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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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The 3-D of structural form made distributions - A case for the Ratities

I failed to fully follow up on Robin's Craw's comments in 2009  ((on-line)(Panbiog-L and in correspondence)) concerning a full investigation into the difference between Ratite distributions and Nothofagus etc in part because I had not fully comprehended Croizat's difference between structural and environmental form-making. 

Recent work on social selection (developed by one of Williams' students (Roughgarden) applied through the vestibular system of turtle head motion had enabled me to understand what in the Principia Botanica had kept me from advancing to Craw's point.  I was then unable to cognize Croizat's notion of 1/2 symmetry non-geometrically.  Now I can see and understand how he applied in the notion of the "aftershaft" as in  a mathematics of these numbers rather in an algebraic sense.  I had missed this before and this prevented me from getting beyond a 2-D vs 3-D perspective.  Further study of multi-model inference offers the means to proceed where abstract algebra infinitesimally would have only been (I had at first thought of this only from catastrophe theory altering. distributions but Kullback-Leibler information numbers can also assist the same apperceptions.

This difference of environmental and structural form-making requires one to uncover the common substance in the force differences of the following map:

With my study on turtle sound energy signals I can understand this and i do see how one can go forward with Craw's suggestions as well as graphs of noded classifications missed wholly by Nelson at that time. The use of multiple model fitting rather than null hypothesis testing provides a means beyond the abstract reasons for approaching this different synthesis.

Robin Craw had asked me some specific questions about ocean baselines and now (2014) I still have not decided absolutely how to represent he difference between a finite number of baselines which can present current understandings of Earth records from an infinite presentation of the baselines so as to incorporate panbiogeography potentially off Earth( baseline issues ), nevertheless I am able to respond to Adrian Paterson's criticism that what the tracks are telling us is not clear.

 It is clear in my mind that his specific objections to his own understanding of ratite track analysis can be gain said.

Taking a synthesis back to Pangea actually helps to understand the points Paterson raised rather than taking away from it. Here is a take home…

Patterson Points To…

1) Moa- Kiwi = same analytically - not so - the fine scale differences can be use to determine relations of track widths to track node-antinode densities and regardless of the mass differences throughout (thus then one describes the anterior and posterior regions of bifurcation)  and especially noted for the ostriches.

2)The two ostrich groups are a secondary bifurcation (running through all track width differences in space) that also affected the graphed Australian ratites via the Madagascar fossils etc  or not into the terminal Kiwii spanning back to the Pangean ancestral difference that explains the fine scale differences into SA as well via the node to baseline relation that can explain how the global sisters related.

3)The fact that Tinamou and Moa are separated by continents is due to the close isolated proximity  of southern Gondwanna when the global ancestral distribution was dividing.

Thus Paterson’s issue is not with panbiogeography but rather whether with what panbiogeography adds to biogeography  if that so far can really overturn accepted visions of species existence times (and thus how to compute the energy per form through time or ( speciation power) ) rather than a finding  of panbiogeography as opaque needing clarification. Panbiogeography is ongoing but not simply a lexicologic phrase like “ontogeny recapitulates  phylogeny”) . Instead  it is a graphical grammetology means to dissect current  (and fossil) distributions.  As such it is a valid research programme that may or may not change projected views back beyond the Pleistocene,  but at least it has helped to bring our vision back that far so far.  My clarification shows that Patterson confounded  the ends in time with ends in space. The forms spoke for themselves!!

Below are the social selection arguments that offered a different dynamics I found compatible with Croizat's use of deduction and induction.

Haeckel described evolutionary causations as if they were proximate ones said Mayr

He said “phylogenesis is …the mechanical cause of ontogenesis” (1874:7)

Now Mayr’s understanding of the domain of mechanics (One Long Argument, Towards a Philosophy of Biology, What is Biology) prevents/prevented him from observing (physically) the possibility that a dynamical invariant within form-making (phylogenesis of/in some certain time) may constrain the relation of ontogeny to phylogeny kinematically.

Social selection sensu Rougharden designed with both proximate and ultimate concerns in mind clearly demonstrates how Mayr may have overanalyzed a difference between physics and biology.  Whether this was due to his attempts to square his concerns about so-called “bean-bag genetics” with actual physiological mechanisms or whether it was simply his failure to see that goal direction on analogy with computer programs need not consider either an advantage of teleological thinking nor a specific law of nature subject to kind of fundamental forces.  A bodily moving force outlined by phylogeny can be a cause effecting a particular class of motions kinematically universal for a particular ontogenetic series of forms.  Countable ontogeny can be described as “the mechanical” cause of phylogeny and phylogeny accounted can describe the dead forces within the physiologically supported mechanics across a sequence in ontogeny.

"The German philosopher Immanuel Kant (1724-1804) developed a concept of descent that is relatively close to modern thinking; he did in a way anticipate Darwinian thinking. Based on similarities between organisms, Kant speculated that they may have come from a single ancestral source. In a thoroughly modern speculation, he mused that "an orang-outang or a chimpanzee may develop the organs which serve for walking, grasping objects, and speaking-in short, that lie may evolve the structure of man, with an organ for the use of reason, which shall gradually develop itself by social culture" (quoted in Evolution from The Internet Encyclopedia of Philosophy.)"

This interpretation does not distinguish Kant’s classification in force vs classifications of forces (moving) no matter whether structure proceeds the reason for IQ adaptation supposed for these primates.  Mayr has rejected that Kant proceeded “in a thoroughly modern speculation”.  This opinion would certainly apply if Kant’s speculation on “evolution” was compared with S. J. Gould’s.


Gould noted, “By moving from the Linnaean four-race system to his own five-race scheme, Blumenbach radically changed the geometry of human order from a geographically based model without explicit ranking to a hierarchy of worth, oddly based upon perceived beauty, and fanning out in two directions from a Caucasian ideal.

Perceived beauty is different from any given sublime taste of beauty.  These are not geographical directions so race or variety ranking is actually of a potentially larger equipollence in a proper continuum combining any objectively grounded notable differences. So it is not “odd”. 

Rather what is not even-handed is Mayr’s analysis of Kant’s “Critique of Judgment”.  The difference reflected on by Kant in that writing is foundational for this larger expansion of geographically compressed representations no matter the relation of the space to the form (regardless of times suggestable).  This is even more foundationally represented in the Opus Postuum where Kant (using Darwin’s Grandfather’s work in the example) discriminates categorically between moving force classifications and  descriptive classifications side-by-side and is materially necessary to discern if it may have been the orang or the chimp or both or neither that is in the structure of the evolution reasonable thought.  Some may say that there is no support for this level of constructable differentiation of difference.  I beg to differ and can. Is it the Orang?

Fisher’s invocation Parental Investment  (“cost” of raising young) to explain  why sex ratios tend to 1:1 even though more could be reproduced if males inseminated many females and the number of females was maximized to produce the most number of offspring assumes  the “infinite” increase of Darwin.  This need not be assumed.

The maximal population number however is not necessarily assumable as the highest geometric increase as if food  (kinds of proteins consumed) had no bearing on the forces( structural form-making)

If runaway forces are from within rather than external the difference between a tetrational and an exponential increase may require a symmetry in sexes rather than an asymmetry but the exponential could be more adaptable than a tetrational if matched to morphological differentiation supporting a particular environmental form-making (Croizat).

When not 1:1 it is supposed there is an “external force” acting to deviate but this may be random sampling of internal forces against a tetrational repulsive emptiness  of the internal moving forces.  Even the “force” of temperature changing the sex ratio in turtles can be internal as well.

It may not be in the cost of raising young but in the difference between genetical penetration and somatic compression that exponentially cellularly narrows the places of loci swapability (alleomorphs).  Thus extension whether tetrational or exponential may be due the different use of attractions versus repulsions in different proteins adapted in different lineages social selected as the infrastructure.

This analysis which aggregates (genes) differently than a simple elastic vs inelastic collision gas model of Fisher points not only to the difference from sexual selection to social selection but must reject the whole sociality that supports productions based on the male-female difference as expressed simply in the background sound of the two lower videos below.

"The point is, you can see how easy it is to write a narrative to these behaviors that can override more dispassionate reasoning. An example may help, however."

Croizat suggested when comparing Fisher and Simpson writ in Space Time and Form that two hares where being run down the same rabbit hole.  This is such a case.

Did Darwin underestimate a potential rate of reproductive increase?

It is a simple popularization of Darwin’s insight beyond others’ view on the transmutation of species that living things posses a powerful capacity of “geometric” increase which he apparently analogized from Malthus.  But in enumerating the actual numbers of creatures and noting that these numbers are finitely divided amongst the species Darwin supposed that at best the actual increase possible for life is arithmetic along with possible increases in the food supply.  Is this synthesis an accurate analysis of the actual ability of living reproduction to increase in quantity?  Does life posses an ability to reproduce beyond geometric measures?  Was Darwin mistaken on how the “checks” to this increase occurs?  Did the finite number of named species confuse Darwin to remain within the mathematical comparison of relative numbers of populations per species than are possible? Do the checks on total growth occur rather by differences in the exponential base of increase rather than in the total number integrally subtracted via an arithmetic measure empirically coordinated?

{\ \mathrm{tet}_b(x) = \ \atop {\ }} {{\underbrace{b^{b^{\cdot^{\cdot^{b}}}}}} \atop {x}}~

As late as 2011, the tetration function has not been listed among elementary functions, it is not implemented in programming languages and it is not used for the internal representation of data in computers.

 f=\mathrm{tet}_b(x)  x,bf=\mathrm{const}.

Does reproduction / fecundity / offspring variation not rather occur via base changes (toward ONE) in tetration rather than via environmental carrying capacity inhibition?  Does the difference between NBS and NCE equilibria work via tetration?

Does social selection's use of cooperation potentially enable it to show that cooperations have higher internal base increase ranges than those in competition.  Darwin thus would have been shown to have overvalued biotic wedging to social and physiological cooperativitiy compared to a different understanding of the biophysical in a different math.  Mayr and Gould failed to evaluate Bateson's meristic vs substantial variation due to thinking a false reductive transition to physics where math was and they put teleology there where teleomatics and non heterochronic growth vaules were.  Does not this support Croizat's notion of structural form-making over Gould's 3 branched core Darwinism in a formal vs functional narrative?

The increase is a result of the difference between expansion and compression as gene coded in distributions of drawing and driving forces.  Fisher is inaccurate to suppose that the relation between among (the amount of) modificatory variance able to affect the heterozygote is such that the amount tends to zero as viability tends to one. 100% viability need not be normalized. The relation of the mutation rate effect in the evolution of recessiveness could be caused rather by different levels of viability 1.4 , 1.8 if the multiplication is chromosomal and related to the entire repulsions and attractions in the genome.  Thus as a complete viability is attained this may be due to populational combinations resulting in larger than an effective 100% (in the behavioral affect) but within the same intrinsic extension (multiple vs single chromosomes etc).  The “handicap” imposed by mutations is not dependent on a 100% viability but rather on the tetrational base that the traits contribution to the push and pulls of the genes expressed.  Thus a different recessive gene may have more or less different effect contribution depending on which specific amino acid is incorporated (mutated to).  This is the missing meaning to the genetic code Lewontin asked for and is circumscribed with Roughgardian social selection Kantianized.   The base is a measure of the total sum of particular amino acids used in the sum of genes per trait. X in the graph could represent time (reproductions) prior to fixation of a particular gene.  The tetrations may go from one prime plateau to another in both the finite and the infinite regions.

Constraints on the two tiers of social selection under the assumption that the infrastructure arose by an unboundedly unbounded game between the sexes – infinite social selection.

Conway has lectured on the situation where a game may continue for an indefinite period of time but that it must end at some time.  In the cases of social selection it may theoretically possibly happen that – that the behavioral tier game whole is structured such that it may outlast the evolutionary tier game part as part of the evolution of the game payoffs themselves if such a Conway game is inherent in social evolution sensu Roughgarden.

What is the population genetics of this situation?  How can the individual behavioral lifetime fitness be summed such that it may outlast the ESS (in theory) but not contraindicate it.  How does the genetics of a particular evolveability direct the infinite phenology of these social selections (what are the internal game motions that restrict the class of equilibriums and to where -- in what specific games, does it occur)? These cannot be external constraints as in Fisher’s view of runaway selection per trait but rather result from the nature of the gamed dynamics as contingently evolved in a particular lineage.

Let us take two populations that genetically have a tetrational asymptote internal to any given niche they exist in(gene vs individual).  Then the populational genetic approximation of one to the other in any F statitistic  of population structure moves in an infinitesimal field of structure that can only be described in Wrights as opposed Fishers or Haldanes frame.  If the equilibria of this structure match a macro extra niche pressure (mutation, migration, selection, drift) situation then it coordination provides a means to traverse the gene perpopulation  adapative landscape vs the population genes landscape as criticized as unworkable by Provine.  So grossone calculus can answer Provine criticism of Wright.

Social Evolution is a deviation from random offspring production but may occur within relative levels of random mating.  This distinction underlies the difference between Wright’s and Fisher’s population genetic maths.  The detailed instantitation of the Kimura’s via Haldane’s however depends on the physiologey of the NBS vs NCE etc. (axiom based vs empirically only determined). The statistical equilibrium of known extracted waveforms formats the difference in the levels of random mating (which is not comprehended in Fisher’s runaway sex difference.

Bateson’s method as an application of morphological visualization in the grossone numerical system – the for D’Arcy Thompson realized.

“The parts of any member of Creatura are to be compared with other parts of the same individual to give first-order connections. 2. Crabs are to be compared with lobsters or men with horses to find similar relations between parts (I.e.., to give second-order connections). 3. The comparison between crabs and lobsters is to be compared with the comparison between man and horse to provide third order connections. (MN, 11)”

Double Description- D’Arcy Thompson’s moving force instantiated in a grossone  numerical system representations of morphology.

Gould doubted that Thompson’s  approach to directly represent original force forming vectors within morphological differences was likely to be involved in expansions of evolutionary theory.  Here we show that this need not be the case and that by using Grossone computer systems detailed differences between serial and bilateral variations can be understood outside of biolegacy teleological thought and known graphically as demonstrated interative functions of combined infinitesimal and infinite numerals algorithmitized.  The grossone presentation of foms permits direct access to Bateson’s third order connections.  The computer system itself enables the bilateral and serial variation for example in a an arthropod’s geographic distribution to edged with variation in mammal spinal chord form for instance panbiogeographically vicariantized.

This is possible because the moving force can be presented from within a volume that contains the morphology but is correlated to different numerical systems not technologized in the instance  being manifested and viewed.  The notion of math as a tool is applied to systematics.  This is coordinatable to biogeography through graph databases of the same data stored. (“what is it in the territory that gets onto the map” Bateson 1970).

Teleology is in the computer system used to visualize the anantomy but this is divided double by the moving forces which are different for different divisions of grossone infintiesimals to infinite. A classified division of grossone sets allows bilateral and serial variations to be composed by the software.

The every more abstract double descriptions are attached to larger gossone relative numerals as the relation between the infinitesimals and infinites is set up.  These can be related to the third biogeographic connections across the phyla.  Because this appears to symptomize hierarchic inference feelings it bears directly on Gould’s idea of attaining an intuition for a hierarchic expansion of evolutionary theory however it requires instead that the levels of orga nization be apprehended before the levels of selection are perceived (else there may be a subreation (through the concepts)).

Grossone one anatomy pertains to nested levels as ONE as Basteson internalized with a crab’s body relative to leg-pattern.  This can be expounded for animals that locomote and plants that drop seeds growing to the sun, to the earth, an earth moving aso to the sun.Double description, insofar as it is a method about a process of classifying the world and using the act of the classification to learn something about both the justification for the classification and its generation is a mode of Kantian metaphysical transition to physics insofar as the moving cause of the construction of the classified objects is part of the form-making of the objects and their position in the classification itself.  Grossone computers permit an anticipation of the analogies thus logically frayed.

There is a difference between motion in a discontinuous space and how the velocities that compound into said motion versus how the space itself aggregates.
Provine misses this difference when he writes that Bateson sought to save evolution from Darwinian gradual evolution via discontinous evolution.
Provine counfounds geometry and algebra with this statement. You can have gradual Darwinian evolution and discontinuous evolution without understanding
how the hypalleomorph in the wild type was reverted to in a unity of gametes per heterozygote NACL like. Bi-sexual ancestry and symmetric socal selection can be
gradual but mendelian.  The evolution of dominance is not the same thing as the dual parental and hybrid contributions
to the force that gametically is cellular.  The motion depends on the infinity in the light (photon) vs the energy levels crossed per repulsion and attraction. Words
used by Provine missed this.

Although there is a formal "purity" of the gametes, they are not screened off
from the individual's ancestry.  This mistaken notion has prevented the creation of
devices that can extract energy from ancestral formations able to survive irreversibilites
otherwise destructive of chemical bonds.  It is possible to run machines by breaking down the
gametic purity of heritage materially.  This is a new untapped source of energy for human consumption and
can be realized once the convergence series and divergent developmental binomial are enumerated in a common
numeral system. The guanosine attachments of microtubules may convey this ancestral information of the triple coded
repulsion attractions in the amino acids purely on. This is relative impenetribility through the filling
of space as alleomorphs change places (sides).