[ExI] mersenne primes again

[spike]

> ...On Behalf Of Mike Dougherty
> Subject: Re: [ExI] mersenne primes again
> 
...
> >
> > More later.  Assignment please: think about everything you know 
> > regarding the definition of statistical significance, and 
> what it means to you.
> >
> 
> Statistical significance is significant only to those who 
> consider statistical signficance.  :)

Mike, here's where I was going with that question.  The notion of
statistical significance is a simplification that draws attention to plenty
of ordinary stuff and distracts attention from plenty of important signals.
The 95%ile criterion is arbitrary, meaningless and often harmful because
statistics teachers and textbooks fail to explain that critically important
point.  Students and later professionals forget what it really means (very
little) and make fundamental mistakes.  

The baby boom/power outage is a fine example: it is impossible to find the
extra infants nine months after a power outage statistically.  The very
slight (theoretical) increase would never be noticed at the obstetric ward.
But turn the question around, and ask the question Drake style: what number
of anomalous births would you expect per million powerless proles?  I get 1
to 4 ish, which you wouldn't expect to find by data analysis. The 2 sigma
statistical significance techniques would put the extra infants at zero by
assuming the null hypothesis.  

Using Drake's notions, can you logically assign the number of anomalous
births from a blackout to a value of zero?  I can't even find assumptions
that would get it all the way to zero.

Another good example is one that interests Damien.  When doing experiments
like having someone guess the next card to measure paranatural phenomena,
you could intentionally insert a few marked cards.  If you do that, but not
too many, our traditional techniques for determining statistical
significance would not detect the funny business.  We are programmed from
our misspent youth to disregard any observation that doesn't make
statistical significance.  Then if it does make that arbitrary criterion for
statistical significance, we are programmed to figure out who was screwing
with the experiment.  If any phenomenon has no theoretical explanation, it
is either missing in the experiemental data or it was a bad experiment.  We
couldn't find real psi if it slapped us in the face.  

Damien, you may use that, with my blessing.  Note I am not saying I think
psi is real, only that we couldn't find it if it is.
 
> ...
> 
> Have you looked a Penrose tiling?...

Early and often.

...
>  Maybe the 'order' in which Mersenne primes manifest is 
> another example of a non-periodic pattern; one with too few 
> examples for us to yet uncover the underlying rules.  ...but 
> that's why we keep searching for more examples, right?

Ja.  It is of particular interest to me, since the field of prognostication
using statistical techniques is so maddeningly fraught with ways to fool
oneself.  I did it myself, with a technique which is described in Damien's
The Spike.  I used superposition of probability distribution functions to
make a prediction of when the next record prime number would be discovered
back in 1999.  I extrapolated the growth rate of GIMPS, then looked at the
cumulative probability over a time span, and just reported the date upon
which we would have accumulated a 50% chance.  

Turns out it was remarkably close to right, but for the wrong reasons: I had
compensating errors.  GIMPS grew much faster than I anticipated, but the gap
was anomalously large.  That flawed technique worked pretty well, three
times in a row.  I fooled myself, but I had fun.  I made a buttload of
"money" on Ideas Futures with that, but I feel the need to return the
"money" somehow, since I wasn't really "right."  There is no way to return
the "money" in IFX.

{8^]

spike