Oliver L. Reiser recognizes that music theory is noncommutative (yet doesn't): The Chordiness of a Whole

 Reiser doesn't seem to understand the true details of time-frequency noncommutativity! Fascinating.

 https://archive.org/stream/promiseofscienti011968mbp/promiseofscienti011968mbp_djvu.txt

But if these symbols refer to concrete "things" (that is, aggregates 
of behavior-stuff), then (z) does not hold, because if you add 
electrons and protons and radiation (a field) you get an atom. In 
that case the behavior of each entity is now a function of the 
properties of the non-additive (emergent) whole. Or if these 
three symbols represent musical notes (c, e, and g, for example), 
you get a musical chord. But for the same reason (the "chordi- 
ness" of a whole), the order in which the units are added is im- 
portant, and in these cases the commutative law no longer holds. 
It is very significant that physicists are coming to recognize the 
importance of wholes in physics. To support this statement I 
quote at length the following passage from Herman Weyl's book, 
The Open World:* 

The state of a physical system is determined when for each physical 
quantity of the system the probability of its taking on each possible value 
is known. It is true therefore that the state of a system consisting of two 
electrons determines the states of both electrons, but the converse does 
not follow. The knowledge of the states of the two parts of a system 
by no means fixes the state of the whole system. We find here a definite 
and far-reaching verification of the principle that the whole is more than 

5 1933-; P* 55- 



RESUME: ARISTOTLE, NEWTON, AND EINSTEIN 103 

the sum of its parts. Modern vitalism, among whose proponents I 
mention first of all Driesch, has attempted to reduce the independence of 
life, its essential distinction from non-organic processes, to the concepts 
of Gestalt or the Whole. According to vitalism the living organism 
reacts as a whole; its functions are non-additive. The manner in which 
its structure is preserved throughout growth, in spite of all outside influ- 
ences and perturbations, is not to be explained by small scale causal 
reactions between the elementary parts of the organism. Now we see 
that according to quantum physics the same applies even to inorganic 
nature and is not peculiar to organic processes. 

Some physicists may be displeased at this introduction of organ- 
ismic conceptions into physics, but we, as philosophers, must not 
overlook the fact that this, at the same time, makes it easier for 
the biological sciences to apply physical notions in physiology 
and psychology. 

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 A more technical illustration of the one-way 
character of psychical duration is found in music in the process of 
chord resolution in melodic and harmonic progressions. It is for 
this reason that playing a phonograph record backward takes the 
"meaning" out of it. 

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 the activities of the individual cells within that rhythm being treated as 
analogous to the "eigenfunctions" of wave mechanics. Finally, 

9 Cf. "The Tan Effect An Example of Psychological Relativity," Science, 1930, Vol. 71, 
pp. 536-537- The quantitative study appears in Journal of Experimental Psychology, 1931, 
Vol. 4, pp. 


SPACE, TIME > MATTER, AMD ORGANISMS ZZ3 

the analogy helps to justify the use of such metaphorical phrases 
as the "music of consciousness/' the "melody" of an instinct, 
and so on, since "panicles' 1 on the undulatory theory of matter 
appear as interference effects, like "beats'* in music, due to the 
superposition of of gra^waves. Thus, in a roundabout way, 
we return to our earlier supposition that the brain may be looked 
upon as a harmonic analyzer and synthesizer, with the melody and 
harmony of conscious life interpreted in terms of the consonance 
of the "fundamentals" and the "overtones" of the wave system 
of the brain-as-a-whole. 

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