Re: Prove that Randomness Exists?

On Nov 9, 9:48 pm, kenkelley.p...@xxxxxxxxx wrote:
On Nov 9, 4:10 pm, tgdenn...@xxxxxxxxxxxxx wrote:



On Nov 9, 3:36 pm, kenkelley.p...@xxxxxxxxx wrote:

On Nov 9, 2:28 pm, tgdenn...@xxxxxxxxxxxxx wrote:

On Nov 9, 2:12 pm, kenkelley.p...@xxxxxxxxx wrote:

Here is what I would consider proof of the existence of randomness.
To wit, I provide a design for a truly random number generator. If
such a generator can be created, then randomness must exist.

--- How to build a truly random (not pesudo-random) number
generator. ---

This generator will produce one random byte per second. It will work
for approximately 1 billion years,

Please elaborate on the failure mode.

-tg

Obviously, eventually enough of the U238 will have decayed that the
results will start to be skewed. The numbers would still be random,
but the distribution would become less even. This will take several
half-lives, so the above estimate is highly conservative.

<

This is where it gets to be fun. What do you mean by the results being
skewed? Or "less even distribution"?

In an "even distribution", each of the 256 possible values would have
the same probability of occurring. In an uneven distribution, the
probabilities would not all be the same. If enough of the U238
decayed that the average number of decay were 100 per second, then the
distribution would be quite uneven. So long as the average remains
above about 1 million per second, the distribution would be almost
perfectly even.

Are you defining random by the outcome or by the process?

"Random" means the "unpredictable", so that would apply to the
outcome. The numbers produced by this generator would not be
predictable. Therefore, they are random. That's what "random" means.

Is random still random for small samples?

Per above, yes. Random means unpredictable. If the average number of
decays per second is 100, then that would be a pretty small sample.
But there is no way to predict whether the number measured in the next
second is 99, 100, 101, etc. Thus the results are random.

Many people seem to conflate "random" with "even distribution". The
reason for this, I think, is that when you want a random number, you
almost always want one distributed evenly over some range. But the
two concepts are independent.


It seemed that you were making that exact 'conflation', hence my
initial question.

I don't think the questions that I'm raising can really be answered,
but it seems worthwhile to clarify the language as much as possible.

-tg

As I just answered them, I would tend to disagree. ;-)


Well, you answered some questions but not really the one that I
raised. :-)

If you are testing the outcome to define 'randomness', then for small
samples it becomes difficult to demonstrate with any confidence. So
when you say, for any smaller number of decays, that the outcome is
still random, you are actually relying on theory or experience
external to the experiment itself.

-tg



.

Relevant Pages

  • Re: issues with statistical test suite from http://csrc.nist.gov/rng/
    ... A distribution, or data set, is symmetric if it looks the ... >> A generator is bad when it fails a test that has a good mathematical ... The most common criteria are lack of correlation and even ... Since some of the best minds in mathematics can't come up with ...
    (sci.crypt)
  • Re: issues with statistical test suite from http://csrc.nist.gov/rng/
    ... >> ses is the standard error of skewness. ... >distribution differs from the expected one. ... >Unfortunately I can't know if a generator under test is good or bad if it ... Kurtosis could be ...
    (sci.crypt)
  • Re: Is Itos Lemma correct?
    ... What algorithm did you use for your random number generator? ... Here's the original location and distribution of Mr. Steve Park: ... It's characterized as "a very accurate approximation of the normal idf". ... could lead to a loop in the RNG. ...
    (sci.math)
  • Re: question on entity generation/termination
    ... use the event based random number generator block. ... be the distribution parameters, and using those you can generate random ... The EML block is a time-based block ... The parameter of the event-based random number ...
    (comp.soft-sys.matlab)
  • Re: question on entity generation/termination
    ... generator " & the "Embeded Matlab Function Block for random time ... Port t is connected to the EMFBRT. ... be the distribution parameters, and using those you can generate random ... The parameter of the event-based random number ...
    (comp.soft-sys.matlab)