Randolph Thompson Dible II (mostconducive) wrote in pytharwinism,
Randolph Thompson Dible II
mostconducive
pytharwinism

The Infinitesimal: There Can Be Only One, but who else believes that?

Does anyone know of anyone else's view of the infinitesimal, unity over infinity in fractional form, which is the unicity of one-ness (any unit) which condenses to singularity (without a multiplicity of singularity, acknowledging the paradox, ignoring the plurality)?

I mean to quote the Highlander "There can be only one" [such entity]. I mean, how could there be another in the same frame of reference? They would condense to being the same one. Newton, Leibniz and Abraham Robinson adopted the definition of infinitesimal[s] as non-zero, but less than 'any known number,' suggestive of the "unknowable" aspect of this number, but its not so much unknowable as not graphically representable. Every point has some dimension, its expression is its extension. So the real dimensionless point (usually considered ideal, in contrast to real) is not visible, but it is because it is the viewer, the point of perspectivity, of the observer. If viewed, it could only be sight in itself, of itself.

The definition "non-zero, but smaller than any known number" opens the discussion for a plurality, and reason would have a multiplicity of such entities as they represent the infinitesimal distinctions all forms of and in our world, which compose it. I contrast this view with the singularity of the infinitesimal, that there can be only one real or true infinitesimal. The only other person (in this case, a mathematician and philosopher) I've found to hold this view is Lorenzo Pena of Spain, editor of the electronic journal Sorities. Is there anyone else?

I don't think multiplicity or plurality doesn't exist, of course it does, but there is no discontinuity of parts, it is contained in the continuum ("the real number line" R in mathematics), the four-dimensional space-time matter-energy continuum in our experiential case. The contents of the continuum plus the continuum compose the totality which we are given, the present. That totality is the unicity of one-ness, the singularity, the Infinitesimal. Other continuums (there must be infinitely many) also condense to the Infinitesimal this way, it is the alpha and omega in common. I identify it with the First Distinction of Spencer-Brown, which cybernetics has taken to. And I set the First Distinction in contrast with the First Dimension, that linearity of the number line (expression of the continuum), the first dimension being the first expression of the first distinction which is ever-present. The First Distinction is the cybernetic Proemial Relation between pure subjectivity and pure objectivity, and every distinction (and keys, key distinctions) are only instances of it. The transcendental distinction (also called difference) is the Spirit which animates us (as the point of perspectivity, the supreme being seeing itself being, that 'negativity within God'), the point at which the pen (-ultimate) strikes the paper (or 'page of assertion,' 'unmarked space') in the book. The abstract pen-point of punctuation is the programmer of all programs, the allegorical writer, the author, one-self, the Spirit as negativity in God, and I've found it to be with mathematical precision "The Infinitesimal."

So my question is, who else demands one true infinitesimal? Or am I to take credit for this radical conception of 'unity over infinity'? Please stop me from that, I don't want to be so alone in this expression. But I've searched a lot, and haven't found much confirmation.
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