Scientific Experiment: Attempts to Converse Across Disciplinary Boundaries Using the Method of Approximation

Shmailov, Maya M.

doi:10.1007/978-3-319-39922-5_3

Maya M. Shmailov⁶

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

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Abstract

The intellectual trajectory of Rashevsky and his group focused on three main subjects which constituted the core of their research for more than a decade. The group adopted Rashevsky’s method of approximation and followed it. The approximation method was developed by Rashevsky in 1937 and was presented in an appendix to his magnum opus, Mathematical Biophysics, published in 1938.

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Notes

1.
Rashevsky, Mathematical Biophysics: Physico-Mathematical Foundations of Biology.
2.
Ibid; ———, “Organismic Sets: Some Reflections on the Nature of Life and Society.”
3.
Rashevsky, Mathematical Biophysics: Physico-Mathematical Foundations of Biology; ———, “Organismic Sets: Some Reflections on the Nature of Life and Society.”
4.
Rashevsky, Mathematical Biophysics: Physico-Mathematical Foundations of Biology; ———, “Organismic Sets: Some Reflections on the Nature of Life and Society.”
5.
Rashevsky, Mathematical Biophysics: Physico-Mathematical Foundations of Biology; ———, “Organismic Sets: Some Reflections on the Nature of Life and Society.”
6.
Rashevsky, “From Mathematical Biology to Mathematical Sociology.”
7.
Ibid.
8.
Ibid.
9.
Ibid.
10.
Ibid.
11.
Ibid.; ———, Mathematical Biophysics: Physico-Mathematical Foundations of Biology; N. Rashevsky, “Advances and Applications of Mathematical Biology”, Bull. Amer. Math. Soc. 47 (1941), 7, no. 9904 (1941); Rashevsky, Mathematical Biophysics Physico-Mathematical Foundations of Biology, Vol. 1 and 2.
12.
Ibid.
13.
Ibid.
14.
Ibid.
15.
N. Rashevsky, Some Medical Aspects of Mathematical Biology (1964); R. Chambers, “Structural and Kinetic Aspects of Cell Division”, Journal of Cellular and Comparative Physiology 12, no. 2 (1938). pg. 6.
16.
Rashevsky, Some Medical Aspects of Mathematical Biology; Chambers, “Structural and Kinetic Aspects of Cell Division”, Pg. 6.
17.
Correspondence with Buchsbaum, June 11, 1940, Box 8, Folder “Buchsbaum”, NRP-SCRC.
18.
G. Ostergren to Rashevsky, December 5, 1949, Box 8, Folder “O”, NRP-SCRC; Rashevsky, Mathematical Approach to Fundamental Phenomena of Biology, n.d.
19.
Kevles and Geison, “The Experimental Life Sciences in the Twentieth Century.”
20.
Rashevsky, “Mathematical Biophysics and Psychology.”
21.
Rashevsky, Mathematical Approach to Fundamental Phenomena of Biology, n.d.
22.
Which did not necessarily correspond in their properties to the actual neurons.
23.
Rashevsky, Mathematical Approach to Fundamental Phenomena of Biology, n.d.
24.
Rashevsky, “Mathematical Biophysics and Psychology.”
25.
Tara Abraham, Doctoral Dissertation, University of Toronto, 2002 and R.G. Frank, “Instruments, Nerve Action, and the All-or-None Principle”, Osiris 9(1994).
26.
N. Rashevsky, “Outline of a Physico-Mathematical Theory of the Brain”, The Journal of General Psychology 13, no. 1 (1935).
27.
Ibid.
28.
Ibid.
29.
AS Householder, “Mathematical Biophysics and the Central Nervous System”, Acta Biotheoretica 8, no. 1 (1946); N. Rashevsky, Mathematical Biophysics: Physico-Mathematical Foundations of Biology (Dover publications, 1960); Vol. II.
30.
Ibid.
31.
Rashevsky, “Mathematical Approach to Fundamental Phenomena of Biology”, n.d. pg, 244.
32.
A detailed account of McCulloch and Pitts paper and its role in the birth of cybernetics is given by Tara Abraham in “(Physio) Logical Circuits: The Intellectual Origins of the Mcculloch-Pitts Neural Networks”, Journal of the History of the Behavioral Sciences 38, no. 1 (2002); Abraham, “From Theory to Data: Representing Neurons in the 1940s.”
33.
Abraham, “(Physio) Logical Circuits: The Intellectual Origins of the Mcculloch-Pitts Neural Networks”; N. Rashevsky, Mathematical Biophysics: Physico-Mathematical Foundations of Biology. Vol. II.
34.
Rashevsky, “From Mathematical Biology to Mathematical Sociology”; N. Rashevsky, “Some Remarks on the Boolean Algebra of Nervous Nets in Mathematical Biophysics”, Bulletin of Mathematical Biology 7, no. 4 (1945).
35.
Ibid.
36.
Rashevsky, “From Mathematical Biology to Mathematical Sociology”, pg. 106.
37.
N. Rashevsky, “Mathematical Theory of Human Relations: An Approach to a Mathematical Biology of Social Phenomena”, Bull. Amer. Math. Soc. 55 (1949), 722–724; ———, “Outline of a Mathematical Theory of Human Relations”, Philosophy of Science 2, no. 4 (1935); ———, “Further Contributions to the Mathematical Theory of Human Relations”, Psychometrika 1, no. 2 (1936); ———, “Studies in Mathematical Theory of Human Relations. Ii”, Psychometrika 4, no. 4 (1939); ———, “Studies in Mathematical Theory of Human Relations”, Psychometrika 4, no. 3 (1939); ———, “Contributions to the Mathematical Theory of Human Relations. Iv”, Psychometrika 5, no. 4 (1940); ———, “Contributions to the Mathematical Theory of Human Relations Iii”, Psychometrika 5, no. 3 (1940); ———, “Contributions to the Theory of Human Relations: Vii. Outline of a Mathematical Theory of the Sizes of Cities”, Psychometrika 8, no. 2 (1943); ———, Mathematical Theory of Human Relations: An Approach to a Mathematical Biology of Social Phenomena (Principia Press, 1947).
38.
R. Rosen, “Anticipatory Systems in Retrospect and Prospect”, General systems yearbook 24, no. 11 (1979), pgs. 11–23 cited in AH Louie, “Essays on More Than Life Itself”, Axiomathes (2011).
39.
Rashevsky, “Foundations of Mathematical Biophysics.”
40.
———, Mathematical Theory of Human Relations: An Approach to a Mathematical Biology of Social Phenomena.
41.
Wilson, “Consilience: The University of Knowledge.”
42.
S.C. Haret, Mécanique Sociale (Paris and Bucharest, Gauthier-Villars, 1910).
43.
Rashevsky, Mathematical Theory of Human Relations: An Approach to a Mathematical Biology of Social Phenomena.
44.
Ibid.
45.
Ibid.
46.
Rashevsky, “Foundations of Mathematical Biophysics.”
47.
Johnston, Pitirim A. Sorokin: An Intellectual Biography.
48.
P.A. Sorokin, “1937–1941. Social and Cultural Dynamics”, New York: American Book Company; ———, “Social and Cultural Dynamics (New York, 1937)”, Vol. II; ———, Social and Cultural Dynamics: Vol. 3: Fluctuation of Social Relationships, War, and Revolution (American Book Company, 1937); ———, The Crisis of Our Age: The Social and Cultural Outlook (Dutton New York, 1941); ———, Social and Cultural Dynamics: Basic Problems, Principles, and Methods, vol. 4 (American Book Company, 1941); ———, Social and Cultural Dynamics: A Study of Change in Major Systems of Art, Truth, Ethics, Law, and Social Relationships (Transaction Publishers, 1957).
49.
There is no evidence to suggest that Rashevsky knew Sorokin and their correspondence is mainly professional.
50.
Correspondence with P. Sorokin, January 10, 1936, translation from Russian is by me. Box 8, Folder “Sorokin”, NRP-SCRC.
51.
Correspondence with P. Sorokin, Box 8, Folder “Sorokin”, NRP-SCRC.
52.
Correspondence with P. Sorokin, April 9, 1941, Box 8, Folder “Sorokin”, NRP-SCRC.
53.
Correspondence with P. Sorokin, Box 8, Folder “Sorokin”, NRP-SCRC.
54.
Correspondence with P. Sorokin, October 5, 1939, Box 8, Folder “Sorokin”, NRP-SCRC.
55.
Correspondence with P. Sorokin, April 14, 1941, Box 8, Folder “Sorokin”, NRP-SCRC.
56.
Rashevsky, “Mathematical Theory of Human Relations: An Approach to a Mathematical Biology of Social Phenomena.”
57.
Correspondence with P. Sorokin, January 24, 1948, translation from Russian, MMS. Box 8, Folder “Sorokin”, NRP-SCRC.
58.
Ibid.
59.
Ibid.
60.
Ibid.
61.
Correspondence with P. Sorokin, January 29, 1948, translation from Russian, MMS. Box 8, Folder “Sorokin”, NRP-SCRC.
62.
Ibid.
63.
Review by F. Mosteller, “General and Theoretical: Mathematical Thinking in the Social Sciences. Paul F. Lazarsfeld”, American Anthropologist 58, no. 4 (1956).
64.
F. Mosteller, “Review of Mathematical Theory of Human Relations: An Approach to a Mathematical Biology of Social Phenomenon by N. Rashevsky”, Journal of the American Statistical Association; Vol. 44, No. 245 (Mar., 1949), pp. 150–155.
65.
B.V. Johnston, Pitirim A. Sorokin: An Intellectual Biography (University Press of Kansas Lawrence, KS, 1995).
66.
Correspondence with P. Sorokin, April 14, 1948, translation from Russian, MMS. Box 8, Folder “Sorokin”, NRP-SCRC.
67.
I. Ponomareva, “Pitirim a Sorokin: The Interconnection between His Life and Scientific Work”, International Sociology 26, no. 6 (2011).
68.
Frederick Mosteller, “Review of: Mathematical Theory of Human Relations: An Approach to a Mathematical Biology of Social Phenomenon by N. Rashevsky”, (Journal of the American Statistical Association; Vol. 44, No. 245 (Mar., 1949), pp. 150–155).
69.
L.F. Richardson, Generalized Foreign Politics: A Study in Group Psychology (The University Press, 1939).
70.
Abraham, “Nicolas Rashevsky’s Mathematical Biophysics”, pg. 337.
71.
Weinberg, The First Nuclear Era: The Life and Times of a Technological Fixer. pg. 7.
72.
Frederick Mosteller, “Review of :Mathematical Theory of Human Relations: An Approach to a Mathematical Biology of Social Phenomenon by N. Rashevsky”, (Journal of the American Statistical Association; Vol. 44, No. 245 (Mar., 1949), pp. 150–155).
73.
D.O. Price, “Mathematical Theory of Human Relations. An Approach to a Mathematical Biology of Social Phenomena. By N. Rashevsky. Bloomington, Indiana: The Principia Press, Inc., 1947” Social Forces 27, no. 2 (1948).
74.
N. Rashevsky, Mathematical Biology of Social Behavior, vol. 256 (University of Chicago Press Chicago, 1951) D.O. Price, “Mathematical Biology of Social Behavior. By Nicholas Rashevsky. Chicago: The University of Chicago Press, 1951”, Social Forces 30, no. 1 (1951).
75.
Ibid. Preface viii.
76.
Ibid.
77.
D.O. Price, “Mathematical Theory of Human Relations. An Approach to a Mathematical Biology of Social Phenomena. By N. Rashevsky. Bloomington, Indiana: The Principia Press, Inc., 1947” Social Forces 27, no. 2 (1948).
78.
Rashevsky, Mathematical Theory of Human Relations: An Approach to a Mathematical Biology of Social Phenomena. pg. 237.
79.
Cull, “The Mathematical Biophysics of Nicolas Rashevsky.”
80.
Rapoport, Certainties and Doubts: A Philosophy of Life; History of the Committee, (1963), Box 2, NRP-SCRC.
81.
Weaver Interviews, July 3, 1938, RG 1.1, Series 216D, Box 11, Folder 148, RAC.
82.
Grant in Aid, October 14, 1936, RG 1.1, Series 216D, Box 11, Folder 147, RAC.
83.
Weaver Interviews, July 3, 1938, RG 1.1, Series 216D, Box 11, Folder 148, RAC.
84.
PK Maini, S Schnell, and S Jolliffe, “Bulletin of Mathematical Biology—Facts, Figures and Comparisons”, Bulletin of Mathematical Biology 66, no. 4 (2004).
85.
Lucas, The Cullowhee Conference on Training in Biomathematics. pg. 14.
86.
Rosen n.d, Weinberg Alvin-personal communications, 2004.
87.
N. Rashevsky, “Physico-Mathematical Aspects of the Gestalt-Problem”, Philosophy of Science 1, no. 4 (1934); Rashevsky, “Foundations of Mathematical Biophysics”; ———, “Mathematical Biophysics and Psychology”; ———, “Physico-Mathematical Methods in Biological and Social Sciences”; ———, Mathematical Biophysics: Physico-Mathematical Foundations of Biology.
88.
Weaver Interviews, June 18, 1940, RG1.1, Series 216D, Box 11, Folder 148 RAC.
89.
By the beginning of the 1938–1939 academic year, the department of psychology was shifted from the Division of Biological Science to the Division of Social Sciences, and a new place had to be found for some of its members, including Rashevsky.
90.
BSD Division Minutes recited in a note dated 15.07.1964 in Beadle Papers, Box 327, Folder 4, BOP-SCRC, University of Chicago Library.
91.
This approach was reflected in the first edition of Rashevsky’s magnum opus “Mathematical Biophysics: Physico-Mathematical foundations of Biology”, University of Chicago Press, 1938.
92.
Rashevsky to R. G. Gustavson, September 24, 1945, Box 214, Folder 6, HOP-SCRC.
93.
Ibid.
94.
N. Rashevsky, Advances and Applications of Mathematical Biology. Chicago, Univ. press (1940); A.S. Householder, “Review: Advances and Applications of Mathematical Biology”, vol. 15, National Mathematics Magazine, (1941): 384–386.
95.
One example is Rashevsky’s work with biologist F.C. Besic on the effects of corrosion of the teeth enamel by various acids.
96.
BSD Division Minutes recited in a note dated 15.07.1964 in Beadle Papers, Box 327, Folder 4, BOP-SCRC.
97.
Discussion with Don Makuleky, December 23, 2012.
98.
Memorandum on “History of the Committee”, (1963), Box 2, NRP-SCRC.
99.
Ibid.
100.
R.M. Hutchins, The State of the University, 1929-1949 (1949):Public Relations Office, University Archives, Pg 13–14; and McNeill, Hutchins’ University: A Memoir of the University of Chicago, 1929-1950. Pg. 102.
101.
Cited in H.S. Ashmore, Unseasonable Truths: The Life of Robert Maynard Hutchins (Little, Brown, 1989), pgs 222–223 and McNeill, Hutchins’ University: A Memoir of the University of Chicago, 1929-1950. Pg. 102.
102.
WH McNeill, Hutchins’ University: A Memoir of the University of Chicago, 1929-1950 (University of Chicago Press, 1991).
103.
Weinberg, The First Nuclear Era: The Life and Times of a Technological Fixer.
104.
History of the Committee, (1963), Box 2, NRP-SCRC.
105.
Weinberg, The First Nuclear Era: The Life and Times of a Technological Fixer. pg. 9.
106.
Correspondence with Arthur Compton, 1942, Box 8, NRP-SCRC.
107.
Ibid.
108.
Rashevsky to R. G. Gustavson, September 24, 1945, Box 214, Folder 6, HOP-SCRC.
109.
Ibid.
110.
Rashevsky to R.W. Harrison, December 27, 1945, Box 214, Folder 6, HOP-SCRC.
111.
Rashevsky to R. G. Gustavson, September 24, 1945, Box 214, Folder 6, HOP-SCRC.
112.
Ibid.
113.
Rashevsky to R. G. Gustavson, September 24, 1945, Box 214, Folder 6, HOP-SCRC.
114.
Ibid.
115.
More on this work, note Landahl, H. D. “Mathematical Biophysics of Cell Respiration.” Growth 1 (1937): 263–77; and Landahl, H. D. “Mathematical biophysics of cell respiration II.” The bulletin of mathematical biophysics 1, no. 1 (1939): 1–17.
116.
Householder, Alston S., and George Gomori. “The kinetics of enzyme inactivation.” The bulletin of mathematical biophysics 5, no. 3 (1943): 83–90.
117.
Rashevsky to R. G. Gustavson, September 24, 1945, Box 214, Folder 6, HOP-SCRC.
118.
Ibid.
119.
Colwell to Gustavson, December 10, 1945, Box 214, Folder 6, HOP-SCRC.
120.
Rashevsky to R.W. Harrison, December 27, 1945, Box 214, Folder 6, HOP-SCRC.
121.
Ibid.
122.
Ibid.
123.
Rashevsky to R.W. Harrison, December 27, 1945, Box 214, Folder 6, HOP-SCRC.
124.
Rashevsky to R.W. Harrison, December 27, 1945, Box 214, Folder 6, HOP-SCRC.
125.
Gustavson to Rashevsky, March 28, 1946, Box 214, Folder 6, HOP-SCRC.
126.
Ibid.
127.
Ibid.
128.
Ibid.
129.
Merle Coulter to Harrison at the central administration on February 28, 1948. HOP-SCRC.
130.
Ibid.
131.
Rashevsky to Bennet, BOP-SCRC, University of Chicago Library.
132.
Correspondence with Householder. March 12, 1948, Box 7, Folder “Householder”, NRP-SCRC.
133.
Weaver Interviews, February 22, 1951, RG1.1, Series 216D, Box 11, Folder 150 RAC.
134.
Letter from Rashevsky to Gustavson, 24 September, 1945, Box 137, Folder 6, HOP-SCRC.
135.
Ibid.
136.
Ibid. pg. 7.

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Interdisciplinary Unit, Bar Ilan University, Ramat Gan, Israel
Maya M. Shmailov

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Shmailov, M.M. (2016). Scientific Experiment: Attempts to Converse Across Disciplinary Boundaries Using the Method of Approximation. In: Intellectual Pursuits of Nicolas Rashevsky . Science Networks. Historical Studies, vol 55. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-39922-5_3

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DOI: https://doi.org/10.1007/978-3-319-39922-5_3
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