642.00 Functions
642.01 Functions are never independent of one another. There is a plurality of coexistent behaviors in nature; these are the complementary behaviors. Functions occur only as inherently cooperative and accommodatively varying subaspects of synergetically transforming wholes. Functions are covariants. Wave magnitude and frequency are experimentally interlocked as covarying cofunctions, and both are experimentally gear-locked with energy quanta. The meaning of a function is that it is part of a complementary pattern. No function exists by itself: X only in respect to Y. Tension and compression are always and only interfunctioning covariables whose seeming relative importance is a consequence of local pattern inspection. Multiplication is accomplished only by division. Universe expands through progressively differentiating out or multiplying discrete considerations.
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Fig. 641.01 Tension Members Tend Toward Arcs of Ever Greater Radius:
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Slack rope and tensed rope: tensed rope tends toward “straight,” i.e.
toward arcs of ever greater radius, but never attains complete “straightness.”
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As tension increases: neutral axis lengthens and girth contracts (becomes more compact). Therefore, the long-dimension profile arcs increase in radius and spiral arcs’ “radii” increase in dimensions but never attain “straightness” of relation between two “fixed” points, as there are no experiences of fixed points and straight points.
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Tension goes toward arcing of larger and fewer different radii all ultimately spirally closing back on self. Tension: inherently comprehensive and finite. Compression goes toward relatively smaller radius and toward more of smaller and multiplying microcosmic differentiation. Compression: inherently local and infinite.
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Tension as gravity: a tension structure is nature’s fundamental pattern-cohering principle.
642.10 Tetrahedral Models of Functions
642.11 Covarying functions are tetrahedrally modelable. A series of covarying tetrahedral models is presented in Secs. 961.10-48.