Here's why I say that the YIN-YANG SCHIZOID nature of MATHEMATICS makes A FLATLAND OF SCIENCE.

As I note elsewhere, the familiar binomials provide t-COMBINATORICS for YANG elements in various structures.

So, for YIN elements, I created partorials as o-COMBINATORICS.

And I noted that t-COMBINATORICS fit (at least, theoretically) VENN DIAGRAMS (t-DIAGRAMS) -- such as for the t-NUMBER, 30 -- so, for o-COMBINATORICS (say, for the o-NUMBER, 360 = 2 x 2 x 2 x 3 x 3 x 5, or PARTORIAL 3), I created o-DIAGRAMS, with "concentric" circles representing DEGREES or ORDERING of element distinction.

I was motivated in this by my (World War II) years as Army Air Force Weather Observer and Weather Forecaster, seeing and drawing ISOBARS in LOWS and HIGHS on weather maps. After I'd drawn a few o-diagrams -- say for FACTORS of 360 -- I realized that they also resembled CONTOUR MAPS of TERRAIN. A map with contours like those in a t-DIAGRAM (VENN DIAGRAM) would represent land which is fairly flat. But land with contours like that of an o-DIAGRAM (even as shallow as that for 360) shows some ELEVATION from FLATNESS. Hence, any science which cannot call upon YIN MATH (allowing distinctions of DEGREE) is FLATLAND.

One way this can arise is by dependence upon PROBABILITY THEORY. But probability theory is based upon STANDARD SET THEORY, which is YANG (not allowing distinctions of DEGREE!).

I can cite two instances of this.

• My motivation for partorials came from a course I was teaching in PROBABILITY THEORY at the University of Maine (Orono), using W. Feller's Introduction to Probability Theory, V. I. Therein, Feller notes that "fermion statistics" derives from the LIMIT FORM OF THE BINOMIAL, whereas "boson statistics" derives from the LIMIT FORM OF THE NEGATIVE BINOMIAL. I realized that my PARTORIALS ARE MEDIAL BETWEEN THE TWO DISCRETE FORMS, hence, can have a LIMIT FORM. I immediately began to search the Physics literature, and found that X. Y. Greenberg had introduced the notion of "parafermions". (Later, this was "legitimatized" as "quark statistics".) But it took about 40 years to make this extension, whereas I did it in a month. Thus, MONOTYPAL in MATH means FLATLAND (NONDEGREE!) in PHYSICS!

• If you search the literature of EVOLUTION THEORY, you find that evolutionary changes of DEGREE have actually been observed. (Example: darkening of wings of moths "living" on tree trunks that have become darkened by coal-pollution.) But evolutionary changes of KIND must be INFERRED from fossils and other historic indicators. Yet BIOLOGY has available only a probability theory that is MONOTYPAL! (In the above hyperlink for my extensions, I show how a PARTORIAL COMBINATORIAL CAN PROVIDE A PROBABILITY DISTRIBUTION not otherwise available. The example there involves a wildlife population, but could be extended.) And, in 1978, I published an extension of "The Hardy-Weinberg Law" -- called by some the "foundation law of evolutionary theory" -- showing that the form is INVARIANT UNDER DISTINCTIONS OF DEGREE! But standard BIOLOGICAL THEORY remains FLATLAND!

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