From: D. J. Schaeffer (golux@mcs.com)
Date: 16-Feb-95 (7:10:36 GMT)
Subj: Symmetry & Tones

Given the apparent devotion to symmetry the TCs have (which I'm not sure has been addressed in any depth), why would they send us operators for unidirectional subtraction and division, as Plotkin has glossed T/U and e/f, when the symmetrical operators I/J ("absolute value difference" and "negative absolute value difference") and M/N ("absolute ratio" and "reciprocal absolute ratio") can do the same tasks?

Also, has anyone given any thought to how the TCs assigned the tones, and what we might learn from those assignments?  For instance, the A-G series is easy: B is the number 1, and stringing it together to run through the numbers makes sense.  A=0 through F=5 makes sense, and then G makes a simple delimiter for the basic lessons.  (Then you're stuck with G as your delimiter.)  But why Q for the number delimiter?  Why are certain related functions grouped or paired (H/I/J, L/M/N, R/S) and others separated by intervening tones (h=cosine from k=sine, for instance, which are separated by i=Boolean AND and j=Boolean OR).

I have no answers to suggest, especially at this late hour, but I think we might be able to determine something about the TCs by looking into these questions.

You all are much better at this than I am.  I am frankly amazed.


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