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*From*: David Bowman <David_Bowman@GEORGETOWNCOLLEGE.EDU>*Date*: Wed, 6 Jun 2001 22:47:24 -0400

Regarding John Denker's method of estimating the earth's circumference:

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.

First off it seems that John has inadvertently made a decimal error of

3 orders of magnitude (probably because of accidentally ignoring the

distinction between a meter and a kilometer).

Secondly, this method would (IMO) constitute an example of "cheating".

If the experiment was done when the meter was defined according to its

original 18th century definition, then this procedure would not really

constitute a *measurement* of the size of the earth. It would really be

merely quoting the definition of the meter. An honest measurement of

some quantity does not use the quantity measured as the definition of the

unit of measurement. The unit of measurement need to be specified

*independently* of the quantity to be honestly measured. For instance

the fact that the vacuum speed of light is exactly 1 ly/yr or exactly

299792458 m/s is not a measurement of that speed. It is really just the

definition of the unit of length.

Even if the experiment was done nowadays using the modern definition of

the meter, then the cheat would be in relying on the fact that

experimentally, the new definition of the meter is numerically close to

the original definition of the meter, and using that numerical fact is

tantamount to merely using a previous measurement of the size of the

earth (made when the new definition was calibrated to agree with the

old one) and then quoting it as some sort of new independent measurement

of the Earth's size.

Another example of another "measurement" of the circumference of the

earth which would constitute "cheating" is to give the circumference in

Nautical miles. Since a nautical mile was originally the surface distance

corresponding to a surface arc angle of 1 minute of arc we know that the

circumference of the earth is 60 x 360 = 21600 naut. mi. by the original

definition of a nautical mile. However, (like other units that have been

"metrified") the current international standard definition of the

nautical mile is exactly 1852 m rather than being based on the size of

the earth.

David Bowman

David_Bowman@georgetowncollege.edu

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