Phanology — the phenotypic study of genetic expressions across generations

In the 70s the controversy amongst phylogeneticists, phenetists and cladists revealed a need to link pathways of evolution to phenotypic traits being taxonomized and classified. Buried in this debate lay a frustration first voiced by Cook in 1912 over the move to abstract the genotype and phenotype. Cook proposed that in addition to the establishment of gens making genotypes there could analogously to the historical use of latent and patent characters arise a discussion of the phans, expression of substantial gens units into phenotypes as mean statistical averages, terms as originally connoted. Galton sought an exploration into how an ideal type might through expression beyond an unknown deviational limit result in a new equilibrium of regression and dispersion into a new statistical mean. The subsequent history of genetics returned this project into it’s own dustbin with the understanding that evolution is a matter of gene frequency changes and that is all. Despite protestations about the modern synthesis leaving out development and failing to fully explain speciation there was never a return to the phenotypic descriptions in the original statistical adumbration as practiced say by Pearson. Phenetics appeared for time to be bringing attention back to the somatic expressions of organisms but in the end cladistics raised the bar by including evolutionary history such that Cook’s original idea was nair to be found. And this is because the spherical properties of the Earth’s revolution and rotation in the gene pool of a high enough level of phenetic taxonomy along geodesics cross the hyperbolic space of organimsal histogenic developments ancestrally from the cells combination of multiple chromosome biochemistry of the ecudeianized gene effects via RNA etc….By using gene pools with spherical geometry we can show that every and anything that can come and go into it transits from the parallels meeting up at poles in which divergences in the chromosomes connect with the hyperbolic perpendiculars of level of organization cells. With this we may be able to predict the future of a population. It is the RNA that makes hyperbolic link to the Eucldedian as the lat long crossings of populations back do it to DNA.

Instead, we find Taylor noting in 2018 that Johansen never a gave a definition of the phenotype or the class extractable genotype recognizing the practical issue of composite genotypes and naturally varying phenotypes. And by calling on the need to engage an understanding that the consequence of the abstractions into which instead DNA and traits are denoted Taylor identified the nexus of the geometric and organic in the use of gaussian normal forms in biometry which can be gain said at a first approximation by a four dimensional consideration of parent, offspring, phenotypic mean and standard deviation — so as to get the genotype class in the transmission phenotype. By forming a hyperbolic statistical triangle from the generant to the parent and offspring on a minmal surface triangle that approximation tologically and algebraically is connected by the postive and negative correlational connections. All of this is embodied in a mendelian transmission of Euclidean gene recombinations distributed out of cells exploring hyperbolic space into small and large populations that by dispersal and vicariance transit a spherical space of the Earth reproductively and selectively as the the Sun gravitates the same.

The recent proof by Perlmann of Thurston’s geometrization conjecture lead Curtis McMullen (https://www.youtube.com/watch?v=v-bpGe3f4VQ&list=RDLV4jdmkUQDWtQ&start_radio=1) to suggest that all forms of any living thing past and present could be described in the language of 3 manifolds. Here I attempt to develop a branch of biology called phanetics which seeks to represent the gens not as genes but as causally transmissible genotypes that when expressed somatically give rise to statistical life forms.

Beginning with a hyperbolic statistical synthesis of parent-offspring transmission via triangular standarizationing of the angle of parallels the regression “line” is converted into a manifold 2 surface from which

I show how linkage groups can be denoted as knots of phanic Galtonian regressions enumerated by the value of the knot complement of the 3 manifold it exists in and I show how using Mendelian and Ancestral Law genetics (newly described) that the expression can be read from the genotype itself. I then apply the theory to the growing discipline of genomics especially in the area of medicine and disease. With the geometrization of the genotype in the phenotype, as the groups of individuals they belong to, it is possible to reply to Galton’s “The limits of deviation beyond which there is no regression, but a new condition of equilibrium is entered into, and a new type into existence, have still to be explored” because the modes of a phenotype differ from it’s means depending on the population it is asserted it regresses to and progresses from. Thus, rather than going historically from the end of regression to the gene we go from the gametic-somatic correlation to the phan.

The Wood Wide Web, the return of the statistical Erscheinungstypus phenotype, and direct causation of offspring variance from ancestral Anlage genotype means periodically selected.

Hyperbolic Statistical Analysis applied to Roy’s data

Johannsen's insistence that the personal phenotype of the parent in no way causes the offspring’s traits is false when Pearson’s progressive evolution beyond Galton’s regression from generants includes extremists correlated with cross family homotypic differentiation of organic correlations of Mendelian traits per biotype. This can appear as subindivdual offspring variance periodically selecting of adult means which simultaneously are the correlated with extremal exogamies and modal endogamies. Apply Kolomologorov…

When excess offspring variance ( beyond the mature parent values) causes exogamy, selection against this in the same parallel direction as ancestral contributions during inbreeding syngergistcally/harmonically add to effect change, from one equilibrium to another and may do so despite a synthetic paring of any of the traits because the family variation of means and standard deviations support alternating cycles of endogamy and exogamy no matter the mutation.

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This can be demonstrated with the ancestral influence via mother trees of the wood wide web with particular seed tree monoplyies in which the offspring variance that is selected against, are from traits that tend to have the offspring not attach to the microrhizal network. Thus periodic selection for offspring attaching to a network prior to maturation results in a shift in the parental means not from the parental mendelian transmission of genes but from the ancestral influences in the mother trees , due to centralizing networking of connected offspring ( Johanesens’ central something)…. The degrees of connectivity of the extremes of the offspring thus force cycles of endogamy and exogamy as the network grows over (this) time and the extremists meet challenges by non-kin and other species and the network itself.

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The extremists can in some cases cause the formation of a new network by not participating in the existing parental/ancestral one and force increase endogamy of the existing relatives ,depend ing on social vs sexual selection... But when periodic selection on the offspring decreases this effect, the network that identifies with the family members over other families can have the parents directly cause the tendency towards extremism (higher variances) in the offspring and this is effected by seed distribution from the parent spatially around it.

This can be developmentally controlled by differing fiboniannci spirals of dispersal which changes the mean without changing the variance.. due to modal increases in the periferphy symmetrically of the means. Antisymmetry provides organic correlations amongst the homotypic correlations within.

This might be shown by seeds dropping from different parts of pine cones on different parts of branches which have cytoplasmic effects in the seeds themselves. ( germinal differences ? from tetrads??) or in Duckweed stipe causations.

From this we can biotype the abmodality of parent and offspring.

Let me explain what this Phanology means

“the more concrete application of phenotype previously made” Whatever it was that was made it was any as others said or an “apparent type” Erscheinungstypus. As we understand what the phan phenotype is we will continue to keep the Anlagetypus or germ-type as abstract genotype non operational until the classification of forces is reached. One fact at a time.

So we keep the major term genotype to be what Taylor and Lewontin mean but we will revert more and more through that’s germ type to an Anglegetypus which has only bifurcatability.

Phanetics is to establish a tradition from the words of Cook 1912.

Cook’s basic use of the phan syllable is to format Johanesen’s later named synthetic genotype of paired heterozygotic traits. — isophans.

These are not the traditional statistical mean phenotype of unity ( in the sense of Pearson’s correlated organs) but is synthetic that can be analyzed back into segregants of distributed isogens.

Phanology enables us to discuss heredity between these isophans by a form of phanetic analysis. The result is that Johanesen did not have a patent on “all true analytical experiments in questions concerning genetics”

It will be the notion that Lewontin and Taylor are working to establish pure line facts but here we will keep to the pure line theory of Johansen in order to turn phanetics through phenetics into phanology.

The chief first point is that adult personal structures do as developed histogenically cause offspring characters abstracted as traits or otherwise personalized ( cladistically).

Thus Phanetics works to disprove Johanesens “The personal qualities of any individual organism do not at all cause the qualities of its offspring”

Swarms of constant biotypes need to be worked back to Galton’s use of numeration per stirp vs Weismannian germ particles so as to get force vs atom. Quality vs Quantity.

What we do is to bring back Pearson’s homotype to differentiate homogenous and heterogenous populations and doing this, without reference to any race.

Instead we find way(s) using the genotypes to bottom up define the generant in which species may have multiple biotypes synthetically dependent on ancestral affects across parentages that possess mendelian and non mendelian abmodalities between parent and offspring.

Once forces are reached and higher Linnean categories are correlated into the Pearsonian constants, then the genotype can be distinguished externally from the phenotype and topology will spell out the negative and positive curvatures per evolution of dominance.???

Thus we will not oppose the genotype conception to the phenotype conception but show how, phenetics and cladistics contribute explain (what) evolution adapts? To spatially.

Constructing ( this) Adaptation

Lineages adapt to the space beyond the natural environments of their ancestors by progressively entering hyperbolic niches otherwise linearly metrizied by mendenlian genes in eucledian cytoplasms.

The cytoplasm is eucledian with respect to the location of mendelian factored gene (divsions) on the chromosomes but the apparent statistical type moves the cytoplasm mitotically and meioutically out into hyperbolic space by avoiding the environments otherwise inhibiting growth into them by viruses and pathologies.

Lewontin was famous for proposing that organisms construct their environments rather than niches’ preexisting to which an organism becomes adapted during evolution. By considering evolution’s environment as a three manifold made up of 8 different geometries ( not Dobshansky’s beetles for Hutchinson) it is possible to refigure Lewontin’s construction as adaptations to different preexisting differences in the geometries relative to the genealogical lines the individual is apart of.

“The standard deviation and coefficient of variation express in a pure race mere temporary conditions of no consequence in heredity. If we could make all conditions of growth and environment the same throughout our pure race, all the evidence indicates that the standard deviation and coefficient of variation would be zero, and this is the positive value of their assistance in determining what shall be the characteristics of the progeny.” -Jennings, AM ER. NAT., 43: 333, 1909.

The biotype can be defined without having to assume a pure race. And this is when the individual has both a mean and standard deviation as found by initially by Roy and Haldane. The zero variation of Jennings is only the notion that the 4-D ring can become the unknot ( becoming zero by deformation of the space) but this does not mean that race is thereby circumscribed nor the zero condition a regular phenomenon. Only that the traits so measured by the zero can be independent of others for the individual in the same biotype ( which never strictly a race at all but a set of relatives). (expanded idea of meaning of lines and points (dualities) per parallel in norms of reactions.

It appears that we might be able to describe the basic idea Erscheinungstypus of the phenotype as the hyperbolic volume of it’s Anlagetypus genotypic knot link. This can retain the original idea of group mean, and may even be able to dissect the polygenic vs alleomorphic variation in the chromosome positions of genes.

The issue of continuity in consideration of the difference of a biotype and genotype is null given Cantor’s design of continuous motion in discontinuous space and shows that removing the statistical basis of the phenotype is mistaken. Irrational numbers are not typological when attached to individual differences which may be due to very small genetic sequence differences, contra Lewontin on the origin question.

By progression of genotypic smaller and smaller differences when homozygotic recessives do not stop the cycles of endogamy and exogamy it is possible to have in this hyperbolic space, the progression stop the regression, during the back tracking caused by increasing ancestral influences (( despite the view of Lewontin and Talyor for any reintegration) ((as their view) depends on the metric from Struvevent of the linear gene)). With multiple chromosomes and all kinds of crossing overs the gene0typtic differences that Johansen thought (genetics should being skeptical with) can be described and all of genetics is subsumed in the apparent phenotypes’ Erscheinungstypus for the actual phenotypes (history of statistical phenotypes Galton onward off of Quetlet (Statistical man) for any cohesion.

Continued inbreeding in which only environmental variability remains, puts the biotypes thus obtained, at the limit of the genetic effect of disease and thus needs to understand pathology genetically ( of double heritages without sex’s twos of Galton) and continue to parse the gentotype molecular biologically no matter the quantitative genetics. This can be done with correlated mutations within copy variants expressed in the quantative genetics.

Pearson’s conclusion on origin (of species) after much inbreeding was speculated without knowledge of expression of phans based on central dogma of molecular biology which with increased ancestrality back tracks the information flow of the minimal factor units on chromosomes. Introns may be further genetic differences to avoid past pathologies. The pathologies interdigitate in the chromosome chemisms between two functionally unified correlated mutations ( for 3d location of the mutation on the protein).

We need to a theory of dominance ( relative to pathology and deviance) based on this continued parsing of the biotype, based on statistical phenotypes which includes gene sequence molecular biology. Disease will continue to produce lineages ”not itself” even when only environmental fluctuating variation remains in homozygotic forms. There may be some apparent “orthogenetic” effect ( orthoselections ) over long geological time if the ecosystem interacts with all lineages. These effects and deformations and deviations thus when the translation and transcription of the phan expression is not-critically-altered-thus, enables species to continue even in extremes where extinction looms. Whether they become different species or merely are able to enter new cycles of endogamy and exogamey requires much research and discovery to find out. In this we work out why it is the Johanesen’s beans had a mother-daughter correlation of .5 to .6 rather than 0, by doing the parsing mentioned above.

The germinal cells of these homozygotes are not identical precisely in the unused copy number variants and in nocoding DNA and in introns with respect to the basic machinery of translation and transcription (metabolism and electron transfer and chemical macrons) and Pearson’s determinantal theory based on Weldon’s notes.

Viruses may exist to enter the hyperbolic space going beyond the linear cytoplasm of hosts’ chemical distributions and could be “evolutionarily physicalities of transspecies ancestral transmissibilities” .

This may be the function the tetrahedron-octohedron geometric capisd and explain the metabolism of giant viruses phoronomy. The adaptation may be constructed in the introns or the noncoding DNA or the copy variants when not segregated!!..as Johansen previously appeared to warn appropo, “but there may be even very narrow limits for this analysis: the entire organization may never be “segregated” into genes! But still there is much to do in carrying through the genotype-conception as far as possible.”

Hyperbolic space mapped to different 1-D segments.

Here with Johansen there is no decrease/simplification in the anlagen during development rather complexification and differentiation of the homotypes that are decreased by increased ancestrality to the parentage as explained by Pearson.

“Weismnann and others, who have suggested that ontogenesis is partly determined or at any rate accompanied by a progressive simplification of the “anlagen” (as we say the “genotype-constitution)” Johansen

Thus developmental sensitive periods are ones in which homotypes differentiate depending on extant organic correlations — in the decreasing variance that can not go to zero comparing the adult and offspring for any periodic selection.

Hyperbolic rules of the cooperative organization of eukaryotic and prokaryotic genomes

Different siblings (same or different pockets) can produce different homozygous line homogeneities of “race” since the homogeneities are smaller than the population as a whole( just sets of relatives ( no relation of genotype to race) and yet the differences will be non-inheritable but not somatic. They are of the nature of the generation and due to the occasional sexual combination (exogamy from two different endogamies). These are not biotypes which are those at the level of the population but are statisical phenotypes nonetheless and present in the wood wide web as well.

This appears because there are levels to a phenotype including higher levels ( multilevel selection).

So because we have a generant and parentage for a group of relatives that may vary independent of the race or geographic differentiation it is a part of , the offspring will possess periodically selectable variation in excess of the said set of genotypes due to the geographic distribution (race)(biotypes that vary by geography) !

When these variation(s) contribute to the somatic characters they alter the relation of the variation to standard deviation of the relatives to ( selection’s Yule) asymptote of the selection as a whole ( between the set of relatives and population and race ( within a species).

Is current racist mania caused by Marxism?

“So has Johannsen’s theory of the genotype as something fundamentally different from the phenotype somehow slipped away without notice?” Taylor

No.

If the fluctuating continuous variation be defined as the evolution of dominance (from a hyperbolic S2 into a third manifold dimension) of a genotype for any deme of phenotypes within the given species (interms of the 3rd dimension from a half plane surreal number line of full recessives and full dominants) and these polymorphisms can be associated with regression of the 2 parameter parent offspring minimal surface tetrahedron, then a tiling between these two representations defines the phenotype missing from Johansens’s original definitioning caused by only access to differences.

The implied cutting of a hyperbolic manifold leads to the knot presentation for the phenotype-genotype relationship and enables one to build a DNA to trait context for the expanded content this development of the notions remands(ing) to the historical shift in meaning observed. By using the homotypic and organic correlation instead of classes of absolute geometric divisions the return to Galton’s use of the “type”( under equilibrium of ancestral regression and family dispersion) is replaced by attractor dynamics of macrons to mediate the connection of the chromosomes to the new model for both the phenotypes as knot complements and genotypes as knot links as the realist empiricism missed as the shift occurred(and ) the reinintegration going (goes)forward and Lewontin’s use of a personal “Darwin” is criticized.

Selection can change the aspect of the evolution of dominance but it can not preclude whether it is recessives or dominants that can sweep a structured population into the original direction of a new species nor can it prevent speciation by vicariance ( of the environment ( under vicariant time)))).

Hyperbolic distance vs angle compared to Eucledian.

“Notwithstanding his definition of “phenotype, no method is discussed in Johannsen(1911) to divide a natural varying population into phenotypes, let alone identify a genotype-as-class in such populations. It is in the restricted realm of his inbred lines of beans that identifying genotypes from phenotypes is possible, albeit not reliably if a phenotype includes a mix of inbred lines.” Taylor

Phenotypes under the Geometrization of 3 Manifolds

“By using the word “phenotype” to mean the prominent statistical center of a group related organisms”(Phenotypes, genotypes and Gens, Cook 1912) it is possible to topologically contain Galton’s original notion of regression of parents on offspring within the geometry of three manifolds in such a way that genotypes may posses causative properties towards the establishment of phenotypes both within organisms and within the group being related. This provides “a concrete sense” (op cit Cook 1912) for the genotype. This new property of genotypes returns, the germ-type or Anlagetypus to it’s developmental linguistic. Here the genotype does make an appearance in pure form from which genotypical (Batesonain differentiate difference in complaint with Pearson’s homotype) differences are derived as already discussed.

From this new theory of anlgetypus on can work to answer Pearson’s need to have an understanding of germinal potentialities which are caused by immature development as the reproductive tissues form.

With this new complication into the relation of latent and patent characters it is possible reason back and forward across generations because transmission and expression are connected by the geometrization of the phenotype as the knot complement space to the genotype as the knot or independent rings not knotted. A totally new biophysics where the knots can cut and reform appears as the offspring process on the gametic -somatic correlation (transversality topologially wise )and a theory emerges that can begin to understand the complicated genomic structuring of coding and non-coding sequences.

Different germinal differences create different distributions for a given gametic-somatic correlation which result in genetic differences that may be expressed as genotypic geometrizations from the phenotypes the somatic cells build. The separate units or gens are not the genes but are the places through which the knots are cut and formed. This provides a complete statistical means for phenotypic unifications of multiple traits genically. The computation of the knot complement as the phan of a gen expresses the theoretical direction first suggested as far as I know by Cook in 1912. Offspring phan expressions may cause panmixia and provide explanation of Roughgardian social selection in the place of sexual selection.

PHANETICS as an alternative research program for reintegration of developmental mechanics and ecological interactions into experimental biology…

One approach is to frame the reintegration from the genotype-conception in opposition to the phenotype conception, but given the correlation of gametes and soma in individual lineages, it is possible to observe from immature offspring variance selected, during growth and development across a range of geographies, different divisions of total population variance such that via hyberbolic statistical analysis, both developmental influences on whole geneotypes and ecolocically constranining and determining interactions, can dynamically subset from the phenotype-genotypes thus being under experimentation an d so experimented with… So terming this concretely as phanology ( Cook 1912) and incorporating both progression and regression in the sense of Pearson ( 1930) it is possible for evolutionary biologists’ to experience this new means of accessing past changes, to lineages in current natural species endemisms (populations’ selections).

By not discounting transmission of phenotypic traits it is possible to describe genotypic difference ( heterozygote vs homozygotes) in ever larger theoretical foregrounds that compound the differences in hierarchies of similarities. This is only possible by being able to describe the expanded population space of different sized populations. That is something that can never appear by the process of differentitiating organic differences genotypically rather than homotypically classifiying similarities phenotypically ( first begun by Haldane in India) because the F1 — F2 vs F2-F3 etc have different statistical life forms.

Furthermore, the apparently forced higher Linnean classifications may through such research acquire classifications of forces that further show how genotypes and molecular genetics are not the only disciplines that move a species from one type to another. A new domain of phanetic biophysics made of electrical, physical and chemical macron interactions is in the offning which may accompany molecular genetics in the work of using genetic variances to understand evolutionary change in quantitative genetics whether by strict breeding controlled praxies or reintegrated abstractions reworked into the concrete lineages found extant on Earth.

By focusing on reiterated subindividual variation, selection of excess immature variance, and Pearsonian dissection of population heterogeneity into homotypic and organic correlations, given a provided gametic to somatic correlation, there is no need to reintegrate abstractions genetically to obtain a better understanding of evolving natural populations that otherwise could be investigated by denying the existence of ancestral ( transmission) influences (the establishment of Remianian metrics coordinated with such ancestral influentialities).

Understanding the norm of reaction via dualities of points and lines

In the debate between Woltreck and Johansen it was observed that environment-trait graphs show somecase confluent rather than parallel relationships between genotypes/biotypes. Johansen maintained that provided there is some difference in the lines per environment it does not matter if genotypes overlap in some places. If a set of such lines possess point — line dualities they may be unified into a homogenous treatment and it could be possible to relate the different genotypes to common biotypes of the individuals involved. If the indiviudals are part of a monophyly in which speciation is determined by the relation of the dual between a point a line in a set of populations framed via hyperbolic projective geometry then it is possible for such clades to superscribe their phenotypic biotypes thus associating genotype and phenotypic for any mutation whether inside the biotype or out.

This enables one to define a discontinuous variation space when point line dualities in the reaction norms are identified, which can be continuously selected from. Fluctuating variation appears as the mutational effects due to out of biotype/population extreme deviance BETWEEN ELEMENTARY (Devries) SPECIES. By finding a Remanian metric unit the phenptypic distances to the genotypic angles permits access to cladal morphospace of these so called elementary species from their compounded biotypes of known populations.

Reversion to type is thus modeled here contra DeVries amongst elementary species rather than within. This is because the family not the race ( wolterek’s daphnia phenotype head identifier) is what determines the generant.

Reversion can go to another elementary species if the ancestral influences by inbreeding reach a point mutation outside the current family composition of geneotypes under certain conditions of the size of the flat ellipses within the current family composed biotype (relating the selectable genotypes and current phenotype). These are not strictly speaking “environmental” effects but rather are topological properties of family compositions to variance in variabilities per means and address Edgeworth’s reference to Pearson no matter Venn criticism of the logic.

Short and broad forms of Johansen’s beans (elementary species) are different individual variants for different family sets of flat ellipse variants.

Transgressive phenotypes (Wolterek) possess common point line dual genotypes.

The reaction norm can be put in a hyperbolic projective geometric space from which the distance among and between individuals'’ phenotypes can be related to biotypes (sets of genotypes) by a Remanian metric of the relevant phenetics.

This formats the reaction norm but it is the relation of the angles it produces to the angles within the cladistical distances of the individual phenotypes separating family members that is transmissible across the generations (and whatever the mutations may have been and may be phylogenetically). The reaction norm is not the phan (or phenotypic potential) of any given genotype. Rather the bifurcative genotype (Johanensens criticism of wolterck) simply locates the eculedian distance stretches that could scale during development from the zygote. It says nothing of the angles wither in the soma or between family members in a deme, no matter the Woodger development. It was a mistake to use Weismann’s concept because one needs to pass instead the Galtonian stirp to the“genotypic” = autogenous, “phenotype” = ectogenous forces for any Russell. That mutations have no relation to the environmental circumstances only means, that they may be within or without the potential infinite growth of the population of organisms in which the mutations may or may not appear Fodor wise. There can in fact be environmental dependence of biotypes (not genotypes) when the genoytpes are ecosystematically parallelized by extra biological chemical heritages sustained by geological processes or viruses (on bacteria).

One can thus show that the historical division of heritable and non-heritable variation is not sound, as there can be a hierarchy of sets of point -line dualisms in which something is phenetically non-heritable for a species within a genus (precisely as the abstract genotype-phenotype distinction models) becomes heritable for another species in the same family given cladogenesis of such phylogenetically extant existent into a higher order dualism to be able to appear.

Part of getting there requires the distinction by Johansen of surface phenotype from its more fundamental level description. I started a college scholar program at Cornell to sketch what a multilevel phenotype of snake scale variation could look like ( from levels of kertain proteins to microscopic scale variation to scale level discontinuous and continuous variations) but this was rejected as not capable of getting me into graduate school. These “organic units” of Galton in terms of Johansen’s bifurcation from genes once connected to monoplyetic speciations, permits the discovery, if it is to be had of these levels of point line dualisms linking geneotypes to biotypes via norms of reactions to be…

Wolterk is correct that extra biological inheritance of reaction energies to the chemicals within these multilevel variations shows that genes do scope out the full relation to the environment but he need not get holistic only (just) show that repulsions and attractions both operate within biological inheritances to connect these environments no matter the extra monoplyletic heritages or lack thereof there. Multilevel phenetics yields not only subindivual variation affects but also cross phyletic biotypic inheritances of energy form transgressions“genotypic” = autogenous, “phenotype” = ectogenous. This gets to the other thing I have been working on for years — extraction of energy from two different phenotypes based on genotypic differences.

Germinal structures of these are not unalterable. Yule on somatic non-heritable variation are alterable from said germinal potentialities of Pearson across all phenotypic levels for Woodgers forward and back embryogenic relations (to and from taxonomy from zygotes functors). These require particular hypotheses that Johansens held back from but that quantitative genetics went forward to find. We get at this by modeling the surface of the statistical metric by using distances for phenotypes and angles for genotypes per Edgeworth on Pearson’s multiple organs correlation.

Johanesens’ apriori genotypical differences are the two trait infinitesimal- infinite connected 2 surfaces of parent offspring in a population of families.

The use of hyperbolic statistical analysis applied to this description of regression and progression can partition phans (expressed gens) of genotypes into phenotypes that may or may not possess mendelian representations. Breeding experiments can further refine the syntheses afforded and pursuit of those possibilities follow. This methodology obviates the need to fully understand the past instances of cycles of endogamy(with respect to identifications of genotypes and phenotypes) and exogamy which are otherwise necessary when sorting out part genotypes from its whole ( this is what “removing the abstraction” seeks to obtain by convoluting symbolically and terminologically and logically the relation of molecular biology to quantitative genetics). The 4d deformable space of offspring, parents, mean and variance topologically cover these cycles through theoretical deformations to the unknot ( under regressions and progressions ). I show how to do this with duckweed which is becoming a desirable new agricultural crop.

Here we set the error variance of the offspring as larger than the parent (both in Pearson’s periodic natural selection and Galton’s familial dispersive effects) and use these in balance with the equation error of a linear parent-offspring regression (gametic to somatic correlation of known value) to determine under what set of genotypes per a phenotype ( of generally variable means and standard deviations) such that the balance achieves a new basin of attraction progressively ( different amounts of ancestral influence) on inbreeding.

Hence the metric is associated with the population structure of demes. The genotypes are assumed independent of the cause of switches between endogamy and exogamy (instead those are subsumed in the error variances of the parent and offspring). An example from nature is presented. This is visualized by knots in 3D of offspring-parent-means that become an unknot in 4d once the(progressive) variances are determined ( under the effects of different mating systems). Thus the mean curves and variances distributions determine the attractor format and given a specific amount of periodic selection progressively change the equilibrium into a new Galtonian balance. The importance of not getting rid of the older transmission concept and the genotype expressed phan is stressed for furthering the reintegration of molecular biology and quantitative genetics with development and ecology. Under an assumption of regression-progression the transmission equation error can be considered minimal for a so obtained somatic to gamete correlation and thus the variance errors function to as much as the scalar mean change does in forming the deviation forward and backward across generations.

“His creed for exactness was a weapon against biometricians who, Johannsen thought,measured precisely, but measured the wrong thing. “Exact biological analysis” meant indeed forhim “the fundamental distinction of true type differences and fluctuations” (Johannsen, 1907,110). Ignoring the existence of biotypes, biometricians worked with ill-defined categories. Interestingly, Johannsen illustrated this point with an analogy taken from the industrial world ofthe second industrial revolution:If anybody makes a study as of the speed of the railway-cars, the botanist noted, he will ofcourse regard every train or type of train separately: express train, local trains, goods trains and so on. (…) But what would be said of an enquirer who, for solving the problem, collectedstatistics as to the speed of the different carriage-classes (…) and by this method found outthat the average speed of the first-class car was much greater than the average speed of thethird-class car — for in the express trains (in the continent at least) there are only (…) first andsecond-class cars, while in the local trains the third-class cars is the majority (…) I must confess that the main part of biometrical work in questions of heredity somewhat resembles suchpreposterous statistics. (Johannsen, 1907, 99)”

https://www.mpiwg-berlin.mpg.de/sites/default/files/Preprints/P343.pdf

“ This can help historians to avoid the plot of the hybrid corn as a Mendelian success story (Bonneuil, 2006) and sharpens the analytical distinction made earlier in this paper between two ways of stressing stability and permanency in biology and heredity by 1900: one taking the hereditary unit or gene as the immutable unit, and one taking the biotype as he immutable unit. These were in fact two “stabilisation” strategies that both emerged from th ewider drive to reshape life in a new industrial time-space of flows. We have developed this argument in detail in this paper as far as the “biotype” or “clone” strategy is concerned. But thesecond strategy of singling out and stabilising immutable genes for valuable traits (disease resistance, productivity, chemical composition adapted to industrial transformation, etc.) has done a similar and complementary job: it has allowed to put “hereditary units” in circulation within a global scientific-economic network of plant breeding, where they were reassembled p104Finally, I must confess a major hole in this article: the material practices have only been superficially discussed here, even though they should be documented in any comprehensive cultural history of the birth of genetics. Although the geneticists of the turn of the century promoted stability and purity as a constitutional and intrinsic property of life (typological conception of biotypes and structural view of purity as homozygosity), they knew, as well as historians know, that the production and maintenance of these pure forms of life necessitated hard work, industrial scale observation and treatment of minute differences, and standardisation activities. As shown by Kohler (1994) with the production of the standard Drosophila, with a stable rate of crossing over in every part of the chromosomes, the coming into being of pure life forms rested upon labor-intensive and capital intensive “networks of purity,” being elements of the control revolution. So an entire aspect that should have been addressed in a more comprehensive essay on the cultural history of early 20th century genetics is the question of the transformations of the material practices of observation, recording, book-keeping, processing and manipulating that were associated with the shifts we have described. Although we have a few good pioneerin gworks (Kohler, 1994; Rader, 1999; Löwy and Gaudillière, 1998; Müller-Wille, 2005)”

The view of biotypes here is not typological ( as Mayr would so criticize it) but depends on the size of the population it is in ( no race).

We are able to distinguish clones and biotypes because clones format on different minimal surfaces while biotypes utilize a particular minimal surface from which a deviation to the continuity of genetic evolution occurs.

The integration of clones and biotypes permits one, with such a tetrahedronic triangulation to remove the bias in the debate that presumes two sexes and hence two pairs for observing linkable genotypes into biotypes. The pair is actually a dual tetrad with an discoverable finite distribution around the hight of the ordinate caused by infintie, infintesimal permuations and gives rise to the genetic code by the co-relation of anti-symmetry to neutrality of triples for mutations of pyrimidines to pyrimidens and purines to purines.

The “purity” for having equal reactions for any actions is in the macrons connecting the homotypes to the biotypes from which the genoytypes differentiate and mutants form organic correlations through which selected phenotypes may given the metric to extralineage inheritance force in some cases a new equilibrium of.

Homotypes possess compatibility conditions with surface curvature connecting the genotypes and phenotypes they are relative to. The biotype constrains the deviations of positive and negartive curvature to it’s zero from which a mutation can alter and result in different linkages of genotypes into changes of the Galtonian type. Hence the Galtonian equilibrium ( racial regression(progression) and family (dispersion) is directly derived from the compatibility conditions that make the total curvature of the biotypes set of phenotypes and geneotyeps = 0.

The establishment of a new equilibrium is the transition of the curvature hills and valleyus amongst the set of genotypes in the biotypes phenotype into a new zero state. This happens differently for different sizes of popuations of relatives depending on the cycles of endogamy and exogamy or clonal heterozygosity vs biotypic homozygosity.

There is no barrier to using biotypes biometrically. To what extent the change is attributed to ancestral characters depends on whether Johansen was correct or not about the relation of the mendelian alleomorphs being mostly only about abnormal changes from the normal and not similiarlty defining metric of groups of geneotypes for agiven phenotype biotypically derived with purity(by macrons connecting the alleomorph variations to the polygenic copies) of the genotypes involved.

This can be biophysically investigated without having to yoke quantittiave genetics to molecular biology. ( differences of collections of mueseums vs origin continuity).

ABMODALITIES

“ How can there be typical differences, in any biological sense, unless groups are compared? The fact seems to be that Johannsen was not using the word type in accord with biological traditions, but in a loose metaphysical way that renders the terms more abstract instead of more concrete.” Cook 1912

I begin by describing the topology involved and emphasizing Cook’s point that hybrids that look alike but have different germinal constitutions (genotypes) do not possess this complete statistical and phenotypic unitie(s). I then describe the 3 manifold geometry in which these statistical unities of phenotypes exist and develop their genotypes as knot links cut into this space. What name shall be given it?

Phanology denies that independence of mendelian traits implies that a new hereditary transmission plausibly replaced the older transmission conception.for Phanetics describes this independence in terms of knot linkages (along a Pearsonian spectrum of Mendelian and Non-Mendelian transmissions).

With duckweed it is easy to combine consideration of cross generational transmission and development if both the morphospace and population space is the same hyperbolic one in which the meristem sizes and differences are on the same metric as the population growth of family dispersion and regression back to the meristems within!!

The pure line as a purely genealogical concept fails because in all cases it requires the gametic- somatic correlation to be parallel (to the chemistry it is coded in) no matter the groups, family or otherwise being compared. There may be no actual parallel and hence the constriction of the older views seems unjustified. There is yet no clear way from the local geneolgical connections of a pedigree to the phylogenetic monophylies of cladistics.

Maxwell doubted whether Galton’s a priori justification of today’s genotype by substance rather than structure and there really is none. Macrons provide the way to mediate between the structure and whatever of substance in biophysically extant. I show the ancestral influence in duckweed by computing the gametic-somatic correlation for width and length of it’s pure homotypes so at to get the pedigree value of the germ plasm of the within and without pocket siblings because the geneotype conception was parallelized with chemistry but it was unable to discover how the forces of repulsion and attraction chemically bear on inheritance substantially.

“.It seems to me that this autocatalysis as well as the compensative and complemental maintainence of genotypical equilibrbrium in the organisms, present some of the greatest enigmas of organic life.” Johansen

“Here is the issue — with phenotypes, and we even haave met withthe idea, that the Daphnias of a lake may in summer diverge in different races or varieties but that in winter they converge into one single race!”

On the theory designed here ,there is no race but instead topology of trait connections with genotypical knots that possess individuals with different combinations of genes and thus it must be clear that geneotypes and races should never be coincident since the population size matters for the race but not for the geneotype of such phenotypes. ( Wrights individuals with gene combinations vs populations of different genes — that Provine said was impossible).

Johansen actually made this (error) incidentally- the establishment of biotypes with Reimannian metrics amongst environments ( norms of reactions) prevents it to be confounded with the population sizes the phenotypes participate in . There is a difference in the geometries ( Thurston types on 3 manifolds) between the populations and environmental metrics.

“however, has been shown by Riedel (19 for vestigial/wildtype. On this basis the heterozygote and homozygous wild type should behave differently with changes in the external environment (Lutz, 1913; Hersh and Ward, 1932; Riedel, 1934; Stanley, 1935; Margolis, 1935). The effect of very high temperature should be even more striking because of the greater differences in the rates of the developmental processes at these temperatures. Normal dominance relations, dependent upon “nor mal” environmental development, should be upset by heat treatment at particular pe riods in development. These periods should, furthermore, coincide with the periods at which the homozygous wild type is affected (since presumably the same developmental reactions are being affected). The data presented show that this has been realized in these experiments. “Dominance has been reversed”” Child

There is no contradiction here on the theory herein as instead Johansen supposed:

. At the same time itoverthrows totally the idea of “organism as being represented by the unities of the “stirp,” ‘pointing out thatthe personal qualities of the or’gavism) ini toto are the results of the reactions of the genotypical constitution”

Pearson bet that the ancestral influence could be shown in pure genotypeical constituions. I will show it to exist as effects on repetitive dna via epigientic methylation personally ( limiting otherwise changes caused by transposons)

This fails to how that organ as stirp and the geneotype can be connected geometrically and hence organically correlated. By not using the homotypic and organic correlation for the correlation of genes Johanensen was not able to see the theory he missed.

“the instance exemplifies the

two incident matters of fact, viz., that apparently simple

“ dimensional “ or meristic characters may be determined

by several different genes, and that one sort of gene may

have influence upon several differei’t reactions”

Phenotypes under the Geometrization of 3 Manifolds

By using the word “phenotype” to mean the prominent statistical center of a group related organisms

(Phenotypes, genotypes and Gens)

It is possible to topologically contain Galton’s original notion of regression of parents on offspring within the geometry of three manifolds in such a way that genotypes may posses causative properties towards the establishment of phenotypes both within organisms and within the group being related. This provides “a concrete sense” (op cit) for the genotype. This new property of genotypes returns the germ-type or Anlagetypus to it’s developmental linguistic. Here the genotype does make an appearance in pure form from which genotypical (Batesonain differentiate difference) differences are derived as already discussed.

From this new theory of anlgetypus on can work to answer Pearson’s need to have an understanding of germinal potentialities which are caused by immature development as the reproductive tissues form.

Johansen replaced sexual substance for Galton’s two (a priori) sexes and denied personal structuring from atoms but even given Clerk Maxwell’s concern that there are not enough molecules for a stirp, a stirp is different than the genotype. The simple geometrical relationship of a stirp as diagramed by Johansen is rediagrammed above

With this new complication into the relation of latent and patent characters, and a means to visualize the expressed genotypic phan it is possible reason back and forward across generations because transmission and expression are connected by the geometrization of the phenotype as the knot complement space to the genotype as the knot or indpendnetn rings not knotted. A totally new biophysics where ethe knots can cut and reform appears as the offspring process on the gametic -somatic correlation and a theory emerges that can begin to understand the complicated genomic structuring of coding and non-coding sequences.

We replace Johanens’s chemisms (around a chromosome) with chemical, electrical and physical macrons.

Different germinal differences create different distributions for a given gametic-somatic correlation which result in genetic differences that may be expressed as genotypic geometrizations from the phenotypes the somatic cells build. The separate units or gens are not the genes but are the places through which the knots are cut and formed. This provides a complete statistical means for phenotypic unifications of multiple traits genically. The computation of the knot complement as the phan of a gen expresses the theoretical direction first suggested as far as I know by Cook in 1912. Offspring phan expressions may cause panmixia.

If spurious heredity by viruses ( and bacteria?) on genotypes through the germ cells were caused by changes in the expression of genes transcription and trnalsation than the phanological diversity may be influenced by past viral inputs marking the changes detected in the structure of pure genoytpes caused by phanological change. Hence disease of correlated mutations being inserted by coding of viruses and disease states of bacteria is remarkable in history and represents ancestral influences. Viruses may be a normal part of evolution despite their deleterious effect on isolated populations and deaths to indiviudals. Viruses only survive by not killing everything off. This may be a function of evolution and not of viral replication. Interactors not replicators in Gould’s sense. There is a difference between normal and pathological ways of life. Evolution puts the pathology to a point per lines evolved.

This was confused with single point of segregatable heterozygosity. It is only in space of projective hyperbolic space with point and line duality that this difference is clearly available.

The extremes of a reaction norm becoming confluent for various purified strains meet at the corners of the phanological cubes combining the abmodalities of groups of relatives. This is how to bring in discontinuous variabilities but requires the addition of Cantorian continuous motion in a discontinuous space.

“In discussing alternative inheritancewe meet with difficulties of the same nature as in regarding fluctuating variability: the inadequacy of phenotype-description as the starting-point for genetic inquiries.”

Phanology makes it possible to use the phenotype-description as the starting point for genetic inquiries. Pearson tried to start this study and inquiry by calling attention to the importance of the gaemetic-somatic correlation, for evolution by natural selection. By moderating the allmacht of selection phanetics builds from the given correlation of gamete and soma into the potentialities of the germinal constitutions via the offspring effect back on the past generations. By being able to reason backward across generations through the corners under Cantorian continua without spandrels a totally new way to discover evolution is afforded ( by motion of the different geometries on 3 manifolds discontinuous genotypically but continuous in multiple trait continuities of knot links). There is never a need to refer to the special creation of species or to special conditions of reaction norms on biotypes per Lewontins organism creates environment and environment creates organism ( because there something to adapt to ( a difference in the geometries used (per Pearsonian organic correlation ( which is also homotypic) for observed angles)) and yet the higher levels of the taxonomists Linnean hierarchy begin to become available when categorizing the forces of change and the changes in forces.

Johanesen gave himself an out and we shall take it.

“The genotype-conception here advocated does not pretend to give a true or full “‘explanation’” of heredity, but

may be regarded only as an implemnent for further critical research, an implement that in its turn may be proved to be insufficient, unilateral and even erroneous as all working-hypotheses may some time show themselves to

be. But as yet it seems to be the most prosperous leading

idea in genetics”

Progressive evolution into hyperbolic space — a selection story for Duckweed.

Some day, perhaps, microscopic research may haveadvanced so far that from a close inspection of germ cells we may learn something of germinalpotentialities. At present we are very far from such knowledge. In all cases we depend for our

prediction on a knowledge of somatic characters in the ancestry, and further we cannot predict what

will certainly be the nature of any individual, but only the type and variance of the whole array.

By using a geometric 3 manifold to model the regression and progression it is possible to derive Pearson’s germinal potentialities by finding how the type is compounded in the array.

Duckweed generants within and without the pouch. Provide there to be some continued deviations (mitotic differences) in homozygous lines. If the two traits are growth perpendicular to the pouch and parallel with both pouches (width and length), then because the opposite pouched siblings will have different selections of ancestors with extraordinary variations for the same inbreeding some differences in trait variations can continue even when homozygous lines become pure. This bifurcation yields a result in hyperbolic space of relative positions but not in one of Euclidean. Thus once the trait for width and height becomes correlated with pouch morphogenesis new species of duckweed could progress via Pearson’s process because there is enough area hyperbolically to realize such increases without producing lethals (the right or left clones can continue to generate provided the opposite pouch indiviudals mostly die or are never birthed). The right and left clone population growth diretums cut this hyperbolic space enabling the Euclidean homozygous mendelian pure line to neverthesess progress dievant wise into the larger surface area from which more intense selections exist for changes with respect to the Sun position.

Pearson believed he had constructed a comprehensive idea of a single midancestor that contained the whole stirp for any family. He wrote, “At any rate let us preserve in future the good word “generant” for the hypothetical individual who possesses, in the manner indicated by the function U, all the midancestral characters which are capable of showing blending inheritance. Such a generant is a sort of mean man for the stirp, who for statistical purposes represents the whole ancestry.” Johanensens 1911 decomposition of a population as a biotype of different genotypes in his continuity of genetic evolution is “blending” in this sense.

withEdgeworth, I think (though) he made the case that for biological processes in which all the organs of a species are correlated and change in the same direction, should credibly possess an extended distribution based on Fs where the modes do not equal the means if one is to be precise. Because multiple organs or multiple traits can change what is the best r during transition from a zero ancestry to a midparentage just as the size of the population may change with respect to the race it may be found in (races may evolve from species or into species) there needs to be some way to represent when the equilibrium of regression (concetration) plus family variability (dispersion) reaches a new tension/attractor/equilibrium and a means to specify what deviatations towards or of the infinite and infinitesimal ( in absolute measures) transversally transit into such a state. I think that Edgeworth suggestion could be used in descrbing how it is that organs are able to move in the same direction for a Pearsonian aggregated generant. If the means are bound by potentially higher modes when possibly changing direction then these could cause correlated organs to move generally together even if some move a little one way and some another as a new total mean U of Pearson arises. I think this would enable one to design a structure that branches out as if from a root from Pearsons’ back into Galton no matter what Galton meant by generant. By associating the modes with particular infintesimals and infinites and structuring a theory of them across multiple traits by knots in 3 manifold space named by surreal numberings it may be possible to show when some types (sets of traits) dominate others, why some vestigial characteristics persist and how disease bifurcates the knot complement space of the traits through which it defects. With this theory in mind it is possible to extend it’s application to cases of non-blending inheritance and the mendelian subsumption of the ancestral law of heredity.

We can start by restricting ourselves to those of skew frequencies as numerated by Kapteyn. We can show that the dependence on x can be geometrized by associating a minimal 2 surface (presenting regression based on deviates from a particular x place)

The size of the 2 surface as defined by its tetredron creates cubes that are joined together to form the curve of abolute numeration extending to zero dimension ( Galton’s ‘ground’), and indefinitely large values (potentially infinite). Because these cubes of E2(approximated on the boundary (of total negative curvature with a average curvature of zero))xC exist as curves in 3 manifold space, different curves representing different trait set types can be combined at their extremes with infinitesiamls on infinitesimal , infninites on infinitnes , or infinites on infinestesimals in two different directions trait wise. These will form tori such that the means exist as axes of revolution. When two or more of them are joined together as links it may be possible to describe the generant as the knot complement of that knot that contains all of the traits involved in that lineage.

In order for one to describe as Galton sought ( and Pearson no where described ( except as best he could in his 1930 paper on progressive evolution) and Edgeworth sought to relate to) at least two mean trait distributions are required for doing so … that … “The limits of deviation beyond which there is no regression, but a new condition of equilibrium is entered into, and a new type into existence, have still to be explored.” Per analysis of the synthetic pairs at least.

The limits of the deviation are read directly off the geometrization of the two traits combined at infnity and infinitesimally as the cubed tetrahedron of minimal surfaced deviates inclined from place of regression of one equilibrium are joined to the a different inclination of the new condition of equilibrium and regression smoothly along the curve connecting the tetrhedrons (made Euclidean??) in the corners. These establish modes different than the means for combination of the two different forms of regression + family variability ( hence there is no race strictly speaking (only population divisionsof indivduals with gene combiations and total population whether the whole species or not).Whether the modes are more towards one equilinrium or the other depend on how family dispersion may depend on the ordinality or cardinality of the family members (and may be different for parents vs offspring, male vs female(gender), or sibling birth order and can be outline by Kapteryn provided the skew is due to a gaussian. If it is pseudo gaussian and of hyperbolic statistical analytic purpose then there is some restriction on how the infinitesimals and infinites can be combined in the ring. The difference of the raising most offspring in the deme vs in the population enmass.

We seek to know for different sets of traits specifying the change of all organs in a concerted direction changes the independence of the “causes”Kapteryn as the different organic relations form and reform. When they are no longer independent then the rings link and knot forms.

If nothing be stable in the physical world except the statistical average, why should we

believe that the germinal cells, even in the most homozygous individual, are identical

There is non coding DNA between homozygous genes.

Because the infinitesimal and infinte can be combined for two traits these will sort differently with respect to the heterozygote and homozygote and thus for multiple mendelian traits there is not sense of pure fixity of the homozygotes the pure line for combinations of traits when the two different traits may have different selective effects when combined as infinites or infintismals no matter the state of heterzogosity. For duckweed the example will be width large with length large, width small with length small, width small with length large , length small with width large. These have different consequences for selection regimes in the hyperbolic space of growth which can sort differently between the sibling types for otherwise selected ancestors in the population genetic deme it is in and can influence the direction of evolution even in a pure homozygote line or under heterozygotic advantage.

The gametic-somatic correlation is not a line between but a geometry without parallels connecting through said correlation.

By two traits connected at the surreal infinite-infinitesimal it is possible to relate the offspring arrays to the change of type as Galton wanted someone to explore and Pearson noted in 1930 had not happened by then. Huxley unfortunately claimed this exploration was not the experience of the evolutionary biologist.

It did not happen since because the non-mendelian aspects were subsumed by issues of environmental rather than chemical repulsion affects. The linking between two Mendels highly polar traits ( green white pea, tall short stems) by their infinites and infintesimals

Builds analytically then synthetically the correlations of the traits or parts of the body and leads to what is a lethal or of selective value for chromoses and parts of them synthetically then …. — what Provine thought Wright slying tried to think he was going to be able to solve with rabbit data.

If antedating is happening in duckweed then it would like be found in the clone sided sibs rather than opposite pouch sibs and thus the rare survival of opposite pouch sibs ( based on their lower number of births) may retain non-disease states and sustain the whole population when a disease condtion emerges in the deme despite being unisexual. This may be the origin of the adaptation to turion formation and heavy starch indiviudals that drop to the botton of the pond. Rna glycans??? In vesicles beyond cells??

Duckweeds may have survived into hyperbolic space because they limited the kind of correlation of somatic characters to reproductive ones.

We could build a Roughgardian social selection theory of exogamous and endogamous associated with progressive changes driven by offspring behavior. Thus offspring behjavior may influence what groups parents mate/reproduce with ( inverting the direction of study in sexual selection theory which may have been biased by assumption of two sexes).

Population structuring by inbreeding as investigated by Wright suggests that it is the shifting balance theory and not Fisher’ whole population in mass directing evolution if progressive evolutionary change dominates speciation.

Test both of past two paragraphs.

Pearson writes “Without random mating, but with inbreeding

or even some degree of assortative mating only, the various sections of a species will not keep

true to type. The basis of differentiation exists in heredity itself, no population is stable, it will

break up into castes, unless random mating keeps it to type. Caste-formation in human societies

is a natural process of race building, rather than an artificial creation, and on this account may

have great evolutionary significance in anthropology.”

Look at Wilson’s theory.

The question however is not “true to type” but true to dynamics of the attractors that move or shift from one type of multiple traits to another double typed set of traits and these may depend on homozygostity and heterozogyistuy, dominance etc via infinties and infintietesimal connections fo the traits in the type to the next corner sets. Stability of a total population and stability of a deme are two different things with respect to the connection fo the traits within the genome vs within the patent expressions. This does not exist a field of biology as of yet. Thus between the deme and very large population needs use of Thurston geometrization hypothesis.

There is no simple single embodiment of “extremists” since it is in double traits per type not just a type with variance and offspring arrary, with as said such doublings extremely ( infinity/infinitesimal) may relate to heterozygotes and homozygotes in different ways.

Pearson did not need consider this when he was only outlining progression from a single typed trait regression being of total deme selective value. The selectivre values that arise on the deme will be different than the extremists from the population at large in Fishers matlthusian encapsulation. This is where phanetics bears on ecology.

Birth from opposite pouches may prove that the Johannsen pure line does not exist all the while the honoygoous lines by breeding maximize the direction of the energy attainment from the sun and hence the ability to grow and reproduce more. Dauermodification vs Woltreck’s old idea of energy to the “gene” (rna glycans)

● Selection of the parent on the offspring in duckweed depends on how the stipes are or are not connected to those parents being selected ust as morphogenically in the wood wide web the network was. This is more for those with connected stipes than not since growth may assist the selective trait if at least weakly correlated. Thus there is a direct ancestral influence here, via personalized “structures”. The mother frond causes variations in the developed daughter frond size and possibly reproduction — investigate to discover this.

Progress is held back by continual regression when there is no stability between the deme and total population.

This continual regression ( not moving necessarily back when assortative mating, sexual selection etc) does have, its own internal deceleration phenomena as it reaches back in ancestry, namely at the higher lineannean divisions species, genus etc …are continually pushing towards patent expression from latent replication, but these divisions substationally begin to effect the balance of repulsion and attractive chemical bond connections and given the metabolic system of the variatey or subsepecies, breeding in demes can not direct regressions backward all the way to the most distant common ancestor and thus the progressive changes and other selective affects move (the )forward despite the general Ancestral Law ( of Galton as modified by Pearson etc). This is in the log exponetials between the the polygenisma and alleomorphism per macron.

The macrons can only resonant as far as the asymptote and this is increased with increasing ancestrality — so the forces of the macrons eventually are blocked in terms of their 2nd law (action reaction) effect. This is a different explanation than that Pearson gives comparing only to special creation ( which explains why creationism continued to exist in America well into the 21st century (intelligent design etc)). for origin vs collection(without Galton’s “two’).

I+++++++++++++++++++++\\

nbreedingl causing a decrease in heterozygosity does not lead to the assumption that the organism was initially heterozygous with local races arising by inbreeind or initially every species of organisms consisted of many homozygous lines that panmixia somehow emerged itself along with heterozygosity or hybridism because it all depends on how the chemical repulsions and attractions are related to extant metabolism and means of obtaiing energy. Because these relations depend on the double traits extremists in the attractor of moving back in type the organism but panmixia did not need to arise to produce the heterozgosity since if the chemical repulsions and attractions are in correspondence with the nature of the biochemistry bonds to get energy the homozygous lines or the inbreeding demes may appear along with a harmony of the cycling endogamy and exogamy — this outside of the phylogeny but carried along in the environment is not lamarkism but a form external physical inheritance chemically and can exist when the entire ecosystem chemical aspects are associated with the regressions back ancestrally.

Current evolutionary theory does not account for this kind of polyphyletic heredity legacy heritage and goes to the issue of when evolution evolves heredity or whether the heredity was part of the vital unit of trait types united in their infinitesimal and infinite dimensions.

?????????

But with deviations, deformaity abnormality and disease it is every present. Because the genotype concept of Johansen found pathology to be normal and kept chemistry to reaction norm the double heritage of disease analysis formerly transgressed without explaining how the two were not needed. This possible chemically when repulsion provide structure to chemical bonds as do attractions auto catalytically

Evolution of heredity in Lemenacae via Hyperbolic Statistical Analysis ( HAS )

“In speaking of the couples of brothers, and of men of the same race who were not brothers, it was the differences of stature that were noted, and not the absolute statures. Differences of stature are identical in value with differences of the departure of either stature from the average of the race. It is, however, under the latter aspect that the mathematician has to consider it.” Galton 1890 to an American audience.

“HSA considers the possibility that deviations (residuals) may exist on a non-flat surfaces with non-Euclidean geometric structures. Hence statistical deviations reflect assumed geometric constructs of the investigator( s) [who is/are extrinsic] observation( s) and/or conclusion( s)” Donato 1993

Duckweed Evolution analyzed via hyperbolic geobiometric statistics

Donato subjectivized hyperbolic statistical analysis and proposed it’s use wherever and whenever orthogonal regression analysis is used. Orthogonal regression analysis may be applied to traditional biometry and can be used to investigate deviations from symmetry in the sum of least squares relation between parents and offspring. By using the area of a triangle and it’s defect in the place of the statistical error concept it is possible to apportion these asymmetries into categories of intrinsic and extrinsic differences. These categories can then be used to analyze heredity given that offspring contain ancestral influences via parents but that parents can be correlated with offspring due to social selection (Roughgarden) maximizing offspring production.

“The old notion was that, the average length of the bone being so and so, and that of the stature of men of the same race being so and so, then if the bone were, say, a twentieth part longer than the average of such bones, the stature of the man to whom it belonged should be estimated at one-twentieth more than the average stature (subject to certain corrections). This we now perceive to be doubly erroneous in principle.”

Because the hyperbolic parametric containment of the dependent and independent biometric variables exist on curved surfaces (with a mean Gaussian curvature of zero) some of the variance otherwise traditionally ascribed to genetic causes is( actually ) hyperbolic statistically attributable to the environment ( with a different sum for additive genetic effects) that may posses different global forms under the same local geometry. When these global forms differentiate monophylies, the evolved speciations between the monophylies contain specific geobiometric compatiblity component condittions (for the surface to exist). I apply this synthesis to an analysis of duckweed evolution by using the right helicoid, left helicoid and catenoid between the unisexual and sexual generations of homotypic fronds via right and left clones sexualized. Thus twist corners are identified in the morphologies of the different species. These twist conditions are modeled by the different geographic populations’ inclination to the direction to the Sun controlling the intensity of natural selection via Gauss-Winegarten equations.

During the course of developing the exemplar, Fisher’s complaint against Wright’s adaptive landscape in the form a like a potential function is evaluated and it is found that Fisher’s use of variance for variation is inadequate to duckweed deme defects of triangulation. The classification of extrinsic data from the intrinsic (curved for local-global united formats) permits the potential to be realized and adaptation to have something to adapt to. A new form of path analysis is introduced to account for hyperbolic parallelism when writing down duckweed mating systems and the Price/Ewens version of Fisher fundamental theorm and…evolutioanary stable strategy with Maynard Smith is shown wanting.

Galton thought that regression happened every generation but Pearson showed that it depends on the multiple correlations amongst the organs and hence across populations of generations in duckweed.

Johansen had asserted that there is no relation between the multiple correlation of organs and instead asserted it all came from the same physico-chemical reactivity of the geneotypes as isolatable. Given Abraham’s macrons of chemical, physical and electrical sourcing the new exploration of Johansen fails to give the genotype access to any and all kinds of formalizable macrons. Pearson bet that selection might show change where Johansen asserted there was none. While is some circumstances this may be in the case/found it is more generally a result of the difference in population sizes per sets of and structures of the factors combinations orderings due to inbreeding resulting in population structure a la Wright that by ecological -evolutionary interactions results in cycles of endogamy and exogamy.

Fisher’s fundamental theorem made these correlations depend genetically on the variance as found from a Euclidean framework of a sum of genes within a genotype but when the perpendicular in the least squares technique for finding the slope of the regressive correlation between parent and offspring is part of a triangle ( of the independent and dependent coordinates) which need no be Eucledian ( sum to 180) and is hyperbolic then the variance is related to the triangle chosen as the standard. This may not be one congruent to that around the mean/median and thus there is no simple additive sum of gene effects that can be removed to discover the how the regression is related across generations and amongst the homozygotes and heterozygotes under any evolution of dominance. Price mistaken. Instead there is a more complex relationship of dominance to the triangle (defining the parallelism of the current demes’ adaptation (place on adaptive landscape)) chosen that may favor homozygotes in some cases and heterozygotes in others. This may be the cause of the confusion noted by Lewontin of some of Dobshanksy’s generation thinking a single homozygote could sweep a population or a single heterzgote in the debate over polymorphisms. The triangle chosen also directs the path coefficents when the causal relations (of endogenous vs exogenous) are decided prior to modeling. This is because the median deviation units from the mean or the standard deviation units from the mean vary depending on the chose standard triangle and the other triangles that appear as one moves from the mean or positionally fixed from the original standard triangle. The only biological import of this change is that it alters how one dissects the relation of homotypic differnentiaion from pure homotypes under the varying organic correlations that may appear when moving various standard deviations away from the mean which also is not necessarily symmetrically homogenous about the mean as noted because again ( by Pearson’s focus point of a regression) due to the different triangles encountered along the correlation/regression lined slope ( which may not be “straight” with respect to sampling representing the whole population ( hence random samples for dispersion is inaccurate as the causes).

A normal mixture of a normal distributions is itself normal. A mixture of normal distributions on hyperbolic space need not be but the pure homotypes (homeostasis of homotypic co-relation to gametes) remain no matter the deme relation to the total population of gene frequencies. The index of midlevel compartment ( aka height of the parent) needs to be associated with standard triangle averaged over the curved reversion line and this can be computed from the path coefficient altered to show which double arrows can be gone in which direction ( they can not be chosen randomly). The central limit thereom is not violated for the entire reversion regressed across organ correlations because of the total curvature being zero populationally even if it is not so in a deme moving up the landscape potentially. Thus the midparents are not at one place but distributed across the organic correlations as the pure homotypes . It is by using hyperbolic statistical analysis that these relations obtain numeration and visualization. In duckweed there is a simple relation of the midparent phenotype to the offspring phenotype in that it is simply divided into left and right sides posessing only a single bifurcation of the tree branching in the hyperbolic space.

In duckweed these stages from the midparent are built up mitotically (personal somatic structure) by the fibonnaci series and format a demic unisexual population of a approaching an equivalent bivariate normal distribution further in the series ( smoothing out the effects of the original triangle selected)

This can be found by combing the left and right helicoid into a catenoid that is bivariate normal.

The bivariate normal is the tangent to the bifurcated tree hyperbolic space.

The two Galton regression lines have the same slope only when the left and right helicoid ( left and right clones) are combined. The evolution of duckweed proceeded by decomposing demes into unisexual lineages of left and right by accidental mutations into more intense selections of birth order effects which increase by mitioic repulsions ? of catenoid centers vs peripheries . with cholrplasts undergoing independent divisions. In right and left clones there is equity in the distributions of the centers and periferies so the causal influences of skew frequency distributions are null compared to the state of the catenoid ( during ancestral and sexual reproductions (Past and future reproductive value of Fisher).

Parent-child and brother-sister relations can not be combined into one correlation as Galton had done. Galton assumed that unisexual reproduction was a defect but with duckweed it is the perfect. Thus by refecting these relations by decompositions into chiral helicoids which enable genetic adaptation to the direction of the Sun duckweeds evolved distinct parent-child regressions and brother-sister reversions that could be spread into speciation with subsequent occasional resexualization. Thus duckweed hyperbolic statistical analysis returns the co-relations in the correlations by finding the causes in the mating system through which the double arrow forward or backward directions are identified by the standard triangle of parallelism of the two data parameters that relate the homotypic to the organic correlations ( diffentiately as said by Bateson).

Individual duckweed differences or variations can not be ascribed to chance per say as Galton supposed for the difference of brothers because the right and left clones will have different effects on distribution of chlolroplasts with respect to sex. Especially in the difference of siblings based on pocket vs based on birth order from the same pocket. We are able to model Galton’s line of tension per incipient structure within the similar local geometry of the catenoid, right and left helicoid.

With hyperbolic statistical analysis unlike that developed by Galton, there is a central standard triangle or form from which departures/variations are measured.

The crucial change that hyperbolic statistics adds is the intrinsic data is different allowing the height as measured from the parent to ground to be different than the offspring to the ground. It is not true when Galton said — “If we were measuring statures, and had made a mark on our rule at a height equal to the average height of the race of persons whom we were considering, then it would be the distance of the top of each man’s head from that mark, upward or downward as the case might be, that is wanted for our use, and not its distance upward from the ground.”

The distance to the ground is needed to determine the extrinsic data as these define the gamete somatic correlation which affects the measure from the average. In H² E space Different proportions of right and left clones make different bivariate normalized like distributions for species differently (especially in noncoding DNA).

H2 E space of ecology for duckweed

By making tori connecting different third dimension circling of the median or mean as knots it is possible to compute the genetic content of noncoding DNA around the genes that make up the coefficient of relatedness as found by Fisher based on large number of Mendelian genes. Hence the Thurstonianization of hyperbolic statistical analysis will enable one to understand how viruses have infected the refections.

Edgeworth ( on Pearson’s correlation of organs changing in the same direction in probable error paper).

“There seems to be here an irreducible element of arbitrariness;comparable to the indeterminateness which baffles us when we tryto define a “random line” on a plane, or a “random chord “ ofa circle. It is a nice question how far such antinomies shouldgive us pause when dealing with a value of r which is in theneighbourhood of zero.*”

we should be able to create a theory of copy order variants and historical gene duplications using this “zero”.

This has to do with the change in variance of the offspring selection variation as noted by Pearson and studied by Weldon ( that the offspring have higher phenotypic variances that are selected away during the growth of the incipent personal structure towards maturity). These higher variances are caused by the smaller accelerating standard triangles ( smallest angles sizes ) permitting many more triangles ( more forward and back arrows in the path diagram) per standard deviation or variance in the sum of additive genetic effects. When in homo or heterozygotes…

Donato begins with a set of two parameter curves bounding of the data points. One curve is the parent and the other is the offspring. Traditionally in biometry there is no difference in the curve for parent or the offspring with respect to evolution independent of the measure of the trait in each. The height parameter for the parent is said to be the same trait in the offspring measured numerically. Height is a biometric measure independent of whether it is measured on a parent or an offspring. Once one introduces parameter curves instead of ordinates and abscissas on which the height is recorded it becomes possible that the numerical rendering must be altered for the type of individual from which the measurement is being taken provided the space on which these alterations meet some requirements ( having no relation of race to prelineage family-suborder division. This is what is in place of the a priori notion of race. These requirements are intrinsic and extrinsic (movements) of the observation point (height in parent and height in offspring) such that all evolved points (are compatible with each other) for the mean curvature of the entire evolutionary points are zero. This is imposed in traditional biometry by disallowing there to be any in the height as measured on a parent or it’s offspring regardless of the generation the ancestor-descendent pair exists in with regard to the origin of the species it is in. In Fisher’s version however there can be a theory in which hyperbolic statistical analysis applies instead.

???

And finally — Galton –

In speaking of the couples of brothers, and of men of the same race who were not brothers, it was the differences of stature that were noted, and not the absolute statures. Differences of stature are identical in value with differences of the departure of either stature from the average of the race. It is, however, under the latter aspect that the mathematician has to consider it.”

So here differences in stature can not be compared to differences in the average of the race because demic structure and relative motion up the same effective landscape will be different and these subpopulations from actual individuals will have different proportions of left and right helicoids and different amounts of intrinsic and extrinscinc data points, so the absolute stature withour regard to the helicoid or cartenoid is the what is needed to continue with Galton.

These minimal surfaces meet at corners of the tetrahedron cubded 2 parameter spaces.

We see that there is no need to presume a racial division of a species under hyperbolic statistical analysis but only a demic decomposition of the local to global geobiometry by conditions of compatibility.

The ordinal and cardinal number do not find the same use in hyperbolic statistical analysis ( being a second brother of the opposite pocket is not the same as first brother of the same pocket on the opposite side by a generation.

Now to the details :

“It is now beginning to be generally understood, even by merely practical statisticians, that there is truth in the theory that all variability is much of the same kind. The theory rests on the grounds that all variability is due to an uncounted number of small independent influences, acting variously in different cases. Mathematicians are able on these purely abstract grounds to develop a singularly beautiful law, known as the law of frequency of error.”

“When dealing with correlated dimensions of the same person, we must take their several scales of dispersion into the account.”

With duckweed this is possible to do based on difference of pouch birth vs birth order.

“n a recent paper [10,11] a chart showing the area-weighted probability density function (pdf) in terms of a geometric shape parameter was presented. This parameter was defined in terms of the ratio of the two principal curvatures kl and k2 where the value of the parameter would be between + 1 and -1. The authors note that (i) when the parameter equals 1, that is, kl = k2 , the material surface is spherical, (ii) when the parameter equals zero, that is, k = ° or k2 = 0, the material surface is cylindrical and (iii) when the parameter equals -1, that is, kl = -k2 , the material surface is pseudo-spherical. The authors then observe that spherical surface elements are very improbable and that cylindrical surface elements are very probable.”

The issue of multiplying r to get uncles from brothers and father sons has to do with the cylinder sides meeting and being transversal independently. Hence multiplication vs correlation.

Cylindrical mitotic surfaces exist throughout most of the soma of duckweed. Spherical surfaces exist along the edge of the reproductive pouch and location of eversion area the sexual meristem, while minimal surfaces exist between the birth order siblings in the reproductive pouch and between the male and female elements in the sexually developing meristem.

“Like Galton, he assurred that correlation coefficients could be sii1y multiplied together to yield values for other correlations; supposing, e • g., that thecorrelation of an uncle and his nephew might be obtained by multiplying together the correlation values for afather arid a son and for two brothers.”

This truth can be tested with hyperbolic statistical analysis as noted above.

“It seemed to foU, that, if a population were to be ‘improved’ by selection, then there would be a reduction of the ‘inprovEnent’ with each generation — for, each successive generation would have only the fraction of the ‘inprovnt’ shcn by the preceding generation.” This is only happening in the catenoid sexual population. The improvement in the clones depends on the distribution of the spherical shape parameters relative to the minimal surfaced ones. As per relation of co-relation correlation balance to chloroplast divisions Pearson’s “jumps in the focus of regression” Pearson did suggest to look for this — “his suggestion that the ‘determination of the focus of

regression for sate organ in selected domestic ducks for several generations

and comparison with the means for wild and general domestic ducks would seem a possibility’,”

This we do by looking at different geographic populations of duckweed and differences in morphology and movement of chloroplasts towards orienteing the tissue towards the sun.

Creating an ancestral law by deviation from racial type can be replaced by correlating proportions of left and right helicoid to an ancestral catenoid. Thus we can get at Pearson’s suggestion. The coefficient of heredity exists for the topological space of the population genetics of set of helicoids and catenoids in the local deme climbing the landscape. Duckweed speciation appears to be due to the fixing of a set of organs per population genetic population no matter the individuals ( hence not a race strictly but defining what amounts to batesonian differentiate differences of total homotypes per species.

“This difficulty would b to sane extent net by introducing a

coefficient which I propose to call the coefficient of heredity,

and consider as capable of being ndif led with regard to both

character and race. As such a law would cover Mr Galton’ s case,

there does not seem any objection to using the nre general formula,

until it is found that the strength of heredity is the sane for all

characters and races. Of course, it may .wel] be arjued

heredity is sanething prior to evolution ,iid denined’ by

it. If this be.. so, its absolute fixity for all organs and races

ought to be capable of observational proof.
” p210 phd thesis

Pearsons assumption falls in line with Galton’s of observing unisexual division as a deviant to sexual but duckweeds show this need not be the case.

“whenever the sexes are equipotent, blend their characters and mate

panganxusly, all characters will be inherited at the sane rate.

Such a result could hardly be. attained if evolution itself had

produced heredity. It suggests that heredity, like variation, is

sarething fundamental to the vital unit, and is not a product of

evolution itself. E”

It is possible that evolution evolves heredity. One way it might do so is via changes to noncoding DNA.

when both Galton slopes are no longer assumed mathematically equivalent there can be a biological theory of regression in the multiple variable corelations.

‘The law of ancestral heredity as founded on the theory of multiple correlation involves no biological theory of regression. The term regression has unfortunately been taken fran statistical theory and interpreted in a biological sense. In statistics the regression is always to the nean of the foreknown character. Further, if there be a number of cognates, we can a priori, i.e before quantitative analysis, riot state the total aniounts they will contribute to the predicate will or will not indicate a biological regression. Again, In l909 Pearson offered” peARSON

‘the law of ancestral heredity is art)raced

in the following statanents’:

(i)In a pop.ilation breeding withcut assortative mating the

regression line for offspring on any ancestor is linear.

(ii)The correlations between offspring arid successive grades

of ancestry form a progression diminishing geanetrically as

we ascend to distant grades; and

(iii) The general relation of an individual to his ancestry can

be closely expressed by the multiple correlation formula.

The regression line need not be linear, multiple correlation can not form the general relation to ancestry.

Once we found and find intrinsic data points around intrinsic geometric connections of compatibilities it is no longer necessary to assert that continued selection on extremes must always give rise to futher new mean values. The means to the components are not longer fluid but divided into the intrinsic and extrinsic and only a certain amount of the selection can change as the space itself has a shape (is not random). If one selects for the correlation of that selected for with the rest of the additive genes then yes it might but otherwise no.

The repeating of place in the 3 manifold space makes spaces of trait combinations that in reality become a subset of the infinite 3 manifold place spaces as the intrinsic and extrinsic data are obtained and classified.

Weldons mixing of the ancestors in various proportions is found in the proportion of unixseaul left and right clones in a given sexual reproducing deme subpopulation. Thus by mutation and sport in unisexual lineages recombined sexually these proportions become altered and speciation may occur,

“r on’A new theory of progressive evolution’, published in the lmnals of

eugenics, he was to be found asserting, quite correctly, that ‘the law does

not depend upon any irethan.thn of the germ plasm’. But, in the meantime, the

world had not stood still, and R.A. Fisher — the future Sir Ronald Fisher

36

- had been at work. We shall return to him and his work in the chapter on

eugenics — but, for the nornent, it Is worth noting that in his frroi…s paper

of 1918, “On the correlation of relatives on the supposition of ?ndelian

inheritance’, he shc’zed that observed correlations between relatives could

be explained in a ?ndelian fashion. Now, as Pearson noted all along, the

coefficients of the ancestral law (e.g., ½,1/4, 18 etc.) — which governed

mid-ancestral deviates — were functionally related to the sirrple correlation

coefficients linking father and son, grandfather and grandson, and so on.

Fisher, therefore, was able to shcM that the law of ancestral heredity was a

consequence of inde1ian genetics — or, at least, that a law of that çieral

form was •”

The issues that hyperbolic statistical analysis raises for Galton and Pearson and Weldon apply even more so to Fisher and the derivation of the ancestral law from mendelian genetics even more so because the variance as used by Fisher is also affected.

Two causes acting together do not always permit a square root of the sum of the standard deviations squared if one cause is a mutation towards the Sun and one in which links sun directed mutations to sex linked traits bearing oppostive effects on chloroplast divisions. One can surely speak of the percentage of causation in those cases where the effects on chloroplast replication are known. Segregation with respect to heterozygosity is not the same thing as different proportions of right and left helicod per mating system.

Fisher starting with random mating assumed multiple small ( unlinked ) factors but by hyperbolic statistical an analysis this way of obtaining the error law for deviations as variation fails to find the cause as coming from skew frequencies caused by different dispersions of gamete — somatic corrleations and these may be united by intrinisic data.

With a shape parameter equal to -1 for x and y axes and total mean curvature equal to zero, the mean of frequency curve is the mean of the curvature. The components curvatures are distributed around the mean of the frequency curve which when summed up produce the mean of the frequency curve. The ‘distorsion” which appear locally the frequency curve made of only a small hillock show how the causes (log normal) change with changing value from the mean. It is log normal? Because it is on a population Malthusian parameter??

If family variability had

been the only process in simple descent that affected the characteristics of a sample

the dispersion of the race from its mean ideal type would indefinitely increase with

the number of generations, but reversion checks this increase, and brings it to

a standstill.”

What checks it is the relation of the distance to the circle of the infinite end the hyperbolic space.

The infinite number of generations can not increase the distance since as it increases it gets smaller progressive while increasing intotal with each generation. Biotic factors overwhelm abiotic factors during the increases going up with each generation. There needs be no check like Galton said. His use of race and ideal type (tipping polygon) is not what actually connects the Linnean hierarch for different clades and monoplylies.

Without the notion of the dispersion of the race from a mean ideal type we instead replace the mean curvature equal to zero where the types are different minimal surfaces the reversion may not be a homogenous across the family.

show how to-measure its degree.

Two variable organs are said to be correlated when the variation of the one is accompanied oni

the average by more or less variation of the other, and in the same direction (p. 135).

The last words seem to us now out of place, but Galton had not yet reached

the idea of negative correlation

These are not out of place because an organ can vary with positive curvature or negative curvature with respect to another as well as positive and negative correlation for zero curvature. This is how it is that one need not consider necessarily the details of Weismanianisms. The places of the later are where Galton had the stirps isolate from the soma during maturity ( under “tension”). Pearson associated this with “balance” when it is in fact an issue of Thurston’s geometries projected onto organ tissues (using Thom’s morphogenesis??). the Calculus of correlations is actually the Kantian cohesion. It is not a “balance” however implemented.

By Galton there is no regression necessary for perfectly common caused organs ( Pearson’s pure homotype) as they would be 1:1 from parent to offspring ( or as left and right is in an individual)

By Galton there is zero regression when there is no cause in common.

Galton’s innovation was to put a single number on the co-relation between 0 and 1. With hyperbolic statistical analysis we have not just number ( slope of a line number( derivative)) but a whole series of higher derivaties that vary according the measure of the organ and the extent of the measure — establishes the causes as well.

The correlations between post-spinous

portion and total carapace length may be cited as illustrations of what Weldon and

Galton were testing:

Plymouth (1000) r = 0 81

Southport (800) r = O-85

Roscoff (500) r = 0 80

Sheerness (380) r = 0 85

Helder (300) r = 0 83

The suggestion that r has the same value for all races of the same species wassupposed to be confirmed by these results. We now realise that without a knowledge of the probable error of r, such a statement is illusory. Buit it was this very series of values which led to the investigation of the probable error of r and so to the extension of the correlational calculus.” Pearson

The probable error of r depends on the proportion of intrinsic to extrinsic data points. There is no need to assume that r is the same for every race of a species. It may be similar when the deme are all moving up the landscape the same way but these may happen in many inclusive ways. The probable error however contains a phase transition or catastrophe which can not predict its value within limits, for instance when right helicoid external edges, match up on the catenoid then go to opposite places in the embedding space of all sub poplations in the species ( without regard to their being defined any race). At these lines of catastrophe it is impossible to determine the intrinsic and extrinsic nature of the data points since the total geometry is undefined and only exists as traditional independence or dependence of relations. If the species can form a genus through which a larger composite geometry (from THurstons?) then it might be possible . This is also how it is that the Linneanean hierarchy may actually have material content that we have been unable to determine the forces of to date. Species, Genus, Family, class and distributions in total morphospace posses real denotations not merely naming connotations. This was kinda what Aggasiz was trying to get at.

The mid parentage in the hyperbolic statistical analysis comes from equal right and left helicoids not two inside out cartenoids unders sexual decomposition.

Galton probably did not write down the equation as Pearson wondered because he might have been worried about what Maxwell said.

This I shall get back to “. Again,I think, his mid-parental correlation is not theoretically

consonant with his parental correlations

”

The dispersion varies as to the relative proportion of intrinsic and extrinsic points. Sampling fails because randomly increasing size one can not systematically be sure to be increasing relative dispersion.

When one uses the pseudo gaussian on the hyperbolic space for the growth plus evolution places (geograhicall and within a pond) of duckweed to the minimal surfaces for the genotypes as expressed in phenotypes then all three of Galton’s three series into correlations come together ( without having to follow the multiple correlation steps taken by Pearson). The dispersions on the psudeo gaussain geographics help to find the focus of regression which Galton did not try to do. Pearson’s did in terms of the variance of the young being larger than the adults but Fisher went a different way.

Hereditary Constraints

How logical is one’s inheritance? Is there a method by which one can show this logic?

Does regression provide such??

If one has a growth morphology like then orthogonal regressions of the shaped sizes in the x and y axes will depend on the size of the angles in any triangle that connects the perpendicular relation of a sibling to another generation’s individual. If we consider the cell division to be isotropic across this propagation geometry and propose that lingulate hyperbolic base form creates two diabolic points in its offspring then it’s clonal ancestry establishes a chirality with respect to the isotropic personalized non-reproductive ( vegetative) structure which establishes the location of the stipe scar.

The search for genes, genic locations responsible for this are likely ones that sort differentially with respect to the sex controlling factors and format a hyperbolic cell replication scheme.If the angles are indeed smaller than 180 for a duckweed triangle from a larger hyperbolic space….then we would be beyond the logic and into the methodological use of it.

Inheritance might be very logical and (mathematically) constrained.

https://www.nature.com/articles/lsa2015101.pdf

Left and right interchange x and y axes with respect to hereditary regressions in this instance.

With Sun location growth as the Gaussian a hyperbolic tree of generations and siblings can have a probability distribution in which the tangent space tracks the stipe scars.

“Variability of family = (square root)Il1 _ r2 X variability of general population.”

This is not true in hyperbolic statistical analysis as there is no constant residual across the range — no homoscedasticity in the arrays of offspring.

Need to integrate over the hyperbolic model of cell division and reproductive production.

dimension perpedicular to the water surface appearing otherwise as the gamete to somatic(nonreproductive) correlation.

Because the histogeny has become adapted to hyperbolic space when stressed by excess electron removal (when placed on a plant fuel cell battery under resistance, the lack of a Eucledian distance connecting the soma and gametes facilities morphogenesis recapitulation back into the ancestral format.

Here I hypothesize that boron chiral ambiguity enabled Duckweed to transition from Eucledian population growth to individual development in hyperbolic space.

Perpendicularity between the parent and the offspring obtains a new meaning in hyperbolic statistical analysis ( and bears on interpretation of the fundamental theorem of Fisher when his method keeps the residuals to remove the additive genetic variance. There is another additive genic variance that is not a straight line regression across all genes but one in which fits a minimal surface across the genes involved. Some sets of genes may possess a more fit combination than others purely due to individuals used to compose it rather than the breeding population it’s gametes appear out of when the this combination nevertheless still has a mean curvature of zero. Because the mean or average may be from a skew frequency curve there are many new kinds of statistical functions relating the x and y axes than Pearson thought and were begun to be explored by looking at the causes of the deviations by …. . Here some of the cause is found in the hyperbolic surface itself. These are additional internal effects that Wright questioned Fisher about and may possibly be out of Pearson’s determinantal non mendelian determinants, and non-coding DNA affects.

Do Duckweeds reproduce and grow in hyperbolic space? Did evolution adapt these plants by balancing tradeoffs between reproduction and growth to maximize total population size surface area? Were different species able to tile hyperbolic distances by using an axis to the sun incident on a surface of Euclidean angles that connects the mitosis and meiosis across the gamete to somatic correlation. Can not Pearson’s original theory of homotyposis supply a statistical division of organic and homotypic tilings in the hyberpolic space evolved?

If unisexual generations determine the flat plane(second annulus), reproductive pockets are determined by the angle of delta to rho within a generation and sex minimizes the ratio of delta to delta-rho

Then the duckweed selection can function to populate the surface with a hyperbolically maximized number of individuals. This would allow natural selection function as a stronger pressure per water surface body since more individuals per time could be produced than if the Euclidean plane constrained the relation of the growth to the number of individuals ( same rate of growth regardless of the number of individuals). Transition to sex will occur when the adaptation to the surface is maximized. If this adaptation is orientation of the chloroplasts to the direction of the Sun then this will be reached when left and right clones ( existing natural form as with two pockets) have a certain number of ruffles and bends ( which will be merely twist forces in the stipes at different individuals in the growth and reproduction sequence). These ruffles and bends will show up in the relative proportion of the chroloplasts that aggregate onto the different cell walls with and without the direction to the Sun.

The overhang of the annuli represent the division of the soma needed for reproductive meristems. Additional same side pocket siblings fill the places between the annuli in some proportion to this overhang. Changes in the length of the annuli represent different species ( Spirodela>Lemna>Wolffia)

When Galton set up regression ( on the basis of least squares) and Pearson extended it to multiple variables, they did without paying regard to any difference in the extrinsic and intrinsic differentiation of data points. The use of standard deviations by Wright and variances by Fisher ( and Haldane) constrained the ability to differentiate nurture from the environment and nature from the genes. Non coding DNA could not be considered genetic.

The suggestion that (requirement of compatibility conditions) the probability density function (pdf) depends on those conditions for the existence of the surface ( connecting the x and y axes, Pearson multiple variables) Donato suggests use of Gauss-Weingarten equations to get them.

In classical biometry the probability density function does not need to assume the existence of a surface since the ordinates are simply numbers of individuals and not generalized variables.

The development of the modern synthesis in Mendelian populations however it is not longer that case and some such surface is assumed. The dispute between Wright and Fisher can be analyzed from this perspective.

By introducing minimal surfaces in place of orthogonal regression, one is in fact supposing mathematical constraints on Galtonian stirps, which would influence how Pearson ( and Weldon) attempted to interpret ancestrality in relation to natural selection, but since Huxley had asserted this was not the experience of biology and the modern synthesis arose ( with its use of variance and standard deviations in path analysis (per mating system))…if one instead used minimal surfaces, it will imply somthething for Fisher’s fundamental theorm and the shifting balance theory however in the logic of the stirp any deteriorations or defects or deviations from the means may ….

With minimal surfaces the correlation of the parent on the offspring existing on these minimal surfaces rather than a Euclidean numericalization may be found to vary within families and among generations homogenously into Fisher’s future reproductive value ( based on past ancestry) and could be one in which organic correlations give rise to homotypic ones ( correlation of organs that Johanesen denied). It may also be able to discriminate drift more easily since the variance in random fluctuations may be less noisy.

So there can be variation caused by the family birth order and type of birth (if polymorphic) ( cardinality with respect to the generation ordinality when the mean curvature by the relation of the homozygote to the heteryzogte altered from random.)

Same local geometry but different global geometry ( left, right helidcoid , catanoid) can place the two parameteric bounding parameters in different incident relations with respect to a higher dimension it is embedded in. If these incidiences are correlated with organ homotypes, family birth orders or types , generational separations, then height may have coherent but variational definition depending on the individual from which it is measured.

Such incidence identifies curvatures in the data points which otherwise appear as errors of sampling. A theory to relate subpopulation discrimination under varying subsampling due to curvatures knowing such incidences could be methodoligcally designed.

A particular type of birth may be incompatible with the overall global geometry the birth is presently in but it may become compatible in a future in which that global geometry becomes replace d by having a unisexual generation become sexual.

Assigning intrinsic genetics aspects to intrinsic geometric properties is possible in hyperbolic statistical analysis but it is not in traditional biometry where there is no distinction of extrinsic and intrinsic data points. This opens the way for symmetrical properties of DNA sequences to be related to phenotypic evolutionary constructs.

Finally diseases, defects, and deviations may disguise alternative global geometries by their exceptionally different local natures. Determining when these are extrinsic or actually intrinsic is immanent. The search for understanding these differences as components that sum to a zero total curvature it the subject of the new hyperbolic biogeometry and may prove to change the way we understand mutations as already mentioned.

Putting this statistics in the service of medicine and applied evolutionary theory is the goal of this new discipline of science.

With an application to duckweed, I will show that right and left clones follow hyperbolic statistics on the right and left helicoid and that sexualization converts them through a catenoid. This will give a means to find the sets of genes on which the intrinsic and extrinsic decompositions might be found.

Yule computed the first regression of parent and daughter Lemmna Duckweed. We can extend this work to cases under hyperbolic geobiometric statistics.

What we find is that a line of tension separates the intrinsic and extrinsic data points. It remains to be determined what density of points may be distributed for a given number intrinsic points and tension lines.

Biologically between heredity and evolution there is homotypic and organic correlation. Homotypic differentiation increases parental deviation and organic development changes offspring deviation. There need not be “incomplete” correlation when regression is the ratio of homotypic over organic correlation relative to pure homotypes and total Galton affinity of personal structure (Pearson’s organic connection vs geometric connection).

Now Fisher supposed — “We mav know this

by considering the difference between brothers ofthe same fraternity: ofthese the whole ancestry is identical,

so that we may expect them to resemble one another rather more than persons whose ancestry, identical in

respect of height, consists of different persons.” This is not the case for duckweed because brothers or daugthers that are of different pockets have adapations to the light twisting in different directions with respect to the questium point of origin ( in the dividing cholorplast macron congruences) which are different than daughters or brother of different birth orders from the same reproductive pocket/pouch.

Since the Mendelian hypothesis depends on the different kinds of brother and daughthers in the fraternity or sorotint in duckweed the correlation from the dilution due regression of the past results tin speciation towards the Wollfia in which there is only one pocket. No infinite fraternity only removal at the infinite hyperbolic distance of the right and left morophology.

By putting the knots in different Thurstonian spaces , higher order relations ( towards all Lemanance) could be obtained in which we reason beyond Fisher’s polarities for any ranged heterozygote and homotzyogte. This is a new theoretical domain. We should be able to determine linkage groups and chromosome composition on this newly advanced theory idea. We have the fisher method of reproducing the parents but not the grandparents at random with the helicoids and catenoids — clones and sexuals.

We should be able to distinguish epistacy from cis trans modulation of gene activity from other places in the genomes.

W The above reasoning as to the effects of dominance applies without modification to the ancestral line,

but in a special class of collaterals requires reconsideration. The reason is that the deviations from linearity are

now themselves correlated. (THIS DEPENDS ON THE KNOTS FOUND FOR THE GENE DUPLICATIONS IN THE HISTORY OF THE SPECIES IN WHICH THE MEASUREMETNS ARE DRAWN IS NOT COVARIANCE ASSOCIATED WITH COPY NUMBER VARIATIONS TAKING DIFFERENT MUTATIONS?? THIS SHOULD GIVE US A WAY TO DETERMINE A STRECH OF DNAS AS “LOCUS” NOT NECESSARILY A SINGLE PLACE DOES DOMINANCE HAVE TO DO WITH THE DISCONTINUITY STRUCTURE OF THESE STRECHES? CAN WE USE Bertrand russell’s logic on this??) In other words, a father who is heterozygote instead of recessive may have

offspring who show a similar variation; but they may also be changed from heterozygote to dominant. In the

case ofsiblings, however, whichever change takes place in one is more likely to occur in the other.e have to do this with duckweed

9 Fisher types by duckweed right light and parent with 3 in each pocket??

Thus with duckweed right and left clones as pure homozygous lines we are able to start to fullfill Pearson’s progressive experiment. Lemna length is inherited with .7 r between mothers and dauthers and thus using this we can begin to show how progression exposes the lengths between genes in the homoygously pure lines.

What we find is that unlike the idea that any deviation can give rise to any amount of increase or decrease (selectively), the infinite and infinteismal connection of multiple traits ( which may be epistatic, etc) set bounds over which selection can go because of the topological binding of the phans. So when a series of selections ceases for a particular trait this does not necessarily mean that a genotype has been selected in, as it may also indicate that the traits that is connected to prevent it from being selected any further.

“he keystone of the pure line arch is the proposition

that selection is ineffective except as a means of separating already existing genotypes. If this keystoneproposition be not sound the whole structure of the

theory crumbles.” I fthis true it might be tested by showing that selection can change a genotype — by converting a knot class into a different knot class.

Suppose there is a phenotype with a knot sub genotype of 4 tangled biotypes, a mutation of the phan of the biotypes is caused by either of two reflections of any two of the biotypes. When one biotype is a right clone and the other is a left clone then the composition of both of them is a rotation. This is modeled with duckweed.

The theory enables us to clearly discriminate segregation of genotypes from heterogeneities in phenotypes. Because there is a difference in the homotypic correlation and organic correlations per segregant when a genotypical difference is observed it can be defined phenotypically into biotypes that might or might not contain segregants linked. If they are always linked prior to any differentiation of the personal structure during development then they form a homotype but if the homotype is not pure segregants can come and go and there is no homotype but an organic correlation amongst other homotypes correlated with linkage in question.

When a frequency polygon is decomposed into different non-homogenous masses of individuals, the homotypes remain constanst no matter the form and nature of the decomposition. Thus biotypes that arise as caused by segregation and the evolution of dominance can either segregates homotyes or change organic correlations. They cannot alter pure homotypes into parts and wholes.

By adding a fourth dimension to a given three manifold of parent-offspring transmission 2 parameter manifold and the third geneotype dimension, where this fourth dimension contains a variable population size it is possible to investigate these differences caused by homotypic and organic correlations because while with organic correlatins the knots can be converted into inknots inthese fourth dimensioned representations the homotypic correlations cannot. This enables the homogeneity and heterogeneity of the statistica population to be discriminated from the individual differences and elmintes the the polemic between the pure linists and the biometricians. With these maths one clearly can say what sets of traits pairs form unknots and how linkage depends on a particular species populations sizes.

The only way to actually test the difference is in a series of cases of signficant subindivudla variation ( in which the individual possesses not just it’s own variance but also skew and kurtosis) . In those situations there may be more variation within the idiv iudal than within the population it is in . It is this variability that can show the Batesonian differentiate of the segregation vs the D-statistic. The genetic code (expression of a gene) is how life ensures that a population does not historically degrade the affect of subindividual variations that bifurcate segregations and homotyical differences.

Poly allelism — polygenism duplicates with in (bangles) vs varationst at each (tangles) into natural biotypes.

Such selection changed the relative proportion of genotypes in the population, not any genotype itself. There could have been room here for reconciliation with the biometrical view of variation in non-experimental populations, but that avenue was not pursued by Johannsen. Instead, like many other exponents of Mendel’s rediscovered work, he chose to dispute the idea that different types of organism could be “evolved from each other by extremely small steps in genotypical change”. Instead, “the mutations really observed in nature have all shown themselves as considerable, discontinuous saltations” (1911: 158; i.e., jumps).

This issue was caused by the statistical observation and belief passed on geometric differences rather than organic correlations and variance by samples from the population rathe than triangels on the surface of two variables. There is still room to recognize changes in the genotypes as sums of log exponentials of places on the chromosome (polygenism) into assyptotic differences in allelisms (poly alleims). This may inform an understanding of the genomics of disease. This does not have to imply that heterozygotes and homozygotes are basic as these go back to the two sexs for Galton nature nurture per Johannes genotype constitutional nature nuture by ambient conditions ( rather than anestaral natural population conditions). I was able to think of this because I had reduced a visualization of Bateson’s criticism of pearson to meristic somatic Tcharacters that vary ( in the D arcy thomposon coordinate transform sense) as log expoentials to an identifying metricsim ( that is non Euclidean in the gene of Johansen). This relation of polyalleism and polygenism should be expressible in knots. , “some method for analyzing the genotypical constitution or genotype as a whole was needed. Johannsen did not provide one.” Thus homo ( two same) and heter zygotics ( two different) come out of a duality in log exponentials informed by dominants and recessives per regression and dispersion not the other way around while mergeing the natural history to the breeding and control experimental. Thus in biology there is as in physical experimental and theorerical physics, there is experimental breeding genetics and theoretical natural population phanetics where experimentally the homozygote and heterozygote are presumed but in the phanetics they are constructed on a case by case basis. Lewontin and Taylor missed the option of building the phenotype rather than genotype at the junction of the meaning of the reaction norm logically ( when and how parralells and convergence apply per niche constructions etc).

Taylor and Lewontin new heredity transmission due to indpenence of the traits only exists when the un knot circle of the two traits being studied do not link. RNA can however as a bangle , tangle up the unknot of said transmission via recombination and create the linkage of the crinkly peas more often on dwarf plants”” in a different species after selection of the increased variance in the mature developmebts of such states.

De vrieanisms can be sorted out in species similiarites on the notion of the genotype herein in 4 dimensions which can never be found by mendeilan segregation (being always the same). These moves in the 4 space when back can show how skew and kurtosis sort into tramsissions of independences of sd and variances per cross generation transmission.

(Indeed, by the 1930s heredity had come to refer to the transmission of and cross-generational patterns in these differences, not to the development of the similarities from which differences depart [Sapp 1987].) Genotype could be applied to classes of organisms with a specific pair of genes (or small set of pairs) or to the specific pairs of genes themselves (matching the connotation of type as an abstraction away from the full set of observed characteristics).

The thing is that the similarities from which the differences depart is what makes a taxa taxogenic, and this is how ancestral forces if not particles can influence endogamy and exogamy. By not arguing against progression as much as regression the heredity studies in the 30s that only looked into differences and the transmission of indpenenedet mendelian traits and cross generation patterns could not a priori reach the needed higher manifold view of the heterozygote and homozygote of divisions of log exponents( some pairs same, some different per asymptote) in such large cross generational manifolds.

Pairs of knot properties as pairs of genes.

Wheldale’s genetic analysis of the color of snapdragon flowers, for example, showed that plants with one or more dominant alleles (i.e., variants of the gene) at a certain locus would show color patterns that she was able to associate with the genotype at three other loci, but plants with two recessive alleles at the first locus would be white no matter what — the homozygote recessive genotype had an epistatic effect over the other genotypes

This is merely relation of the cut of clones to infinity vs infitnesimal in the direction of the evolution of domaince in the higher dimensional representation. Just very complicated to dissect but not impossible.

Thus the mendelian view can not get to the proportion of genes shared by relatives relative to the effect of the heterozygote and homozygote the proportion of genes per “race” this can be oriented given a pa particular eov lution of domnaince in the higher dimensions.

Quantitive genetics can not find this effect of the deme moving up the landscape in different ways? By selection coefficients??/

“, namely, a difference that makes a difference (see entry on causation and manipulability). (The serious debate about whether statistical analysis can distinguish causal from non-causal differences that “make” a difference should be noted; Hernán et al. 2002.) The connection between an association within some population and causal mechanisms is susceptible to disconfirmation by experiments. At the same time, doing such experiments invites scrutiny of the relationship of experimentally altered dynamics to the original dynamics that generated the data that were analyzed to show the original statistical association (Taylor 2015).

Most importantly given the framing of this entry around control and reintegration: Any experimental as well as statistical association is also conditional on the subset of the population or species studied and the situations where they are observed (Lewontin 1974b). Understanding associations and formulating manipulations based on them requires attention to what has been experimentally or, at least, statistically held constant. In other words, in controlled conditions the direction of the arrow labeled identification in Figures 2 and 3 may be reversed and given a causal connotation, but the causality is conditional on the factors, including the rest of the organism, held constant.”

By using progression as well as regression and the orthogonal regession on a surface rather than the stats on the plane by variances that are not triables for the observations of the geometric and organic correlations we do not have to reach the program of Lewontin and Taylor because the phanology supports a robust genotype capable of having the traits Lewontin and Tylory wanted DNA to be gentoyrpe of .

Waddington’s interpretation is that a genotype (in the sense of a specific set of pairs of genes) had arisen in the population that switched on development of large papillae. Presumably, this could happen through reassortment of genes into new genotypes, not a random mutation. An alternative hypothesis, which places more emphasis on the dynamics of development, is that, if many pathways in a non-inbred population can produce the same response (e.g., enlarged anal papillae in response to salt), selection results in a population of individuals that have a concentration or redundancy of the various pathways. If pathways arise within this concentration where large papillae develop without the salt stress, that is not a logical process to be modeled by population genetic or quantitative genetic models, but a contingent outcome of the dynamics of development in a realm in which a variety of genotypes can influence a variety of paths to a trait. In this light, to call traits phenotypes, and thus suggest that they have a direct association with a specific genotype, is to make it more difficult to conceive and pursue a program of reintegration in which researchers examine cases of traits that are acquired as an appropriate response to environmental condition and then increase in frequency in a population. M

I do this with four dimensional return of the knot to the unknot?? And answer the quantitiativ e genetic lacunae by the wrong notion of the environment for the forces in the energy and when the log exponetials are not particulate but are macrons wise associatable.

Does not selection of the immature offspring variance change the genotype? Can not selection for offspring behavior under social selection change within genoytpes?

Can homotypes be defined as groups of copied gene regions that depending on expression of them result in differentiations and the multiple alleomorphs of them cause different organic correlations amongst the differentiations of the homotypes?

Distance to the ground from the mean of parents different than offspring to the infinitesimal permits different population size effects as when the infintiesimals are so small that no force can change the effects. Variablity to the infinite for each curve to ground however shows that Pearson? was mistaken to think that all variation is of the same kind coming from the law of error/

““It is now beginning to be generally understood, even by merely practical statisticians, that there is truth in the theory that all variability is much of the same kind. The theory rests on the grounds that all variability is due to an uncounted number of small independent influences, acting variously in different cases. Mathematicians are able on these purely abstract grounds to develop a singularly beautiful law, known as the law of frequency of error.””

One neat development of this theory is that the Darwin’s wedging of indviuals in dense ecologies will be ableto be defined interms of geometries between different species extant popualtions

The new corner relations to the environment in atttactions and repulsions can be computed up to varaitions in error in the r ( correlation regression , reversion,)

We will finally be able to answer Kant’s force in classificzationa sn classififcations of forces byt showing how certain linnean herirchies can be overdetermined by Thurstonian geometrical hierarchies