Propositions

Propositions - converting the plurivocal to the identity of a unified consensus in axiomatic panbiogeography

Proposition 2.1 - If l and m are any two distinct generalized tracks that are not parallel, then l and m have a unique point in common.
if this point is a node then there is a derivative at the node
if this point is not a node then the continuousness (continuity) in the area is a plane boundary cutting collinear points.

Proposition 2.2 - For every individual track or geographic variation there is at least one node outside the area in the vicinity of which Catastrophe theory of (Thom 1975) can be applied.

Proposition 2.3 - For every collection there is at least one individual track or geographical variation not passing through it's area (principle of terminal taxons)

Proposition 2.4 - For every collection locality there exist two distinct tracks oriented from some baseline that pass through the geographic coordinates of the locality.
Notice - let MrN be three points reconstructing the baseline, Prop. 2.4, there fore an individual baseline's exsitence is or co-exsitence was (at least)

Proposition 2.5 There exist 3 distinct lines such that form Space + Time + Form; either the two distinct lines of Prop 2.4 are not time or time is correctly inferred and is Craw's (1983) reduction of the information content of a cladogram.

“The surprising fact is the amount of infinitesimal and infinitely large numbers which such a positional numeral system can represent.:”

http://vixra.org/pdf/1012.0011v1.pdf

On Sergeyev’s Grossone: How to compute effectively with Infinitesimal and Infinitey large Numbers.

The ability for the gross powers to be recursively defined in terms of prior gross one numbers allows for this large but not cardinally inaccessible size of representation. How far it can be empirically utilized where other larger infinites are at play remains to be seen and how to populate a set of grosspowers and grossdigits via path analysis for instance (where the two directional arrows represent undetermined divisions within the a posteriori instantiated empirics) needs to be materialized.

Consider any given set of distribution points as having an association with some number with the Natural Number set N as a grossnumber numeral.

This particular division would be suitable wherein the distributions shows two lineages and where the the track^node^mass^baseline organizational difference between the two is simply a shift relative to the baseline.

One way to find this shift as the data for both lineages are populated into the outline and framework is by the constraint that N also presents grossone squared at the same time. One is thus left with the more less difficult task of describing the track^node^mass^baseline coefficients as the cross (vicariant) diagonal through ordered pairs of actual distribution collection localities.

To do this the lineages without shift (relative to sister) are demonstrated in the upper half of the x illustrated diagonal. How high grossone minus one goes before it is subtracted (in data actually inputted) may depend on the masses actually present. The lower end of the x may be those areas wherein the node antinodes are clearly directed to the baseline.

Axiomatic Panbiogeography

offers an application of incidence geometry to historical biogeography by defining collection localities as points, tracks as lines and generalized tracks as planes.