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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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Spatial Evolution - is more than biogegraphy.  It includes any way that humanity changes the way space itself is understood and viewed.  It changes in time.

Torquexs’  Phoronomy – A case of applied metaphysics

These applications are geared to display the metaphysical elaboration of Kantian phoronomy. The use of inputs and outputs in digital technology enables actual demonstrations of all of the philosophical distinctions that Kant adumbrates. Special computer programs that interact with human biomechanics permit direct effects otherwise only mentally accessible.  This website will show that one can get quite well beyond the description of the state of the art on the topic as presented below.  In particular technology associated and used with this website will present the elaborations of Kant’s unutilized observation(s) on the relation of space and velocity, bodily.   velocities may indeed be subsetted differently than spaces are.  He cited the application to fluid motion in creatures noting the flow of blood compared between man and bird but also simply the rotation of the body Earth compared to the Sun.  E-commerce on this site will also show that the notion of absolute space has not had it’s last laugh despite thoughts that it was a dead force for change a long time ago.

The first chapter of the Metaphysical Foundations, the Phoronomy, considers the quantity of motion of matter and how it is to be constructed in intuition a priori (so as to produce the kind of rules that are necessary for our experience of matter in motion). Since extension and impenetrability are not directly relevant to how different magnitudes (or degrees) of motion can be represented, Kant restricts his discussion in this chapter to matter considered as a point. Since the motion of a point in space can be represented straightforwardly, the main issue is how to represent the composition of two different motions. Kant's primary claim in this chapter is that due to the relativity of space (i.e., the fact that every motion can be viewed arbitrarily as either the motion of a body in a space at rest, or as a body in a state of rest in a space which is in motion in the opposite direction with the same velocity) “the composition of two motions of one and the same point can only be thought in such a way that one of them is represented in absolute space, and, instead of the other, a motion of the relative space with the same speed occurring in the opposite direction is represented as the same as the latter” (4:490). The proof of this Theorem considers the three possible cases for the composition of two motions: (i) The two motions are in the same direction; (ii) the two motions are in opposite directions; (iii) the two motions enclose an angle. Kant then shows how one can construct a priori in intuition a single motion out of the two motions described in cases (i)-(iii).

Very little has been written directly on Kant's Phoronomy. (Kant's philosophy of mathematics, by contrast, has received considerable attention.) The most extensive discussions of the Phoronomy are by Palter (1972) and Pollok (2001).


  • Palter, R., 1972, “Kant's Formulation of the Laws of Motion,” Synthese, 24: 96-111.
  • Pollok, K., 2001, Kants 'Metaphysische Anfangsgründe der Naturwissenschaft'. Ein kritischer

Application of the principles of Phoronomy

Quantity of the movable -- various measures of software use.

Internal construction --  the motion conducted through Powerball* hand-“gyroscopes” and communicated to digital computers .

Quality of movability  -- Whatever can be done with a hand-gyroscope physically by a user and programmed out of hardware receptive to qualitative changes in motion.

Motion therein (velocity and direction) – Torque applied to a hand-gyroscope accelerates its rotation rate which changes the spinning velocity. In Torquex1.0 direction will be wholly within the computer display of these changes ( accelerations and retardations) although future versions may permit this to be explored from the degrees of freedom of the hand-gyroscope itself as it is torqued.


With these understandings or definitions one can move from reading Kant’s Observation 1 through his Explanation 1 INTO Observation 2.  Knowledge of absolute space is outside this application (as if) of Phoronomy embodied through the rotational motion of hand-gyroscope parts displayed on computers.  One person may move the computer representation of the motion per display faster or slower than another thus showing without regard to the fluids involved Kant’s idea of “return” and thus dictating consequently a directum towards absolute space somewhere. Otherwise the actual use of the application will have to argue against Kant’s metaphysics philosophically even while it was designed with it in mind.

Explanation I.

Matter is the movable in space; space, which is itself movable, is termed material or relative space; that in which all motion must in the last resort be conceived (which is therefore itself absolutely immovable), is termed pure or absolute space.

Observation 1.

As in Phoronomy nothing is to be discussed but motion, its subject, namely matter, has here no other quality attributed to it than movability. It can therefore itself be valid for one point so far, and in Phoronomy we abstract from all internal construction, hence also, from the quantity of the movable, and concern ourselves only with motion, and what can be regarded as quantity therein (velocity and direction). If the expression body is sometimes used here, it occurs only to anticipate in a measure the application of the principles of Phoronomy to the following more definite conceptions of matter, in order that the exposition may be less abstract and more comprehensible.

          One is able to feel the equal and opposite force of the motion of the gyroscope exactly in the sense that Kant describes later the ability to sense attraction rather than not repulsion. This feeling both sensically and as manipulatible on screen,  provides a material empirical space (in Observation #2) that in different computer program versioning will be larger material spaces (both as the program grows and changes and as more people use the software). The experience of one user/programmer is different than another.

Observation 2.

If I am to explain the conception of matter not by a predicate, applying to it as object, but only by the relation to the faculty of knowledge, in which the presentation can be primarily given me, matter is every object of the external sense, and this would be its mere metaphysical explanation. But space would be simply the form of all external sensuous intuition (whether this accrued to the external object we call matter in itself, or remained merely in the construction of our sense, a point which does not enter into the present question). Matter, in contradistinction to form, would be that which in external intuition, is an object of feeling, and consequently the properly empirical of sensible and outward intuition, because it cannot be given at all à priori. In all experience something must be felt, and this is the real of sensuous intuition. In consequence, space, in which we are to institute experience respecting motions, must be capable of being felt, that is, of being indicated by that which can be felt, and this, as the sum-total of all objects of experience, and itself an object of the same, is called empirical space. Now this, as material, is itself movable; but a movable space, if its movement is to be able to be perceived, presupposes again an enlarged material space in which it is movable, and this again another, and so on to infinity.

Physical universality of real compass understood in an idea for hand-gyroscope use.

Motion in this thing.

Observation 1.I have already laid the conception of matter at the basis of the conception of motion; but, as I wished to determine the latter independently of the conception of extension, and thus could consider matter only in one point, I had to admit the use of the common explanation of motion as change of place. Now that the conception of matter is to be explained universally, and therefore as applicable to moved bodies, this definition is inadequate, for the place of every body is a point. If one wishes to determine the distance of the moon from the earth, one wishes to know the distance of their places, and to this end one does not measure from any point of the surface, or of the interior of the earth, to any point of the moon at pleasure, but takes the shortest line from the central point of the one to the central point of the other, and therefore, in each of these bodies there is only one point that constitutes its place. Now a body may move without changing its place, as the earth in turning on its axis; but its relation to external space changes notwithstanding, for it presents for instance its different sides to the moon in the course of the twenty-four hours, from which all kinds of transformative effects result on the earth. Only of a movable, i.e., physical point can one say: motion is always a change of place. It might be objected against this explanation that internal motion (e.g., fermentation) is not included therein; but the thing which one speaks of as in motion must so far be regarded as unity. That matter, as, for instance, a cask of beer, is in motion signifies something different to the beer in the cask being in motion. The motion of a thing is not one and the same with motion in this thing; but the question is here only of the former. The application of this conception to the latter case is afterwards easy.

Croizat Method 






  On Panbiog-L  

    More optionsFeb 20 2009, 2:47 am

From: Crawzat <>

Date: Thu, 19 Feb 2009 22:47:52 -0800 (PST)

Local: Fri, Feb 20 2009 2:47 am

Subject: Ghosts of Gondwana and Vicariant Time

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"Nothing wraps a man in such a mist of errors as his own curiosity in
searching things beyond him". Owen Feltham Resolves (1623), Of
Curiosity in Knowledge , p.xxvi
Members may be familiar with George Gibbs' 2006 book "Ghosts of
Gondwana", reviewed by Grehan in "Biogeografia". Grehan's review is
too diplomatic for Gibbs, like Morrone, is a recuperative decadent
with an even more ambitious plan - to synthesize Darwin and Croizat,
dispersal and vicariance through molecular clock-time: "The title of
his [Croizat's] last major work "Space, Time, Form", held the clue to
what was missing in his approach- the time factor. Clearly we need an
idea of when each particular biogeographical event took place in order
to be able to match it with the everchanging map of the world. This is
now becoming available with molecular clock analysis and improved
means of dating fossils" (Gibbs 2006:44).
Gibbs' concept of time in biogeography as a particular
palaeogeographical and/or fossil molecular clock-time is impoverished:
it immobilizes`and spatializes time as a binary opposition of late
Cretaceous-Paleogene Gondwanic vicariance age against a post-Oligocene
trans-oceanic dispersal age. But to Croizat biogeographical evolution
is the flow of life by form, through time and in space, along and
amongst the rifts, cracks, fractures and fissures of the earth - a
general process of becoming, not being, over the sum of
palaeogeographical and present space. Gibbs confuses the concept of
age with that of time in Croizat : "Let us conclude then that nothing
can be taken for granted and that time in evolution is not tantamount
to age...." (STF, p.6). In a very real way age and chronology are part
of the concept of space in Croizat.
The passage or passing from a molecular clock-time of vicariance or
dispersal in particular ages/epochs/places to an understanding of
vicariant time is the death of Darwinism, and entry into a vicariance
of times :
"Immanency is the supreme standard of life much sooner than particular
motion and change" (STF, p. 549).
Why pose and publish Gibbs on an author you have never read, let alone


Comparative biogeographers argue that big biogeography must come together over areas.  This will not work.  There has to be both biogeographic and geographic congruence. Time is not adequate here and here is why, creationism.  As Ebach and Parenti note area endemism was originally thought of as separate creation.  Creation scientists have their own way of understanding groups of creatures in the mendelian populations and as biogeography works it way from a discipline of past distributions to future ones the geography that creationists may develop without an evolutionary history will have to incorporated.  This will be worked out as population genetics and biogeography are more fully integrated.  Example with snake baramins and eco-justice populations.


My own understanding of biogeography however is actually an inversion of the statement (page) “Without a biogeographical classification that incorporates natural biotic area groups based on a phylogenetic classification, we must explain each incidence of conformation to a pattern as if it were not part of the pattern.  In effect we give up the opportunity to compare.”


This  is true in a popular way of thinking.  Axiomatic panbiogeography however was the attempt to reach back through what counts as “area groups based on phylogenetic classification” to the invidual conforming incidences.  It suggests that there is a science of biogeography available by starting with incidences and getting the patterns.  This enables math itself to be a tool for the biogeographer and sets the context that biogeographic thought resides. This prevents a religious content from dominating the patterns recoverable but also suggests that there is a law like behavior in biogeography and not simply a qualitative earth and life evolve to gehter as could as well be applied to Margulis’s notion of Darwin’s “Check” in endosymbiosis.


Parenti and Ebach write (page 43) Area homology differs from the concept of spatial homology sensu Croizat (1952): the spatio-temporal relationship among areas considered independently of biotic relationships

The notion of “independence” as referred to AND used, however confounds the distinction made by Kant in his Introduction to Logic between something that can be judged based on verisimilitude or probability (By probability we are to understand an assent from inadequate reasons, which however bear a greater proportion to the adequate reasons than do the reasons for the opposite. By this definition we distinguish probability (probabilitas) from mere verisimilitude (versimilitudo), which is an assent from inadequate reasons in so far as these are greater than the reasons for the opposite.”(Immanuel kant Introduction to Logic  Philosophical Library New York 1963)). As Kant said, “contrarie opposita” may both be false, propositionally (Kant op.cit. page 62).

Croizat’s 1952 notion of space is never an opposite of biotic areas as cognized by comparative biogeography but two area homology proposals may be contrary opposites and thus both not true(the opposite case may go across the goal of monophyly not achieved).  They need not be but they could be on Kant’s logic which only finds opposites subject to verisimilitude while no probability need apply (independent or otherwise) . This conceptual distinction is also responsible for the inadequate assertion in Comparative Biogeography that apparent temporal divergences have no a priori basis.  They failed to make clear what the difference of synthetic and analytic apriority is or is not.  It is true that prima facie divisions of distributions into ages makes the finding of patterns difficult and may even be at odds with technical stoichiometery of various methods it does follow that one need claim there is no a priori basis unless one was committed to a definte non-concept of separate creation for an area of endemism for instance. Even that may not be sufficient, logically.

With a further developed panbiogeography some amount of taxonomic projection in space should not be out of order.

This is where and how the notion of spatial evolution comes in.  Croizat knew it.  Above was a partial framing of it within Kant’s metaphysics


"A perfectly elastic collision is defined as one in which there is a no total loss of kinetic energy in the collision. An inelastic collision is one in which part of the kinetic energy is changed to some other form of energy in the collision. Any macroscopic collision between objects will convert some of the kinetic energy into internal energy and other forms of energy, so no large-scale impacts are perfectly elastic. Momentum is conserved in inelastic collisions, but you are unable to track the kinetic energy through the collision since some of it is converted to other forms of energy. Collisions in ideal gases approach perfectly elastic collisions, as do scattering interactions of sub-atomic particles, which are deflected by the electromagnetic force. Some larger-scale interactions like the slingshot type gravitational interactions between satellites and planets are perfectly elastic. Collisions between hard spheres may be nearly elastic, so it is useful to calculate the limiting case of an elastic collision. The assumption of conservation of momentum as well as the conservation of kinetic energy makes it possible to calculate the final velocities in two-body collisions. (University of Waterloo, 2010)"

What we are to investigate is how evolution’s form is different depending on whether the population of genes be considered as elastic or inelastic.  Fisher thought there was some comparison but the form of his notion of sexual selection under runaway is not a compatible with tetrational view of socially selected social infrastructures given alternative  series of changes as illustrated by Wright in 82.

We will locate where in these relationships between genotype and phenotype the mean free path and the virial are for gradients of elastisity under common repulsion and attraction. This falls within spatial evolution when the difference of wild gene vs wild type per morphology of domestic vs natural phenotypic variance is ignored. This is an environment of translations, reflections and rotations wherein a volume (of energy) can be decided (without regard to texture and figure) if a wavelength can be extracted (and bounded).  The frequency of  which can be used to connect Kimura's through Haldane's in between Fisher's compared to Wright's network.

To usefully think of the heterozygote it is important to consider what Mendel thought.  Olby has pointed out that Mendel did not think of the heterozygote as it has been in genetics well beyond Bateson. He at least pointed to evidence that Mendel’s F1 hybrid vs constant character representations (homozygotes) are not the heterozygote.

So  now Fisher wishes to think of the a heterozygote as possessing dyadic/bilateral variance in either a potential or latent form.  The substance of this form in some elemental materiality is supposed to not disappear when homozygotes are mated but is rather “stored” in some order through which serially it may later reappear. He appears to think that the difference between kinetic and potential energy can fall categorically within his ideas of potential and apparent variance.  Feynmann however simply pointed out that this difference is divisible into elastic and chemical energy which crosses over itself as to forms of energy subject to the 1st law of thermodynamics. It is as if Fisher required that cohesion is comprehendable fully from  no longer being latent and appearing either as a potential or a kinetic energy that may be through inelastic or elastic bindings.  It does not seem to follow however that cohension elasticity in compression need be wholly of the form or shape of chemical energy potentials and kinetics especially because living things do interact directly with  gravity (through calcium in plants) or magnetic forces( magnetitie in bacteria) etc .  So the coheshion will be latent that becomes apparent that is not simply potential but could be moving as moving forces themselves move regardless of any way to store or keept in memory of the possible motions.

This may explain how Fisher did have to correct his equations based on feedback from Wright. It is possible that Mendel had a better idea. This notion was confused by Provine between phase transitions and Wright as a determinist (Laplacian).  No. it is about moving force classifications in Darwin s grandfather's nervous vs muscle dissection.  Huxley explicitly refused to think about this dyanmics elementally. Mendel only had it mathematically.