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Topic: "Equals divide by Equals": Temperature Scales


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Subject:   "Equals divide by Equals": Temperature Scales
Author: Sonny
Date: Jul 23 2004
Jargon: "Equals added to equals gives equals"; "Equals subtracted from equals
gives equals"; "equals times equals gives quals"; "Equals divided by equals
gives equals". Correct for numbers. But only conditionally for measures, as in
temperature. 5/9(xdegF - 32degF) = ydegC, because, at freezing of water, 32deg F
= 0degC; at boiling of water, 212degF = 100degF. Hence, ratio of (212 - 32)/(100
- 0) = 180/100 = 1.8 = 9/5. Thus: 50degF = 10degC; 68degF = 20degC;
86degF=30degC; 104degF=40degc; etc. Since 68degF = 20degC, and 50degF = 10degC,
to say "Equals divided by equals gives equals", would bere become "68/50 equals
2-/10"! Incorrect! What goes wrong? Explanation
derives from a Theory of Measurement Scales by the Harvard psychophysicist, S.
S. Stevens. (During WWII, psychophysicist Stevens designed airplane instrument
panels so that critical dials were
easiest to see. Steven's seminal work, "Psychophysics", 1975, sells ONLINE.)
This theory is not taught in our schools, and not used by National Institute of
Standards and Technology (formerly National Bureau of Standards). Stevens bases
his measyre classification upon: (1) transformattion group;  (2) appropriate
statistics. NOMINAL MEASURE, as in proper names, technical terms; identity
transformation group; mode(s). TYPOLOGICAL MEASURE: taxonomy of plants and
animals,
etiology of diseases; permutation group; mode(s). ORDINAL MEASURE: Moh mineral
hardness scale, IQ scores, Ricter-Kanamouri earthquake scale; isotonic group;
median, range. INTERVAL MEASURE: denities; temperature scales; linear group;
arithmetic mean, variance. RATIO MEASURE: weight, lenght, etc.; similarity
group; all statistics. If our problem involved a RATIO measure, the "equals
divided by ..." would "work"; however, being an INTERVAL MEAURE, this obviously

doesn't. The LINEARITY, y = ax + b, is implicit in the F-to-C transformation
rule. (The RATIO MEASURE relates to the similarity equation: y = ax.) However,
DIFFERENCES OF INTERVAL MEASURES WILL PASS THE RATIO TEST, since this subtracts
out the INTERVAL (LINEAR) CONSTANT. Thus: (104degF - 68degF)/(86degF - 60degF) =
36/36 = (40degC - 20degC)/(30degC - 10degC) = 20/20 = 1.--A related matter
exists in quantum theory wherein the phase of a wavefunction is not conserved
under transformation, but differences of phases are conserved. Presently, "The
Standard Model of Particle Theory" is based upon "gauge theories", where the
term "gauge" is a misnomer, due
to historical circumstances. Many in the literature note that it should be
"phase theories". (More on this at
http://members.fortunecity.com/jonhays/measure.htm . Also,
http://www.rasch.org/rmt/rmt11n.htm .)

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