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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.
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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 underlying  this 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.


Programs  for 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 ontological  in 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,


it is not so absolutely infinitely impossible.Cantorian abstraction: A reconstruction and defense


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 of  system of simultaneous equations of a high degree over one  with 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 under  social 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 number  class 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 in  1966

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. ‘Cantorian  Abstraction: 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.