371

Academic Vita of Norbert Wiener!

1894 Born on November 26 in Columbia, Missouri, to Bertha Kahn Wiener and Leo Wiener, a professor of foreign languages at the University of Missouri.

1895 The family moved to Cambridge, Massachusetts, where Leo Wiener became a professor of Slavic languages at Harvard.

1901 Entered the third grade at the Peabody School, but was removed shortly and taught by his father until 1903.

1903 Entered Ayer High School. 1906 Graduated from Ayer High School and entered Tufts College where he

studied mathematics and biology. 1909 Received an A.B. degree, cum laude, from Tufts, and entered the

Harvard Graduate School to study zoology. 1910 Entered the Sage School of Philosophy at Cornell University with a

scholarship, and studied with Frank Thilly, Walter A. Hammond, and Ernest Albee.

1911 Transferred to the Harvard Graduate School to study philosophy, and studied with E. V. Huntington, Josiah Royce, G.H. Palmer, Kar! Schmidt, and George Santayana.

1912 Received an M.A. degree from Harvard. 1913 Received a Ph.D. degree from Harvard; dissertation under J. Royce,

but supervised by K. Schmidt of Tufts College. Appointed a John Thornton Kirkland Fellow by Harvard, and entered Cambridge University. Studied logic and philosophy with Bertrand Russell, G.E. Moore, and J.M.E. McTaggart, and mathematics with G.H. Hardy and J.E. Littlewood.

1914 Joined the University of Gottingen and took the courses of David Hilbert, Edmund Husser!, and Edmund Landau. Appointed a Frederick Sheldon Fellow by Harvard; returned to Cam­bridge University to study mathematics and philosophy. Received the Bowdoin Prize from Harvard.

1915 Studied philosophy under John Dewey at Columbia University. Appointed an assistant and a docent lecturer in Harvard's Philosophy Department for 1915-1916, and lectured on the logic of geometry.

1916 Served with Harvard's reserve regiment at the Officer's Training Camp in Plattsburg, N.Y. Appointed instructor of mathematics at the University of Maine in Orono for 1916-1917.

This data is extracted from the Chronology in the spiral-bound publication entitled the "Inventory of Norbert Wiener, 1894-1964", processed by Mary Jane McCavitt, September 1980.

372

1917

1918

1919

1920

1924 1925

1926

1928

1929

1931-1932

1933

1934

1935

1936

1937

1938 1940

Academic Vita of Norbert Wiener

Served with the Cambridge ROTC; briefly worked as an apprentice engineer in the turbine department of the General Electric Corp. in Lynn, Massachusetts. Appointed a staff writer for the Encyclopedia Americana in Albany, N.Y. Joined the Aberdeen, Proving Grounds of the U.S. Army under O. Veblen, and worked on computations of ballistic tables. Joined the American Mathematical Society. Served as an Army private at the Aberdeen Proving Ground, Mary­land. Worked as a journalist with The Boston Herald. Appointed instructor of mathematics at MIT. Attended the International Mathematical Congress in Strasbourg as MIT's representative and presented a paper on Brownian motion. He also visited Cambridge and Paris. Appointed assistant professor of mathematics at MIT. Attended the International Mathematical Congress in Grenoble and the British Association for the Advancement of Science meeting in Southampton; visited Gi:ittingen University. Elected fellow of the American Academy of Arts and Sciences. Married Marguerite Engemann. Received a Guggenheim Fellowship to study in Gi:ittingen and in Copenhagen during 1926-1927. Collaborated with Harald Bohr, and taught a course of general trigonometric developments at Gi:ittingen. Addressed the Symposium on Analysis Situs of the American Math­ematical Society. Appointed associate professor of mathematics at MIT. Lectured at Brown University as exchange professor during 1929-1930. Visiting lecturer at Cambridge University; lectured on the Fourier integral and its applications at Trinity College. Appointed professor of mathematics at MIT. Attended the International Congress of Mathematics, Zurich, as MIT's representative. Awarded Bocher Prize by the American Mathematical Society. EleCted to the National Academy of Sciences. Began participation in the interdisciplinary seminar at Harvard Medical School under Arturo Rosenblueth. Collaborated with REAC. Paley. Delivered the AMS Colloquium Lectures at Williamston, Massa­chusetts. Patented electrical network systems with Yuk Wing Lee. (Two more patents were issued in 1938.) Lectured at Stanford University and in Japan on his way to China. Visiting professor at Tsing Hua University in Peiping, China, during 1935-1936. Attended the International Congress of Mathematicians in Oslo, Nor­way, and lectured on Tauberian gap theorems. Collaborated with Harry Ray Pitt at MIT during 1936-1937. Delivered the Dohme lecture at Johns Hopkins University on Tauberian theorems. Lectured on analysis at the semicentennial of the AMS. Appointed chief consultant in the field of mechanical and electrical aids to computation for the National Defense Research Committee.

Academic Vita of Norbert Wiener 373

1941 1945

1946-1950

1946

1947

1948 1949

1950

1951

1952

1953

1953~1954

1955~1956

1956 1957

1959

1960

Consultant with the NDRC's Office of Scientific Research and De­velopment, Statistical Research Group and Operational Research Lab­oratory at Columbia University. Consultant to the War-Preparedness Committee of the American Mathematical Society. Joined a team at MIT under S. H. Caldwell to study the guidance and control of antiaircraft fire. Worked on the theory and design of fire control apparatus for anti­aircraft guns with Julian Bigelow, under NDRC Project. Resigned from the National Academy of Sciences. Participated in a study group set up by John von Neumann, and attended a meeting on communication theory in Princeton. Collaborated with Arturo Rosenblueth at the Instituto National Car­diologia in Mexico, and attended the Mexican Mathematical Society's Conference held in Guadalajara. With Arturo Rosenblueth received a five-year Rockefeller Foundation grant that allowed them to collaborate in Mexico and at MIT on alternating years. Received an honorary Sc.D. degree from Tufts College. Attended the first three Josiah Macy, Jr. Foundation Conferences and the Conference on Teleological Mechanisms sponsored by the New York Academy of Sciences. Lectured at the National University of Mexico. Visited England and France, and gave lectures on harmonic analysis in Nancy, France. Spoke at the AMS's Second Symposium on Applied Mathematics. Received the Lord & Taylor American Design Award. Delivered the AMS's Josiah Willard Gibbs Lecture at the annual meeting. Attended the seventh Macy conference. Lectured at the International Congress of Mathematicians at Harvard University. Lectured at the University of Paris, College de France, under a Ful­bright Teaching Fellowship, and also lectured in Madrid. Received an honorary Sc.D. degree from the University of Mexico. Received the Alvarega Prize from the College of Physicians III

Philadelphia. Delivered the Forbes-Hawks Lectures at the University of Miami. Lectured on the theory of prediction at the University of California at Los Angeles. Taught a summer school course with Claude Shannon and Robert Fano on the mathematical problems of communications theory. Lectured at the Tata Institute of Fundamental Research, Bombay, attended the All-India Science Congress, and visited research centers. Visiting professor at the Indian Statistical Institute in Calcutta. Lectured in Japan and gave a summer school course at UCLA. Received an honorary Sc.D. degree from Grinnell College. Awarded the Virchow Medal from the RudolfVirchow Medical Soci­ety. Gave a summer school course at UCLA. Appointed institute professor at MIT. Lectured at the University of Naples in Italy, and visited the USSR.

374 Academic Vita of Norbert Wiener

Received the ASTME Research Medal. Retired from MIT, and appointed institute professor emeritus.

1961 Gave a summer school course at UCLA. 1962 Lectured at the Institute of Theoretical Physics, University of Naples,

Italy. Delivered the Terry Lectures at Yale University, titled "Prolegomena to Theology".

1963 Gave a summer school course at UCLA. 1964 Received the National Medal of Science from President Johnson. 1964 Visiting professor and honorary head of neurocybernetics at Nether­

lands Central Institute for Brain Research, Amsterdam. Lectured in Norway and Sweden. Died on March 18 in Stockholm, Sweden.

375

Doctoral Students of Norbert Wiener!

Shikao Ikehara Ph.D. 1930 Sebastian Littauer Sc.D. 1930 Dorothy W. Weeks Ph.D. 1930 James G. Estes Ph.D. 1933 Norman Levinson Sc.D. 1935 Henry Malin Ph.D. 1935 Bernard Friedman Ph.D. 1936 Brockway McMillan Ph.D. 1939 Abe M. Gelbart Ph.D. 1940 Donald G. Brennan Ph.D. 1959

1 Reprinted with the kind permission of Professor Irving Ezra Segal of MIT.

376

The Classification of Wiener's Papers

Mathematical Papers A Mathematical philosophy and foundations B Potential theory C Brownian movement, Wiener integrals, ergodic and chaos theories, tur­

bulence and statistical mechanics D Generalized harmonic analysis and Tauberian theory E Classical harmonic and complex analysis (orthogonal developments,

quasi-analyticity, gap theorems, and Fourier transforms in the complex domain)

F Hopf-Wiener integral equations G Prediction and filtering H Relativity and quantum theories I Miscellaneous mathematical papers

II Cybernetical and Philosophical Papers A Philosophical papers B Cybernetical papers

III Social, Ethical, Educational, and Literary papers IV Book Reviews, Prefaces, and Obituaries

A Book reviews and prefaces B Obituaries

V Abstracts VI Books and Other Publications.

In the accompanying Bibliography, Wiener's publications have been classified into six broad categories labeled I, ... , VI, and these larger categories have been divided into subcategories labeled A, B, C, ...

The publications are indexed by the official year of their appearance. The internal ordering of the publications appearing in a given year is not chronological but according to the categories mentioned in the last paragraph: a run down the list a, b, c, ... for a particular year entails a run down the list of categories lA, lB, ... , usually with omissions and repetitions, as will be apparent from a glance at the right-hand columns in the bibliography. For instance, [33d] means "the dth paper, according to category, which appeared in a journal marked 1933".

References in the book indicated by numbers in square brackets preceded by MC, e.g. [MC, 57], refer to the Manuscript Collection of Wiener in the MIT Archives. Roman numerals in square brackets, e.g. [IV], refer to Defense Department Docu­ments pertaining to Wiener, listed after the Bibliography. (Symbols in braces, e.g. {K3}, which refer to other authors, are listed at the end of the book.)

[13a]

[l4a]

[14b]

[l4c]

[14d] [15a]

[15b]

[16a]

[16b]

[16c]

[16d]

[l7a]

[17b]

[ISa]

[ISb]

[ISc]

[lSd]

[lSe]

I Sf]

Bibliography of Norbert Wiener

On a method of rearranging the positive integers in a series of ordinal numbers greater than that of any given funda­mental sequence of omegas, Messenger of Math. 43 (1913), 97-105. A simplification of the logic of relations, Proc. Cambridge Philos. Soc. 17 (1914), 387-390. A contribution to the theory of relative position, Proc. Cambridge Philos. Soc. 17 (1914), 441-449. The highest good, J. Phil. Psych. and Sci. Method 11 (1914), 512-520. Relativism, J. Phil. Psych. and Sci. Method 11 (1914), 561-577. Studies in synthetic logic, Proc. Cambridge Philos. Soc. 18 (1915), 14-2S. Is mathematical certainty absolute?, J. Phil. Psych. and Sci. Method 12 (1915), 568-574.IA Mr. Lewis and implication, J. Phil. Psych. and Sci. Method 13 (1916),656-662. The shortest line dividing an area in a given ratio, Proc. Cambridge Philos. Soc. 18 (1916), 56-58. Review of Cassius J. Keyser, Science and Region: the Rational and the Superrational, J. Phil. Psych. and Sci. Method 13 (1916), 273-277. Review of A.A. Robb, A Theory of Time and Space, J. Phil. Psych. and Sci. Method 13 (1916), 611-613. Certain formal invariances in Boolean algebras, Trans. Amer. Math. Soc. 18 (1917), 65-72. Review of C.J. Keyser, The Human Worth of Rigorous Thinking, J. Phil. Psych. and Sci. Method 14 (1917), 356-361. Review of Edward V. Huntington, The Continuum and Other Types of Serial Order, J. Phil. Psych. and Sci. Method 15 (1918), 7S-S0. Aesthetics, in Encyclopedia Americana, 1915-20 edition, vol. I, 19S-203. Algebra, definitions and fundamental concepts, in Encyclopedia Americana, 1918-20 edition, vol. I, 3S1-385. Alphabet, in Encyclopedia Americana, 1918-20 edition, vol. I, 435-43S. Animals, chemical sense, in, in Encyclopedia Americana, 1918-20 edition, vol. I, 704. Apperception, in Encyclopedia Americana, 1918-20 edition, vol. II, 82-S3.

377

IA

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IA

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lA

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IVA

IIA

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IIA

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IIA

378 Bibliography of Norbert Wiener

[18g] Category, in Encyclopedia Americana, 1918-20 edition, vol. VI, IIA 49.

[18h] Dualism, in Encyclopedia Americana, 1918-20 edition, vol. IX, IIA 367.

[18i] Duty, in Encyclopedia Americana, 1918-20 edition, vol. IX, IIA 440-441.

[18j] Ecstasy, in Encyclopedia Americana, 1918-20 edition, vol. IX, IIA 570.

[19a] Geometry, non-euclidean, in Encyclopedia Americana, 1918-20 I, I edition, vol. XII, 463-467.

[19b] Induction, in logic, in Encyclopedia Americana, 1918-20 edition, IIA vol. XV, 70-73.

[19c] Infinity, in Encyclopedia Americana, 1918-20 edition, vol. XV, IIA 120-122.

[19d] Meaning, in Encyclopedia Americana, 1918-20 edition, vol. IIA XVIII, 478-479.

[1ge] Mechanism and vitalism, in Encyclopedia Americana, 1918-20 IIA edition, vol. XVIII, 527-528.

(19f] Metaphysics, in Encyclopedia Americana, 1918-20 edition, vol. IIA XVIII, 707-710.

(19g] Pessimism, in Encyclopedia Americana, 1918-20 edition, vol. IIA XXI, 654.

[19h] Postulates, in Encyclopedia Americana, 1918-20 edition, vol. IIA XXII, 437-438.

[20a] Bilinear operations generating all operations rational in a domain IA Q, Ann. of Math. 21 (1920), 157-165.

[20b] A set of postulates for fields, Trans. Amer. Math. Soc. 21 (1920), IA 237-246.

[20c] Certain iterative characteristics of bilinear operations, Bull. Amer. IA Math. Soc. 27 (1920), 6--10.

[20d] Certain iterative properties of bilinear operations, G. R. Strasbourg IA Math. Congress, 1920, 176--178.

[20e] On the theory of sets of points in terms of continuous transforma- IA tions, G.R. Strasbourg Math. Congress, 1920, 312-315.

[20f] The mean of a functional of arbitrary elements, Ann. of Math. (2) IC 22 (1920), 66--72.

[20g] Review of C. 1. Lewis, A Survey of Symbolic Logic, J. Phil. Psych. IVA and Sci. Method 17 (1920), 78-79.

[20h] Soul, in Encyclopedia Americana, 1918-20 edition, vol. XXV, IIA 268-271.

[20i] Substance, in Encyclopedia Americana, 1918-20 edition, vol. IIA XXV, 775-776.

[20j] Universals, in Encyclopedia Americana, 1918-20 edition, vol. IIA XXVII, 572-573.

[21a] A new theory ofmeasurement: A study in the logic of mathematics, IA Proc. London Math. Soc. 19 (1921), 181-205.

[21 b] The isomorphisms of complex algebra, Bull. Amer. Math. Soc. 27 IA (1921), 443-445.

[21c] The average of an analytic functional, Proc. Nat. Acad. Sci. U.S.A. IC 7 (1921), 253-260.

[21d] The average of an analytic functional and the Brownian movement, IC Proc. Nat. Acad. Sci. U.S.A. 7 (1921), 294--298.

[2Ie]

[22a]

[22b]

[22c]

[22d]

[22e]

[23a]

[23b]

[23c]

[23d]

[23e]

[23f]

[23g] [24a]

[24b]

[24c]

[24d]

[24e]

[24f]

[24g]

[24h]

[24i] [25a]

[25b]

Bibliography of Norbert Wiener

A new vector method in integral equations (with F.L. Hitchcock), J. Math. and Phys. I (1921), 1-20. The relation of space and geometry to experience, Monist 32 (1922), 12-60, 200-247, 364-394. The group of the linear continuum, Proc. London Math. Soc. 20 (1922), 329-346. Limit in terms of continuous transformation, Bull. Soc. Math. France 50 (1922), 119-134. The equivalence of expansions in terms of orthogonal functions (with J.L. Walsh), J. Math. and Phys. I (1922), 103-122. A new type of integral expansion, J. Math. and Phys. 1 (1922), 167-176. On the nature of mathematical thinking, Austral. J. Psych. and Phil. 1 (1923), 268-272. Nets and the Dirichlet problem (with H.B. Phillips), J. Math. and Phys. 2 (1923), 105-124. (Reprinted in [64f].) Discontinuous boundary conditions and the Dirichlet problem, Trans. Amer. Math. Soc. 25 (1923), 307-314. Differential-space, J. Math. and Phys. 2 (1923), 131-174. (Reprinted in [64f].) o szeregach L~(± Iln}-Note on the series L~(± lin), Bull. Acad. Polon. Ser. A, 13 (1923), 87-90. Note on a new type of summability, Amer. J. Math. 45 (1923), 83-86. Note on a paper of M. Banach, Fund. Math. 4 (1923), 136-143. Certain notions in potential theory, J. Math. and Phys. 3 (1924), 24-51. The Dirichlet problem, J. Math. and Phys. 3 (1924), 127-146. (Reprinted in [64f].) Une condition necessaire et suffisante de possibilite pour Ie problt'!me de Dirichlet, C.R. Acad. Sci. Paris 178 (1924),1050-1054. The average value of a functional, Proc. London Math. Soc. 22 (1924), 454-467. Un probleme de probabilites dfmombrables, Bull. Soc. Math. France II (1924), 569-578. The quadratic variation of afunction and its Fourier coefficients, J. Math. and Phys. 3 (1924), 72-94. Review of four books on space, Rudolf Carnap's Der Raum: Ein Beitrag zur Wissenschaftslehre, E. Study's Mathematik und Phy­sik: eine erkenntnistheoretische Untersuchung and Die realistische Weltansicht und die Lehre vom Raume: zweite Auflage; erster Tei!, and Hermann Weyl's M athematische Analyse des Raum-problems. Vorlesungen gehalten in Barcelona und Madrid, Bull. Amer. Math. Soc. 30 (1924), 258-262. Review of E. Study, Denken und Darstellung: Logik und Werte; Dingliches und Menschliches in Mathematik und Naturwissenschaf­ten, Bull. Amer. Math. Soc. 30 (1924), 277. In memory of Joseph Lipka, J. Math. and Phys. 3 (1924), 63-65. Note on a paper of o. Perron, J. Math. and Phys. 4 (1925), 21-32. The solution of a difference equation by trigonometrical integrals, J. Math. and Phys. 4 (1925), 153-163.

379

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IA

IA

IE

I, I

IA

IB

IB

IC

IC

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I, I IB

IB

IB

IC

IC

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IVA

IVA

IVB IB

ID

380

[25c]

[25d]

[25e]

[25f]

[26a]

[26b]

[26c] [26d]

[26e]

[26f]

[27a]

[27b]

[27c]

[27d]

[27e]

[27f]

[27g]

[27h]

[27i]

[27j]

[27k]

[28a]

[28b]

[28c]

Bibliography of Norbert Wiener

On the representation of functions by trigonometrical integrals, Math. Z. 24 (1925), 575-616. Verallgemeinerte trigonometrische Entwicklungen, Goltingen Nachr. (1925), 151-158. Note on quasi-analytic function, J. Math. and Phys. 4 (1925), 193-199. A contribution to the theory of interpolation, Ann. of Math. (2) 26 (1925),212-216. The harmonic analysis of irregular motion, J. Math. and Phys. 5 (1926),99-121. The harmonic analysis of irregular motion (Second Paper), J. Math. and Phys. 5 (1926), 158-189. The operational calculus, Math. Ann. 95 (1926), 557-584. A new formulation of the laws of quantization of periodic and aperiodic phenomena (with M. Born), J. Math. and Phys. 5 (1926), 84-98. Eine neue Formulierung der Quantengesetze fur periodische und nichtperiodische Vorgiinge (with M. Born), Z. Physik 36 (1926), 174-187. Analytic approximations to topological transformations (with P. Franklin), Trans. Arner. Math. Soc. 28 (1926), 762-785. The spectrum of an array and its application to the study of the translation properties of a simple class of arithmetical functions, Part I, J. Math. and Phys. 6 (1927), 145-157. (Part II: On the translation of a simple class of arithmetical functions, by K. Mahler, ibid, pp. 158-163). A new definition of almost periodic functions, Ann. of Math. (2) 28 (1927), 365-367. On a theorem of Bochner and Hardy, J. London Math. Soc. 2 (1927), 118-123. Une methode nouvelle pour la demonstration des tMoremes de M. Tauber, C.R. Acad. Sci. Paris 184 (1927), 793-795. On the closure of certain assemblages of trigonometrical functions, Proc. Nat. Acad. Sci. U.S.A. 13 (1927), 27-29. Quantum theory and gravitational relativity (with D.J. Struik), Nature 119 (1927), 853-854. A relativistic theory of quanta (with D.J. Struik), J. Math. and Phys. 7 (1927), 1-23. Sur fa tMorie relativiste des quanta (with D.J. Struik), C.R. Acad. Sci. Paris 185 (1927) 42--44. Sur la tMorie relativiste des quanta (N ate), C. R. Acad. Sci. Paris 185 (1927), 184-185. Laplacians and continuous linear functionals, Acta Sci. Math. (Szeged) 3 (1927), 7-16. Une generalisation des fonctions a variation bornee, C.R. Acad. Sci. Paris 185 (1927), 65-67. The spectrum of an arbitrary function, Proc. London Math. Soc. (2) 27 (1928), 483--496. A new method in Tauberian theorems, J. Math. and Phys. 7 (1928), 161-184. The fifth dimension in relativistic quantum theory (with D.J. Struik), Proc. Nat. Acad. Sci. U.S.A. 14 (1928), 262-268.

ID

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ID

ID

ID IH

IH

I, I

ID

ID

ID

ID

IE

IH

IH

IH

IH

I, T

I, T

ID

ID

IH

[28d]

[29a]

[29b]

[29c]

[29d]

[2ge]

[29f]

[29g]

[29h]

[29i]

[29j] [30a]

[30b]

[31a]

[31b]

[31c]

[32a]

[32b] [32c]

[32d] [32e]

[32f]

[33a]

[33b] [33c]

[33d]

Bibliography of Norbert Wiener

Coherency matrices and quantum theory, J, Math, and Phys, 7 (1928), 109-125. Harmonic analysis and group theory, J. Math. and Phys. 8 (1929), 148-154. A type of Tauberian theorem applying to Fourier series, Proc. London Math. Soc. (20) 30 (1929), 1-8. Fourier analysis and asymptotic series. Appendix to V. Bush, Operational Circuit Analysis, New York, John Wiley, 1929, 366-379. Hermitian polynomials and Fourier analysis, J. Math. and Phys. 8 (1929), 70-73. Harmonic analysis and the quantum theory, J. Franklin Inst. 207 (1929), 525-534. On the spherically symmetrical statical field in Einstein's unified theory of electricity and gravitation (with M.S. Vallarta), Proc. Nat. Acad. Sci. U.S.A. 15 (1929), 353-356. On the spherically symmetrical statical field in Einstein's unified theory: A correction (with M. S. Vallarta), Proc. Nat. Acad. Sci. U.S.A. 15 (1929), 802-804. Mathematics and art (Fundamental identities in the emotional aspects of each) , Tech. Rev. 32 (1929),129-132,160,162. Einsteiniana (Facts and fancies about Dr. Einstein's famous theory), Tech. Rev. 32 (1929), 403-404. Murder and mathematics, Tech. Rev. 32 (1929), 271-272. Generalized harmonic analysis, Acta Math. 55 (1930), 117-258. (Reprinted in [64f] and [66b].) Review of A. Eddington's Science and the Unseen World, Tech. Rev. 33 (1930), 150. Ober eine Klasse singuliirer Integralgleichungen (with E. Hopt), Sitzber. Preuss. Akad. Wiss. Berlin, KI. Math. Phys. Tech., 1931, pp. 696-706. (Reprinted in [64f].) A new deduction of the Gaussian distribution, J. Math. and Phys. 10 (1931), 284-288. Reportsfrom Cambridge-1931, Tech. Rev. 34(1931), 82-83,131, 218, 220. Tauberian theorems, Ann. of Math. 33 (1932),1-100 (Reprinted in [64f] and [66b].) A note on Tauberian theorems, Ann. of Math. 33 (1932), 787. Back to Leibniz! (Physics reoccupies an abandoned position), Tech. Rev. 34 (1932), 201-203, 222, 224. Reports from Cambridge-1932, Tech. Rev. 34 (1932), 62, 74. Review of A.S. Besicovitch, Almost Periodic Functions, Math. Gaz. 16 (1932), 275-277. Analytic properties of the characters of infinite Abelian groups (with R.E.A.C. Paley), Abstract, Int'1. Math. Congr., Ziirich, 1932,95. Notes on random functions (with R.E.A.C. Paley and A. Zyg­mund), Math. Z. 37 (1933), 647-668. A one-sided Tauberian theorem, Math. Z. 36 (1933), 787-789. Characters of Abelian groups (with R.E.A.C. Paley), Proc. Nat. Acad. Sci. U.S.A. 19 (1933), 253-257. The total variation of g(x + h) - g(x) (with R. C. Young, Trans. Amer. Math. Soc. 35 (1933), 327-340.

381

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V

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ID

382 Bibliography of Norbert Wiener

[33e] Notes on the theory and application of Fourier transforms (with IE R.E.A.C. Paley) I, II, Trans. Amer. Math. Soc. 35 (1933), 348-355; III, IV, V, VI, VII, Trans. Amer. Math. Soc. 35 (1933), 761-79l.

[33f] Putting matter to work (The searchfor chapter power), Tech. Rev. IlIA 35 (1933), 47-49, 70, 72.

[33g] Review of Harald Bohr, Fastperiodische Funktionen, Math. Gaz. IVA 17 (1933), 54.

[33h] R.E.A.C. Paley-In Memoriam, Jan. 7, 1907-Apr. 7,1933, Bull. IVB Amer. Math. Soc. 39 (1933), 476.

[33i] The Fourier Integral and Certain of Its Applications, Cambridge VI University Press, New York, 1933; reprint, Dover, New York, 1959; review by E.C. Titchmarsh in Math. Gaz. 17 (1933),129.

[34a] Random functions, J. Math. and Phys. 14 (1934),17-23. IC [34b] A class of gap theorems, Ann. Scuola Norm. Sup. Pisa, E IE

(1934-1936), I-6. [34c] Quantum mechanics, Haldane, and Leibniz, Philos. Sci. I (1934), IIA

479-482. [34d] Fourier Transforms in the Complex Domain (with R.E.A.C. VI

Paley), Amer. Math. Soc. Colloq. Publ. 19, Amer. Math. Soc., Providence, R.I., 1934.

[34e] Aid for German-refugee scholars must come from non-academic IIID sources, Jewish Advocate (December 1934).

[35a] Fabry's gap theorem, Sci. Repts. of Nat'1. Tsing Hua Univ., Ser. IE A, 3 (1935), 239-245.

[35b] Limitations of science (The holiday fallacy and a response to the IIIA suggestion that scientists become sociologists), Tech. Rev. 37 (1935), 255-256, 268, 270, 272.

[35c] The student agitator (Is he accepting radicalism as an opiate?) IIIC (with Carl Bridenbaugh), Tech. Rev. 37 (1935),310-312,344,346.

[35d] Mathematics in American secondary schools. J. Math. Assoc. IIIC Japan for Secondary Education (Tokyo) 17 (1935), 1-5.

[35e] The closure of Bessel functions, Abstract 66, Bull. Amer. Math. V Soc. 41 (1935), 35.

[35f] Once more ... the refugee problem abroad, Jewish Advocate IIID (February 5, 1935).

[36a] A theorem of Carle man, Sci. Repts. of Nat'1. Tsing Hua Univ., Ser. IE A, 3 (1936), 291-298.

[36b] Sur les series de Fourier lacunaires. Theoremes directs (with S. IE Mandelbrojt), C.R. Acad. Sci. Paris 203 (1936), 34-36.

[36c] Series de Fourier lacuna ires. Theoremes inverses (with S. Man- IE delbrojt), C.R. Acad. Sci. Paris 203 (1936), 233-234.

[36d] Gap theorems, C.R. de Congr. Int'1. des Math., 1936, 284-296. IE [36e] A Tauberian gap theorem of Hardy and Littlewood, J. Chinese IE

Math. Soc. 1 (1936) 15-22. [36f] Notes of the Kron theory of tensors in electrical machinery, J. I, I

Electr. Engrg., China 7 (1936), 277-29l. [36g] The role of the observer, Philos. Sci. 3 (1936), 307-319. IIA [37a] Taylor's series of entire functions of smooth growth (with W. T. ID

Martin), Duke Math. J. 3 (1937), 213-223. [37b] Random Waring's theorems, Abstract (with N. Levinson), Science V

85 (1937), 439.

[38a]

[38b]

[38c]

[38d]

[38e]

[38t]

[38g] [38h]

[39a]

[39b]

[39c]

[39d]

[3ge]

[39t]

[39g]

[39h]

[40a]

[40b]

[40c]

[40d]

[41a]

[41b]

[42a]

[43a]

Bibliography of Norbert Wiener

The homogeneous chaos, Amer. J. Math. 60 (1938), 897-936. (Reprinted in [64t].) On absolutely convergent Fourier-Stieltjes transforms (with H. R. Pitt), Duke Math. J. 4 (1938), 420-440. Fourier-Stieltjes transforms and singular infinite convolutions (with A. Wintner), Amer. J. Math. 60 (1938), 513-522. Taylor's series of functions of smooth growth in the unit circle (with W.T. Martin), Duke Math. J. 4 (1938),384-392. The historical background of harmonic analysis, Amer. Math. Soc. Semicentennial Publications Vol. II, Semicentennial Addresses, Amer. Math. Soc., Providence, R.I., 1938, 513-522. Remarks on the classical inversion formula for the Laplace integral (with D. V. Widder), Bull. Amer. Math. Soc. 44 (1938), 573-575. The decline of cookbook engineering, Tech. Rev. 40 (1938), 23. Review of L. Hogben, Science for the Citizen, Tech. Rev. 40 (1938), 66--67. The ergodic theorem, Duke Math. J. 5 (1939), 1-18. (Reprinted in [64t].) The use of statistical theory in the study of turbulence, Proc. 5th Int'l. Congr. of Applied Mechanics, Sept. 12-16, 1938, Wiley, New York, 1939, 356--358. On singular distributions (with A. Wintner), J. Math. and Phys. 17 (1939), 233-246. Convergence properties of analytic functions of Fourier-Stieltjes transforms (with R. H. Cameron), Trans. Amer. Math. Soc. 46 (1939), 97-109; Math. Rev. 1 (1940), 13; rev. 400. A generalization of Ikehara's theorem (with H.R. Pitt), J. Math. and Phys. 17 (1939), 247-258. Review of Roger Burlingame, March of the Iron Men, Tech. Rev. 41 (1939), 115. Review of W. George, The Scientist in Action, Tech. Rev. 41 (1939), 202. A new method in statistical mechanics, Abstract 133 (with B. McMillan), Bull. Amer. Math. Soc. 45 (1939), 234; Science 90 (1939), 410-411. Review of M. Fukamiya, On dominated ergodic theorems in Lp(p~l), Math. Rev. 1 (1940), 148. Review ofM. Fukamiya, The Lipschitz condition ofrandomfunc­tion, Math. Rev. I (1940), 149. Review of Th. De Donder, L'imergetique deduite de la mixanique statistique generale, Math. Rev. 1 (1940), 192. A canonical series for symmetric functions in statistical mechanics, Abstract 133, Bull. Amer. Math. Soc. 46 (1940), 57. Harmonic analysis and ergodic theory (with A. Wintner), Amer. J. Math. 63 (1941), 415-426; Math. Rev. 2 (1941), 319. On the ergodic dynamics of almost periodic systems (with A. Wint­ner), Amer. J. Math. 63 (1941), 794-824; Math. Rev. 4 (1943),15. On the oscillation of the derivatives of a periodic function (with G. P6Iya), Trans. Amer. Math. Soc. 52 (1942), 249-256. The discrete chaos (with A. Wintner), Amer. J. Math. 65 (1943), 279-298; Math. Rev. 4 (1943), 220.

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[43b)

[44a)

[45a)

[45b)

[46a)

[46b)

[47a)

[47b)

[48a)

[48 b) [48c)

[48d)

[48e)

[48f]

[49a)

[49b)

[49c)

[49d)

[4ge)

Bibliography of Norbert Wiener

Behavior, purpose, and teleology (with A. Rosenblueth and J. Bigelow), Philos. Sci. 10 (1943), 18-24. Review of Hugh Gray Lieber and Lillian R. Lieber, The Education of T. C. Mils; What Modern Methematics Means to You, Tech. Rev. 46 (1944), 390, 392. La teoria de la estrapolacibn estadistica, Bol. Soc. Mat. Mexicana 2 (1945), 37--45; Math. Rev. 7 (1946), 461. The role of models in science (with A. Rosenblueth), Philos. Sci. 12 (1945),316-322. A generalization of the Wiener-Hopf integral equation (with A. E. Heins), Proc. Nat. Acad. Sci. U.S.A. 32 (1946), 98-101; Math. Rev. 8 (1947), 29. The mathematical formulation of the problem of conduction of im­pulses in a network of connected excitable elements, specifically in cardiac muscle (with A. Rosenblueth), Arch. Inst. Cardiol. Mexicana 16 (1946), 205-265; Bol. Soc. Mat. Mexicana 2 (1945), 37-42; Math. Rev. Sur les fonctions inde{iniment derivables sur une demi-droite (with S. Mande1brojt), C. R. Acad. Sci. Paris 225 (1947), 978-980; Math. Rev. 9 (1948), 230. A scientist rebels, Atlantic Monthly 179 (1946), 46; Bill. Atomic Scientist 3 (1947), 31. Time, communication and the nervous system, Ann. New York Acad. Sci. 50 (1948), 197-220; Math. Rev. 10 (1949), 133. Cybernetics, Scientific American 179 (1948),14-18. An account of the spike potential ofaxons (with A. Rosenblueth, W. Pitts, J. Garcia Ramos, and the assistance of F. Webster), J. of Cellular and Comparative Physiol. 32 (1948), 275-318. A rebellious scientist after two years, Bull. Atomic Scientists 4 (1948), 338-339. Review of L. Infeld, Whom the Gods Love. The Story of Evariste Galois, Scripta Math. 14 (1948), 273-274. Cybernetics, or Control and Communication in the Animal and the Machine, Actualites Sci. Ind., no. 1053; Hermann et Cie., Paris; The MIT Press, Cambridge, Mass., and Wiley, New York, 1948; Math. Rev. 9 (1948), 598. Partly reprinted as Rigidity and learn­ing: ants and men, in Classics in Biology (A Course of Selected Reading by Authorities), Philosophical Library, New York, 1960, pp. 205-213. Sur la tMorie de la prevision statistique et du filtrage des ondes, Analyse Harmonique, Colloques Internationaux du CNRS, No. 15, pp. 67-74. Centre National de la Recherche Scientifique, Paris, 1949; Math. Rev. 11 (1950), 376. A statistical analysis of synaptic excitation (with A. Rosenblueth, W. Pitts, and J. Garcia Ramos), J. of Cellular and Comparative Physiol. 34 (1949), 173-205. A new concept of communication engineering, Electronics 22 (1949), 74-77. Sound communication with the deaf, Philos. Sci. 16 (1949), 260-262. Some problems in sensory prosynthesis (with J. Wiesner and L. Levine), Science 110 (1949), 512.

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Bibliography of Norbert Wiener 385

[49t] Obituary-Godfrey Harold Hardy, 1877-1947, Bull. Amer. Math. IVB Soc. 55 (1949), 72-77.

[49g] Extrapolation, Interpolation, and Smoothing of Stationary Time VI Series with Engineering Applications, The MIT Press, Cambridge, Mass., Wiley, New York; Chapman & Hall, London, 1949; paper-back edition with the title Time Series, The MIT Press, 1964; Math. Rev. 11 (1950), 118.

[49h] Review of Philipp Frank, Modern Science and its Philosophy, New iVA York Times, Book Review, August 14, 1949, sec. 7, p. 3.

[50a] Some prime-number consequences of the Ikehara theorem (with L. ID Geller); Acta. Sci. Math. (Szeged) 12 (1950), 25-28, Leopoldo Fejer et Frederico Riesz LXX annos natis dedicatus, Pars B; Math. Rev. II (1950), 644; Math. Rev. 12 (1951), 1002.

[50b] Comprehensive view of prediction theory, Proceedings of the Inter- TG national Congress of Mathematicians, Cambridge, Mass., 1950, vol. 2, pp. 308-321; Amcr. Math. Soc., Providence, R.I., 1952, Expository lecture; Math. Rev. 13 (1952), 477.

[50c] Some maxims for biologists and psychologists, Dialectica 4 (1950), IIA 186-191.

[50d] Purposeful and non-purposeful behavior (with A. Rosenblueth), IIA Philos. Sci. 17 (1950), 318-326.

[50e] Cybernetics, Bull. Amer. Acad. Arts and Sci. 3 (1950), 2-4. lIB [50t] Speech, language, and learning, J. Acoust. Soc. Amer. 22 (1950), lIB

696-697. [50g] Entropy and information, Proc. Sympos. App!. Math., vol. 2, lIB

Amer. Math. Soc., Providence, R.I., 1950, p. 89; Math. Rev. 11 (1950), 305.

[50h] Too big for private enterprise, Nation 170 (1950), 496-497. IlIA [50i] Too damn close, Atlantic 186 (1950), 50-52. lIlA [50j] The Human Use of Human Beings, Houghton Mifflin, Boston, VI

1950; paperback edition by Doubleday, Anchor, Garden City, N.Y., 1954. Chapter 3 reprinted in Classics in Biology (A Course of Selected Reading by Authorities), Philosophical Library, New York, 1960, pp. 205-213.

[50k] The brain (short story), Tech. Eng. News 31 (1950), 14-15,33-34, VI 44, 50. (reprinted in paperback anthology, Cross-roads in Time, ed. Groff Conklin, Doubleday, Garden City, N.Y., 1953.)

[5Ia] Problems of sensory prosthesis, Bull. Amer. Math. Soc. 57 (1951), IIB 27-35. (Reprinted in [64t].)

[51 b] Homeostasis in the individual and society, J. Franklin Inst. 251 lIB (1951), 65-68. (Reprinted in [64f].)

[5Ic] Mathematical relationships of possible significance in the study of ITA human leukemia (with P.F. Hahn), Federation Proc. 10 (1951).

[52a] Cybernetics (Light and Maxwell's demon), Scientia (Italy) 87 lIB (1952), 233-235.

[52b] The miracle of the broom closet (short story), Tech. Eng. News 33 VI (1952), 18-19,50. (Reprinted in the Magazine of Fantasy and Science Fiction, ed. Anthony Boucher, February 1954, pp. 59-63).

[52c] Cybernetics, in Encyclopedia Americana Annual 1952 edition, lIB 187-188.

[53a] Optics and the theory of stochastic processes, J. Opt. Soc. Amer. 43 IG (1953), 225-228; Math. Rev. 17 (1956), 33.

386

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[53c]

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[53e]

[53f]

[53g]

[53h]

[53i]

[53j]

[53k]

[54a]

[54b] [54c]

[55a]

[55b]

[55c]

[55d]

[55e]

[56a]

[56b]

[56c]

Bibliography of Norbert Wiener

A new form for the statistical postulate of quantum mechanics (with A. Siegel), Phys. Rev. 9 (1953),1551-1560; Math. Rev. 15 (1954), 273. Distributions quantiques dans l'espace differentiel pour lesfonctions d'ondes dependant du spin (with A. Siegel), C.R. Acad. Sci. Paris 237 (1953), 1640-1642; Math. Rev. 15 (1954), 490. Les machines a calculer et la forme (Gestalt), Les machines a calculer et la pensee humaine, Colloques Internationaux du Centre National de la Recherche Scientifique, Paris, 1953, pp. 461-463; Math. Rev. 16 (1955), 529. The concept of homeostasis in medicine, Transactions and Studies of the College of Physicians of Philadelphia (4) 20 (1953), No.3, 87-93. Problems of organization, Bull. Menninger Clinic 17 (1953), 130-138. The future of automatic machinery, Mech. Engrg. 75 (1953), 130-132. Ex-prodigy: My Childhood and Youth, Simon and Schuster, New York, 1953; The MIT Press, Cambridge, Mass., 1965 (paperback edition, The MIT Press); Math Rev. 15 (1954), 277. The electronic brain and the next industrial revolution, Cleveland Athletic Club Journal (January, 1953). The machine as threat and promise, St. Louis Post-Dispatch (December, 1953). We can't attain truth without risk of error (from This I Believe radio show), Minneapolis Tribune (November, 1953). Men, machines, abd the world about, in Medicine and Science, New York Academy of Medicine and Science, ed. I. Galderston, International Universities Press, New York, 1954, pp. 13-28. Conspiracy of conformists, Nation 178 (1954), 375. Automatization (with Donald Campbell), St. Louis Post-Dispatch (December, 1954). Nonlinear prediction and dynamics, Proc. Third Berkeley Sym­posium on Mathematical Statistics and Probability, University of California Press, Berkeley, Calif., 1954/5, pp. 247-252; Math. Rev. 18 (1957), 949. On the factorization of matrices, Comment. Math. Helv. 29 (1955), 97-111; Math. Rev. 16 (1955), 921. The differential-space theory of quantum systems (with A. Siegel), Nuovo Cimento (10) 2 (1955), 982-1003, No.4, Supp!. Thermodynamics of the message, in Neurochemistry, ed. K.E.C. Elliott, Thomas, Springfield, 1955, pp. 844-849. Time and organization, Second Fawley Foundation Lecture, Uni­versity of Southampton, 1955, pp. 1-16. On a local L 2-variant of lkehara's theorem (with A. Wintner), Rev. Math. Cuyana 2 (1956), 53-59. The theory of prediction, in Modern Mathematicsfor the Engineer, ed. E.F. Beckenbach, McGraw-Hill, New York, 1956, pp. 165-187. "Theory of Measurement" in differential-space quantum theory (with A. Siegel), Phys. Rev. 101 (1956),429-432.

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Bibliography of Norbert Wiener 387

[56d] Pure patterns in a natural world, in The New Landscape in Art and IIB Science, ed. G. Kepes, Paul Theobald and Co., Chicago, 1956, pp. 274-276.

[56e] Brain waves and the interferometer, J. Phys. Soc. Japan 18 (1956), IIB 499-507.

[56f] Moral reflections of a mathematician, Bull. Atomic Scientists 12 IlIB (1956), 53-57. (Reprinted from [56g].)

[56g] I Am a Mathematician. The Later Life of a Prodigy, Doubleday, VI Garden City, New York, 1956; paperback edition by The MIT Press, 1964; Math. Rev. 17 (1956), 1037.

[57a] The definition and ergodic properties of the stochastic adjoint of a IC unitary transformation (with E.J. Akutowicz), Rend. Circ. Mat. Palermo (2) 6 (1957), 205-217, Addendum, 349; Math. Rev. 20 (1959), rev. 4328.

[57b] Notes on Polya's and Tur(m's hypotheses concerning Liouville's ID factor (with A. Wintner), Rend. Circ. Mat. Palermo (2) 6 (1957), 240-248; Math. Rev. 20 (1959), rev. 5759.

[57c] On the non-vanishing of Euler products (with A. Wintner), Amer. ID J. Math. 79 (1957), 801-808.

[57d] The prediction theory of multivariate stochastic processes, .Part I IG (with P. Masani), Acta Math. 98 (1957), 111-150; Math. Rev. 20 (1959), rev. 4323.

[57e] Rythms in physiology with particular reference to encephalography, IIB Proceedings of the RudolfVirchow Medical Society in the City of New York, vol. 16, 1957, pp. 109-124.

[57f] The role of the mathematician in a materialistic culture (A IlIA scientist's dilemma in a materialistic world), Columbia Engineer-ing Quarterly, Proceedings of the Second Combined Plan Confer-ence, Arden House, October 6-9, 1957, pp. 22-24.

[57g] The role of the small cultural college in education of the scientists; mc a speech given at Wabash College, Indiana, October 10, 1957.

[57h] Cybernetics, in The Universal Standard Encyclopedia (abridgment IIB of The New Funk and Wagnall's Encyclopedia), Standard Refer-ence Works Publishing Co., New York, 1957, p. 180.

[58a] Logique, probabilite et methode des sciences physiques, in La IH Methode dans les Sciences Modernes, Editions Science et Indus-trie, ed. Franyois Le Lionnais, Paris, 1958, pp. 111-112.

[58b] The prediction theory of multivariate stochastic processes, Part II IG (with P. Masani), Acta Math. 99 (1958), 93-137; Math. Rev. 20 (1959), rev. 4325.

[5Sc] Random time (with A. Wintner), Nature 181 (1958),561-562. IIB [58d] Sur la prevision lineaire des processus stochastiques vectoriels a IG

densite spectrale bornee. I (with P. Masani), C. R. Acad. Aci. Paris 246 (1958), 1492-1495; Math. Rev. 20 (1959), rev. 4324a.

[SSe] Sur la prevision lineaire des processus stochastiques vectoriels a IG densite spectrale bornee. II (with P. Masani), C. R. Acad. Sci. Paris 246 (1958), 1655-1656; Math. Rev. 20 (1959), rev. 4324b.

[58f] My connection with cybernetics. Its origins and its future, Cyber- IIB netica (Belgium) I (1958), 1-14.

[5Sg] Time and the science of organization, Part II, Scientia 93 (1958), JIB 225-230.

[5Sh] Science: The megabuck era, New Republic, 13S (1958), 10-11. IlIA

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[59a]

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[60b]

[60c]

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[60e]

[60f]

[60g]

[61a]

[61b]

[61c]

[62a]

[62b]

Bibliography of Norbert Wiener

Nonlinear Problems in Random Theory, The MIT Press, Cam­bridge, Mass., and Wiley, New York, 1958; paperback edition, The MIT Press, 1966. A factorization of positive Hermitian matrices (with E.J. Akuto­wicz), J. Math. Mech. 8 (1959),111-120. Nonlinear prediction (with P. Masani), in Probability and Statis­tics, The Harald Cramer Volume, ed. U. Grenander, Stockholm, 1959, 190-212. On bivariate stationary processes and the factorization of matrix­valuedfunctions (with P. Masani), Teor, Verojatnost, i Primenen. 4 (1959), 322-331. (English trans I. Theor. Probability App. 4 (1959), 300-308). Man and the machine (Interview with N. Wiener), Challenge (The Magazine of Economic Affairs) 7 (1959), 36-41. The Tempter (novel), Random House, New York, 1959. The application of physics to medicine, in Medicine and Other Disciplines, New York Academy of Medicine, ed. 1. Galderston, International Universities Press, 1960, pp. 41-57. The brain and the machine (Summary of an address), in Dimensions of Mind, ed. S. Hook, Collier Books, 1960, (Proceedings of Third Annual New York Univ. Institute of Philosophy held on May 15-16,1959), pp. 113-117. Kybernetik, Contribution to Worterbuch der Soziologie, F. Enke Verlag, Stuttgart, 1960, pp. 620-622. Some moral and technical consequences of automation, Science 131 (1960), 1355-1358. The duty of the intellectual, Tech. Rev. 62 (1960), 26-27; reprinted almost in entirety in The grand privilege, Sat. Rev. 43 (1960), 51-52; also in Technion 18 (1961), 86-87-"A professor tells what a professor is." Preface to Cybernetics of Natural Systems, by D. Stanley-Jones, Pergamon Press, London, 1960, pp. v-viii. Possibilities of the use of the interferometer in investigating macromolecular interactions, in Fast Fundamental Transfer Pro­cesses in Aqueous Biomolecular Systems, ed. F. O. Schmitt, Department of Biology, MIT, Cambridge, Mass., June 1960, pp.52-53. Uber Informationstheoreie, Naturwissenschaften 48 (1961), 174-176. Science and society, Voprosy Filosofii (1961), No.7, 117-122; reprinted in Estratto Rivista Methodos 13 (1961), 1-8, and in Tech. Rev. 63 (1961), 49-52. Excerpts in Science 138 (1962), 651. Cybernetics, Second edition of [48f] (revisions and two additional chapters), The MIT Press and Wiley, New York, 1961; paperpack edition, The MIT Press, 1965. A verbal Contribution to Proc. of the International Symposium on the Application of Automatic Control in Prosthetics Design, August 27-31, 1962, Opatija, Yugoslavia, pp. 132-133. The mathematics of self-organizing systems, in Recent Develop­ments in Information and Decision Processes, Macmillan, New York, 1962, pp. 1-21.

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Bibliography of Norbert Wiener 389

[62c] Short-time and long-time planning, originally presented at 1954 IlIA ASPO National Planning Conference. Jersey Plans, An ASPO Anthology (1962), 29-36.

[63a] Random theory in classical phase space and quantum mechanics IH (with Giacomo Della Riccia), Proc. Internat. Conference on Functional Analysis, Massachusetts Institute of Technology, Cambridge, Mass., June 9-13, 1963; Analysis in Function Space, The MIT Press, Cambridge, Mass., 1964, pp. 3-14.

[63b] Introduction to neurocybernetics (with J.P. Schade) and Epilogue, lIB in Progress in Brain Research, vol. 2 of Nerve, Brain and Memory Models, Elsevier Publishing Co., Amsterdam, 1%3, pp. 1-7, 264-268.

[63c] The lonely nationalism of Rudyard Kipling (with K. Deutsch), Yale llID Rev. 52 (1963), 499-517.

[64a] On the oscillations of nonlinear systems, Proc. Symposium on Sto- lIB chastic Models in Medicine and Biology, Mathematics Research Center, U.S. Army, June 12-14, 1963, ed. John Gurland, Uni-versity of Wisconsin Press, Madison, Wisconsin, 1964, pp. 167-177.

[64b] Dynamical systems in physics and biology, Contribution to series lIB "Fundamental Science in 1984", The New Scientist (London) 21 (1964), 211-212.

[64c] Machines smarter than men? (Interview with N. Wiener), U.S. lIlA News and World Rept. 56 (1964),84-86; abbreviated in Reader's Digest 84 (1964), 121-124.

[64d] Intellectual honesty and the contemporary scientist (Transcript of lIlA talk given to Hillel Group at Massachusetts Institute of Technol· ogy), Tech. Rev. 66 (1964),17-18,44-45,47.

[64e] God, Golem, Inc.-A Comment on Certain Points Where Cyber. VI netics Impinges on Religion, The MIT Press, Cambridge, Mass., 1964; paperback edition, The MIT Press 1966.

[64t] Selected Papers of Norbert Wiener with expository papers by VI Y. W. Lee, Norman Levinson, and W. T. Martin, The MIT Press, Cambridge, Mass., 1964.

[65a] L'homme et la machine, Proc. Colloques Philosophiques Inter· IlB nationaux de Royaumont, July, 1962; Le concept d'in/ormation dans la science contemporaine, Gauthier-Villars, Paris, 1965, pp. 99-132.

[65b] Perspectives in cybernetics, Progress in Brain Research 17 (1965), IIB 399--408.

[65c] Cybernetics in Collier's Encyclopedia, U.S.A., ed. William D. Hal· IIB sey, The Cormwell·Collier Publishing Co., New York, 1965, pp. 598-599.

[66a] Wave mechanics in classical phase space, Brownian motion, and IH quantum theory (with G. Della Riccia), J. Math. Phys. 7 (1966), 1372-1383.

[66b] Differential Space, Quantum Systems and Prediction (with A. VI Siegel, B. Rankin, W. T. Martin), The MIT Press, Cambridge, Mass., 1966.

[66c] Generalized Harmonic Analysis and Tauberian Theorems (paper· VI back edition of [30a] and [32a]), The MIT Press, Cambridge, Mass., 1966.

390 Bibliography of Norbert Wiener

[75a] Cybernetics (with F. Landis), in Funk and Wagnall's New Eney- lIB c1opedia, Funk & Wagnall, New York, 1975, p. 228.

[85a] Letter covering the memorandum on the scope, etc., of a suggested lIB computing machine (September 21, 1940), Coli. Works, IV, pp. 122-124, ef. {MIO}.

[85b] Memorandum on mechanical solution of partial differential equa- lIB tions, Coil. Works, IV, pp. 125-134, ef. {MIO}.

[85e] Muscular Clonus: Cybernetics and Physiology (with A. Rosen- lIB blueth and J. Garcia Ramos), Call. Works, IV, pp.466-51O, ef. {MIO}.

391

Defense Department Documents!

Ia. S.H. Caldwell, Proposal to Section D2, NDRC (3 p.), November 22, 1940.

lb. N. Wiener, Principles governing the construction of prediction and compensating apparatus (8 p.) accompaniment to la, November 22, 1940.

II. K.T. Compton, Letter to Dr. Warren Weaver, NDRC, May 13, 1941.

III. J.H. Bigelow, Minutes of Conference held at Bell Laboratories on June 4, 1941.

IV. N. Wiener, Letter to Dr. Warren Weaver, NDRC, December I, 1941.

V. G. R. Stibitz, Note on prediction networks a la Wiener (14 p.), February 22, 1942.

VI. Warren Weaver, Letter to Dr. J.C. Boyce, MIT, March 24, 1942.

VII. N. Wiener, A.A. Directors, Summary Report of Demonstration (17 p.), June 10, 1942.

VIII. Demonstration by Wiener and Bigelow at MIT, July I, 1942, Diary of G.R. Stibitz, Chairman, Division D2, July 23, 1942.

IX. N. Wiener: Final report on Section D2, Project No.6 (8 p.) submitted to Dr. Warren Weaver, NDRC, December I, 1942.2

X. N. Wiener, Letter to Dr. Warren Weaver, NDRC, January 15, 1943.

XI. R. S. Phillips and P. R. Weiss, Theoretical calculation on best smoothing of posi­tion data for gunnery prediction, MIT Radiation Laboratory Report 532, February 16, 1944.

XII. N. Wiener, Automatic Control Techniques in Industry, Industrial College of the Armed Forces, Washington, D.C., 1952-1953.

NDRC stands for National Defense Research Committee. 2 This report is accompanied by a Report to the Services, No. 59, of March 27,

1945, entitled "Statistical Method of Prediction in Fire Control".

392

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A2 American Mathematical Society Bulletin 72 (No.1, Part II) (1966), dedi­cated to Norbert Wiener.

A3 Ampere, Andre-Marie, Essai sur la philosophie des sciences ou exposition analytique d'une classification naturelle de toutes les connaissances humaines, Paris, Bachelier, 1838, premiere partie; 1843, seconde partie.

A4 Ashby, W.R., Design for a Brain, Wiley, New York, 1960. AS Ashby, W.R., Principles of the self-organizing system, pp.255-278, in

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A6 Ashby, W.R., An Introduction to Cybernetics, Wiley, New York, 1963. A 7 Augustine, St., Concerning the nature of good, in Basic Writings of St. Augus­

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B1 Barnes, J.L., Information-theroretic aspects of feedback control systems, Automatica 4 (1968), 165-185.

B2 Bass, J., Stationary functions and their applications to the theory of turbu­lence, J. Math. Appl. 47 (1974), 354-399, 458-503.

B3 Bass, J., Fonctions de correlation,fonctions pseudo-aleatoires et applications, Masson, Paris, 1984.

B4 Bell, D., The Cultural Contradictions of Capitalism, Basic Books, Inc., New York, 1976.

B5 Bell, E. T., Men of Mathematics, Simon & Schuster, New York, 1965. B6 Benedetto, J., Spectral Synthesis, Academic Press, 1975. B7 Bergman, S., The Kernel Function and Conformal Mapping, Math. Surveys 5,

Rev. Ed., Amer. Math. Soc., Providence, R.I., 1970. B8 Bernal, J.D., The Social Function of Science, George Routledge & Sons,

London, 1946. B9 Bernstein, J., Einstein, Fontana/Collins, Glasgow, 1973.

BIO Birkhoff, G.D., Intuition, reason and faith in science, Science 88, (1938), 601-609.

Bll Birkhoff, G.D., The principle of sufficient reason, Rice Inst. Pamphlet Vol. 28, Jan. 1941,24-50.

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400

Name Index

Acheson, George 197 Aeschylus (525-456 B.C.): 370 Aiken, H.H. (1900-1973): 239 Alaric (3707-410): 332 Albertson, Ralph A. (I RR6-1951): 30,

392 Alexander, J. W. (1888-1971): 63, 68 Ambartsumian, V. (b. 1908): 337 Ampere, Andre Maric (1775-1836): 252,

253, 392 Anaxagoras (5007-428 B.C.): 62 Anderson. Clinton (1895-1975): 312 Aquinas, Saint Thomas

(l225?-12747): 41,62,277,344 Archimedes (287-212 B.c'): 345 Aristotle (384 322 B.c'): 203, 277, 327,

368 Ashby, W. Ross (1903-1972): 212,250,

255, 256, 258-260, 262, 292, 293, 333, 367, 392

AtanasofT, V.J. (b. 1903): 172 Augustine, Saint (354-430): 318-321,

324, 329, 331, 344, 392 A vogadro, Count Amedeo

(1776-1856): 82, 148

Babbage, Charles (1791-1871): 162,171, 219, 220, 254

Bach, Johann Sebastian (1685-1750): 293

Bacon, Francis (1561-1616): 41, 62 Bacon, Roger (l214?-12947): 41, 62,

259, 277, 368 Baker, H.F. (1866-1956): 47 Banach, Stefan (1892-1945): 76 Barlow, John Sulton (b. 1925): 235,250 Barnes, John L. (1906-1976): 159,392 Barnett, 1. Albert (1894-1975): 77,167 Bartlett, Sir Francis C. (1886-1969): 56 Bass, J. 151,392 Beethoven, Ludwig van (1770-1827): 18,

200 Behrend, B.A. (1875-1942): 340 Bell, Daniel (b. 1919): 287,392 Bell, E. T. (18831960): 59, 392 Benedetto. J.J. (b. 1939): 114,392 Benke, G. 114 Berger, Hans (1873-1941): 233

Bergman, Stefan (1898-1978): 232, 393 Bergson, Hcnri (1859-1941): 42,57,60,

152, 254, 255, 277, 366 Bernal, J.D. (1901-1971): 261,359,393 Bernard, Claude (1813-1878): 253 Bernstein, Felix (1878-1956): 60 Bernstein, J. (b. 1924): IS, 393 Besicovitch, A.S. (1891-1970): 104,117,

141 Bessell, F.W. (1784-1846): 104,107 Bigelow, Julian 182-186, 188, 194, 20 I,

211,218,239,373,391 Birkhoff, G. D. (18841944): 64, 85, 93,

126,127,132,139,141,145,241,254, 326, 341, 360, 361, 363, 393

Blair, C. 297,311,314,393 Blaschke, Wilhelm (1885-1902): 136 Bliss, G.A. (1876-1951): 68 Bloch, Andre (1893-1948): 352 Bloy, Reverend Myron 370 Bocher, Maxime (1867-1918): 34,108 Bochner, S. (1899-1982): 101, 112, 195 Bode, IIendrik W. (19067-1982): 182,

189 Bohm, D. 129, 130,393 Bohr, Harald (1887-1951): 104,105,

251,372 Bohr, Niels (1885-1962): 55, 123, 128,

393 Boltzmann, Ludwig (1844-1906): 54,81,

122,143,146,148,149,155,158,159, 254

Bolyai, J. (1802-1860): 73 Bonaventura, Saint (1221-1274): 343,

346, 393 Boole, G. (1815-1864): 22 Borel, E. (lR71-1956): 90,354 Born, Max (1882-1970): 111,115,

117-119,132,155,157,241,366,393 Bouligand, C. D. 92 Boyce, J.c. 192,391 Bourbaki, N. 348 Bradley, F.H. (1846-1924): 56,60 Bray, Hubert (18890-1978): 68 Brazier, Mary A. B. 235 Brelot, Marcel (1903-1987): 86, 393 Bridgman, P.W. (1882-1961): 121,393 Brillouin, L. 155

Name Index

Broad, C.D. (1877-1971): 72 Broglie de, L.V. (1892-1987): 26,119,

122, 123, 125, 129, 130,241,345 Brown, G.S. (b. 1907): 163,396 Brown, Robert (1773-1858): 81, 82 Browning, Robert (1812-1889): 30 Buchdahl, H.A. 157,393 Bush, Vannevar (1890--1974): 96, 101,

160--162,165,166,170-172,174,175, 179, 239, 241, 264, 295, 296, 366, 393

Butler, Nicholas Murray (1862-1947): 61

Butler, Samuel (1835-1902): 35

Cairns, T. 205 Caldwell, Samuel H. (1904-1960): 181,

184,373,391 Cameron, R. H. (1908-1989): 151, 266,

271,393 Cannon, J.W. 85,393 Cannon, Walter B. (1871-1945): 34,168,

197, 198,203, 361 Cantor, Georg (1845-1918): 48,50, 59,

76,93 Caratheodory, C. (1873-1950): 94, 157 Carnap, R. (l87l-l970): 49,54,72,218,

223, 393, 394 Carnot, Sadi (1837-1894): 147, 148,254 Carroll, Lewis (1840-1921): 335 Cartwright, Mary (b. 1900): 136 Cassirer, E. (1874-1945): 25,326,394 Caton, R. 233 Chafetz, Morris E. 339 Chase, M. W. (b. 1905): 248 Chiang Kai-shek (1887-1975): 302 Christopherson, D.G. 180 Church, A. (b. 1903): 220 Clausewitz, Karl von (1780-1831): 298,

302-303,307,308,313,314,316,394 Cockcroft, Sir John D. (1897-1967): 367 Compton, Karl T. (1887-1945): 92, 192,

391 Conant, James Bryant (1893-1978): 361 Coomaraswamy, A.K. (1887-1947): 329,

343, 346, 394 Courant, Richard (1888-1972): 105 Cousins, Norman (b. 1912): 311 Cramer, Harald (1893-1985): 194 Croce, Benedetto (1866-1952): 136

Daniell, P.J. (1889-1946): 78,79,90, 394

Dante, Alighieri (1265-1321): 293,343 Darwin, Charles Robert

(1809-1882): 249 Davenport, H. (1907-1969): 47 Dean, Gordon 310 Dedekind, J.W.R. (1831-1916): 50 Deem, G. 151 De Kruif, Paul (1890--1971): 340,341 Delbruck, Max (1906-1981): 245,248

401

Democritus (b ab 460 B.c.): 143 Descartes, Rene (1596-1650): 277 Deutsch. Karl (b. 1912): 288,289,330,

336, 394 Dewey, John (1859-1952): 61,62,

277-279, 371, 394 Dickens, Charles (1812-1870): 287 Dirac, Paul A.M. (1902-1984): 119,260,

345, 368 Doob, J. L. (b. 1910): 83, 394 Draganescu, M. 253, 394 Duns Scotus, John (1265'1-1308): 62

Eckhart, Meister J. (l260?-1327): 343 Eddington, Sir Arthur (1882-1944): 26,

57, 152, 345, 394 Edwards, C. B. 71 Ehrenfest, P. (1880--1903): 147 Ehrenfest, T. 147 Einstein, Albert (1879-1955): 19,25,26,

47, 53, 55, 72, 79, 80-83, 85, 90, 102, 113, 115, 120, 121, 129, 130, 136, 143, 241, 258, 267, 268, 292, 296, 324, 325, 330-334, 344-346, 369, 394

Eisenhower, Dwight D. (1890-1969): 295,299,310,312

Eliot, T.S. (1888-1965): 60,61,279,331, 366, 394

Ellis, H. Havelock (1859-1939): 342 Emerson, Ralph Waldo (1803-1882): 93 Engels, Friedrich (1820--1895): 260,277,

293,314,395 Engemann, Marguerite (see Margaret

Wiener) Euclid (3651-275? B.C.): 326, 368 Euler, Leonhard (1707-1783): 62, 97,

345 Euripides (480?-406? B.C.): 370 Evans, W. 114

Fano, Robert (b. 1917): 373 Faraday, Michael (1791-1867): 24,99,

176 Faramelli, N.J. 333, 395 Ferry, D. K. (b. 1940): 173, 174 Feynman, R.P. (b. 1918): 84,128 Fisher, Sir Ronald A. (1890-1962): 153,

254, 395 Fisk, James B. (b. 1910): 312 Fock, V. (1898-1974): 121, 125,271 Foias, C. 193 Folin, Otto (1867-1934): 34 Forrester, Jay W. (b. 1914): 175 Forsyth, G. E. (b. 1917): 296 Foures, Y. 182,395 Fourier, Jean-Baptiste Baron de

(1768-1830): 97-99,104,144,163,177 Fowler, Henry Watson (1858-1933): 70 Francis of Assisi, Saint (1182-1226): 318 Frank, Philipp (1884-1966): 115, 136,

395

402

Frankel-Conrat, H.L. (b. 1910): 248 Frankfurter, Felix (1882-1965): 362 Franklin, Philip (1898-1965): 68,71 Frechet, Maurice (1878-1973): 74-77 Fredholm, I. (1866-1927): 163 Freudenthal, Hans (b. 1905): 349, 353,

355, 395 Frege, G. (1848-1925): 49-50,59 Freundlich, E.F. (1884-1964): 133 Freyman, M. 251 Friedrichs, K. (1901-1983): 101 Fuller. H.J. 280, 395

Gabor, Sir Dennis (1900-1979): 111 Gage, F.D. 393 Galileo (1564-1642): 315,368 Gallie, W.B. (b. 1912): 314,317,395 Galois, E. (1811-1832): 345 Garno, Hideya (b. 1924): 111 Gandhi, M.K., Matatma

(1869-1948): 318, 351, 395 Garcia Ramos, J. 197,205-208,248,

395 Gauss, Karl F. (1777-1855): 59,87 Gelfand, I.M. (b. 1913): 108 Getting, Ivan A. (b. 1912): 349 Gibbs, Josiah Willard (1839-1903): 55,

79, 122, 139, 143, 145, 146, 254, 354 Gilbreth, Frank (1868-1914): 254 Gilbreth, Lillian (1878-1972): 254 Giuculescu, A. 256, 395 Gleason, A.M. (b. 1921): 128,395 Glimcher, Melvin J. (b. 1925): 230 Glushkov, Y.M. (b. 1923): 260,261,395 Giidel, Kurt (1906-1978): 50,51,52,56,

136,219,220,261,346, 395, 396 Goethe, J.W. (1749-1832): 32,316,341 Golden, Reverend 370 Goldstine, H.H. (b. 1913): 175,232,

239, 396 Gordon, W. 120 Gould, K.E. 162,396 Goursat, E. (1858-1936): 353 Grattan-Guiness, I. (h. 1941): 43, 64,

396 Gray, T.S. (b. 1906): 162, 163,396 Green, G.F. (1793-1841): 87 Green, Gabriel Marcus (1891-1919): 77,

363 Greenberg, D. S. 361, 396

Hadamard, Jacques (1865-1963): 169, 170, 325, 396

Haldane, J.B.S. (1892-1964): 121-127, 136, 168, 248, 251, 254, 260, 293, 366, 396

Halmos, P.R. (b. 1914): 345-347,396 Hamilton, Sir William R.

(1805-1865): 142, 147, 345 Hantschius 127

Name Index

Hardy, G.H. (1877-1947): 22,47,55, 78, 94, 105-107, 135, 136, 335, 344, 345,353,371,396

Haug, E. 233 Hausdorff, F. (1868-1942): 84 Hazen, H.L. (1901-1980): 163,396 Healy, Sister E. T. 343, 393 Heaviside, Sir Oliver

(1850-1925): 100-103,336,340,346 Hegel, G.W. (1770-1831): 60 Heims, S. (b. 1926): 20, 242, 248, 293,

308,314,333,334,396 Heine, Heindrich (1797-1856): 335,341 Heins, A. E. 134 Heisenberg, Werner (1901-1976): 117,

118,121,184,241 Helmholtz von, H.L.F.

(1821-1894): 148 Heraclitus (6th-5th cent. B.C.): 268 Hermite, C. (1822-1905): 270 Heron of Alexandria (c. 100 A.D.): 256 Hershey, Alfred D. (b. 1908): 249 Hertz, H. (1857-1894): 24, 25 Hewitt, E. (b. 1920): 108, 114,396 Hilbert, D. (1862-1943): 26,59,60,94,

240, 371 Hill, G. W. (1838-1914): 207 Hille, Einar (1894-1980): 108 Hitchcock, Alfred (1899-1980): 94,

338-340 Hocking, William E. (1873-1966): 66 Hodgkin, Sir Alan Lloyd (b. 1914): 208 Homer (c. 850 B.C.): 293, 335 Hopf, Eberhard (1902-1983): 132-135,

139, 186, 196,396 Horace (65-8 B.c'): 335 Huntington, E.Y. (1874-1952): 43,46,

73-75, 89, 371 Hurewitz, Witho1d (1904-1956): 349 Husser!, Edmond (1859-1938): 59, 371 Huxley, A.F. (b. 1918): 208 Huygens, C. (1629-1695): 125

Ikehara, Shikao (l904?-1984): 107, 168, 375

Inge, W.R. (1860-1954): 369 Ingham, A. E. (1900-1967): 105 Ito, K. (b. 1915): 83,86

Jackson, Dougald C. (1865-1951): 96 Jacobs, W.W. (1863-1943): 316 Jacquard, J.M. (1752-1834): 219,220 James, William (1842-1910): 39,62 Jesperson, Otto (1860-1943): 280 Jewett, Frank (1879-1949): 18,356,360,

361 Johnson, Lyndon B. (1908-1973): 15,

364, 374 Jones, Rufus (1863-1948): 218

Name Index

Kac, Mark (1914~1984): 83,84,86,128, 396

Kahn, Henry 30 Kailath, T. (b. 1935): 135 Kakutani, S. (b. 1911): 88,130,151,

266,271,397 Kaluza, Th. (1885~1954): 119,121 Kant, Immanuel (1724-1804): 41,59,

71,72, 120,277,316,341 Karamata, J. 108 Kellogg, O.D. (1878~1932): 86,87,91,

361 Kelvin, Lord (Sir William Thompson)

(1824-1907): 102,103,161,254 Kennedy, Peggy (see Peggy Wiener) Kepler, Johannes (1571~1630): 19,25,

345 Kerensky, A.F. (1881~1970): 32 Ketner, K.L. 221 Kettering, C.F. (l876~1958): 340 Keynes, Lord J.W. (1883~1946): 284,

397 Keyserling, Leon (b. 1908): 274 Khinchine, A.L. (1894-1959): 86,113,

149,194 Kipling, Rudyard (1865~1936): 335, 336 Kirchoff, G.R. (1824~1887): 176 Kleene, S. C. (b. 1909): 220 Klein, Felix (l849~ 1925): 225 Klein, O. 120, 121, 125 Kline, J. R. 167 Koebe, P. (l882~1945): 18 Kolmogorov, A.N. (1903~1987): 86,90,

149, 193~195, 241, 261, 397 Konoye, Prince (1891 ~ 1945): 298 Kosambi, D.D. (1907~1966): 363,397 Kronecker, L. (1823~1891): 59 Kropotkin, Prince P.L. (1842~lnl): 34

Lafargue, Paul (1842~1911): 292,397 Lagrange, J.L. (1736-1813): 87,99,345 Laguerre, E. (l834~ 1886): 164, 165, 270 Lambert, J.H. (l728~1777): 107 Landau, Edmund (1877~1938): 17,59,

60,371 Langmuir, Irving (1881~1957): 245 Laplace, P.S. (1748~1827): 87 Laski, Harold (l893~ 1950): 362 Lau, K-S. (b. 1948): 114,397 Lazarsfeld, P.F. (b. 1901): 290 Leahy, William D. (1875~1959): 296,

298 Lebesgue, H. (1875~1941): 77,78,83,

92, 139, 145, 147, 354 Lee, Yuk Wing (b. 1904): 165~168, 178,

187, 195,212,235,239,240,372,397 Legendre, A.M. (1752~1833): 163 Leibniz, G.W. (1646-1716): 19,39,76,

121,122,125,126,161,162,171, 219~222, 239, 254, 277, 319, 363, 366, 368

Lemaitre, Cannon G.H. (l894~1966): 170

403

Lenard, P.E.A. (l862~1947): 315 Lenin, V.1. (1870~ 1924): 122, 260, 275,

397 Leontovich, M. 86 Leray, J. (b. 1906): 101 Lettvin, Jerome (b. 1920): 218 Levinson, Norman (l912?~1975): 92,

172, 349, 350, 353, 355, 375, 397 Levy, Hyman (l889~1975): 59,261 Levy, Paul (1886-1971): 86, 194 Lewis, Albert C. 18 Lewis, T. 204 Lichenstein, Leon (1878~1933): 136, 167 Liddell Hart, Sir Basil H.

(1895~1970): 298, 398 Lilienthal, D.E. (b. 1899): 311 Lindsley, D.B. (b. 1907): 236 Liouville, J. (l809~1882): 147 Littlewood, J.E. (l885~1977): 47,

105~1O7, 135, 136,368,371 L1ull, R. (1225~1316): 254 Lobatchevsky, N.1. (1793~ 1856): 73 Locke, John (l632~1704): 368 Lorente de No, R. (b. 1902): 239 Lovelace, Lady (Ada Byron)

(l815~?): 219 Lovell, C.A. 182, 189, 192 Lowell, Abbot Lawrence

(l856~ 1943): 32, 66, 362 Lucretius (9?~55 B.C.): 122 Lynd, Albert 280, 398

Mach, E. (1838~1916): 54,277 Mackey, G. W. (b. 1916): 128, 398 Maimonides, Rabbi Moses

(1135~1204): 41,43,398 Malliavan, P. 114 Mandelbrojt, Szolem (l899~ 1983): 170,

251 Mandelbrot, Benoit (b. 1924): 85,291,

368, 398 Mann, Robert W. (b. 1924): 230, 231 Marcinkiweicz, J. (1910-1940): 114 Marquand, A. 221 Marshall, George C. (1880-1959): 296 Martin, K. 362, 398 Martin, W. T. (b. 1911): 151,266,271,

393 Marx, Karl (1818~ 1883): 260, 277, 284,

292, 314, 322, 398 Masani, P.R. (b. 1919): 112,265,333,

398 Masaryk, Thomas (1850-1937): 31, 136 Maupertius, P.L. (l698~1759): 121 Maxwell, James Clerk

(1831~1879): 23~25, 81, 99,109,116, 143, 146, 155,254,258,334,345

McCulloch, Warren S. (l898~1969): 200, 205, 218, 219, 222, 223, 225, 227, 232,

404

236, 238, 239, 243, 248, 346, 366, 367, 398, 399

McMillan, Brockway (b. 1915): 151,375 McTaggart, 1.M.E. (1866-1925): 56,60,

371 Mehra,l. 118,398 Mendel, Gregor (1822-1844): 249 Menger, Karl (b. 1902): 136, 167 Mercer, J. (?-1932): 47 Meyer, Ella J. (Mrs. J. Franklin) 353 Michaelangelo, B. (1475-1564): 293, 347 Michaelson, A.A. (1852-1931): 110 Mill, John Stuart (1806-1873): 35 Millikan, Robert Andrew

(1868-1953): 366 Milton, lohn (1608-1674): 293 Milyukov, P.N. (1859-1943): 32 Minkowski, H. (1864-1909): 346 Mobius, A.F. (1790-1868): 63 Moliere (1. B. Poqug1in)

(1622-1673): 342 Monod, 1. (1910-1971): 249,398 Moore, E.H. (1862-1932): 77 Moore, G.E. (1873-1958): 56,371 Moore, O.K. 191 Moore, R.L. (1882-1974): 75 Mordell, L.l. (1888-1972): 47 More, Saint Thomas (1478 1535): 335 Morgenstern, O. (1902-1977): 268, 290,

296, 303,401 Morishima, M. (b. 1923): 314,399 Morris, William (1834-1896): 277 Morse, Marston (1892-1977): 108 Mozart, W.A. (1756-1791): 93,259 Muller, H.J. (1890-1967): 312 Mumford, Lewis (b. 1895): 284, 336,

337, 369, 399 Munsterberg, H. (1863-1916): 46

Nagy, B. Sz. (b. 1913): 193, 399 Napoleon, B. (1769-1821): 300,304 Nelson, Edward (b. 1932): 83, 128, 130,

241, 399 Nelson, Lord Horatio (1758-1805): 304 Neurath, O. (1882-1945): 336,399 Newton, Sir Isaac (1642-1727): 19,76,

87, 122, 342, 345 Nordhoff, C. (1830-1901): 29,399

Odob1eja, Stefan (1902-1976): 253,399 Ogden, C. K. (1889-1957): 56 Ohm, G.S. (1787-1854): 176 Oppenheimer, J. Robert

(1904-1967): 311, 313, 363 Orey, S. (b. 1928): 91 Osgood, W.F. (1864-1943): 71, 77, 353,

361 Osher, W.l. 205 Ostwald, W. (1853-1932): 54

Name Index

Paley, R.E.A.C. (1907-1933): 84, 136-138,140,166,169,177,197,372

Palmer, G.H. (1842-1913): 43,46,371 Parkinson, C. Northcote (b. 1909): 286,

287, 399 Pascal, B. (1623-1662): 19,161, 171,

239, 254 Pauling, L. (b. 1901): 312 Peano, Giuseppe (1858-1932): 53,59,

147 Pearl, Raymond 65 Peirce, Charles Sanders

(1839-1914): 15-17,22,39,55,62,74, 93,221,255,277,369,399

Perrin, J.B. (1870-1942): 79,81,82,84, 293, 366, 399

Perry, Ralph Barton (1876-1957): 43. 46,66

Phelan, G.B. (b. 1892): 367,399 Phillips, H.B. 71,88,171, 180 Phillips, Ralph S. (b, 1-913): 349,391 Pierce, J.R. (b. 1910): 155,257,399 Pincus, 1. 135 Pitt, Harry Ray (b. 1914): 108,372 Pitts, Walter (1923-1969): 201,207,208,

218,219,223-225,227,232,236,239, 243, 248, 398, 399

Planche rei, M. (1885-1967): 98, 147 Planck, Max (1858-1947): 117,130,156 Plato (427-347 B.C.): 15,24,43, 122,

124, 252, 253, 255, 259, 260, 297, 327, 335, 344, 363, 368

Poincare, H. (1854-1912): 59,62,207, 315

Poisson, S.D. (1781-1840): 87 Pollack, Rabbi Herman 370 P6lya, George (1887-1985): 47 Pope, Alexander (1688-1744): 342 Post, E.L. (1897-1954): 220 Potra, F. 232 Prokhorov, Yu. (b. 1929): 86 Pupin, M.1. (1858-1935): 336 Pythagoras (572-501 B.C.): 24, 345, 368

Quevedo, Tores y 304 Quine, W.V. (b. 1908): 52,54,55,399

Rabi, I. (b. 1894): 312 Raisbeck, Barbara (see Barbara Wiener) Ramanujan, S. (1887-1920): 345,350 Randell, Brian 173, 175, 180, 399 Rashevsky, N. (b. 1899): 218 Rayleigh, Lord 1.W.S. (1842-1919): 102,

103, 111 Rechenberg, H. 118,398 Reuther, Walter (1907-1970): 16,62,

273-275,299,300,302, 303, 314 Riccia, 1. Della 128 Richards, LA. (b. 1893): 56 Rickover, Hyman (1900-1986): 281,299 Riemann, B. (1826-1866): 107,346

Name Index

Riesz, F. (1880- I 956): 75 Robinson, E.A. (b. 1930): 297 Roosevelt, Franklin D.

(1882- I 945): 296, 298 Rosenblith, W.A. (b. 1913): 235 Rosenblueth, Arturo (\ 900- I 970): 34,

197-205,207,208,210,21 1,218,225, 233, 239, 240, 243, 248, 249, 25 I, 36 I, 366, 367, 373, 399

Rosenthal, A. 147 Ross, K. A. (b. 1936): 108, I 14, 396 Rousseau, J.J. (1712-1778): 277 Royce, Josiah (1855-1915): 43,46,361,

371 Rudin, W. (b. 1921): 137,399 Runge, C. 180 Ruskin, John (\819-1900): 335 Russell, Bertrand (1872-1970): 18, 22,

45,47-52, 55, 56, 59, 60-64, 72, 79, 93, 199, 220, 239, 277, 297, 303, 335, 346, 366, 371,400, 402

Russell, H.N. (1877-1957): 243 Rutherford, Lord Ernest

(1871-1937): 123,322

Saeks, R.E. (b. 1941): 173,174,400 Samuel, A. L. (b. 1901): 306,400 Santayana, George (1863-1952): 43,61,

371 Santillana, George de 18 Sarvagatananda, Swami 370 Schetzen, M. (b. 1928): 271,400 Schickard, W. (1592-1635): 254 Schiller, J.C.F. (1759-1805): 341 Schmidt, K. 43, 46, 371 Schmidt, Robert 105-106 Schopenhauer, A. (1788-1860): 341 Schottky, W. 85 Schrodinger, E. (1887-1961): 120, 122,

123, 130, 241, 249, 345, 400 Schroeder, F. (1841-1902): 43,48 Schuster, Sir Arthur R.

(1851-1934): 102-104, 11 I-I 13,400 Schwartz, Laurent (b. 1915): 100, 251 Schweitzer, Albert (1875-1965): 318 Scimone, Frank J. 352-353 Segal, I.E. (b. 1918): 241,395 Shakespeare, William (1564- I 616): 347 Shannon, Claude E. (b. 1916): 50, I I I,

153-155, 159, 182,221,224,253,262, 356, 373, 400

Sheffer, Henry Morris (1883-1864): 55, 74

Siegel, Armand (b. 1914): 128, 129, 131 Simeone, S.A. 198 Sinclair, Upton (1878-1968): 362 Singleton, H. E. (b. 1916): 211 Smith, Adam (1723-1790): 281 Smoluchowski, M.V. 55,79,241 Snow, Sir C. P. (b. 1905): 359,400 Sobolev, S. L. (b. 1908): 101

Socrates (470-399 B.C.): 93 Sophocles (496-406 B.C.): 370 Southwell, R. V. 180

405

Speiser, Andreas (1885-1970): 341 Spinoza, Baruch (1632-1677): 39,43,

277, 366, 370 Stalin, Joseph (\ 879-1953): 325 Stewart, Duncan 192 Stewart, H. R. 393 Stibitz, G.R. (b. 1904): 172,187,190,

391 Stieltjes, TJ. (\856--1894): 84, 107 Stimson, H. L. (1867-1950): 296 Stirling, J. (1696--1770): 159 Stokes, G.G. (1819-1903): 23 Stone, M.H. (1903-1989): 241 Stoughton, T R. 296 Strauss, Lewis, J. (1896--1974): 312,313 Struik, Dirk Jan (b. 1894): 120, 293,

349-351,353,368,400 Swift, Jonathan (1667-1745): 335,342 Szasz, Otto (1884-1952): 60,167 Szilard, Leo (1899-1964): 155,296

Tamakrin, J.D. (1888-1945): 108 Tasaki, I. 208 Taub, Abraham H. (b. 191 I): 120,3\3,

400 Tawney, R.H. (1880-1962): 284,400 Taylor, Frederick (1856-1915): 254 Taylor, Sir Geoffrey I. (1886-1975): 79,

102, 103, 113, 400 Teller, Edward (b. 1908): 311 Tennyson, Alfred (1809-1892): 299 Tesla, Nicola (1856--1943): 340 Thackeray, W. M. (1811-1863): 335 Thilly, Frank (1865-1934): 41,371 Thompson, Kenneth (b. 1943): 305 Tillich, P.J. (1886-1965): 324,400 Tinbergen, Jan (b. 1903): 285 Titchmarsh, E. C. (1899-1963): 47 Tolstoy, Count L. (1828- 1910): 31 Toynbee, Sir Arnold J. (1889-1975):

3 \3, 401 Tran, L. T. 91, 401 Trentowski, S. 252 Truman, Harry S. (1884-1972): 273,

295,296,298-300,310,311 Turing, A.M. (1912-1954): 50,219,220,

243,246,251,401

Ulam, Stanislaw (1909-1984): 51,295, 311,314,401

Vallarta, M. S. (b. 1899): 120, 203 Van de Graaff, Robert J. 367 Veblen, Oswald (1880-1960): 63,68,75,

85,95, 167,363 Verne, Jules (1828-1905): 37,335 Vico, Giambattista (1668-1744): 62, 255,

277, 325

406

Vigier, J.P. 129 Vinci da, Leonardo (1452-1519): 18,343 Voltaire, F.M. (1694--1778): 122 Volterra, Vito (1860-1940): 77,163,264,

266, 271 Von Foerster, Heinz 248 Von Laue, Max (1879-1960): 111 Von Mises, R. (1883-1953): 86 Von Neumann, John (1903-1957): 50,

51-52,109,119,129,131,140,141, 184, 225, 232, 237, 239-242, 247, 248, 268,290,295,297,303,310-315,335, 345, 373, 396, 400, 401

Walsh, J. L. (1895-1973): 360 Walter, W. Grey (1910-1977): 212,234,

237,240,251,401 Walton, E. T. S. (b. 1903): 367 Watson, J.D. (b. 1928): 20,401 Watt, James (1736-1819): 252 Watts, A.W. (1915-1973): 25,401 Weaver, Warren (1894--1978): 183, 192,

207, 391 Weiss, P.R. 391 Wells, H.G. (1866-1946): 37,335 Weyl, Hermann (1885-1955): 53, 115,

120, 151,200,225, 345, 368, 369, 401 Whitehead, Alfred North

(1861-1947): 21,25,43,45,50,56,59, 72,93, 199,220,259,277,324,334, 346, 361, 367, 368, 369, 402

Whittaker, Sir Edmund (1873-1956): 118,402

Wiener, Barbara (daughter) (b. 1928): 94

Wiener, Bertha (sister) (b. 1902): 30, 35

Name Index

Wiener, Bertha Kahn (mother) 30, 371 Wiener, Constance (sister) (b. 1898): 30,

35 Wiener, Fritz (brother) (b. 1906): 30 Wiener, Leo (father)

(1862-1939): 29-47,67,94,335,361, 371

Wiener, Margaret (wife) (b. 1894): 38, 94, 95, 372

Wiener, Peggy (Margaret) (daughter) (b. 1929): 94, 339

Wiener, Philip P. (b. 1905): 369 Wiener, Solomon (grandfather) 29 Wiesner, J. (b. 1915): 211,212,228 Wigner, E.P. (b. 1902): 367,402 Wilder, R.L. (b. 1896): 77 Wilhelm II, Emperor (1871-1918): 32 William of Ockham (c. 1200-1259): 62 Wilson, Woodrow (1856-1924): 67 Witner, A. (1903-1958): 141, 151,204 Wittgenstein, Ludwig (1889-1951): 52,

53, 57,402 Wold, H. 193 Wolf, J. 111, 393 Wolfson, Harry A. (1887-1974): 69 Womack, J. Printise 275-276 Wrinch, Dorothy 245

Yaglom, A.M. 113,193,401 Young, L. C. (b. 1905): 136 Young, R. C. 136 Young, W.H. (1863-1942): 136

Zangwill, Israel (1864--1926): 34 Zermelo, E. (1871-1953): 51 Zygmund, A. (b. 1900): 84

Subject Index

Aberdeen Proving Grounds 61, 63, 68, 372

Abduction 62 Academie Francaise 358, 359 Accademia dei Lincei 358 Active and passive mechanisms 202 Albany, New York 67 Algorithm 219,220 Alice in Wonderland 93, 152 American Mathematical Society

1934 Colloquium Lectures 137, 372 1940 Dartmouth meeting 172 1949 J.W. Gibbs Lecture 373

American Society of Mechanical Engineers 277

Analysis situs 63 Angelos 251 Animal feedback (homeostatic, postural,

voluntary) 210-211 Anti-aircraft fire control 181

cranking errors 189 error of performance 186, 187 predictor 187 transient errors 189

Arabian Nights 316 Art

Dante's view of 343 Eckhart's view of 343 presentative aspect of 344 representative aspect of 344

Arthasastra 287 Artist and Artisan 343, 346 Atomic diplomacy 295, 311 Atomic energy

and Oakridge National Laboratory 312

and Price-Anderson Act 312 Atomic warfare

atomic bomb 301,310 atomic bombing of Japan 296, 298 civil defense 301 Litianthal Report 311

Attica prison 351-353 Automata theory

game-playing automata 304, 305, 306, 355-356

type-classification in 52, 306 Automatic control 272

Automatic factory 272-273 Automatization 15,25,51,272,273 Avogadro's Law 148 Avogadro's number 82 Ayer High School 37, 371 Axons 207, 213

Banach algebras 108, 241 Banach space 76, 114 Ballistics 68, 187 Bangor, Maine 65

407

Bell Telephone Laboratories 228, 305 Bergsonian philosophy 57, 58 Bergsonian time 151-153 Bertrand Russell Editorial Project 18 Bessell identity 104-105, 107 Binary scale 172 Birkhoff's ergodic theorem 110, 132,

139, 140, 141, 149, 150 Bocher Prize 108, 372 Bochner's theorem 113 Boolean algebra 73, 74, 89, 221 Borel measurability 83, 90 Boston 362 Boston Arm (and Elbow) 229-231 Boston Herald 71, 372 Boston police strike 362 Brain 214 Brain-mind dualism 198, 306 Brain-wave encephalography 227, 233,

234, 235-236 Bridge on the River Kwai 338 Brownian motion 55,79-86,88,90,91,

102 and heat equation 84 and potential theory 88 and quantum mechanics 128-131 and random measure 130-131 and shot effect 85 as input 264-266 as noise 143 Einstein's theory of 81-83 flow of 140-141 idealized 83-86

Bureaucracy 92-93, 170, 286-287, 338 Bush differential analyzer 160, 181

408

Bush integraph 160, 161 Bush network analyzer 160

Calculi (logical) 54 Calculus of variations 186 Calculus ratiocinator 219, 221 Cambridge University 45,66, 122, 136,

372 Causal operators 101 Causality and analyticity 101, 134-135 Cell, complexity of 244-245 Chaotic integrals 265 Chess-playing automata 304-305,

355-356 Child training, Leo Wiener's views

on 35 Clonus (see Muscle clonus) Coherence of light 110--111 Coherency matrix 110--111 Cold War 313 Columbia Medical School 218 Columbia University 61, 371 Communication 152 (see also

Information) and time scales 307-308 as social cement 288 channels of 288-289 communal information and

cohesiveness 288 communications engineering 101-102,

206 Communism 332 Communists 293, 294 Complementarity 116-117 Complex number field C 89 Computer (see also Turing machine)

abacus 171 all-purpose 219 analogue 110, 160-161 as prosthesis for the brain 232, 233 data-storage by tape 172, 173, 174 digital 171 electronic 15, 172, 224 ENIAC 174, 239, 244 exchangeability of time and

space 226-227 necessity for high speed 171-172, 173 program 220, 238 special purpose 171 special purpose digital 219 solution of PDE's by scanning

179-180 transistorized 174 use of vacuum tubes in 172, 174

Computing machines (see Computer) Conditional Banach spaces 114 Consonance 253 Contest 268 Control (see Anti-aircraft fire control;

Automatic control; Homeostasis; Animal feedback)

Subject Index

Controlled experiment 152 Convex bodies 72 Convolution filters 10 I, 107, 163-164,

177-179 Convolution integrals 101, 106, 107, 264 Copyright 338 Curl 23 Cybernetics (defined) 256

cybernetical attitude 239-240, 253-256 Cybernetical Circle 239 origin of idea of 56, 57, 58 origin of name of 251-252 Soviet attitudes toward 260-261

Deterministic dynamical system 141-142 Diagonalization procedure 48 Dialectic duality 25-26 Dialetic materialism 293 Dirichlet problem 87-88, 171, 180 Docent Lectures 62-64 Dual nature of light 25-26, 116 Duty 66, 125, 327 Dynamical system

coefficients of inertia 157 conservative 142 deterministic 141-142 Hamiltonian 142, 157 Hamilton's canonical equations 142 kinetic energy 157 phase space 142 potential (energy) 87, 157 state space 142

Econometrics 291 Economic planning 285-286, 329 Economic system (U.S.) 281-283

acquisitiveness in 283, 284 alienation in 284 and hard-work ethic 283 credit-card hedonism in 283-284 entrepreneurship in 282 investments in 282-283 irreligious aspect of 284 market as n-person game in 281 promotion in 283 volatility of 283

Education 277-281 and Parent Teachers Association

(PTA) 281 and teachers' colleges 280 and teachers' trade unions 281 damage from harshness in 35 decline of in U.S. 281 John Dewey's ideas on 277-280 quackery in public schools 280

Electric engineering 10 I-I 02 Electric filters

amplitude response function 165 causality (physical realizability) 101,

138, 163-164

Subject Index

frequency response function 164, 165 linearity 101 lumped-passive 164, 176 phase-response function 165 weighting function 163

Electric networks (see Electric filters) Electrodynamometer 160 Electroencephalogram (EEG) 233 (see

also Brain-wave encephalography) Electromagnetic theory of light 24, 109 Electron microscopy 245, 246 Electronic computer 15, 172, 224 Electronic Age 25 Encvclopedia Americana 67 372 Energy 87, 148, 157 ' ENIAC 174, 239, 244 Entrainment of frequency 237 Entropy (see Thermodynamics) Ergodic hypotheses 146-147 Ethics 58, 125, 311, 327

altruism 125, 327 conscience 58 duty 66, 125, 327, 328 vocation 327

Evil analogy of, with entropy 319 as corruption 319 (see also Fall of

man) moral 319, 322 natural 319 non-eradicability of 319 phylogenetic origins of 319, 320 St. Augustine's views on 318,319 321

Explication 72 ' Extensive abstraction 56

Fall of man 321,323-324 Feedback 169,201,202 (see also Animal

feedback) anticipationary 191 double 210 negative 202

Feedback circuit, in muscular clonus 206

Field 99, 208 Final cause 203 Flight prediction, statistical aspect 184,

190 Foreign policy (U,S,)

Eisenhower-Dulles 311 Truman-Acheson 295,311

Fourier's series; Fourier transform' Fourier-Stieltjes transform (sce ' Harmonic analysis)

Fractals 85, 291 Function

Borel measurable 90 Hermite 270 Laguerre 164--165

non-differentiable 79, 84 periodic 97

Functional integration 84

Gadget-worship 171

409

Game theory 268-269, 286, 287, 290, 303, 306, 309

Gating mechanism 236 Gauge theory 120 Gene- reproduction 124 General Electric 67 Generalized Harmonic Analysis

(GHA) 102, 104--105, 184 almost periodic functions 104, 141 (auto-)covariance (or correlation)

function 102, 110, 113, 186 cross-covariance 110 Einstein's contributions to 112-113 Generalized Bessel identity 104--105 generalized Fourier coefficients 141 generalized Fourier transform 104 periodogram 104 spectral distribution and densitv 104,

112, 113 ' total mean-power 109

Geometry Einstein's views on 53, 72 Euclidean 73, 342 Greek conception of 73 Kant's views on 71-72 non-Euclidean 73

German intellectual tradition 32-33 German romantic movement 341, 342 Gestalt (see Pattern) Glasnost 293 Gleason's theorem 128 God (Logos) 25, 292, 330, 332-334

Jehovah 333 of Spinoza 25, 292, 333, 345 personal 333

Giidel number 346 Giidel incompleteness

metatheorem 52-53 Gorgias 252 Giittingen University 56, 59-60, 105,

117, 371 Gravitational force 23 Guggenheim Fellowship 105, 372 Gulliver's Travels 335

Harmonic (Fourier) Analysis 96--100, 245-246 characters 97-98, 100 Fourier coefficients 97-98. 100 Fourier series 97-98, 107, 135 Fourier-Stieltjes transform 98-99, 104.

112, 195 Fourier (and Planche reI)

transforms 98, 101, 104-105, 107, 112,114,115,134.136-137,177

410

pure tone 96 sin usoidal curve 97

Harmonic analyzer 161 Harvard Lampoon 362 Harvard reserve regiment 66--67, 371 Harvard University 39-41, 43-44,

63-64, 361-362 Hausdorff dimension 83, 85, 90, 91 Heart, human 204

auricles 204 dis tole 204 fibrillation 204 flutter 204 sistole 204 tonic-clonic cortical responses 204-205

Heat equation 84 Heaviside operational calculus 100, 160 Hebraiche Melodien 335 Helices (spirals) 108, 114, 195 Hidden parameters 129 Hidden periodicities 104, 112-113 Highest good 58 Hilbert space 26, 108, 114, 118-119,

128-129, 131, 193, 195,241 Hilbert transform 165-166 History, episodic view of 297-298, 302 Hitopedesa 287 Holography III Homeostasis 34

breakdown of 331 homeostatic diseases 211 homeostatic feedback 210

Homeostat 212 Hominids 322, 323 Homogeneous chaos 149 Homogeneous random fields 141 Homo peccator 322 Homo sapiens 322 Hopf-Wiener integral equation 133-134,

186,241 Hunting 201

Idealization 72, 116, 122, 184,258-259, 326

Incoherent signals 110-111 Indeterminism 146, 253, 254-255, 290,

291,318 (see also Uncertainty principle)

Indian Statistical Institute 193, 285, 351, 373

Industrial revolutions (First, Second, Third) 249,272,273,281,346

Infinite (actual) 59 Information theory 153-156

communal 288 informative value of a

message 153-154 loss of 228, 229 misuse of 288-289 optical III, 228

Subject Index

Inquiry 268 Instruments 186, 187

limitations of 143, 146 response time (or latency) 109

Instrumentation theory 186, 187, 195, 196

Integraph 160,161,162,175-176 International Copyright Convention 337 International Mathematical Congresses

1920 Strasbourg 75, 372 1932 Zurich 136, 166,372 1936 Oslo 170,231,372 1950 Cambridge, Mass. 373

Iron lung 229 Isomorphism 200

Jacquard loom 219 Japan, atomic bombing of 296, 298, 323 Jewish Numeras Clausus 32,361-362,

363 Jewish question 30-32,41-43, 59 John Thornton Kirkland Fellow 44, 371 Josiah Macy Foundation 205, 373 Judaism 42 Juniata College 94

Kinesthetic organs (proprioceptors) 213 Klein-Gordon equation 120 Kolmogorov-Wiener prediction

theory 193 Korean War 273, 299, 300

Labor, American migrant 275-277 retraining of 277

Lag mechanisms 19 I Laguerre functions 164-165, 177 Laplace's equation 87 Latency 191 Lead mechanisms 191 Learning 152-153,262-264 (see also

Education) Learning mechanisms (machines) 58,

262 Lebesgue integral and measure 78, 83,

99, 104, 140 Lee-Wiener network 163-165,177-179,

195, 264, 270 Leibnizian philosophy 121-122,

125-128,219 calculus ratiocinator 219,220 machina ratiocinatrix 219, 220 monads 121, 125-126 principle of identity of

indiscernibles 121 principle of sufficient reason 121-122,

126 Leukemia 211 Libertinism 47 Linear operator 99-100 Linear partial differential equations 99

Subject Index

Little Doritt 287 Logic 22, 48---49 Logical empiricism 53, 54 Logos (see God)

Machine 256 Machine intelligence, creativity,

tropism 212, 346--348 (see also Computers) Homeostat (machina sopora) 212 machina ratiocinatrix 219-222 machina speculatrix ("tortoise") 212 "moth-bedbug" 211 reproducing machines (see Self-

reproducing mechanism) Machine-man concatenation 188-189,

310 "Mad Tea Party" of Trinity 56 Manhattan Project 310 Marxism 292, 293, 294 Massachusetts General Hospital 234 Massachusetts Institute of Technology

(MIT) 71,92,96, 181,207,218,234, 372

MIT Autocorrelator 234, 235 MIT Radiation Laboratory 349 Masters, The 359 Mathematician's credo 341 Mathematics

aesthetical aspects of 22-25, 54 as fine art 341-343, 344, 345 Halmos's views on 345 philosophies of 54 role of in the empirical realm 23-28,

53-54, 258, 259 Mathology 345, 346 Mathophysics 345, 346 Maximal ideal 114 Maxwell's demon 155-156,325 Maxwell's equations 24, 119 McMaster University 18 Memory 152 Mengenlehre 368 Merton College, Oxford 60 Message 19,239,251,256-257 Metalanguage 50, 57 Metamathematics 50, 55, 56-57 Metric space 76 Mexican Mathematical Society 203, 373 Mexico 203 Michelson interferometer 110 Military mind 296 Military science (see also War)

continual reconnaissance 307-308, 310, 354-355

type classification in 303-305, 309 Mind, human

computing abilities of 223, 224 pattern recognizing abilities

of 225-226 Misinformation 289

Molecular biology 248-250 Monads 121, 125-126 (see also

Leibnizian philosophy) Monkey's Paw, The 316 Monogenism 321,323-324 Monte Carlo method 151 Multivariate prediction 193, 297 Muscle clonus 205-207

411

Music, musical notation 116 Mutualistic Societies in America 29-30 Myopia 37 Myths 324-325 Mythic mode of perception 25, 324-326 Mythology 325-326

Name and object 325 National Academy of Sciences

(U.S.) 356--358,360-361,373 National Defense Research Committee

(NDRC) 181-182,373 Project DJ.C. 5980 182

National Institute of Cardiology, Mexico 197,207

National Medical of Science 15,364 National University of Mexico 373 Negentropy 155 Nerves 215 Nervous system, human 213,243

action potential 213 afferen t nerves 215 autonomic 215 center of nerve 215 central 202,213 efferent nerves 215 gating 236 gray matter 213 mixed nerves 215 parasympathetic 215 peripheral 214 physiological clock 236 reflex action 208 spatial summation 214 sympathetic 215 synapse 213 synaptic delay 214 synaptic excitation 208 temporal summation 214 white matter 213

Neuron 213 association 214 axons 207, 213 cytoplasm 213 dendrites 213 excitatory 214 firing of 213,214 inhibitory 214 irritability of 213 motor 214 nucleus of 213 quiet 214 refractory period of 214

412

resting state of axon 2 \3 sensory 214

Neurophysiology 249, 250 analogical aspects of 244, 262-263

New England (democracy of) 34, 38, 289

New York Times 15,229 Newtonian mechanics (see Dynamical

system) Noise 19,143 Non-linear filters (networks,

transducers) 264-267,270--271 Nucleic acid complexes 249

Observation, photometic nature of 119 Observer-observed coupling 127-128,

289, 290, 291 On a Balcony 30 Ontogenetic learning 262-263 Operationalism 121 Operator

linear 99-100 non-linear 264

Optics 109-112 brightness 109 coherence 110-111 Michelson interferometer 110 photometer 109 polarized light III

Optical depth 132 Ordered pair (couple) 55 Organization 96

Paley-Wiener criterion 138 Paradise Lost 93 Paradoxes 48-50, 52 Parkinsonianism 210 Partial differential equations 99

parobolic 174 Particle-wave dichotomy 26, 27, 121 Pa th integral 128 Pattern (Gestalt) 96, 244

as group-invariant 225 Pattern recognition 15, 225-226

apparition 225 limitations of theory of 244

Peabody School 35,37,371 Peano's postulates 53, 65, 73 Perception

logical mode of 25 mythic mode of 25, 325 sensory 199-200

Philosophies of mathematics 54 Philosophy of Science Club 197 Photometer 109 Photosynthesis 156 Phylogenetic corruption 321,323-324 Phylogenetic learning 263-264 Physiological clock 236-237 Planning 285, 329 Platonism 258-260

Subject Index

Plattsburg, New York 66 Poetry 25 Polarization of light III Polynomial chaos 150 Postulate systems 73-79 Potential theory 86-88

capacity 88 Dirichlet problem 87-88 the potential 87

Potentiometer 160 Power engineering 102 Pragmaticism 62 Pragmatism 39, 57, 62 Prediction theory 193 Prime number theorem 107 Principia Mathematica 45, 48, 50, 52, 53,

54, 55, 93, 220, 240 Principle of least action 121 Probability distribution 86 Probability theory 86 Project D.LC. 5980 182 Prometheus 325, 332 Proprioceptors (kinesthetic organs) 213 Prosthesis (muscular-skeletal and

sensory) 227-231 Boston Arm 229-231 Iron lung 229 sound communication with the

deaf 228-229 Protein molecule 124 Psychic signs 325 Pure tone 96, 115 Purpose (see Teleology) Purpose tremor 20 I Purposive action 124

Quantum mechanics 26,115-131 degeneracy 123 hidden parameters 129, 131 potential barrier 123 pure state 128, 131 role of Brownian motion in 128-131 self-repair in 123 state 128

Quasi-analytic functions 169 Quasi-ergodic hypothesis 147 Quickening 191

Radiative equilibrium 132 Ramakrishna Vedanta Society of

Boston 370 Recursion 50, 53 Reflex action 208-209 Refugee scientists 167-168 Relation structure 199, 200 Relation theory 50, 55, 63-64 Relativism 57, 58, 60 Relativity theory 26, 120 Religion (see also Evil; Fall of man; God)

"acts of God" 330 "acts of Grace" 330, 332

Subject Index

Adam and Eve 321 and science 324, 330, 333-334 Black Mass 315-316 Grace 321 role of death 319 self-alienation 322 simony 316 sin 322

Republic 43, 67 Retrospective operator 101 Riemann zeta function 107 Ritual 324 Robot arm 232-233 Rockefeller Foundation 205, 207 Royal Society 358, 359 Russell's antinomy ("paradox") 48-50,

52

Sage School of Philosophy 40, 41, 371 Scannmg 171, 173, 179-180,226-227 Schwartz distribution 100 Science fiction 335-336 Science and human welfare 285,291,

292,311,314-315,329-330 Scientific methodology

centrality of relation-structure 198, 199,200

complementarity 116-117,127-128 cybernetical augmentation of 253-255,

257 explication 72 faith as a part of 24-25, 326 function of science 358 idealization as a part of 258-260, 326 incomplete orderliness of the

world 146 instrumental limitation 143, 146 logical empiricist theses 53-54 mythic perception as a part of 25,

324-326 nature of inquiry 268-269 nature of logic 53-54, 222-223 observer-observed coupling 127, 289,

290, 291 organization of empirical data 41, 72 place of electronic computer in 232

233 ' propaedeutic role of mathematics

in 22-28, 367, 368 Secrecy 191, 192, 299 Self-alienation 322 Self-organizing systems 236, 237, 246 Self-reproducing mechanisms 246,

263-264, 266-267, 269 Semi-exact sciences 290 Sensory prosthesis (see Prosthesis) Servomechanisms 189,202,210 Set, concept of 48 Shannon-Wiener information theory (see

Information theory) Sheffer's connective 74

Shot effect 85 Signal 19, 102 (see also Information

theory) Signal detection 257 Simony 316 Sin 322 (see also Evil) Sinusoidal curve 97 Social cohesiveness 289 Society for the Advancement of

Management 276, 277 Sociology, observer-observed coupling

in 289 Sorcerer's Apprentice 316 Sorcery 316

413

South Tamworth, New Hampshire 38 Soviet attitudes 229,251,260-261,314 Space-time continuum 26 Spectral distribution and density 104,

112, 113 Spectral synthesis 108, 114 Spectral theory of operators 193 Spike potential 207,215-217

differential equation of 217 Hermann model 216

Spinal cord 208, 209 Spinoza's God 25, 292, 333, 345 Spirals (helices) 108, 114, 195 State, the 328, 329 Stationary random measure 149 195 Stationary sequences 193, 195 ' Statistical mechanics

and communications engineering 102, 154-155

Boltzmann's H-theorem 149 complexion of a gas 159 ergodic hypothesis 146 ergodic theorem for homogeneous

chaos 150 Maxwell's demon 155-156 325 microstate of a gas 158 ' quasi-ergodic hypothesis 147 statistical entropy 148

Statistical thermodynamics 148 Stochastic integration 84, 150 Stokes's theorem 23 Stratagem 267-269, 286-287, 303-306,

307,309,316-317 Strategic evaluations 306 Strategic learning 268 Switching networks 221 Symbolism, mathematical 21-28 Synthetic a priori 71,72 Synthetic logic 63 Synapse 213

Tala Institute of Fundamental Research 373

Tauberian theory 105-108 Tchestnost 293 Teleological Society 239

414

Teleology 57, 124, 152-153,201-202, 253, 368 purposive mechanism 202, 262, 268 teleological mechanism 202, 226

Television scanning 171, 173 Templer, The 336 Tensor 26 Terry Lectures 306, 331, 374 Theory of messages 251 (see also

Message) Thermodynamics

absolute temperature 148, 157 adiabatic transformation 147, 157 Caratheodory's principle 157 empirical temperature 157 entropy 147, 157 Helmholtz free energy 148 internal energy 157 state space J 47

Time anistropic 57. 152 Bergsonian 58, 152 Newtonian 58

Time Series· Topological transformation 75 Topology 62-63,74-75 Traclatus logico-philosphicus 53, 54 Trade union consciousness 275 Tragedy and catharsis 331-332 Transducers 256, 308 Transfinite induction 48 Transformation (see Operator) Tsing Hua University 168, 372 Tufts College 39, 371 Turbulence 79, 151 Turing machine 173,219,220,221,222,

223, 238, 346, 348 Type theory 47, 50-52

Uncertainty principle 115-117, 119, 129 Unified field theory 120 United Automobile Workers of America

(UA W) 273-275

• This term, occurring in Wiener's lexi­con, and meaning a function on the time-domain the values of which are empirical data, is replaced in the book by terms such as input signal, output signal, signaL

Subject Index

Universal Turing machine (see Turing machine)

University of London 94 University of Maine 65 University of Melbourne 94 University of Missouri 30 University of Nancago 251 USSR 313,314 (see also Soviet

attitudes)

Values (see Ethics) Vector 23, 75-76 Vector space (metric, normed) 75-76,78 Virus 244-245, 248 Vocation 327 Vocoder 228 Voluntary activity 188-189

War (see also Military science) absolute 303, 313, 316-317 effects of on scientific morale 298-299 military and political phases of 302,

313,316-317 real 302, 313, 316-317 war games 306-307

Wave equation 24 Wavicle 26 Wiener class S 102-104, 184 Wiener integraph 162,175-176 Wiener measure 83 Wiener process (see Brownian motion,

idealized) Wiener-Hermite representation 271 Wiener Tauberian theorem 107 Wiener, Norbert

absentmindedness of 349 analogical mind of 366, 367 as lecturer 353-355 doctoral dissertation of 43-44 early suffering of 16, 35, 41-43 ideas on historical continuity

of 368-369 literary style of 354 marriage of 94 military thought of 300-302,309-310 premature writings of 18, 358 quirkishness of 349, 350 temperament of 16, 19,20,349,350,

351 vegetarianism of 59

"Yellow peril" 182

415

Photograph Index and Credits

Norbert Wiener. 1945 (Frontispiece, p.2). Courtesy of Mrs. Margaret Wiener.

America's first Leibniz (p. 17). Courtesy of Dr. William A. Stanley, National Ocean­ic and Atmospheric Administration, Washington, D.C.

Figure 1 (Chalice or face profiles?) and Fig­ure 2 (The wave-particle or "wavicle") (p. 27). Reprinted from: James Jeans: New Background of Science, New York 1933, Frontispiece.

Bertha and Leo Wiener, parents of Norbert Wiener (p.31). Courtesy of The MIT Museum (Photo NW 81).

Norbert Wiener at age seven (p. 36). Cour­tesy of The MIT Museum (Photo NW 39).

Norbert Wiener in 1912 just before he re­ceived his doctorate from Havard (p. 44). Courtesy of the MIT Museum (Photo NW 60).

Bertrand Russell (p.51). Reprinted from: Autobiography of Bertrand Russell, Lit­tie, Brown & Co., Boston 1968, p. 277.

Norbert Wiener in army uniform (p. 69). Courtesy of The MIT Museum (Photo NW 46).

Albert Einstein (p. 80). Reprinted from: G. Kuznecov: Einstein. Leben-Tod-Un­sterblichkeit, Birkhiiuser Verlag, Basel 1977, Abb. 5.

J.B. Perrin (p. 81). Courtesy of Dr. Francis Perrin.

Marguerite Engemann in 1926 (p.95). Courtesy of The MIT Museum (Photo NW 89).

Lord Kelvin (p. 103). Courtesy of The Royal Society, London.

Lord Rayleigh (p. 103). Courtesy of The Royal Society, London.

Sir Oliver Heaviside (p. 103). Reprinted from: O.K. McClerey: Introduction to Transients, New York 1961, Frontis­piece. Courtesy of Wiley & Sons Inc.

Sir Arthur Schuster (p. 103). Courtesy of The Royal Society, London.

Sir Geoffrey Taylor (p. 103), Reprinted from: The Scientific Papers of G.1. Tay­lor, Vol. 4, ed. by G.K. Batchelor, New York 1971. Courtesy of Cambridge Uni­versi ty Press.

G.H. Hardy (p. 106): Courtesy of Birk­hiiuser Boston Inc.

Wiener with Max Born (p. 118). Courtesy of The MIT Museum (Photo NW I).

Gofffried Wilhelm Leibniz (p. 126). Cour­tesy of Dr. E. A. Fellmann, Euler Archiv Basel.

J.B.S. Haldane (p. 127). Reprinted from: Living Philosophers, New York 1931, p. 324. Courtesy of Harper and Row Publishers Inc.

Eberhard Hopf (p. 133). Courtesy of The MIT Museum (Photo EH I).

R.E.A. C. Paley (p. 137). Copyright Elwin Neame. Reprinted from: Fourier Trans­forms in the Complex Domain, R.E.A.C. Paley and N. Wiener, Ameri­can Mathematical Society Colloquium Publications (1934), Vol. 19, by permis­sion of the American Mathematical Soci­ety.

J.-B. Fourier (p. 144). Reprinted from: I. Grattan-Guinness: Joseph Fourier 1768-1830, MIT Press, Cambridge MA 1972 (Plate 4). Courtesy of Archives de l' Academie des Sciences de Paris.

H. Lebesgue (p. 144). Courtesy of Birk­hiiuser Boston Inc.

J. W. Gibbs (p. 145). Courtesy of AlP Niels Bohr Library.

G.D. Birkhoff (p. 145). Reprinted from: G.D. Birkhoff: Collected Mathematical Papers (1950), by permission of the American Mathematical Society.

C. E. Shannon (p. 155). Courtesy of The MIT Museum (Photo CES 1).

416

Vannevar Bush (p. 166). Courtesy of The MIT Museum (Photo VB 2).

Y. W. Lee (p. 167). Courtesy of The MIT Museum (Photo YWL 2).

Wiener with colleagues (p. 169). Courtesy of The MIT Museum (Photo NW 67).

Julian Bigelow (p. 183). Courtesy of Mr. Julian Bigelow.

Academician Andre Kolmogorov (p. 194). Courtesy of Birkhiiuser Boston Inc.

Arturo Rosenblueth (p. 199). Courtesy of Mrs. Virginia Rosenblueth.

Norbert Wiener with Drs. J. Weisner and Y.K. Lee (p. 212). Courtesy of The MIT Museum (Photo NW 26).

Warren McCulloch (p.222). Courtesy of The MIT Museum (Photo WSM 4).

Walter Pills (p. 224). Courtesy of The MIT Museum (Photo WHP I).

The Boston Arm (p. 230). Courtesy of Mr. T. Walley Williams, Liberty Mutual In­surance Company, Boston.

The Boston Elbow (p. 231). Courtesy of Mr. T. Walley Williams, Liberty Mutual In­surance Company, Boston.

W. Grey Walter (p. 235). Courtesy of Bur­den Neurological Institute.

John von Neumann (p. 247). Courtesy of the Niels Bohr Institut.

Henri Bergson (p. 255). Reprinted from: Willy Haas: Nobelpreistrager der Litera­tur. Ein Kapitel Weltliteratur des zwan-

Photograph Index

zigsten Jahrhunderts. Heinz Moos Ver­lag, Heidelberg 1966.

William Ross Ashby (p. 259). Courtesy of Professor N. N. Rao, Electrical & Com­puter Engineering Department, Uni­versity of Illinois.

Walter Reuther (p. 274). Courtesy of Mrs. Norma Bogovich, UA W Public Rela­tions and Publications Department De­troit, MI. Photo by Alexander Archer, UAW Solidarity Magazine.

John Dewey (p. 278). Reprinted from: Living Philosophers, New York 1931, p. 21. Courtesy of Simon & Schuster.

Chess playing automaton, built by Tores y Quevedo in 1890: (p.304). Courtesy of The MIT Museum (Photo NW 55).

Chess pla,ring automaton, the Belle (p. 305). Courtesy of Dr. Kenneth Thompson, Belle Telephone Laboraties.

St. Augustine in His Stu,~v (p. 320). Cour­tesy of Scala Istituto Fo\ografico Edito­riale S.p.A., Firenze.

Homo peccator (p. 323). Courtesy of Rin­gier Dokumentationszentrum Ziirich. (Photo WK 2 Japan II Dukas, Hiro­shima (G 0136232)).

Norbert Wiener in the Soviet Union (p. 364). Courtesy of The MIT Museum (Photo NW 14).

Norbert Wiener at the White House (p. 364). Courtesy of The MIT Museum (Photo NW 51).