🚀 go-pugleaf

In article <55805@mentor.cc.purdue.edu> hrubin@pop.stat.purdue.edu (Herman Rubin) writes:
>In article <1130@kepler1.rentec.com> andrew@rentec.com (Andrew Mullhaupt) writes:
>>1.	Says who they're _really_ random? Sure we like to think so, but
	[what about the prcision of the measurement device?]

>Thes problems you have stated are not the major ones.  If one uses 
>radioactive counts, the process is as close to independent as it
>is unbiased, and long-term effects are essentially impossible.
>HOWEVER, there is no way of testing them beyond the .001 level
>of randomness, and there are good reasons for questioning .00001
>on the physical grounds of the asymmetry of counters when changing.

I am not complaining that the radioactive decay has long term
correlations. I am pointing to the fact that there is a problem with
controlling oscillations in the measurement device. You will be well
within your rights to claim that a time base can be established to
much better than 1 part in 10^10, but it is expensive to do so at
bandwidths that can compete with algorithmic generators.

Now I think 10^7 bps is a reasonable rate to compete with workstations,
and so we need to control the frequency standard of the counter to drift
less that 1 Hz per hour. This is do-able, but you have some thermal
questions to worry about if you put the device in the computer. This
gets you to the level of correlations you get with 32-bit algorithms,
but I doubt this will be viewed as a vast improvement. But when you
want to go to the level of performance of a 48-bit generator, you have
to control your time base to 1 Hz per 60K hours. If this is not a _major_
problem for an economically viable device I'm surprised. But nonetheless
I can go to a 128 bit generator and there is no hope left for the analog
generator. 1 Hz per 10^28 hours is not in the cards, (10^28 hours = longer
than the life of the universe so far, and by a long chalk.)

>There are ways to overcome this, and they are not complicated.  If
>one combines with XOR several streams, the problems should disappear.

Not at all. If they have the same resonance, XOR'ing two streams together
will not (generically) do anything for the correlations.

>One problem of pseudo-random numbers is the problem of either having
>a not good enough, or a too good, frequency response.  By chance, there
>should be a few rather large spectral points.

You mean white noise samples aren't white? OK. But if you have a resonance
in the measurement device, all your samples will have the _same_ resonance,
and I don't call that white noise.

>>3.	You can't prove theorems about their outputs very easily. This
>>	is similar to (1), but it can also be a defect of some algorithms
>>	too.
>
>I do not see that this is a problem, if the points I have mentioned above
>are taken care of.

I'm unconvinced that you can take care of them. Call me new-fashioned, but
I'm happier about precise descriptions of digital circuits than I am
with analog devices.

>>The way I look at it, the problem with 'natural' RNG is that the market
>>is small for it, and so the use of general purpose hardware is always
>>economically favored - i.e. algorithmic RNG.
>
>Algorithmic RNG is likely to have some hidden flaws.  There is the 
>matter of cost, but it seems that some physical random numbers are
>needed to give reasonable assurance that they will not occur.  

Actually, I like the idea of blowing off white noise altogether, and
using known deterministic equidistributed systems for the theory. There
is a certain motion in this direction with special algebraic points to
do integration instead of Monte Carlo.

One 'cute' example would be to use succesive digits of pi as uniformly
distributed digits. How do statisticians view this heresy? 

Later,
Andrew Mullhaupt