## Measurement

Copyright © 1996 by H. Goldstein, J.L. Gross, R.E. Pollack and
R.B. Blumberg
(This is the third chapter of the first volume of
The Scientific Experience, by Herbert Goldstein, Jonathan
L. Gross, Robert E. Pollack and Roger B. Blumberg. The
Scientific Experience is a textbook originally written for the
Columbia course "Theory and Practice of
Science". The primary author of "Measurement" is Jonathan L. Gross,
and it has been edited and prepared for the Web by Blumberg.
It appears at MendelWeb, for non-commercial
educational use only. Although you are welcome to
download this text, please do not reproduce it without the permission
of the authors.)

**The sensible answer to Question 1 is no, of course.** It is a mistake in
physics to identify the concept of "warmth" with measurements on the Celsius
scale. Suppose the temperature drops to 1° C on Tuesday. Was it
really twenty times as warm on Sunday? What if it drops to 0.1° C on
Wednesday. Was it ten times as warm on Tuesday, and 200 times as warm on
Monday? Perhaps by Thursday the temperature drops to -5°. Was it
-4 times as warm on Monday as on Thursday?

The Fahrenheit scale is another interval scale for temperature that is not
a ratio scale. The comparable Fahrenheit readings for Sunday, Monday,
Wednesday, and Thursday would be 50° F, 68° F,
32° F, and 22° F. Their ratios make no more sense than
ratios on the Celsius scale.

The point is that, if a scale is not a ratio scale, then inferences based
on the calculation of ratios of its data points may be utterly misleading.

**Question 2:** Using the Celsius temperature measurements given in
Question 1 and its answer, is it correct to say that the temperature difference
between Monday (20° C) and Sunday (10° C) was about twice
as great as the temperature difference between Monday and Wednesday
(0.1° C)?

( yes ) ( no )

(This is the third chapter of the first volume of
The Scientific Experience, by Herbert Goldstein, Jonathan
L. Gross, Robert E. Pollack and Roger B. Blumberg. The
Scientific Experience is a textbook originally written for the
Columbia course "Theory and Practice of
Science". The primary author of "Measurement" is Jonathan L. Gross,
and it has been edited and prepared for the Web by Blumberg.
It appears at MendelWeb, for non-commercial
educational use only. Although you are welcome to
download this text, please do not reproduce it without the permission
of the authors.)

MendelWeb was conceived and created by Roger B. Blumberg
rblum@netspace.org