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History Re-Imagined

2. HISTORICAL REEVALUATION – pre to post Synthesis

William Provine states, “ If true, Pearson’s homotyposis theory would have been a stunning contribution to biology.” But Will situates Mendelism and discontinuous evolution on one side and biometry and Darwinian evolution on the other. In that he was mistaken.


What were the biological foundations of Pearson’s theoretical argument? What were his assumptions and were they dubious? Pearson claimed that the data showed numbers similar enough but what is the error? What are the chance distributions from which one can determine that the 0.4570 was close enough to 0.4479.

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Pearson claimed that the two ways to obtain these values were from the same phenomenon. Bateson challenged Pearson on how one was to determine what parts of organisms were to be considered as homotypes and what were not. Pearson said that homotyposis appeared mathematically when there was evidence of undifferentiation – no correlation to environment , etc. Bateson thought that this was simply evidence of evolved symmetry differences. How this relates to the creationism and evolution debate in the US will be considered in a sequal.

What was weak about Pearson’s argument that led Provine to claim that the theoretical argument was weak? Because Pearson considered both the gametes and repetitive parts within an individual to potential homotypes and because he considered the offspring to be representative of the parents Bateson thought that differentiant variation united all of these but in this Pearson found heterogeneity and thus he would have been unable to separate out the data. Regardless of the answer to the question.


Fisher’s work provides a way in which the homotyposis can be reconsidered if we include the modern finding that the genetic factors are genes on chromosomes.

Provine seems to have thought that by using Mendel’s theory Bateson could have “devasted Pearson’s theory” because says Will, ( that )Pearson had assumed the sperm cells and ova were undifferentiated like organs. What Pearson said was that there are, appeared to be, a lack of evidence in what we could know of the variation and differentiation in germ cells so that one could by default consider them homotypes in addition to those other parts already thought to be classified such.


Bateson wanted assistance in trying to understand the variability and differentiation in gametes given Mendel’s ideas but found that Pearson was not helping him (ref). Mendel had suggested that what we now call the heterozygote contained a dual developmental state of hybrid and parent and the union was forced after gametogenesis (ref). Provine thinks that Mendel’s experimental realization that germ cells were differentiated - when Bateson says that he realized it is the gamete and not the zygotes that needed to be computed from - but Pearson simply says that there is a lack of correlation in whatever this differentiation is – so that they can be warranted to be in the homotypic rather than the organic ( individual growth fit to a common end) category. What Will never made clear was that arguing from Mendel the way he does misplaces the history of understanding because at that time, this was postitive eugenics not modern synthesis criticism.


Pearson never applied cross-homotyposis to gametic structures that might be identified. I will do this below. It is possible that some gametic differentiation may be organic and that cross-homotyposis may exist. This will be most clear in the third example (on the origin of the Edicarian biota since the cross direction is purely mathematical in that case). It was not because the differentiating bodies may or may not be material. This will come out more clearly as we understand the parity rules relative to waves of advantageous gene flows.

Bateson thought that symmetry under genetic transmission – heredity and inheritance itself - could explain the differentiation from the variation. Pearson does not discount this – he only says that in that case there should be a heterogenous distribution that different chance causes would reveal on further study. This does not mean to say that catching chance is the only way to find information in biochemicals. Provine was of the opinion that Bateson’s vibration theory of heredity does not fit with a materialist one that may be associated with the chromosome theory of heredity. It is true Pearson could not understand how to use the vibration idea but he also could not understand how to use the symmetry ideas – statistically.

Considering chromosome segment duplication as a homotype we can see that all of this is a confused attempt to understand the differences of opinions.


Provine said that “evidently Bateson misunderstood or rejected what Mendel had said”. He believes Provine found Bateson agreeing with Pearson, in that the “relationship and likeness between two brothers is an expression of the same phenomenon as the relationship and likeness between two leaves on the same tree,..between repeated parts generally”. Provine thought that Mendel’s differentiation of the gametes implies materially that the difference between the differentiation during development and differentiation of the germ plasm meant there was a fundamentally (absolute) different kind of variation in a single plant from the variation in the offspring of the plant. Provine never spelled out what the physical regularity of this irregularity is.


(But) Provine here is relying on an abstract notion of the variation which can be recognized if one attempts to derive the homotypic correlation from the correlation of repeated parts within an organism using post modern synthetic understandings but Pearson said that Bateson’s argument about this was not what he was saying.


Instead Pearson was asking about how the mid parent or one in each generation in past lineages should relate to what makes the difference in the distribution and makes them heterogenous or not.

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AGAIN Provine brought in modern post evolutionary synthesis ideas to make this point as I will explain with my reuse of Fisher advantageous wave model…Wright had developed path analysis specifically be able to handle the kinds of questions Pearson was asking but Provine simply asserted that there was never a demic structure component to the difference but only a simple one of variation in the offspring vs the parent. He never tried to show how the maths of Fisher and Wright differed. He also never worked in Haldane’s ideas which were even more different since neither parent was necessarily certain.

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Now it is possible to use Fisher to show that Bateson’s differentiant evolution he wanted to ascribe to Pearson whether using vibrations or not may be able to unite what Provine asserted was a contradiction.

Now before we do a little historiography and craft an example that counter’s Provine’s position I set the stage for a general differentiat evolution without respect to any kind of vibration. The counter example depends on certain claims about the relation of the vibration to the materiality ( chemical bonds)

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Differentiant Molecular Evolution

High correlation is due to the need for “fit”:

Correlation due to the need for “fit” is not homotypic:

Therefore, High correlation is not homotypic.

William Bateson, Variation and Differentiation in Parts and Brethren


Pearson never responded in public to Bateson’s response to Pearson’s reply to Bateson’s criticism (or at least I have not seen it ( counter rejoinder vs venue). As such the debate never resolved and history has left a irreconcilable difference in it’s place (as Provine has said). Conway’s discovery of surreal numbers provides a means through which we can now fully respond to Pearson and Bateson in their place.


Bateson thought that Pearson never responded to his theoretical position. In Pearson’s public response before Bateson wrote, Pearson addressed Bateson’s criticism most substantially by saying that if Bateson had bothered to read far enough he would have found that Pearson has discussed “cross-homotyposis” and cross evolution but one can find no where in the literature - later - any attempt to develop and draw out this statistical discipline. Instead we find Haldane supporting studies of sub individual variation Pearson’s name and most recently the continuation of this study. This work however has nothing to do with the theoretical point that Bateson claimed to have made.


The theoretical criticism relied on the need to have clear way to understand the difference of organic and homotypic correlation in the materials of evolution, how differentiation, variation, position and symmetry are related and how they can be logically associated with parallelized lines of evolution.


By a priori defining one purine base less than another and creating distributions where the other purine is the negative of the first and by accumulating distributions of higher number of concatenations of bases one is always able to find a symmetrical distribution from which the average homotyposis remains defined because the depth of the line is infinitely deep while also being able to find larger and larger numbers of bases sequences. This permits a clear definition of the difference of homotypic and organic variation. Bateson’s second point can be handled IN THE SAME SET OF DISTRIBUTIONS if a mirror surreal line above the practical one is theoretically added to resort the current distributions through. Reflection operations permit parallels to be swapped in the process of resorting and all of Bateson’s theoretical and practical concerns can be addressed.


Bateson’s concern that position challenges Pearson’s average homotyposis is well formed. However because there is a new infinity with each Day line in the surreal number line it is always possible to reposition the distribution into a different potential infinity for representation ( because of the relation of value and form). And when cross-homotyposis applies (which segment to use, or radial vs bilateral etc) one simply searches across the reflection plane for the quadrant in which the base distributions need to be reorganized into. Once this quadrant is recovered the additional refraction operations are detailed to put the organic and homotypic correlations back into the same cause of the logical answer to Bateson’s syllogistic rescritption of the issue. Kant had already addressed how to do this but with Conway’s numbers we can see how to do it with evolutionary theory itself.


For reasons I may explain below, consider A bases to be less than G then if we start with an A

Then it’s surreal number is -1 and G is +1, Then we consider the pyrimidines and we find (given an additional a priori rule , that since T goes with A , T is less than G. Hence the four bases are ordered by less and greater than as A<G: T<C here I assume that complements need to be on each side of zero rather than being spread across it. I may be wrong - but it seems that we need to keep the linearity of the DNA strand covalent bond heritiability not the cross strand hydrogen bond hybridization when it comes to how chemical bonds are related to adaptability and evoleability. Whether TT< GG however I am not certain but I think GG<TT for stemming from the reason I did not say I wanted A<G. But think this is not symmetrical enough.

A<T<G<C

AA<AT<AG<AC<TA<TT<TG<TC<GA<GT<GC<GG<CA<CT<CG<CC

AA<AT<AG<AC<TA<TG<TT...?

AAA<AAT<AAG<AAC…


Given the A is electrotonic quantum mechanically insulating we are able to get to the infinite ordinals while G with the this double set theory of Von Neumann sets as Conway did and this is because the electrical macrons thus produced can interact with the physical macrons of cell divisions. This will enable one to bridge the gap and integrate on the surreals. Since the quantum electrotonics always puts numbers on the left the individual evolves/marches to the right. The eletrotonic A never places any numbers on the right which is the A being mostly insluators ( at least not electrotonic – transferring electrons). You are only saying that the sequence is always more ( more electrons transferred) from a nothing/vacuum/insulator and this gives you the von Nuemann ordinals in sequence positioning. Thus the gravitational collapse of the protons may have more of a massive effect on the neutral bases but the transfer of the electrons permits the ordinals to be accessed in sequences ordered by increasing surreal numbers. This increase is dependent on atomic electron orbits that form infinite series when observed in flame spectra and which are composed from hydrogen on up the periodic table. How these cross the infintesimals given one line at infinity projected is what appears cytoplasmically and biologically.



Fisher spread of a advantageous allele in two directions explains how we can not have Bateson’s fit of claw on the left and the right with half fit one way in a population and half the other way in half of the same population since both ways are traversed at the same evolutionary time. Bateson’s idea is that of the deme. This destroys his scruple that “Parts are not homotypes if their correlations affect the “welfare” of the individual”.

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3. Example 1 – Counter to Provine

Exclusive Exosomic Inheritance : through Differntiant Evolution

The divergence between observed results and theoretical expectations is not what soley determines the relation of the Mendelian population to the study of its contribution to evolutionary theory. Rather, exclusive inheritance may in some Mendelian cases be inclusive of speciation. I describe contra Fisher's opinion and Haldane's declination that phenotypic discontinuity can in at least a class of genes be recursively connected through reductive segregations by advancing waves of mutated exosomes. Whether this qualifies as a case of Mayr’s genetic revolution I leave to the reader to judge.

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