Re: counts in an interval

[Ludwik Kowalski <KowalskiL@MAIL.MONTCLAIR.EDU>]

John Denker wrote:
> IMHO, if you start by assuming/stipulating that the Geiger
> counter is a highly reliable source of clean data, then you
> cannot possibly be in a position to verify the randomicity
> of various theories...

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. Use a more
complicated function, if you prefer.

I would not be "in a position to verify" this with a counter
which is not reliable. The "clean data" term was used to
express this obvious fact. A counter of nuclear particles,
like any other real instrument, can be used in a mathematical
investigation. John would probably disagree by saying
that pure mathematicians do not need instruments. But then
he would make an exception for an instrument called computer.
The author of a book I was reading several months ago
claimed that, seen from the kitchen entry , mathematics is
an experimental science. He was contrasting this with ways
in which mathematical findings are "officially justified".
In other words many specific observations before formal
proofs.

I agree with John that a Geiger counter may have many
more uses in a "math lab" than in a physics lab. Is it better
than a simulation? Hmm. Probably not, unless the purpose
is to show that mathematics makes good predictions about
reality. It is not an instrument for testing consequences of
various assumptions, as a computer can be.
Ludwik Kowalski