[Bell Historians] Weights and the Olympic Bell

[Frank King]

Dear Carl,

You say...

> If this essay is TMI (Too Much Information),
> I shan't apologize...

Quite right.  This essay should be compulsory
reading for all first-year University science
students who should be asked to make critical
comments.  The good ones will applaud it and
complain only that the essay could have been
longer!

> I would welcome correction of any misstatements.

You have been delightfully cautious in your use
of language and it is hard to find fault but that
won't stop me trying!

Subject to some assumptions which you clearly state
you say:

  Then the exact weight, if one could measure it
  with greater precision, must be in the range

     22.91 plus or minus .005 metric tonnes

Given your assumptions this assertion is correct.

One tiny quibble is that I prefer 0.005 to .005
but only on aesthetic grounds!

A minor quibble is that this is not the usual way
in which "plus or minus" is interpreted when
quoting quantifiable observables.

More commonly a measurement quoted as:

                    x +/- y

is not to be interpreted as a *range* within
which the true value is guaranteed to lie but
rather a range within which the true value is
expected to lie with some implicit probability.

Commonly y is the "standard error" and, subject
to a host of assumptions, the expectation is
that the true value will lie in the range
x-y to x+y with a probability of about 0.68 so
there is a fair chance of being outside this
range.  To be safer, the probability of being
in the range x-2y to x+2y is about 0.95 but
there is still a 1 in 20 chance of being
outside even this extended range.

You do not, of course, claim that the standard
error for the Olympic Bell is 0.005 metric tonnes
but (making woolly assumptions) it is probably
not far from this value.

I don't know what kind of kit is used these days
to weigh objects of around 23 metric tonnes and
would be interested to hear.

I should be even more interested to hear what
kit could be used to satisfy your assertion:

  It is theoretically possible to measure the
  weight of the Olympic Bell to the nearest
  microgram

I don't dispute this but I'd sure like to know
how you would do it!  I would expect the lifting
gear to rub off a few micrograms and sticky fingers
to leave a few micrograms of crud on the bell.  It
is not at all clear that these effects would balance
one another!

Frank H. King
The University Bellringer
Cambridge, U.K.