Ending the Karl Pearson Controversy (1904): Over the Incomplete Couplets Produced by Mendel’s Fraction-Addition Method

Conrado Ruiz-Hernández

doi:doi:10.11648/j.ijgg.20140206.14

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Ending the Karl Pearson Controversy (1904): Over the Incomplete Couplets Produced by Mendel’s Fraction-Addition Method

Conrado Ruiz-Hernández

Published in International Journal of Genetics and Genomics (Volume 2, Issue 6)

Received: 28 November 2014 Accepted: 23 December 2014 Published: 6 January 2015

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Abstract

Early in the 20th Century, leading mathematicians found a link between Mendel’s Laws and Newton’s Binomial. This enabled multigenerational studies of entire populations. In this regard, K. Pearson in 1904 raised objections to Mendel’s predictions that the ‘pure’ (dominant and recessive) descendants of hybrid ancestors turn out to be incomplete assemblies when using the sum of fractions used by Mendel in his 1866 article “Experiments in Plant Hybridization”. This algorithm is analyzed as a model for the case of just one hereditary characteristic, within an axiomatic framework that necessitates the formulation of a theorem in order to elucidate whether it was, on the one hand, a genuine mistake or, on the other, it is what Mendel, with all conviction and consideration, intended to say. We take into account the contemporary (1850-1870) knowledge of the cell and the structures involved in the transmission of inherited characteristics that this pioneer in the field of genetics would have had available for his deliberations at a time when this discipline was not yet a science. There follows the analysis of an unspecified intermediate member of the sum of fractions (not included in the Mendel’s original paper), which, from a mathematical standpoint, helps us resolve the incomplete assemblies (‘pure’ descendants) enigma.

Published in	International Journal of Genetics and Genomics (Volume 2, Issue 6)
DOI	10.11648/j.ijgg.20140206.14
Page(s)	121-125
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2024. Published by Science Publishing Group

Keywords

Mendel’s Laws, Transmission of Inherited Characteristics, Mendel’s Fraction-Addition Method, Hardy- Weinberg Law, and Newton’s Binomial

References

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[2]	Bowler PJ: The Mendelian Revolution. The John Hopkins University Press, Baltimore 1989.
[3]	Coleman W: Biology in the Nineteenth Century, Problems of Form, Function, and Transformation, Cambridge University Press, New York 1977.
[4]	Corcos A, Monaghan F: Gregor Mendel’s experiments on plant hybrids: a guided study, New Brunswick: Rutgers University Press 1993.
[5]	Di Trocchio F: Mendel’s experiments: a reinterpretation, Journal of the History of Biology 1991, 24: 485-519.
[6]	Edwards AW: G.H. Hardy (1908) and Hardy-Weinberg Equilibrium, Genetics 2008, 179: 1143-1150.
[7]	Franklin A: The Mendel-Fisher controversy: an overview. In: Ending the Mendel-Fisher Controversy (Allan Franklin et al, Editors), University of Pittsburgh Press, Pittsburgh (PA) 2008, p. 1-77.
[8]	Fisher RA: Has Mendel’s work been rediscovered? Annals of Science 1936, 1: 115-137.
[9]	Hull LW: History and Philosophy of Science: An Introduction. Longmans, London 1959.
[10]	Hartl D, Orel V: What Gregor Mendel Think He Discovered? Genetics 1992, 131: 245-253.
[11]	Iltis H: Gregor Johann Mendel, Springer Verlag, Berlin 1924.
[12]	Ledesma-Mateos I: Historia de la biología, AGT Editor, Distrito Federal (México) 2000.
[13]	Losee J: (Fourth Edition), A Historical Introduction to the Philosophy of Science, Oxford University Press, New York 2001, p. 72-85.
[14]	Mark H: Gregor Johann Mendel on Pisum sativum: Archives of Ophthalmology 1966, 75: 287-289.
[15]	Mendel G.: Experiments in Plant Hybridization (1866). In: Stern, C., and E. Sherwood, The Origin of Genetics: A Mendel Source Book. W. H. Freeman, San Francisco 1966, p. 16, 24, 29-30.
[16]	Olby RC: Mendel no Mendelian? History of Science 17: 53-72. Reprinted with minor changes in The Origins of Mendelism, 2nd ed., 1979, pp.234-258. Chicago: Chicago University Press, 1985.
[17]	Olby R: Mendel, mendelism and genetics. This essay appears, exclusively at Mendel Web 1997.
[18]	Orel V: Gregor Mendel: the first geneticist, Oxford University Press, Oxford 1996.
[19]	Pearson K: Mathematical contributions to the theory of evolution. XII. On a generalized theory of alternative inheritance, with special reference to Mendel’s laws, Philosophical Transactions of the Royal Society 1904, 72: 505-509.
[20]	Ruiz HC: Corrección a una equivocación de Karl Pearson (1904): la suma de fracciones de Mendel no produce acoplamientos genéticos incompletos. Ciencia ergo sum, 2014, 21(1): 67-70.
[21]	Sandler I: Development: Mendel’s Legacy to Genetics. Genetics 2000, 154: 7-11.
[22]	Schwartz J: In pursuit of the gene: from Darwin to DNA, Harvard University Press, Cambridge (Massachusetts) 2008.
[23]	Sturtevant A: (Republished Edition), History of genetics, Cold Spring Harbor Laboratory Press, @Foundations of Classical Genetics 2001.
[24]	Wilczynski J: Contributions to the theory and evolution of mendelian generalizations. Acta Biotheoretica, 1942, 6: 97-152.
[25]	Wood R, Orel V: Genetic prehistory in selective breeding: a prelude to Mendel, Oxford: Oxford University Press 2001.

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Conrado Ruiz-Hernández. (2015). Ending the Karl Pearson Controversy (1904): Over the Incomplete Couplets Produced by Mendel’s Fraction-Addition Method. International Journal of Genetics and Genomics, 2(6), 121-125. https://doi.org/10.11648/j.ijgg.20140206.14

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ACS Style

Conrado Ruiz-Hernández. Ending the Karl Pearson Controversy (1904): Over the Incomplete Couplets Produced by Mendel’s Fraction-Addition Method. Int. J. Genet. Genomics 2015, 2(6), 121-125. doi: 10.11648/j.ijgg.20140206.14

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AMA Style

Conrado Ruiz-Hernández. Ending the Karl Pearson Controversy (1904): Over the Incomplete Couplets Produced by Mendel’s Fraction-Addition Method. Int J Genet Genomics. 2015;2(6):121-125. doi: 10.11648/j.ijgg.20140206.14

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@article{10.11648/j.ijgg.20140206.14,
  author = {Conrado Ruiz-Hernández},
  title = {Ending the Karl Pearson Controversy (1904): Over the Incomplete Couplets Produced by Mendel’s Fraction-Addition Method},
  journal = {International Journal of Genetics and Genomics},
  volume = {2},
  number = {6},
  pages = {121-125},
  doi = {10.11648/j.ijgg.20140206.14},
  url = {https://doi.org/10.11648/j.ijgg.20140206.14},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijgg.20140206.14},
  abstract = {Early in the 20th Century, leading mathematicians found a link between Mendel’s Laws and Newton’s Binomial. This enabled multigenerational studies of entire populations. In this regard, K. Pearson in 1904 raised objections to Mendel’s predictions that the ‘pure’ (dominant and recessive) descendants of hybrid ancestors turn out to be incomplete assemblies when using the sum of fractions used by Mendel in his 1866 article “Experiments in Plant Hybridization”. This algorithm is analyzed as a model for the case of just one hereditary characteristic, within an axiomatic framework that necessitates the formulation of a theorem in order to elucidate whether it was, on the one hand, a genuine mistake or, on the other, it is what Mendel, with all conviction and consideration, intended to say. We take into account the contemporary (1850-1870) knowledge of the cell and the structures involved in the transmission of inherited characteristics that this pioneer in the field of genetics would have had available for his deliberations at a time when this discipline was not yet a science. There follows the analysis of an unspecified intermediate member of the sum of fractions (not included in the Mendel’s original paper), which, from a mathematical standpoint, helps us resolve the incomplete assemblies (‘pure’ descendants) enigma.},
 year = {2015}
}

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Author Information

Conrado Ruiz-Hernández

Departments of History of Biology and Environmental Education at the National Autonomous University of Mexico: UNAM-Iztacala, Los Reyes Iztacala, Tlalnepantla-Estado de México, México. 54090

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APA Style

Conrado Ruiz-Hernández. (2015). Ending the Karl Pearson Controversy (1904): Over the Incomplete Couplets Produced by Mendel’s Fraction-Addition Method. International Journal of Genetics and Genomics, 2(6), 121-125. https://doi.org/10.11648/j.ijgg.20140206.14

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ACS Style

Conrado Ruiz-Hernández. Ending the Karl Pearson Controversy (1904): Over the Incomplete Couplets Produced by Mendel’s Fraction-Addition Method. Int. J. Genet. Genomics 2015, 2(6), 121-125. doi: 10.11648/j.ijgg.20140206.14

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AMA Style

Conrado Ruiz-Hernández. Ending the Karl Pearson Controversy (1904): Over the Incomplete Couplets Produced by Mendel’s Fraction-Addition Method. Int J Genet Genomics. 2015;2(6):121-125. doi: 10.11648/j.ijgg.20140206.14

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@article{10.11648/j.ijgg.20140206.14,
  author = {Conrado Ruiz-Hernández},
  title = {Ending the Karl Pearson Controversy (1904): Over the Incomplete Couplets Produced by Mendel’s Fraction-Addition Method},
  journal = {International Journal of Genetics and Genomics},
  volume = {2},
  number = {6},
  pages = {121-125},
  doi = {10.11648/j.ijgg.20140206.14},
  url = {https://doi.org/10.11648/j.ijgg.20140206.14},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijgg.20140206.14},
  abstract = {Early in the 20th Century, leading mathematicians found a link between Mendel’s Laws and Newton’s Binomial. This enabled multigenerational studies of entire populations. In this regard, K. Pearson in 1904 raised objections to Mendel’s predictions that the ‘pure’ (dominant and recessive) descendants of hybrid ancestors turn out to be incomplete assemblies when using the sum of fractions used by Mendel in his 1866 article “Experiments in Plant Hybridization”. This algorithm is analyzed as a model for the case of just one hereditary characteristic, within an axiomatic framework that necessitates the formulation of a theorem in order to elucidate whether it was, on the one hand, a genuine mistake or, on the other, it is what Mendel, with all conviction and consideration, intended to say. We take into account the contemporary (1850-1870) knowledge of the cell and the structures involved in the transmission of inherited characteristics that this pioneer in the field of genetics would have had available for his deliberations at a time when this discipline was not yet a science. There follows the analysis of an unspecified intermediate member of the sum of fractions (not included in the Mendel’s original paper), which, from a mathematical standpoint, helps us resolve the incomplete assemblies (‘pure’ descendants) enigma.},
 year = {2015}
}

Copy | Download

TY  - JOUR
T1  - Ending the Karl Pearson Controversy (1904): Over the Incomplete Couplets Produced by Mendel’s Fraction-Addition Method
AU  - Conrado Ruiz-Hernández
Y1  - 2015/01/06
PY  - 2015
N1  - https://doi.org/10.11648/j.ijgg.20140206.14
DO  - 10.11648/j.ijgg.20140206.14
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JF  - International Journal of Genetics and Genomics
JO  - International Journal of Genetics and Genomics
SP  - 121
EP  - 125
PB  - Science Publishing Group
SN  - 2376-7359
UR  - https://doi.org/10.11648/j.ijgg.20140206.14
AB  - Early in the 20th Century, leading mathematicians found a link between Mendel’s Laws and Newton’s Binomial. This enabled multigenerational studies of entire populations. In this regard, K. Pearson in 1904 raised objections to Mendel’s predictions that the ‘pure’ (dominant and recessive) descendants of hybrid ancestors turn out to be incomplete assemblies when using the sum of fractions used by Mendel in his 1866 article “Experiments in Plant Hybridization”. This algorithm is analyzed as a model for the case of just one hereditary characteristic, within an axiomatic framework that necessitates the formulation of a theorem in order to elucidate whether it was, on the one hand, a genuine mistake or, on the other, it is what Mendel, with all conviction and consideration, intended to say. We take into account the contemporary (1850-1870) knowledge of the cell and the structures involved in the transmission of inherited characteristics that this pioneer in the field of genetics would have had available for his deliberations at a time when this discipline was not yet a science. There follows the analysis of an unspecified intermediate member of the sum of fractions (not included in the Mendel’s original paper), which, from a mathematical standpoint, helps us resolve the incomplete assemblies (‘pure’ descendants) enigma.
VL  - 2
IS  - 6
ER  -

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