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Re: Would you like to share some data?

At 10:49 AM 6/6/01 -0400, David Bowman wrote:

How would you expect to determine the surface distance between the
various observation sites (as well as determine your latitude and
your longitude)? If you expect to use a map and a ruler, that will
probably be cheating since the map will have been made with a
cartographic scale and a projection that is cognizant of and accomodating
of the radius of the earth.

These remarks raise an important point, but it can be dealt with.

Key idea: The baseline distance _could_ be determined without using
advanced cartographic techniques.

Just because it is possible for the students to cheat on this experiment in
a hundred ways, that doesn't mean they will.

As a general rule:
No matter what you are doing, you can always do it wrong.
... but that doesn't prevent us from doing it right if we choose.

In fact, if you use a highway map (even a
small regional one) you can determine the size of the earth directly from
it without even making any solar shadow measurements at all. All you
have to do is pick two widely separated points on the map and note their
indicated latitudes and longitudes.

Again: This is an important issue, but there is an easy work-around. Set
up a double-blind protocol where one team looks at a map, determines the
baseline distance, and reports that (and only that!) to another team which
does the data reduction. The second team should not even know the latitude
and longitude of the observation sites, so they can only calculate using
the distances and the independently-observed angles.


The issues David raises crop up every time one makes a measurement,
especially every time one measures something that has been measured before.

Measuring the size of the earth is an extreme case, because the answer is
so well known. Indeed, you don't even need a highway map! To get a good
estimate of the circumference of the earth, you can just measure the length
of a meter stick (which is pretty easy :-) then multiply by 40,000. Even
in less extreme cases, known quantities manage to insinuate themselves into
measurements in all sorts of ways.

A particularly insidious example is the measurement of mass and/or
weight. Sometimes you get a scale that measures mass; sometimes you get
one that measures weight; sometimes you get a bizarre linear
combination. The known value of g often insinuates itself into the


One should be careful about using terms like "cheating". There are two
very different things that could be happening:
1) Inadvertent use of un-accounted-for knowledge.
2) Intentional use of un-accounted-for knowledge.

The latter is clearly cheating. It tends to make the measured values more

The former probably should not be called cheating. It is an error. It is
sometimes a serious error. It sometimes makes the measured value less
accurate, and it often causes the uncertainty of measurement to be
seriously underestimated.

Remeasuring a known quantity requires discipline and integrity, not just
raw observational and analytical skill. One notorious example concerns the
measurement of the charge of the electron:

Remember Feynman's principle of scientific integrity:
The first principle is that you must not fool yourself
-- and you are the easiest person to fool.


The really subtle and challenging part here is explaining to students _why_
it is important to make an independent measurement. Normally when I assign
a problem, I make it clear that they are expected to use _all_ the
information at their disposal -- not just the ideas we covered in class
this morning. So why the sudden change of rules?

The answer has to do with "error bars". Every measurement has a
best-estimate value and an uncertainty. The usual procedure when
remeasuring something is to make an _independent_ measurement (call it A +-
a). In a !later! step this can be combined with previous result (B +- b)
to get a new combined result (C +- c). If your measurement (A +- a) is
_dependent_ on the old results (B +- b) in some undocumented way,
calculating C +- c will be a nightmare.

So the answer is that we _will_ bring in the other knowledge we have, but
we need to do it systematically, later. First we need to get a clean
estimate of the uncertainty of the new measurement.