globe
is the size of a football stadium).  Air is blown up thru
the balls, causing them to dance about, and a ball is selected
at random by a vacuum cleaner hose inserted thru a hole in
the globe.  A ball is selected, the number is tested for 
primeness.  If composite, the ball is tossed back and a
new ball is selected, but if prime the ball is retained.
About 95% of the balls are tossed back.

The game is to guess the leading digit.    

If one is aware of the n/ln(n) trick, one would guess
1 every time (We disallow leading zeros for sake of argument),
leading to an anomalous 8.81 percent higher than expected
win rate compared someone who liked 9 and always picked that
number.

The next post on this topic is about what all this has to 
do with psi, uploading, evolution, extropy and everything 
like that. I had a blinding flash, a mind-blowing epiphany 
while doing these calcs.

spike