entropy

[Les]

On Mon, 2010-01-11 at 18:27 +1030, Tim wrote:
> On Sun, 2010-01-10 at 03:47 -0800, Don Quixote de la Mancha wrote:
> > it's just like a bunch of Physicists to go to all the trouble to
> > build a randomness source out of a Geiger counter.  A noisy resistor
> > or diode would have done the job just as well.
> 
> One of my very old computers had a white noise generator for use by the
> random number function.  One day I decided to test it by repeatedly
> polling it and using alternate polls as X and Y co-ordinates to place a
> mark on a graph.  The images was, predominately, two fat parallel
> diagonal bars.  The effect was rapidly noticeable, and didn't even out
> over a prolonged time.
> 
I can see this happening even with some kinds of "cosmic" number
generators.  Even the friendly neighborhood geiger counts can be
affected by environment and yield less than optimal noise.  However
there are some quite good white noise diodes available from commercial
houses that do considerable analysis of their noise results, and will
yield quite good histogram distributions and even multi-axis
distributions.  However the experiment you did was a bit biased in its
setup if you modified the output to generate the two axis, for example
limiting the binary data to say 8 bit numbers, they you essentially get
a distribution running from 0-511 which would have a gaussian curve if
the random numbers were uniform.

	Random numbers are a rather esoteric study in and of themselves, and
understanding the limits of a particular algorithm or measurement is
always helpful.  Noise algorithms used in a noisy environment tend to
produce gaussian results due to aliasing of local noise sources into the
data, 60 hz or 50 hz is a common issue.  If a wireless lan is present,
it will produce some odd effects due to the headers and other protocol
bits adding non random data into the mix.

A common tactic of using the trailing bits of a PI calculation is also
an interesting approach.

Regards,
Les H