Monday, February 4, 2013

Between Unity and LoF

The simplest of all cases would be undifferentiable or at least undifferentiated unity.

Unity was primitively recognized and denominated as "abyss", "void", "nameless" and "chaos".

And the simplest of all analyses would be such what might be called "unarics", limited to such recognition and denomination of unity, with no calculation possible.

The simplest of all cases which permit calculation are those analyzable in terms of two indexes, which analyses, calculuses, arithmetics and algebras are called binarics here, and of which George Spencer Brown's Laws of Form (LoF) of course presents a most elegant and thorough description and development.

Note, however that LoF's law of calling

[ ] = [ ] [ ]

can be, but law of crossing

[ [ ] ] =

cannot be, represented on a line, by segments of different colors.

This proves that there exist still simpler cases and corresponding binarics than that presented in LoF, binarics in which the law of calling but not the law of crossing is valid, but which cases and binarics like that of unity and "unarics" are incalculable.

And it also suggests some correspondence of form and representation on the one hand and dimensionality on the other.

But note too that calling involving more than two indexes and therefore similarly simplified what are called here enarics of number of indexes N > 2 can be represented on a line, by use of line-segments of more than two colors, which proves that there exist cases and such enarics in which the law of calling but not that of crossing is valid.

And could there not equally be cases and enarics where the law of crossing but not calling is valid?

Keywords: abyss, analysis, binarics, calculation, calling, chaos, crossing, dimension, enarics, George Spencer Brown, Laws of Form, LoF, nameless, unity, void