MATH ESTABLISHMENT IDEOLOGY

MATHEMATICS IS BIFURCATED INTO TWO SECTORS -- which I call "YIN" and "Yang". (This classification overlaps with and o-logomath, cited elsewhere).

The difference between Yin and Yang involves OPERATIONS WHICH ARE AUGMENTABLE (NONABSORPTIVE) and OPERATIONS WHICH ARE NONAUGMENTABLE (ABSORPTIVE). (An OPERATION is AUGMENTABLE if the AUGEND INCREASES IN VALUE.)

A Yin system has one or more primary operations which are Augmentable, but nonAbsorptive, whereas a Yang system's primary operations are nonAugmentable, but Absorptive.

Please consider the system [E, #, =, ¹], where E is a set of elements; where # is a binary, associative, comutative operation; where =, ¹ are equivalence, nonequivalence relations.

• If (for e in E) e # e ¹ e, then operation # is Augmentable, nonAbsorptive, and the system is Yin.
• If e # e = e, then # is nonaugmentable, Absorptive, and Yang if this is so for all primary operations.

Yin systems have a Yang subsystem, for natural reasons. And Yang-like measures are found in many physical systems, for good and useful purpose.

Yin systems have a Yang subsystem, for natural reasons. And Yang-like measures are found in many physical systems, for good and useful purpose. But the Yin-Yang Bifurcation in Mathematics exists only because of 2500-year-old philosophical prejudices!

In the above system, [E, #, =, ¹], let E be the set of (rational, irrational) real numbers, # a mean (averaging) operation, and =, ¹ the equivalence, inequivalence relations.

• Let # º arithmetic mean. For any real number e, e # e = e -- absorptive. For example, if e = 2, 2 # 2 = 1/2(2 + 2) = 2; etc.

• Let # º geometric mean. For any real e, e # e = e -- absorptive. For example, if e = 3, 3 # 3 = √(3 x 3) = 3; etc.

• Let # º harmonic mean. For any real e, e # e = e. For example, 4 # 4 = 1/[1/2(1/4 + 1/4)] = 1/[1/2(2/4)] = 1/(1/4) = 4; etc.
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• And if # is any other mean, then e # e = e -- absorptive.

As I note elsewhere, all means are averages. Other averages are the MODE and the MEDIAN, and these are absorptive also. In fact, when the numbers are all the same, all averages trivially yield the same result -- clearly absorptive.

We find absorptive measures in physics.

• In general physics, we find a well known absorptive measure: density (mass per unit volume). Thus,
• In thermodynamics, an absorptive measure is called "intensive"; a nonabsorptive measure, "extensive". An intensive example is temperature; an extensive is volume. Thus, 1 pint of water at 75 degrees Fahrenheit combined with 1 pint of water at 75 degrees Fahrenheit yields 2 pints of water (extensive -- nonabsorptive) at 75 degrees Fahrenheit (intensive -- absorptive).

• In electromagnetics, we find correspondents of extensive, intensive properties as (respec.) magnitudes, intensities. Intensities are electromagnetic densities. Thus,electric field force, F is a magnitude ("extensional", nonabsorptive) which becomes electric field intensity, E ("intensional", absorptive), when divided by charge, Q. Other intensities are useful in electromagnetics, but are called "densities", although they are not rated to volume, but to charge. However, "proper" densities (rated to volume), also appear in electromagnetics, such as in charge density: charge per unit volume.

  This is just one of many reasons why the language of science (here, physics) confuses students and citizens, contributing to what the late Carl Sagan said about SCIENCE:
  "We've arranged a global civilization in which the most crucial elements ... profoundly depend on science and technology. We have also arranged things so that no one understands science and technology. This is a prescription for disaster. We might get away with it for a while, but sooner or later this combustible mixture of ignorance and power will blow up in our faces .....", Carl Sagan, The Demon-Haunted World"

  You may now return to the Schizoid discussion.