On replacing the biological notion of homology with a new transfinite genetics or preliminary quotations in preperation to JUDGE the alternative of Collet apparently contrary Thom that either the continuum is not well-ordered OR the 3 infinite proper subsets and inversion of the natural ordering of two of these substets exist (aka can Lewontin's coupled differential equation be disqualified by an answer to inspection as Collet requested by an intergration in adjudication.). I will accomplish this by talking MORE than Bertrand Russel who in PRINCIPLES OF MATHEMATICS delimted the worked thru creation/evolution confusion to the harmonic tune of "The kind which belongs to the rational numbers, and consists in having a term between any two we have agreed to call compactness; and to avoid confusion, I shall never again speak of this kind of continuity."
but we shall code the polymorphous set whether encoded or incodingj to the sound of the compaction that definitionally is continuous in the application of nanotechnology to mole bio with RNA between any DNA
for we shall find while testing Wolfram's NEW KIND OF SCIENCE that biodiversity informatic IT and bioinfomatics platforms will more efficiently become integrable during this judgement. There will be also criticism independent of the length of prolonging beyond Russel due to concommittant Macrothermodynamcis or better statistical mechanics of the dual translation and transcription into adherence, coherence and inherence classes for Haldanes putting of Wright use of geometric progreesion witll not be discarded apriror nor out of hand. This will become increasinlgy apparent in the lower limit of biological discouse as it will be herein stipulated that Kervran's potentially weak force biological transmutations will not be considered real in the sense of Cantor wanted religously or not to distinguish real and reel numbers no matter whehter one agrees with me or GOuld on Mayr etc as we mrshall with Cantor and Russell but agaisnt Dauben and others the non-existence of the infintiesmals as far as Wolfram's analgogy of natural selection and engineering goes (Immunology has the competence to make it practical as to the extent of LOGICal disagreement IN BIOLOGY) with linear numbers (no matter the "fractal" but with WOODGERS logic of the bauplan) learning to seperate and keep seperate IN COMPUTERS geometric and arithmetic statistics (of biometry)
Huxley-Evolution:The Modern Synthesis Chp3 Mendelism and Evolution 1. Mutation and Selection "The essence of Mendelian heredity is that it is particulate. The genetic constitution is composed of discrete units. Each kind of unit can exist in a number of discrete forms. The hereditary transmission of any one kind o funit is more or less independent being a partial one, concerned with the phenomenon oflinkage." p47
Dauben-p293 "Cantor had never been content with a purely mechanical physics. Above all else, it seemed destined to promote materialism which he attributed in large measure to Issac Newton and to Newton's faulty metaphyiscs.74 As an antidote, Cantor sought what he called an organic theory of nature determined with the same mathematical precision as Newton had brought to his materialistic, mechanical philosophy. The key to this new organic approach was to be found, Cantor believed, in his transfinite numbers:
The elements of the set M in question are to be thought of as seperate; in the intellectual copy of M^_, which I call its order type, the units are nevertheless joined into an organism. In a certain sense these order types may be regarded as a composite of matter and form; the conceptually distinct units contained therein comprise the matter, while the order of these elements corresponds to their form.75"
Quantity
Mendelp8 "Henceforth in this paper those characters which are transmitted entire, or almost unchanged in the hybridization, and therefore in themselves consitute the characters of the hybrid, are termed dominant, and those which become latent in the process recessive. The expression "recessive" has been chosen because the characters thereby designated withdraw or entirely disappear in the hybrids, but nevertheless reappear unchanged in the their progeny, as wioll be demonstrated later on."
This reappearence may be signaled by the collection of ordinals forming a cardinal apparent in the progeny. However to be as fair as possible in the end to Fisher one must either actuall discount Huxley account of mendelizing gene diffences in the absolute (by failure ot analyize with the simply ordered sets?)or in particular some sematics lexically determinatble of his claim historically about the dropping of Medel's characters being false. This is a false fact in evolutionary law when not also simply the failure BOTH to have the French and recent Englsih translations of Cantor distinguish the real and reel numbers and the failure of geneticits to work the EXTERNAL variable no matter the approximation of the data to 3:1 to INFINITE I N I T E G E R S thus it may simply be that Huxley took Mendel's NOTION of REapperence of the recessive (defined and termed by Mendel) in the F2 as a PHSYICAL PRIOR disapperence WHERE if an infinite and not a finite integers rules the statical result is never THOUGHT as SPATIAL removal. This gets back to Russel notion that the SPACE would at least on Cantors notion be "religously" different and defendable with transfinites no matter the natura/naturatta distinction Dauben quite scholarly remanded BETWEEN philsophy and mathtmeatics so if molecualr biology can use continiuty of the rational power no matter the response to COllet with Thom or aginst Lewontins non-use of catastrophe theory in working in the EVOLUTION in topobiology then Huxley's HISTORICAL claim about genetics would be showable in a court of genetic paradigms to be the false fact I have already indicated it is.
A cardinal characterization of the hybrid thenleads to a search of the cardinals N0 , N1, N2,... to find an accessible one that the ordinals generated from this number created a numbering ( that is the difference of finite and infinite if you do not know this theology) thru the sexual union of ordinals that generates a next cardinal distributing simply ordered sets epigentically in the offspring as a form of the ordinals per ordertype.
As the sign Mendel used was A + 2Aa + a somehow the transfinite nimber in this taxa must have twice as much ordertype formation than the format of the cardinals and ordinals involved no matter the infinite symbol for the simply ordered sets involved in the well-ordering as expressed by the actually finite # reproductions per bio-change to some other well-ordering.
Quality
Mendel's Experiment with Hybrids of other Species of Platns @ "In Pisum it is known that the characters of the flower- and seed- colour present themselves unchanged in the first and further generations, and that the offspring of the hybrids display exclusively the one or the other of the characters of the original stocks. It iws otherwise in the experiment we are consdering" that this notion of Cantor's ASSUMPTION that every set could be well-ordered.
Is the difference of stress of cardinal numbers from the Grundlagen to the Beitrage and failure to
Magnitude
Mendel- "These two experiments are important for the determination of the average ratios, because with a smaller number of experimental plants they show that the very considerable fluctuations may occur. In counting the seeds, also, especially in Expt.2, some care is requisite, since in some of the seeds of many plants the green colour of the albumen is less developed, and at first may be easily overlooked. The cause of this partial disappearence of the gree colouring has not connection with the hybrid-character of the plants, as it likewise occurs in the parental variety. This peculiarity [bleaching] is also confined to the individual and is not inherited by the offspring. In luxuriant plants this appearance was frequently noted.
Dauben - "Again, since there was no largest element, one could imagine another number representing the entireity, in order, of numbers w+v. Denoting this entirety by 2w, it was possible to continue further:
2w, 2w+1,2w+2,...2w+v,...
In attempting ot characterize this mode of generation, Cantor allowed that w could be regarded as a limit which the natural numbers N (increasing monotonically) approcahed but never reached.^10 Lest the analogy seem entirely mistaken, he added that by this he meant only to emphasize the character of w taken as the first whole number following next after all the numbers nEN. The idea of w as a limit served to satisfy its role as an ordianl, the smallestg integer larger than any integer nEN.
This then was the second principle of generation. Whenever a set of numbers could be considered as limitless in extent, new transfinite numbers could always be generated by positing the existence of some least number larger than any in the given class. Cantor expressed the essential feature of this second principle of generation in terms of tis logical function:
I call it the second principle of generation of real [realen] whole numbers and define them more precisely: if any definite succession of defined whole real numbers exists, for which there is no largest, then a new number is created by means of the second principle of generation which is thought of as the limit of those numbers, i.e., it is defined the next larger of all of them.^11
By succesive application of the two principles it was always possible to produce new numbers and alsways in a completely determined succession in their most general formulation, such numbers could be wrtten as follows:^12
5.1) vow^u + v1w^(u-1)+...+vu."
Towards use of this transfinite presentation to better the goal of electronic species publishing by incorporting mutiatonal taxonomy phentically into classificatory biology
Huxley - "The particulate nature of inheritance enables calcualtions to be made as to the proportions of offspirng of didfernt types in different generations afters a xross. Like the atomic theory in chemisty, it si the basis of qunatiative treatment."
Mendelp34 It is otherwise with the exceptional cases cited. Gartner confesses even that the exact determination whether a form bears a greater resemblance to one or the other of the two upon the subjective point of view of the observer. Another circumstance could, however, contribute to render the results fluctuating and uncertain, despite the most careful observation and differentiation. For the experiments, plants were mostly used which rank good species and are differentiated by a large number of characters. for the experiments, plants were mostly used which rank as good species and are differentiated by a large number of characters. In addition to the sharply defined characters, where it is a question of greater or lesser similarity, those characters must also be taken into account which are often difficult to define in words, but yet suffice, as every plant specialist knows, to give the forms a peculiar appearance."
Dauben 132 Cantor reinforced his study of the philosophical status of his new numbers with a simple analysis of the familiar and accepted natural whole numbers. For both finite and infinite integers, they could be considered in essentially two ways. Insofar as they were well-defined in the mind, distinct and different from all other components of thought, they served "in a connectional or relational sense to modify the substance of thoughjt itself This reality which the whole numbers as expressions or images of processes in the world of physical phenopmena. This aspect of the whole numbers, be they finite or infinite, he termed transsubjective or tansient.
Cantor asseerted the reality of both the phyeical and ideal aspects of the number concept. These dual realityes, in fact, were always found in a joined sense, insofar as a concept possessing any immanent reality always had a transient reality as well. It is one of the most difficult problems of metaphysics to determine the nature of the connection between the two.
Recapitualtion--Huxley-"For ordinary natrual selection involving a simple dominant with a selective advantage of 1 in 1,000 (i.e. where the ratio of dominant to recessive changes from 1 to 1.001 in each generation) it will take nearly 5,000 generations to increase the proportion of the dominant from 1 to 50 percent, and nearly 12,000 more to raise it to 99 percent. For the early stages of selection of a single mutation which constant effects, when the tgeen is still very rare, dominants can spread much more rapidly than pure recessives, unless a certain degree of inbreeding occurs."
Andthus we have explained why Provine thought that no frcitional light between Fisher and Wright resulted in the kind of advance in thinking Mayr thought would have to occurr if the bag of beans meant anything for Boston Tea Party and as I had analyzed this situation before I had:Toward saving web generations my first analysis of this synthesis was without Corinthians: Acts:1-2; JOEL
Mendel*should* (no)(sic!) have expected 1:2 ratios with a chi square p=.99993 but rUther ("farther", further, futher) some deviation/clinamen addition due to small number of seeds, chance chromosome events and yet what Mendel said, was; "The dominant character can have here a double signification vz. that of a parental character, or hybrid-character. In which of the two significations it appears in each seperate case can only be determined by the following generation." (The translation^* said "determined" not "obtained" and is thus in fidelity to any conception of induction Mendel may have possessed) that when generalizing the computation to maximal universality no matter the equivalent sophistication this signification is dissolved (by so-called Provine "continuous diffusive effects")
The faliure of the mathematics of biology seems to have accurred wholy beacuse Fisher sided with Mendel's choice of the Cardinal while It increasingly looks to me like the more coordinated view of Wright (shifting balance) is likely to come out on top when the evolution not development aspects of topobiology are squared with development not evolution view of Mendel. There still is the reveresiblity when BOTH reverse lexicographic encoded polymorphic traits and entropy per any 2nd law of therm acutality in Macrothermodynacis is dynamized IN THE SYMBOLS (extra Gibbs term etc) outstanding in the grammer which either indicates an grammetological error on Mendel's part with USE of double signification, time for more use beyond Faraday's "bipolarization" of cause electronically and electrically flexible with Newton's "spirit" else any metrics involved in Einstein's rod and clock communityis acutlly compassed at least biologically.
- - - - - - - - - = = = - - - - - - - -- ---
But this only seems to establish that Collet's discrete correction by Thom if it exists in more truth is only that panthesism rules the continuum NOT (so) well-ordered no matter the application in biology.
Species' relation to the Ecosystem by answer to the above question prior to masters' review.
Cardinal + 4(1/2 ordertype) + ordinal= Mendel hybrid (baramincally or not?)
I use 4(1/2)=2 because Mendel noted spotting in progeny absent in progenitoprs and sister outp group compared IN COLOR.
Daubenp220 "Neither artithemetic nor the concept of number should be tied to any narrow domain of particulars - point sets,for example.
I assert that even if there were two reversed lexicograpic molecular biological ordering of the gene code available these would not even be constitutive in these point sets. Is not a point set of the collection localities of the hybrids' geographic distribution beyond the garden but a matter merely of the finite number of 1/2ed ordertypes between the distance isolation by distance (Wright) created multiplied by an integer (such as those Weyl asserts for aij; p100 between latice bases multipole Four in the same question Edelman opens both his own book TOPOBIOLOGY and Shcrodinger's WHAT IS LIFE??
Is this not a genetic basis fot the deductive biogeography Croizat sought for Panbioegoraphy but is yet to show expression with the Fourier Math of Cantor's ascending P SYMBOLS interms of Croizat "topography" but made metric in Wright's isolation by distnace reactived in transfinite terms?
References
Collet, F. What is the missing axiom in our trying of a well-ordering on the Continuum? in Bio-Math Bio- Mathematique & Bio-Theorique Tome XXXVIII 3`eme trimestre 2001 (N^o 151)
Dauben, Joseph Warren 1990 Georg Cantor His Mathematics and Philosophy of the Infinite Princeton University Press, Princeton New Jersey
Gould, Stephen Jay, 2002 The Structure of Evolutionary Theory The Belknap Press of Harvard University Press Cambridge Massachusetts
Huxley, Julian 1964 Evolution: The Modern Synthesis John Wiley & Sons, Inc., New York
Lewontin, Richard 2000 The Triple Helix Gene, Organism and Environment Harvard University Press Cambridge, Massachusetts
Mendel, Gregor 1965 Experiments in Plant Hybridisation Harvard University Press Cambridge
Russel, Bertrand 1903? Principles of Mathematics W.W. Norton & Company INC, New York
Weyl,Herman 1952 Symmetry Princeton Univeristy Press, Princeton New Jersey
Wolfram Stephen 2002 A New Kind of Science Wolfram Media, Inc. Champaign Ill.
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