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An Overview: Rashevsky’s Mathematical Biology

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Intellectual Pursuits of Nicolas Rashevsky

Part of the book series: Science Networks. Historical Studies ((SNHS,volume 55))

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Abstract

Francis Crick once commented that “cosmologists are … less inhibited than chemists in regard to scientific speculations.” When Rashevsky had a chance to discuss this statement with Crick in 1959, he jokingly pointed out to him that “mathematical biologists are much worse than cosmologists!” Independent of whether he was being facetious, he had a point: it was precisely this speculative and abstract nature of mathematical biology that prompted others to habitually accuse Rashevsky and his fellow mathematical biologists of being entirely disconnected from biology. Rashevsky set out to prove them wrong. Driven by his dream of establishing the counterpart to mathematical physics in biology, he was shaking the very core of biology and often found himself under attack by the biologists to whom his ways seemed unrealistic, overly theoretical, oversimplified and even arrogant. His strong personality played a major role in his incursion into biology as he continuously fought to turn his dream into reality. Following his dream through, he advanced his views aggressively, defended them when attacked by his peers and prominent biologists, manipulated and exploited available opportunities to receive funding to sustain his enterprise, and employed a mixed strategy of self-aggrandizing and self-deprecation to champion his cause. At times arrogant and domineering, Rashevsky had a sense of self importance and presumptuousness that led to alienation from his colleagues. Undoubtedly, his personality played a major role in the fortunes of his science.

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Notes

  1. 1.

    Correspondence with G. Gamov, June 26, 1959, Nicolas Rashevsky Papers (Hereinafter: NRP), Box 10, Folder G, Special Collections Research Center, University of Chicago, IL, (hereinafter SCRC).

  2. 2.

    EF Keller, Making Sense of Life: Explaining Biological Development with Models, Metaphors, and Machines (Harvard Univ. Pr., 2003); Abraham, “Nicolas Rashevsky’s Mathematical Biophysics” 2004.

  3. 3.

    O.W. Richards, “The Mathematics of Biology”, The American Mathematical Monthly 32, no. 1 (1925): 30–36.

  4. 4.

    E.B. Wilson, “Some Aspects of Progress in Modern Zoology”, Science 41, no. 1044 (1915), G.E. Allen, Life Science in the Twentieth Century (John Wiley & Sons, 1975); J. Maienschein, “Shifting Assumptions in American Biology: Embryology, 1890-1910”, J. Hist. Biol 14, no. 1 (1981); ———, “Experimental Biology in Transition: Harrison’s Embryology, 1895-1910”, Stud. Hist. Biol 7(1983); R. Rainger, K.R. Benson, and J. Maienschein, The American Development of Biology (Rutgers Univ Pr, 1991); R. Creath and J. Maienschein, Biology and Epistemology (Cambridge Univ Pr, 2000); D.J. Kevles and G.L. Geison, “The Experimental Life Sciences in the Twentieth Century”, Osiris 10(1995).

  5. 5.

    R.G. Harris, “Mathematics in Biology”, The Scientific Monthly 40(1935):504–510.

  6. 6.

    “Paper and Pencil Biology”, Research Reports, Vol.1, No. 5, 1950, University of Chicago, Nicolas Rashevsky Biographical File, SCRC.

  7. 7.

    RC Lewontin, “Epilogue: Legitimation Is the Name of the Game”, in Harman and Dietrich eds., Rebels, Mavericks, and Heretics in Biology (2008), 372–380.

  8. 8.

    Ibid.

  9. 9.

    Ibid.

  10. 10.

    GWI, 2004.

  11. 11.

    R. Rosen, Life Itself: A Comprehensive Inquiry into the Nature, Origin, and Fabrication of Life (Columbia University Press, 1991), pages 112–113.

  12. 12.

    Personal communications with Mrs. Gwen Rapoport, widow of Anatol Rapoport, Rashevsky’s student and a close friend (2010–2011), in author’s possession.

  13. 13.

    Lucas, The Cullowhee Conference on Training in Biomathematics, page 351.

  14. 14.

    Keller, 2003, personal communications with late Lee Segel and Alvin Weinberg in 2004. Notes in the author’s possession.

  15. 15.

    Rashevsky to Jack Cattel, editor of American Men of Science, February 25, 1946, Box 8, Folder “Cattel”, NRP-SCRC,. Rashevsky repeated statements in this vein repeatedly throughout his scientific life when approached by the editors of scientific directories in their requests to include his name. Rashevsky was so vehemently against publication of his biography that in one instance, he threatened the A.N. Marquis Company, publisher of the “Who’s Who in America”, that he would bring the matter to litigation should they dare to publish his biography.

  16. 16.

    Ibid.; Rosen, “Autobiographical Reminiscences of Robert Rosen”, pgs. 1–23, courtesy of Tara Abraham.

  17. 17.

    In “The moral un-neutrality of science”; Speech delivered in 1960 to the American Association for the Advancement of Science; published in C.P. Snow and W. Cooper, The Physicists (Macmillan, 1981). pp. 180–188; see also C.P. Snow et al., “The Moral Un-Neutrality of Science”, Science 133(1961).

  18. 18.

    Rashevsky to Edward Levi, July 3, 1953, Box 1, restricted Folder, NRP-SCRC.

  19. 19.

    A. Rapoport, Certainties and Doubts: A Philosophy of Life (Black Rose Books Ltd, 2000).

  20. 20.

    Emily Rashevsky to C. Bowen, Director of MIT press, draft of a letter circa 1967. The book in question was N. Rashevsky, Looking at History through Mathematics (The MIT Press, 1968).

  21. 21.

    “Reminiscences of Nicolas Rashevsky”, Robert Rosen, n.d.; Nicolas Rashevsky Biographical File, SCRC.

  22. 22.

    F.M. Snell and R. Rosen, Progress in Theoretical Biology, vol. 2 (Academic press, 1972). pp. xi–xiv.

  23. 23.

    Letter of reference by Paul H. Dike, Box 12, misc. NRP -SCRC Rashevsky worked under Paul H. Dike’s supervision at the Robert College in Constantinople. After completing his doctorate in physics at the University of Wisconsin in 1911, Dike taught physics at Cornell College in Iowa, the University of Missouri, and Robert College. Dike returned to the United States circa 1923 to teach at the Universities of North Carolina and Vermont before joining the Leeds and Northrup Research Department in 1925. A fellow of the American Physics Society, Dike was a specialist in pyrometry and “made important contributions to the development of precision resistors and of radiation-type detector for determining temperature”. In “Paul H. Dike”, Physics Today 9, no. 8 (1956).

  24. 24.

    A. Rapoport, Certainties and Doubts: A Philosophy of Life (Black Rose Books Ltd, 2000); Personal Communication with Rashevsky’s granddaughter, Dr. Vibeke Strand. Emily’s father, an officer in the army, was killed during WWI and the only other remaining family member was her brother, George. Her brother was sent with the French troops, and prior to her departure to the US, attempts to locate him and release him from service were unsuccessful. Not dated letter in French from Emily to Army officers in Folder “correspondence”, Box 12, NRP-SCRC.

  25. 25.

    Robert College was founded in 1863 by two Americans, philanthropist Christoper Rhinelander Robert and American school master Cyrus Hamli. Robert was a wealthy American industrialist who succeeded in establishing under the Ottoman Empire a modern university offering an “American-style” education with instruction in English. It was an American-sponsored school with benefactors that included John S. Kennedy, Olivia Stokes, and members of the Dodge and Huntington Families. In the early twentieth century, Robert college had evolved into a leading institution in the Middle East: R.H. Davison, “Westernized Education in Ottoman Turkey”, Middle East Journal 15, no. 3 (1961).

  26. 26.

    Ibid.

  27. 27.

    “Biography of Nicolas Rashevsky”, Folder “Miscellaneous”, Box 11, NRP-SCRC.

  28. 28.

    Folder “reprints”, Box 11, NRP-SCRC.

  29. 29.

    Folder “reprints”, Box 11, NRP-SCRC; N. Rashevsky, “Light Emission from a Moving Source in Connection with the Relativity Theory”, Physical Review 18, no. 5 (1921).

  30. 30.

    Boxes 11 and 12, Folders “Correspondence”, NRP-SCRC.

  31. 31.

    Paul Dike to Rashevsky, March 7, 1923, Box 11, Folder “correspondence”, NRP-SCRC.

  32. 32.

    Cited in P. Dike to Rashevsky, November 30, 1923, Box 11, Folder “correspondence”, NRP-SCRC.

  33. 33.

    With the rush of Russian émigrés to US in the 1920s, the Russian Student Fund was established to offer assistance in the form of loans and contacts assisting over some 650 persons. For more on the fund and the Russian émigrés, see A.R. Wiren, “The Russian Student Fund 1920-1945”, Russian Review 5, no. 1 (1945), and T. Schaufuss, “The White Russian Refugees”, Annals of the American Academy of Political and Social Science 203(1939).

  34. 34.

    R. Boer, The Engineer and the Scandal: A Piece of Science History (Springer Verlag, 2005); R.E. Goodman, Karl Terzaghi: The Engineer as Artist (American Society of Civil Engineers, 1999).

  35. 35.

    Paul H. Dike to Rashevsky, April 20, 1924, Lawrence Moore to K. Terzhagi, April 24, 1924, Box 11, NRP-SCRC.

  36. 36.

    Records and ship manifests of Ellis Island Foundation. Inc.; Emily and the girls joined Rashevsky relatives in France and eventually arrived on the Aquitania on October 3, 1924.

  37. 37.

    “Why we are Trying to Make Gold”, Scientific American 131, 389–389 (December 1924).

  38. 38.

    “Scientific Notes and News”, Science 60, no. 1547 (1924).

  39. 39.

    The cause and nature of the disagreement has not been documented.

  40. 40.

    “Minutes of the Washington Meeting April 23 and 24, 1926”, Physical Review 27, no. 6 (1926). Correspondence with Paul Dike, 1925, Box 11, NRP-SCRC.

  41. 41.

    Correspondence with Jerome Alexander, 1932, Box 11, NRP-SCRC; While no other records corroborate this fact, the title “engineer in Biophysics and X-Ray Group, under the Physics Division” appears under Rashevsky’s signature in the correspondence.

  42. 42.

    Exchange in Box 11, NRP –SCRC indicates that Rashevsky made ends meet by translating articles and preparing English abstracts from the Russian Journal Electrichestwo for the journal Electrical World.

  43. 43.

    Rashevsky to Robert Grant, President of the Bureau, May 1, 1926, Box 12, Folder “correspondence”, NRP-SCRC.

  44. 44.

    Abraham, “Nicolas Rashevsky’s Mathematical Biophysics” (2004); N Rashevsky, “On the Size-Distribution of Colloidal Particles”, Physical Review 31, no. 1 (1928).

  45. 45.

    Ibid.

  46. 46.

    D.J. Kevles, The Physicists: The History of a Scientific Community in Modern America (Harvard University Press, 1995), pg. 201.

  47. 47.

    Abraham, “Nicolas Rashevsky’s Mathematical Biophysics”; e.g. Rashevsky, “On the Size-Distribution of Colloidal Particles.”

  48. 48.

    Abraham, “Nicolas Rashevsky’s Mathematical Biophysics” (2004).

  49. 49.

    Snell and Rosen, Progress in Theoretical Biology.

  50. 50.

    N. Rashevsky, “Some Theoretical Aspects of the Biological Applications of Physics of Disperse Systems”, Physics 1, no. 3 (1931), pg. 144.

  51. 51.

    Rosen, Life Itself: A Comprehensive Inquiry into the Nature, Origin, and Fabrication of Life. Pg. 110.

  52. 52.

    Cited in W. Bechtel, “Integrating Sciences by Creating New Disciplines: The Case of Cell Biology”, Biology and Philosophy 8, no. 3 (1993).

  53. 53.

    Cited in Ibid.

  54. 54.

    For an account of the development of general physiology in the early 20th century, see e.g. P.J. Pauly, “‘General Physiology and the Discipline of Physiology, 1890–1955”, Gerald L. Geison (ed.) (1987).

  55. 55.

    E.V. Cowdry, General Cytology (Univ. Chicago Press, 1924).

  56. 56.

    Abraham, “Nicolas Rashevsky’s Mathematical Biophysics.”

  57. 57.

    D’Arcey. Thompson, “Review: Nicolas Rashevsky, Mathematical Biophysics. Physicomathematical Foundations of Biology, Dr. Rashevsky has a way of his own” Nature 142, 1938, 931–932.

  58. 58.

    Thompson, “Review: Nicolas Rashevsky, Mathematical Biophysics. Physicomathematical Foundations of Biology, Dr. Rashevsky has a way of his own”; A.F. Huxley, “Review: Nicolas Rashevsky, Mathematical Biophysics” Nature 165(1950). pg.292.

  59. 59.

    Allen, “Mechanism, Vitalism and Organicism in Late Nineteenth and Twentieth-Century Biology: The Importance of Historical Context.”

  60. 60.

    Ibid.

  61. 61.

    Ibid.

  62. 62.

    J. Schaxel, “Über Die Natur Der Formvorgänge in Der Tierischen Entwicklung”, Development Genes and Evolution 50, no. 3 (1922). Cited L. Bertalanffy and J.H. Woodger, Modern Theories of Development: An Introduction to Theoretical Biology (Harper Torchbooks, 1962), pg. 2.

  63. 63.

    Amidon, “Adolf Meyer-Abich, Holism, and the Negotiation of Theoretical Biology”; C.S. Minot, Modern Problems of Biology (Blakiston, 1913), Pg 113 Bertalanffy and Woodger, Modern Theories of Development: An Introduction to Theoretical Biology.

  64. 64.

    Bertalanffy and Woodger, Modern Theories of Development: An Introduction to Theoretical Biology.

  65. 65.

    Schaxel, “Über Die Natur Der Formvorgänge in Der Tierischen Entwicklung.”

  66. 66.

    Bertalanffy and Woodger, Modern Theories of Development: An Introduction to Theoretical Biology.

  67. 67.

    Ibid. pg. v.

  68. 68.

    Ibid.; Allen, Life Science in the Twentieth Century.

  69. 69.

    Ibid.

  70. 70.

    G. Israel, “On the Contribution of Volterra and Lotka to the Development of Modern Biomathematics”, History and Philosophy of the Life Science 10, no. 1 (1988).

  71. 71.

    Cited in Ibid.

  72. 72.

    G. Israel, “A glance at the history of the mathematization of biological phenomena”, lecture delivered at Bar Ilan University, Ramat Gan, 20.02.2006.

  73. 73.

    Ibid.

  74. 74.

    Ibid. Millán Gasca, “Mathematical Theories Versus Biological Facts: A Debate on Mathematical Population Dynamics in the 1930s”.

  75. 75.

    Israel, “On the Contribution of Volterra and Lotka to the Development of Modern Biomathematics.”

  76. 76.

    S.E. Kingsland, “Mathematical Figments, Biological Facts: Population Ecology in the Thirties”, Journal of the History of Biology 19, no. 2 (1986); Millán Gasca, “Mathematical Theories Versus Biological Facts: A Debate on Mathematical Population Dynamics in the 1930s”.

  77. 77.

    For a more comprehensive discussion of the attempts and the complexities of introducing mathematical thinking see, e.g. Israel and Millán Gasca, The Biology of Numbers: The Correspondence of Vito Volterra on Mathematical Biology; and further publications mentioned in footnote 42.

  78. 78.

    SE Kingsland, Modeling Nature (University of Chicago Press Chicago, 1995); Abraham, “Nicolas Rashevsky’s Mathematical Biophysics.”

  79. 79.

    Kingsland, Modeling Nature. Abraham, “Nicolas Rashevsky’s Mathematical Biophysics”; K. Pearson, “On the Fundamental Conceptions of Biology”, Biometrika 1, no. 3 (1902); E.S. Pearson, Karl Pearson: An Appreciation of Some Aspects of His Life and Work (CUP Archive, 1938).

  80. 80.

    A. Rapoport, “Beachheads in Mathematical Biology”, n.d. circa 1950, Anatol Rapoport’s Papers, University of Toronto Archives Center (ARP-TUL).

  81. 81.

    D Thompson and JT Bonner, On Growth and Form (Cambridge University Press Cambridge, 1942, second edition first published in 1917).

  82. 82.

    Millán Gasca, “Mathematical Theories Versus Biological Facts: A Debate on Mathematical Population Dynamics in the 1930s” page 352.

  83. 83.

    Ibid. page 352.

  84. 84.

    Bonner, in editor’s view in Thompson and Bonner, On Growth and Form.

  85. 85.

    Ibid.

  86. 86.

    Ibid. pp. 7–8.

  87. 87.

    Ibid.

  88. 88.

    Provine, “The Origins of Theoretical Population Genetics”; editor’s introduction, Sarkar, The Founders of Evolutionary Genetics: A Centenary Reappraisal.

  89. 89.

    Sarkar, Ibid.

  90. 90.

    Abraham, “Nicolas Rashevsky’s Mathematical Biophysics.”

  91. 91.

    S. Sarkar, “The Founders of Evolutionary Genetics: A Centenary Reappraisal”, Boston studies in the philosophy of science (142(1992); R.C. Lewontin, “Theoretical Population Genetics in the Evolutionary Synthesis”, The Evolutionary synthesis: perspectives on the unification of biology, no. 787 (1980); Harman, The Price of Altruism: George Price and the Search for the Origins of Kindness (2010); pg. 59–85.

  92. 92.

    Ibid.

  93. 93.

    Ibid. Millán Gasca, “Mathematical Theories Versus Biological Facts: A Debate on Mathematical Population Dynamics in the 1930s.”

  94. 94.

    Sarkar, “The Founders of Evolutionary Genetics: A Centenary Reappraisal.”

  95. 95.

    Provine, “The Origins of Theoretical Population Genetics.”

  96. 96.

    Ibid.

  97. 97.

    E. Mayr, “Where Are We?” (1959).

  98. 98.

    RC Lewontin, “What Do Population Geneticists Know and How Do They Know It”, Biology and epistemology (2000).

  99. 99.

    Lewontin, “Theoretical Population Genetics in the Evolutionary Synthesis”, pg. 58.

  100. 100.

    Ibid.

  101. 101.

    See e.g. Kingsland, Modeling Nature; Israel and Millán Gasca, The Biology of Numbers: The Correspondence of Vito Volterra on Mathematical Biology.; Francesco M Scudo, “Vito Volterra and Theoretical Ecology,” Theoretical Population Biology 2, no. 1 (1971); Francesco M Scudo and James R Ziegler, The Golden Age of Theoretical Ecology, 1923-1940: A Collection of Works by V. Volterra, VA Kostitzin, AJ Lotka, and AN Kolmogoroff, (Springer-Verlag, 1978); Francesco M Scudo, “The ‘Golden Age’ Of Theoretical Ecology; a Conceptual Appraisal,” Revue européenne des sciences sociales(1984).; Francesco M Scudo and James R Ziegler, “Vladimir Aleksandrovich Kostitsin and Theoretical Ecology,” Theoretical Population Biology 10, no. 3 (1976). Kingsland, Modeling Nature; Israel and Millán Gasca, The Biology of Numbers: The Correspondence of Vito Volterra on Mathematical Biology.

  102. 102.

    G Israel, “The Scientific Heritage of Vito Volterra and Alfred J. Lotka in Mathematical Biology,” La matematizzazione della biologia. Storia e problematiche attuali, P. Cerrai, P. Freguglia (eds), Quattro Venti, Urbino(1999).

  103. 103.

    Ibid.

  104. 104.

    G. Israel, “A glance at the history of the mathematization of biological phenomena”; Israel, G. “Vito Volterra, Book on Mathematical Biology (1931)”, Chapter 73 in Grattan-Guinness, Ivor, ed. Landmark writings in Western mathematics 1640-1940. Elsevier Science, 2005.

  105. 105.

    Ibid.

  106. 106.

    Ibid.

  107. 107.

    Ibid.

  108. 108.

    Israel, “On the Contribution of Volterra and Lotka to the Development of Modern Biomathematics”. pg 12.

  109. 109.

    Ibid. Israel and Millán Gasca, The Biology of Numbers: The Correspondence of Vito Volterra on Mathematical Biology.

  110. 110.

    Israel, G. “Vito Volterra, Book on Mathematical Biology (1931)”, chapter 73 in Landmark Writings in Western Mathematics 1640–1940 (2005).

  111. 111.

    G. Israel, “A glance at the history of the mathematization of biological phenomena.”

  112. 112.

    Ibid.

  113. 113.

    AJ Lotka, Elements of Physical Biology (Williams & Wilkins company, 1925); AJ Lotka, Elements of Mathematical Biology (Dover Publications, New York, 1956).

  114. 114.

    Abraham, “Nicolas Rashevsky’s Mathematical Biophysics”; Kingsland, Modeling Nature.

  115. 115.

    G Israel, “The Scientific Heritage of Vito Volterra and Alfred J. Lotka in Mathematical Biology”.

  116. 116.

    Ibid.

  117. 117.

    J.R. Jungck, “Ten Equations That Changed Biology: Mathematics in Problem-Solving Biology Curricula”, Bioscene 23, no. 1 (1997); L Edelstein-Keshet, Mathematical Models in Biology (Society for Industrial and Applied Mathematics Philadelphia, PA, USA, 2005).

  118. 118.

    Kingsland, “Mathematical Figments, Biological Facts: Population Ecology in the Thirties”; ———, Modeling Nature.

  119. 119.

    Ibid.

  120. 120.

    Ibid.

  121. 121.

    Rashevsky, “Foundations of Mathematical Biophysics”. Pg 196.

  122. 122.

    ———, “Organismic Sets: Some Reflections on the Nature of Life and Society”. Pg. 2.

  123. 123.

    ———, “Foundations of Mathematical Biophysics.”

  124. 124.

    ———, “Organismic Sets: Some Reflections on the Nature of Life and Society.”

  125. 125.

    E.g. N. Rashevsky, “Foundations of Mathematical Biophysics,” Philosophy of Science (1934); N. Rashevsky, “Physico‐Mathematical Methods in Biological Sciences,” Biological Reviews 11, no. 3 (1936).

  126. 126.

    Rashevsky, Mathematical Biophysics: Physico-Mathematical Foundations of Biology.pg. vii.

  127. 127.

    Ibid. pages vii–viii.

  128. 128.

    Correspondence with Mortimer Spiegelman, February 28, 1950, Box 8, Folder S, NRP-SCRC; N. Rashevsky “Birds eye view at Mathematical Biology” in Lucas, The Cullowhee Conference on Training in Biomathematics. AJ Lotka, Elements of Physical Biology (Williams & Wilkins company, 1925).

  129. 129.

    Abraham, “Nicolas Rashevsky’s Mathematical Biophysics.”

  130. 130.

    Lotka, Elements of Physical Biology.

  131. 131.

    Ibid.

  132. 132.

    N. Rashevsky, Mathematical Approach to Fundamental Phenomena of Biology, n.d., Box 9, Folder “Misc”, NRP-SCRC.

  133. 133.

    N. Rashevsky, Mathematical Approach to Fundamental Phenomena of Biology, n.d., Box 9, Folder “Misc”, NRP-SCRC.

  134. 134.

    Rashevsky, Mathematical Biophysics: Physico-Mathematical Foundations of Biology.pg. viii.

  135. 135.

    N. Rashevsky, Mathematical Approach to Fundamental Phenomena of Biology, n.d., Box 9, Folder “Misc”, NRP-SCRC.

  136. 136.

    Ibid.

  137. 137.

    N. Rashevsky, “Physico-Mathematical Methods in Biological Sciences”, Biological Reviews 11, no. 3 (1936).

  138. 138.

    N. Rashevsky, “Mathematical Biophysics”, Nature 135, (1935), 1938.

  139. 139.

    P. Cull, “The Mathematical Biophysics of Nicolas Rashevsky”, Biosystems 88, no. 3 (2007), 178–184.

  140. 140.

    Rashevsky, “Foundations of Mathematical Biophysics”, pg. 176–196.

  141. 141.

    Ibid. pg. 176–196.

  142. 142.

    Ibid; N. Rashevsky, “Physico-Mathematical Methods in Biological and Social Sciences”, Erkenntnis 6(1936).

  143. 143.

    Rashevsky, “Physico-Mathematical Methods in Biological Sciences.”

  144. 144.

    ———, Mathematical Biophysics: Physico-Mathematical Foundations of Biology.

  145. 145.

    Abraham, “Nicolas Rashevsky’s Mathematical Biophysics”, 2004; History of the Committee, (1963), Box 2, NRP-SCRC.

  146. 146.

    Robert Rosen, “Reminiscences of Nicolas Rashevsky”, n.d.

  147. 147.

    Rashevsky to RR. Mellon, 10, April, 1928, Box 11, Folder “correspondence”, NRP-SCRC; affirmation to the collaboration with RR Mellon is also found in “Photograph onion light; rays stimulate growth,” New York Herald Tribune, 28 December 1928, p. 7.

  148. 148.

    Ibid. It is interesting to note in this program’s outline that Emily Rashevsky was also involved in the program, doing some work on the radiation emitted by living tissue. While Emily Rashevsky’s name does not appear in any of the scientific papers or exchange in the NRP, this record indicates that at least at the beginning, Rashevsky’s interest in biology was shared by his wife; her name was indicated as one of the scientists to execute a section of the outlined program. Her name would appear in his books as a contributor to editing and preparations of miscellaneous appendixes, but no scientific contributions to the new discipline have been recorded.

  149. 149.

    R. Rosen, Life itself, 1991; D’Arcey Thompson, “Review: Nicolas Rashevsky, Mathematical Biophysics”, 1938.

  150. 150.

    US Patent US1,840,130 and British patent GB 271885 listing Rashevsky as an Inventor, 1926; R. Rosen and D.P. Agin, eds., Foundations of Mathematical Biology (Academic Press New York,1972).

  151. 151.

    Rashevsky, “Some Theoretical Aspects of the Biological Applications of Physics of Disperse Systems”, pg. 143–153; Rashevsky, “Foundations of Mathematical Biophysics.”

  152. 152.

    Ibid.

  153. 153.

    Rashevsky, “Foundations of Mathematical Biophysics.”

  154. 154.

    N. Rashevsky, “From Mathematical Biology to Mathematical Sociology”, ETC., A Review of General Semantics (1951).

  155. 155.

    Abraham, “Nicolas Rashevsky’s Mathematical Biophysics.”

  156. 156.

    Ibid. R.S. Lillie, “The Physiology of Cell-Division.—I. Experiments on the Conditions Determining the Distribution of Chromatic Matter in Mitosis”, American Journal of Physiology—Legacy Content 15, no. 1 (1905); ———, “The Relation of Ions to Contractile Processes.—I. The Action of Salt Solutions on the Ciliated Epithelium of Mytilus Edulis”, American Journal of Physiology—Legacy Content 17, no. 1 (1906); ———, “The General Biological Significance of Changes in the Permeability of the Surface Layer or Plasma-Membrane of Living Cells”, Biological Bulletin (1909); ———, “The Physiology of Cell-Division.—Ii. The Action of Isotonic Solutions of Neutral Salts on Unfertilized Eggs of Asterias and Arbacia”, American Journal of Physiology—Legacy Content 26, no. 1 (1910); ———, “The Relation of Stimulation and Conduction in Irritable Tissues to Changes in the Permeability of the Limiting Membranes”, American Journal of Physiology—Legacy Content 28, no. 4 (1911); ———, “Increase of Permeability to Water Following Normal and Artificial Activation in Sea Urchin Eggs”, Amer. J. Physiol 40(1916); ———, “The Physiology of Cell Division. Vi. Rhythmical Changes in the Resistance of the Dividing Sea-Urchin Egg to Hypotonic Sea Water and Their Physiological Significance”, Journal of Experimental Zoology 21, no. 3 (1916).

  157. 157.

    Rashevsky, “Physico-Mathematical Methods in Biological and Social Sciences”, Erkenntnis 6(1936).

  158. 158.

    Abraham, “Nicolas Rashevsky’s Mathematical Biophysics”, 2004.

  159. 159.

    Abraham, “Nicolas Rashevsky’s Mathematical Biophysics”, 2004.

  160. 160.

    N. Rashevsky, “Outline of a Physico-Mathematical Theory of Excitation and Inhibition”, Protoplasma 20, no. 1 (1933), 42–56.

  161. 161.

    AV Hill, “Excitation and Accommodation in Nerve”, Proceedings of the Royal Society of London. Series B, Biological Sciences 119, no. 814 (1936):305–355.

  162. 162.

    C. Hodson and LY Wei, “Comparative Evaluation of Quantum Theory of Nerve Excitation”, Bulletin of Mathematical Biology 38, no. 3 (1976):277–293.

  163. 163.

    F. Offner, “Excitation Theories of Rashevsky and Hill”, The Journal of General Physiology 21, no. 1 (1937):89–91.

  164. 164.

    GWI, 2004.

  165. 165.

    Scattered correspondence with H.A. Blair, 1933–1939, Boxes 6 and 8, NRP-SCRC.

  166. 166.

    F.F. Offner, “The Excitable Membrane-Biophysical Theory and Experiment”, Bulletin of Mathematical Biology 35, no. 1 (1973):101–107.

  167. 167.

    The letter was eventually published in 1937 as an article by Offner, “Excitation Theories of Rashevsky and Hill.”

  168. 168.

    Correspondence with H.A. Blair 1933–1939, Box 8, NRP-SCRC.

  169. 169.

    N. Rashevsky, “Some Physico Mathematical Aspects of Nerve Conduction”, Physics 4, no. 9 (1933):341–349.

  170. 170.

    Correspondence with H.A. Blair 1933–1939, Box 8, NRP-SCRC.

  171. 171.

    R. Pearl, “Review: Nicolas Rashevsky, Mathematical Biophysics. Physicomathematical Foundations of Biology”, Bulletin (New Series) of the American Mathematical Society 45, no. 3 (1939): 223–224.

  172. 172.

    Huxley, “Review: Nicolas Rashevsky, Mathematical Biophysics”.

  173. 173.

    Rashevsky to Weaver, September 24, 1936, RG 1.1, Series 216D, Box 11, Folder 147, RAC.

  174. 174.

    e.g. N. Rashevsky, “Foundations of Mathematical Biophysics”, Philosophy of Science (1934).

  175. 175.

    ———, “Mathematical Biophysics and Psychology”, Psychometrika 1, no. 1 (1936).

  176. 176.

    Weaver to Rashevsky, September 19, 1936, RG 1.1, Series 216D, Box 11, Folder 147, RAC.

  177. 177.

    N. Rashevsky, “Mathematical Biophysics: Physico-Mathematical Foundations of Biology”, Bull. Amer. Math. Soc. 45, 2(1939), 223–224.

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    Maya M. Shmailov

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Shmailov, M.M. (2016). An Overview: Rashevsky’s Mathematical Biology. In: Intellectual Pursuits of Nicolas Rashevsky . Science Networks. Historical Studies, vol 55. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-39922-5_1

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