Chronology Current Month Current Thread Current Date
[Year List] [Month List (current year)] [Date Index] [Thread Index] [Thread Prev] [Thread Next] [Date Prev] [Date Next]

Re: randomness, experiments versus theory

Does anybody wants to verify that what JohnD is saying (see below)
is correct? I will be happy to supply 3000 counts (or 60,000) from
the Geiger counter. I suppose John will agree to supply an equal
number of simulated counts (with identical mean and identical
standard deviation). My prediction is that one set of numbers will
not be better than another (in terms of randomness) to a reasonable
level of confidence. We must agree on that level before starting.

I am not denying a possibility that deviations from non-randomness
can be detected in the Geiger counts (when the contribution of the
dead time is neglible, that is at a low counting rate). I simply do not
believe it will happen. Many would probably be very interested in
the outcome of this nontrivial project. And we can learn something
worth knowing.

John Denker wrote:

At 04:16 PM 3/29/00 -0500, Ludwik Kowalski wrote:

As far as I can see, the Geiger counter is a very good instrument to produce
really random events, even when nothing is known about the source causing
the clicking.

I'll bet the output of the pseudo-random number generator (PRNG) on my
computer is more random (i.e. passes more tests for randomness) than the
output of your Geiger counter. OTOH people may point out that a PRNG spews
out a lot of bits, but not any real entropy. And they're right. So let's
not talk about PRNGs.

I have on occasion put together crypto systems to protect a great deal of
valuable information. The integrity of these systems is contingent on the
quality of the random numbers. For such machines I have implemented true
random number generators (TRNGs). Sometimes the TRNG exploits thermal
noise in a pair of resistors. Sometimes it exploits the hydrodynamics of
the spinning disk.

In my mind a Monte Carlo simulation belongs to theory. A validation of
something by the Monte Carlo method is not equivalent, at least in principle,
to a validation by experiments. Drawing tickets from an urn is an experiment,
producing them with with pseudorandom numbers is not. Yes, I know that
the outcomes are indistinguishable but a line between theory and experiments
has to be drawn somewhere.

Let's see. In experiment "A" we have a Geiger-Muller tube which responds
to random radioactive events. That's physics. It's connected to a scaler
which is (gasp!) a piece of electronics. From there the data goes to a
computer and gets analyzed.

In experiment "B" we have a resistor in which the electrons fluctuate due
to thermal noise. That's physics. It's connected to a Soundblaster card
which is (gasp!) a piece of electronics. From there the data goes to a
computer and gets analyzed.

In experiment "C" we write numbers on tickets, toss them in an urn, and
shake. That's physics. Then we draw them out, type something into the
computer, and analyze it.

In experiment "D" we use a pseudo-random number generator.

I agree that a line can be drawn that separates case D from the
others. But from among A, B, and C, I see no distinction in principle, and
the main distinctions in practice are that "C" has hard-to-control
nonidealities, and "A" requires expensive and complicated equipment.

In all cases, if you want really random numbers, you would be well advised
to run your experimental data through a cryptologic hash function to
"whiten" it.