Re: Radioactive decay

["John S. Denker" <jsd@MONMOUTH.COM>]

Ludwik Kowalski wrote:
> Unless the number of pencils (or coins etc., as you
> suggested) is very large, averaging is unavoidable when
> the purpose is to demonstrate that N=No*exp(-lambda*t).
> Note that neither averaging nor rounding was necessary
> in a program when No was 10,000.

To which I replied:
> > I disagree!  The indivisibility of pencils accuratly
> > models the indivisibility of atoms -- so why fight it?
> > Averaging detracts from the accuracy and from the
> > realism.

The key phrase above is "... when the purpose is to
demonstrate ..."

We need to negotiate a little about what the purpose is.

It seems to me that the purpose of the experiment ought
to be to see what happens.  One should not jigger the
procedure for the purpose of making the outcome agree with
a preconceived notion.

        (Note this makes contact with the other thread
        today:  the importance of scientific evidence
        and objectivity.)

> Because individual outcomes fluctuate widely  ...

My point is that these fluctuations are real.  Don't
jigger the procedure to conceal them.

The exponential decay formula is not "the" law of radioactive
decay.  The real physics includes fluctuations.  In some
cases when the fluctuations are small, a simple exponential
behavior emerges.

> Following your,
> approach, John, I would do the averaging over decay
> sequences rather than averaging at the level of each step.

Then we agree!  I think this is a fine idea:  take the
data _without_ averaging.  Record the decay sequences,
fluctuations and all.  Observe that the decay is approximately
described by an exponential, but with fluctuations above
and below.

Repeat the process.  Take the average, or (better) the sum.
Observe how the sum converges toward a simple exponential.
Remark that taking the sum is equivalent to using a larger
number of pencils.

By doing it in stages we get several benefits:
 -- we don't need to buy as many pencils
 -- we get to see and understand the fluctuations
 -- we get some appreciation for "preliminary results"
    and we get to see how preliminary results lead to
    other results.