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Re: counts in an interval

At 12:23 PM 7/10/00 -0400, Ludwik Kowalski wrote:
John would probably disagree by saying
that pure mathematicians do not need instruments.

What I say is:
a) Pure mathematicians do not strictly "need" instruments like Geiger
counters.
b) They are free to use whatever instruments they choose.
c) If a mathematician has a choice of instruments, and chooses one that
is more expensive, less reliable, and less convenient than another
readily-available instrument, people might start asking questions.

I agree with John that a Geiger counter may have many
more uses in a "math lab" than in a physics lab.

Actually that's the opposite of what I've been saying.

Let me try again: A couple of weeks ago I gave a seminar about my work on
True Random Number Generators. A large fraction of the audience was
wondering why I didn't just use a Geiger counter as a source of random
numbers. I had to explain that even if you consider it an axiom of physics
that radioactive decay is truly random, it is _not_ axiomatic that the
counts from a real Geiger counter are truly random; there are live-time
effects and all sorts of other cruft. There is also no reason to believe
that radioactive decay is more truly random than, say, Johnson noise in a
resistor. Finally, True Random Numbers are needed only for certain special
purposes. In contrast, for purposes such as investigations of the
mathematics of randomness, or for Monte Carlo integrations, a good software
Pseudo Random Number Generator is vastly more suitable than a Geiger counter.

Suppose I react to a claim that atomic nuclei do not disintegrate
randomly. The claim is that under certain conditions the
probability of decay per unit time has an oscillating component.
For example, L=Lo+A*sin(w*t), where A=Lo/10.

That is a fine example of what a Geiger counter _should_ be used for. If
that is the purpose of the experimental setup, then we can ask detailed
questions about whether the setup has the required sensitivity, et cetera.

Remember, all along I have been questioning whether a particular setup is
suitable for achieving its stated purpose. If the statement of purpose
changes, so do the questions.