Re: [Phys-L] the physics of randomness

[John Denker <jsd@av8n.com>]

On 02/18/2014 09:07 AM, Paul Nord wrote:
> That’s the trouble with randomness, you can never be sure…
> http://www.nsftools.com/misc/DilbertRandom.gif

Yes.

See also:   http://xkcd.com/221/

On Feb 17, 2014, at 5:44 PM, John Denker <jsd@av8n.com> wrote:
> > More to the point, statistical testing like this is a one-sided
> > proposition.  As Dykstra was fond of saying:  Testing can demonstrate
> > the presence of bugs.  It can never prove the absence of bugs.

On a more positive note, I should add that when validating a
random number generator, it is pointless to audit the numbers 
that come out.  Instead you validate the /process/ that
produces the numbers.  You can build an industrial-strength 
RNG by starting with thermal noise, e.g. Johnson noise.
  http://www.av8n.com/turbid/

Since the dawn of the computer age, people have tried and
failed to write a program for generating randomness.
This is why it is nice to know some physics.  Programming
cannot solve the RNG problem, but physics can.

Again:  You validate the /process/ that produces the numbers.
In other words, you validate the distribution.  This is
related to what I said before:  There is no such thing as
a random number
 -- If it's a number, it's not random.
 -- If it's random, it's not a number.
 -- You can have a random distribution over numbers, but
  then the randomness is in the distribution, not in any
  particular number that might be drawn from the distribution.

A distribution is different from a number as surely as an
infinite-dimensional vector is different from a scalar.

This is also related to the important physics topic of 
uncertainty and "error bars".
  -- A raw data point cannot possibly have error bars.
   It cannot have any width.
  -- You can have a distribution over data points, but
   then the width is in the distribution, not in any
   particular point that may have been drawn from the
   distribution.

It is extra work *and* conceptually wrong to put error bars
on a raw data point.

It is conceptually wrong to use "sig figs" (or anything else)
to suggest that a raw data point has width.
   http://www.av8n.com/physics/uncertainty.htm