These remarks are from a discussion which took place at
the ISI meeting in Istanbul, August 1997, on the teaching
of probability and statistics in the natural sciences.
The complete discussion is available from me by email
(and will appear in the Bulletin of the ISI)

Comments by R.D. Gill
=====================

I would like to make some comments on physics versus statistics (the
latter includes for present purposes probability).

As has been said by others we statisticians have a lot of difficulties
trying to `sell our wares' to physicists. Physicists are renowned for
their arrogance. They believe there is nothing much to know about
statistics and that they can easily invent it for themselves if
necessary. And one has to admit they are dammed clever and for instance
do mathematical calculations with more ease and speed and originality
than most mathematicians. This is certainly some cause for us to
adopt some humility when dealing with them. The sheer amount of things
they know is amazing and the finely tuned intuition about physical 
reality with which they home in on the right answer despite getting
logico-mathematical arguments usually wrong is amazing too.

However I think they are wrong (about knowing already what they
need to know about statistics) and that we do know something they
do not know, and do need to know. And I believe that although we 
should adopt a certain amount of
humbleness in our dealings with these uebermenschen, we should at the same 
time counter their arrogance with some of our own.

The trouble is that elementary probability is pretty boring and
elementary statistics even more so. Clearly we should not be teaching
these topics to such clever people by starting at the beginning, 
as we can do (?) with mathematicians.
Rather we should assume a certain amount of sophistication and
maturity and step in at the deep end with exciting topics which they
will appreciate. For instance: Gibbs sampling, simulated annealing,
Metropolis... :  using ideas from physics to solve hard numerical
and combinatorial optimisation problems certainly appeals to them.  What about
the beautiful results and challenging problems in random polymers,
interacting particle systems, percolation,...?  Did you know that
a recent book about the so-called Inflationary Universe by a famous
cosmologist whose name I forget uses results from percolation theory
to explain what must have happened during the first ten to the minus
god knows how many seconds of the universe, in order that we could all
be here today?

Another nice topic is The Bootstrap; another is Statistical Inverse Problems
(the Grenander estimator, the Wicksell problem ...) where NPMLE
automatically does the regularisation which one otherwise has to
invent oneself.  Physicists will be excited by using Splus and using
the internet resources which are out there for Splus.
Random Number Generation is an exciting topic; especially when you
tell them about the modern insights from cryptography and
lend them Marsaglia's CD-ROM to test the generator which is built into
their package. Let us teach maximum likelihood, not least squares.

I must admit that the time when I gave a lecture on the bootstrap to
a physics audience the physicists were so enthusiastic that they went
away and did it. Two days later they came to me with their results and
a problem since it did not seem to be working --- indeed their problem
was about the largest eigenvalue of a random matrix and this is
precisely a problem where the classical bootstrap does not work!

Some physicists are beginning to realise that randomness does play a
major role in some of their ventures. For instance I have been consulting
with seismologists who realise that the measurement errors in the
data which goes into a big inverse problem can be a source of bias when
doing a proper non-linear inversion. We found it could pay off
to linearise and do a linear inversion.

There are certainly a lot of difficulties to be overcome. In Utrecht
University the maths curriculum for physicists is monopolised by analysists and algebraists
so that `we' don't get a chance to teach probability or statistics at an
early stage. 
The physicists think they have learnt statistics from their
first year course on measurement and experimental design and statistics,
in which they learnt  1) all errors are normally distributed;
2) how to do least squares calculations by hand for fitting $y=a+bx$;
3) this was all there is in statistics [and there is no connection
between 1) and 2)].  A course on probability is not part of the
curriculum. Instead they pick up some funny (and interesting) ideas on probability
from courses on statistical mechanics, together with some odd (and interesting)
ideas from an optional course on the foundations of physics
including some philosophical stuff on probability/quantum/foundations of
statistics.  
In view of this brainwashing, which as far as I know has been going on the whole century, it is not so surprising that physicists don't hold
statisticians in such high regard.

Another problem to be overcome is that physicists are such incredibly
deterministic thinkers (along with computer scientists, lawyers,  and
many engineers). They cannot see that there is something there
in our field.  They are taught just to go ahead and ask for some
more millions of dollars and do a better and bigger experiment. Or do some
even more truly fundamental thinking to get to the (deterministic?) bottom of things.

Yet another problem is that they are so incredibly bad at logical reasoning.
They do not know the difference between a theorem and an example and a 
counterexample. They do not distinguish between the equality sign
of mathematical equality, and an approximate equality derived under
some assumptions and only holding asymptotically. 
I attended a fascinating advanced physics course on thermal and statistical physics
and was amazed how one time the lecturer wasted half an hour 
(of his precious 2 times 3/4) by not being
able to use standard (and basic) ideas from measure theory or 
differential geometry in order to explain concisely what he means by a uniform
distribution on a curved manifold...the students are bright and realise 
something is being hidden from them. The lecturer is certainly not daft
either, so it is really strange...

Yet another problem is that they are fairly incapable of distinguishing
between (physical) reality and (mathematical) models. They have been
taught that the RIGHT model is THE TRUTH hence no need to distinguish.
Their models are so bloody good they can also be excused from this
mistake. Anyway this makes it hard to talk to them. Statisticians on
the other hand are the most professional persons I can think of in
making this distinction and benefiting from it.

Finally I would like to bring up my current hobby horse - quantum 
statistics. As you all know quantum mechanics is an essentially
stochastic theory of the world. As such you might expect it to be
`our business' too. Of course it is a difficult field, but worse still,
generations of physicists AND of mathematicians have been
spreading the dogma that it is a different kind of probability from
the kind we use in the statistics of sample surveys or of dice throwing.
This is really bad and we have to do something about this, especially
since a) there is a lot of money and a lot of good science and exciting
technology and the most fundamental problem of
cosmology being studied there at the moment, read your newspapers, and b)
it seems to me that the randomness which goes on in measuring the
polarisation of a photon is the most true randomness you will ever find
in the world - the toss of a dice on the other hand is a completely understood and
completely deterministic business (there are even pretty mathematical
theorems saying that there can be no respectable deterministic theory
behind quantum physics). We should be collectively ashamed not to
know anything about quantum mechanics. I would like to see all introductory
texts in probability theory going a little into the physical (quantum)
theory behind the geiger counter before using some data of alpha
particle counts as an illustration of the Poisson process; I would like
a discussion of the Bell inequalities together with a modicum of
quantum mechanical background to show how elegant probabilistic reasoning
shows that the quantum world is truly random (unless you would like
to go for an even more weird non-local deterministic theory).
It was interesting to see in a recent book the famous physicists
Penrose and Hawkings debating whether the famous measurement problem -
which is all about randomness in quantum mechanics - is the holy grail
of physics (Penrose), or a red herring (Hawking). My money is on Penrose.

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