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Re: Radioactive decay, evidence versus authorities



Ludwik Kowalski wrote:

I agree that sums are better than averages and recording
outcomes as they are (instead of averaging at each step)
is more to the point. Here are my new data.
...
The end result is the same as before but there is no need to truncate
fractions. That is a big improvement.

Yup. The original version was nifty but this is niftier.

... Rightly or wrongly many
authors refer to the exponential formula as the "low of decay."

That sounds like an appeal to authority!

This point is not worth arguing now, IMHO.

Sorry, I can't resist. This is a too-perfect illustration of
the points Michael E. and others were making this morning.

Here we have an authoritative theory that says one thing,
and we have first-hand data that says something else.

Somehow there seems to be a widespread temptation to
conclude that there is something wrong with the data.
DO NOT GIVE INTO THIS TEMPTATION!!!!!!!!!!!!!!!!!!!!

I can't find strong enough words to say this:
-- It is not the experimentalist's job to find a way to
make the experiment agree with the theory.
-- Sometimes if theory and experiment disagree, it's because
there is something wrong with the experiment. But sometimes
not. And this should not be the primary way of deciding
whether there is something wrong.

In this case we have PERFECTLY CLEAR evidence that the
theory is wrong.

If you want to be polite, you can say that the exponential-
decay law is "outside its range of validity". But that means
the same thing; using a theory outside its range of validity
is wrong.

Whenever a theory is presented, it is the presenter's duty
to specify the range of validity. For instance, equating
kinetic energy to 1/2 m v^2 is valid only in the non-relativistic
limit. The decay "law"
N=No*exp(-lambda*t)
is only valid in the large-N limit.

A single run of Ludwik's experiment does not attain the
large-N limit. And that does !!NOT!! mean that the experiment
is wrong. The experiment is fine. The experiment is beautiful.
It just cannot be compared to the large-N theory. A more
refined theory is needed. If the authorities don't provide
a small-N theory, that's the authorities' problem.

DO NOT APOLOGIZE for the small-N data. Data is data.

This has the makings of a really, really important lesson.
Do the experiment. Compare it to "the" theory. FACE THE
FACTS. The fact is that the data doesn't fit the theory.
Do not duck the issue. Do not fudge the issue.

I'm not suggesting this is easy. There is a tremendous
psychological barrier that must be overcome. People have
such a strong expectation that properly-taken data will
always fit "the" theory that have a hard time facing
contrary facts, no matter how clear the facts.

The skill of squarely facing unexpected facts is sometimes
a life-and-death issue. I see this a lot in student pilots.
Airplanes are so reliable that if something goes wrong during
takeoff, they cannot believe it. They continue the takeoff,
passing up a whole series of opportunities to save the situation
by discontinuing the takeoff. Nobody believes me when I
lecture about this. They all think they are smart enough
to do the right thing. But the first time I spring this
situation on them, they get it wrong. Every single one of
them. I've got lots of data on this. (On subsequent
occasions, they do much better.)

I suppose we should count our blessings: It's nice to live
in a world where most things we experience agree with expectations.
But if you want to be a scientist, you have to learn to deal
with -- indeed relish -- unexpected facts.