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

Use of geographic distribution vertices to organize algorithms for parallel processing

When Grossone (2) and (3) etc

application objects are being considered (within some outlined dendogram/thamnograme reference) it appears that one is clearly in the relam of arbitrary object dependence definitions.

http://www.gabbay.org.uk/papers/arboms.pdf

If one is able to coordinate the logical partioning of big data on distrubute servers within this notion of Fine's then a graph database representation of the moving forces subsistent can be materially instantiated. The would encompass panbiogeography in other galaxy should life be demonstrated beyond the Mily Way.

Cantor – Grundlagen – translated 1950s

“If somehow actual- infinitely small quantities did exist,
i.e. were definable, they would certainly stand in no direct relationship to those
familiar quantities which are in the process of becoming infinitely
small.”

Kant’s infinity of the Opus Postumum works continually through
this becoming.Thus Cantors distinction
in this sentence makes the philosophy-math difference of Kant real for a
subject.Cantor’s expression of this
object however is merely indicative.Current biology provides, with the discovery of DNA, a substantial moving
force basis from which this becoming was and is simply found in the transition
to physics (centripetal – centrifugal) with Cantor’s numbers replacing Darwin’s
thinking of the relative difference between arithmetically increasing and
geometrically increasing quantities.Data and livingness are not at odds with each other.

Vertex parallels
amongst different monophyletic lineages will provide data objects to sort and
direct parallel processing but underlyingthis is a complex biology of cause and effect in which the 2-dimensional
unit (bio&geo-graphy) decomposed panbiogeographically have members in actual populations.Ordertypes can be found to provide an
instrument to explore the metrics between the tracks noded massed and baselined even when on parallels. Classes of transcendentals programmatically flag and partially order (Fine arbitary) object dependency that is in line with a classification of biogeographic forces supplied from graphical data.

Programsfor homogneous sets of quaternions as
arbitrary objects within transfinite collections of frieze patterns distributed
in Euclidean space.

Wolfram Hinzen "Constructive Versus Ontological Construals of Cantorian Ordinals"

struggles to relate the computational and the ontologicalin defenses of Cantorian numbers.

It is true that,

computational instances of
Cantorian reasoning have been made for instance in the derivation of a given
transcendental number but when an attempt to specify what compositions of
arbitrary objects are and what the difference between a particular arbitrary
object (continuous material object) and its rigid body parts is,

Spontaneity ought not be confounded with receptivity. Unordered
sets provide the realm of receptivity in which Kantian spontaneity may occur.
One cannot go from a set to a cardinal untill both feet stand firm but thinking
of an arbitrary spontaneity is different than an arbitrary receptivity.

Transfinite Ordertype Algebra – Infinite Path Analysis with
Arbitrary Objects

Wright (1954) brought out that the method of path analysis
“is by no means restricted to relations that can be described as ones of cause
and effect.It can be applied to purely
mathematical systems of linear relations and merges into the methods of multiple
regression and multivariable vectorial analysis when applied to the symmetrical
systems of relations that characterize these methods”.

Transfinite Path analysis constricts the difference of
opinion between Fine and Hinzen on the application of reasoning with arbitrary
objects to Cantorian numbers and provides a tool to operate the inverse
operation Wright never applied to evolution. This permits a better
understanding of somatic programs and social selection.One is able to do “ the inverse problem”
applied to game theory mutations and deduce the path coefficients from known
correlations and a given pattern of relations (variable relation relation
variable) even though it depends on the solution ofsystem of simultaneous equations of a high
degree over onewith the tediousness by
similarities in parts of ordertypes of different ordinal and cardinal numbers.
(I am thinking but could be wrong).So
rather than find population genetic correlations amongst mutation, immigration
and selection we use correlations of game strategy pleasure based teamworks
operating amongst mutation and immigration (isolation by distance) to determine
path coefficients that change payoffs over populational time under different
orthoselections.

Sense is involved in the receptivity while
spontaneity can be immanent.Both the
ontological extension and the computational manifestation are realized in
programs for homogenous sets of quaternions applied within monophyletic
lineages undersocial selection of
abandoning former threat points vestibularly in the space of different densities
of infinite frieze patterns.How dense a
given volume may be-- may be computationally limited even if it is not
necessarily so ontologically. Well orderings may be imposed on the sets but not
necessarily on the points in actual space as these depend on the biological future and past population potential enumerations (Malthus refined). ReasoningWith Arbitrary Objects

This is where Kant discussed monods, mistaken monodology (instead), and the
frustration of the metaphysican vs the geometrician. Poincare pointed this out to Russell. Cantor just made this
dilemma sharper. Russell insisted that ordinals must be something(like color or tones) against Dedekind but Dedekind was not incorrect. It did not go away.Some attempts such as Godel on Husserl can be looked at from this
perspective.

That (where the mistake appears) depends on the mathematical intuition not the applied
mathematical intuition. As Cantor said we need EITHER to “enlarge our mind” in
the infinite or predicate “infinity” differently (Grundlagen).

Since there is no rush to consider Cantorian
sciences (no general spontaneous acceptance across the board) it will take the
construction of sense enhancing computer programs that increase receptivity of
transfinite sets (envisioned here in terms of rotations, translations and
reflections in freize patterns in the environment of the mean free paths of
molecules carried evolutionarily) (and the predications humans complete in the process) that will possibly
enable both of Cantors suggested to be real.

With the inner ear striola indicating the location of the
unit Remanian sphere Norths of the 3 complex plane motion canal flows it is
possible to comprehend Cantor’s “ “insertion of finite numbers in the reals” as
Kant’s posited insertion and is that amount of translations , rotations, and
reflections forced by differently ponderable matter onto the repulsive and
attractive penentrations of other matter. One must use Cantor’s numbers, not
Russel’s, Quine’s, or Kroneckers. “since the manner described a definite
extension of the region of the real numbers into the infinitely great has been
attained it would not be possible to do the same with equal success for the
infinitely small, or, what might turn out to be the same, whether it would be
possible to define finite numbers (which would appear as limiting vaules of
series of irrational numbers) which would not coincide with either the rational
or the irrational numbers but would insert themselves among the real numbers as
the irrational numbers among the rational or the transcendental numbers into
the texture of the algebraic numbers.”

These are the interpolations I suppose turtle brains perform
vestibularly with their behavior computers. Former threat points are abandoned
insertions which nevertheless bind the point manifold connectivity of the
irrationals to the real (subsets in each lineage spatial evolution).This is why the continuum hypothesis has
never been proved as it depends on what the actual physical forces are utilized
between the compression of the cohesion and the penetration of the repulsions
no matter the attraction (if it as correct that organisms could transmute the
elements via the weak force things would be different than they are, if
macrothermodynamic influence extends to that which works at the nuclear level
then… etc (for use of neutrinos or other baryons explicitly etc etc) with or without teleology (in the attraction) but with teleonomics for sure. There are ontological consequences when one purposively builds mechanical and dynamical devices that interact with the teleonomic programs or associable teleomatic law backgropund(s). Kant's mistake about the Sun's dynamism causes philosophical miscategorizations of his views which result from the combined inverse atrtractionsquatede and repuslsioncubed distances.

It is possible to read the Opus postumum with ontological differences between the cohesion of organic and inorganic nature (and to assume that Darwin had thought of this somewhat) but this difference is systematic between as revised Linnean system and the forces that are used to rewrite it. They are clearly not Freudian for instance. One must abstract from the NorthStar (gaze vs locomotion) and Logic in different rational modes of orientation. The vestibular system encodes this kind of difference. How gravity is synthesized in this physiology does weigh on Kant's note in his time of a evidential lack of data (within the Earth) that past historical forms had not been found (to change species parentally over time). Forms can and do change. The confusion of Kant's use of a tree for cause and effect reciprocity comes from his mistaken view of the Sun and the difference of evergreen and decidious trees tracking different galaxy perspectives as their seeds fall both to the Earth and the Earth to the Sun(paticipation of gravity directly in the form-making of trees (between nodes)). Kant remained phronomically with his Solar System systematic constitution and analogically comet tails etc.

Each canal’s complex point at infinity combines with the
other two via these finite numbers defined through a limitation of a given
series of irrational numbers to from a directum Remanian North which combined
bilaterally is symmetrically dependent on the “south” direction anteriorily
(infinitely small per biology rotation induced division of the freize
patternable space placed and or extended with blinking fractal praxis).This
physiology appears to provide what Cantor asked for and is IN SOUND the
apodictic certainity that Bertrand Russell said he was looking for but never found.
He heard it all along but he never simply believed what he heard. Those who
have an ear let them hear. Evolution provides a well enough ordering to get
this result.It is thus silly to deny
evolution because one believes in an infinite God.In fact evolution gives God more logical
reality than otherwise.Prime
factorizations of the transfinite freize patterns can be one to one and onto
the finite limiting values of the various irrationals presenting the motion in
the canals. This provides a tool like fourier analysis. It can be used to
process panbiogeography vertex parallels as well.

Translation, rotation, reflection (in a point or a line) are all isometries. Isometery is a linear transformation of the plane (or space) that preserve distances between points.

Phoronomy is a kind of study of distance invariants formally divided between moving forces and bodies moved.

Bodies can be represented in 3D Euclidean space and thus the insertion of the body in this space phoronomically preserves distances no matter the relative rotation, translations and reflections both inside and outside the body inserted.

The volume of such at a given velocity composition (sun earth man bird fluid flow comparaed example) can have varying densities. How densities change with velocity for a given volume and how the volume can be scaled depends on how many rotations there may be for each set of translations and relflections. This is a purely morphological kinematics the dynamics of which can be decomposed by infinite prime factorizations of the finite insertions once presented as finite values of irrational series geometrized from its imaginary form.

A definition such as the Anzahl of the moons of Jupiter is
the extension of the the concept ‘equinumerous with the concept “moon of
Jupiter” is possible for turtle foreclaw pulsations but Cantor’s finite Anzahl
is already infinitely counted (quantitively determinate).That was Cantor’s point for the reality vs
the logic of the case. General extensions depend on particular physiology of sense
when a determination is to be made.If
infinite numbers are accepted in this processing then the finite quantitiave
determinations by higher numberclass
counts preceeds the general any cardinal counter. These must be counted (moons
of Jupiter) before the extension can be said to exist. We insert as we do count. Frege was mistaken about Cantor's criticism.

Structural Equation Modeling reasoned with Arbitrary Objects

Fine (1998) has proposed a reasoning of arbitrary objects to
solve an understanding of Cantors’ “numbers” and even suggested that the
application may provide concrete “types” of scientific discourse (if correct).

Hinzen (2003 ) has objected to Fine’s ontological
justification for using arbitrary objects as a means to recognize the meaning
of Cantorian ordertypes and instead prefers to emphasize the computational
interest when operating infinite abstraction however thought.

Path analysis as developed by Wright ( biologically motivated) contains infinite linear
representations and has become used rather extensively as part of structural
equation modeling.

Here the dependence – independence relation of arbitrary
objects are used manufacture path analysis within arbitrary object ordertypes
providing structural equation modeling a new platform to compute the forward
and inverse problems ( between path coeffieincts and correlations and from
correlations to path coeficients) and thus showing that Hinzen’s concerns
against the new ontological objects is unfounded.

It improves on Wright’s use of symbols by making clear how
the ontological objects are related to the grammar involved.

This will show that Fine’s account of Cantor’s ordertype is “correct”
as far as the application of sampling error/drift (unordered set prior to
abstraction) goes in the practical intrication of social evolution through
social selection as well as in other uses put to SEM.

Some had considered Wright’s Path Analysis as “lost” (Columbia 2008 op cit) until
it was applied in sociology in1966

and others have asserted
it is a “subset” of SEM

http://online.sfsu.edu/efc/classes/biol710/path/SEMwebpage.pdf“the multivariate procedure that, as defined
by Ullman (1996), “allows examinagtion of a set of relationships between one or
more independent variables, either continuous or discrete, and one or more
dependent variables, either continuous or discrete”.

The relationship between numbers and sets phylogenetically will make clearer
in the computations vs the ontology (of graphs) a better philosophy of cause and causation
in social evolution where Fisher attempted to think with elastic and nonelastic
motions where path analysis backward in geological time existed.Paths of game theory mutations can be related
to path coeffients in the dependence –independence relations of arbitrary objects
when COMPUTED.Applications of cantor’s
use of the diagonal argument for the computation of transcendental numbers is
applied the infinite linear representations in Path analysis and infinite prime
factors become available to work the inverse problem through arbitrary object
typing back from the correlations to the path coefficients or payoff evolutions
locally selectable on a background of structural orthogeny (Croizat read
through Wright).This opens up a totally
new tool to understand payoff changes in time beyond that of Levin Akcay et al and Roughgarden Akcay et al.

Fine, K. 1998. ‘CantorianAbstraction: a Reconstruction and Defence’,
The Journal of Philosophy XCV,
599-634.

Wolfram Hinzen 2003.‘Constructive Versus Ontological Construals
of Cantorian Ordinals’, History and
Philosophy of Logic, 24:1, 45 - 63

The applied nature of grossone as a theoretical addition to
natural science is both at once hindrance to its pure acceptance and a future
benefit.The close relationship between
its mathematical manipulation and a
particular physical epistemological cycle of experiment and observation remands
that its acceptance beyond the idea or avenue is in the correlational stoichiometry
of a codifed and empirically verified horizon of causal processing.

Here Grossone is used to create a cybernetic feedback system
for the vestibular system that permits pleasure based neuronal circuitry to be
integrated with dynamic (force impact and sound representations) sensation by
untwisting the grossone divisions of blinking fractals simulatable on a
computer.The original thought was to
use two fundamental series of reversed
sense with w^2 but the notion of blinking fractals permits a generalization and
a richer signal figure for a given texture and is not tied to a particular
transfinite ordinal in the organization.