Hi folks
> Humans are notoriously good at finding patterns in
> cluttered data. Problem is, they're also good at
> finding patterns in random data.
The supposed clustering is in fact typical of 'random' data. Ask a human being to pick
lottery numbers, the human perception of randomness is 'equally spaced' (so much so,
the *average* human probably wouldn't pick two consecutive numbers but the probability
of that happening is surprisingly high).
There's an older version of the Noll Island Conjecture that goes something like this.
You can wait for a bus for hours and hours, then two come along at once. This was not
called the Bus Island Conjecture - because it's common experience.
Humans are notoriously bad at applying their statistical intuition to the extreme
circumstances, particularly when probabilities are low over a large number of trials.
'Expectation' and all those sorts of measures relating to the central limit theorem
just no longer hold up. The distribution of low-probability events such as very large
Mersenne primes, buses arriving on a random schedule, clicks on a Geiger counter
behave very differently from coin tosses.
> #4: The Noll Island Theory is not valid. As more
> Mersenne primes are collected, statistical effects
> due to our small sample size will be lessened.
Actually I think the "theory" is valid, at least in that we'd expect these sort of
clusters - significance testing as you say is pretty much a lost cause with only 38
data. The problem though is it makes no difference where the next one is, you can
always shape the conjecture to fit the existing data.
Could anyone pick *one* new Mersenne prime that would either confirm or deny the
island theory? I don't think you can. Just move the goalposts if you need to.
Chris Nash
Lexington KY
UNITED STATES
_________________________________________________________________
Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm
Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers
