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Home , Eberhard Hopf, Homeostat, Norbert Wiener, Roger Burlingame

371 Academic Vita of !

1894 Born on November 26 in Columbia, Missouri, to Bertha Kahn Wiener and , a professor of foreign languages at the University of Missouri. 1895 The family moved to Cambridge, Massachusetts, where Leo Wiener became a professor of 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 and . 1909 Received an A.B. degree, cum laude, from Tufts, and entered the Harvard Graduate School to study . 1910 Entered the Sage School of at 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, , 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 , 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 , Edmund Husser!, and . Appointed a Frederick Sheldon Fellow by Harvard; returned to Cam• bridge 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 Academic Vita of Norbert Wiener

1917 Served with the Cambridge ROTC; briefly worked as an apprentice engineer in the turbine department of the Corp. in Lynn, Massachusetts. Appointed a staff writer for the Encyclopedia Americana in Albany, N.Y. 1918 Joined the Aberdeen, Proving Grounds of the U.S. Army under O. Veblen, and worked on computations of ballistic tables. Joined the American Mathematical . 1919 Served as an Army private at the Aberdeen Proving Ground, Mary• land. Worked as a journalist with The Boston Herald. Appointed instructor of mathematics at MIT. 1920 Attended the International Mathematical Congress in Strasbourg as MIT's representative and presented a paper on . He also visited Cambridge and Paris. 1924 Appointed assistant professor of mathematics at MIT. 1925 Attended the International Mathematical Congress in Grenoble and the British Association for the Advancement of Science meeting in Southampton; visited Gi:ittingen University. 1926 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. 1928 Addressed the Symposium on Analysis Situs of the American Math• ematical Society. 1929 Appointed associate professor of mathematics at MIT. Lectured at Brown University as exchange professor during 1929-1930. 1931-1932 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. 1933 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 . Collaborated with REAC. Paley. 1934 Delivered the AMS Colloquium Lectures at Williamston, Massa• chusetts. 1935 Patented electrical network 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. 1936 Attended the International Congress of in Oslo, Nor• way, and lectured on Tauberian gap theorems. Collaborated with Harry Ray Pitt at MIT during 1936-1937. 1937 Delivered the Dohme lecture at Johns Hopkins University on Tauberian theorems. 1938 Lectured on analysis at the semicentennial of the AMS. 1940 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

Consultant with the NDRC's Office of Scientific Research and De• velopment, Statistical Research Group and Operational Research Lab• oratory 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 anti• aircraft guns with , under NDRC Project. 1941 Resigned from the National Academy of Sciences. 1945 Participated in a study group set up by , and attended a meeting on in Princeton. Collaborated with Arturo Rosenblueth at the Instituto National Car• diologia in Mexico, and attended the Mexican Mathematical Society's Conference held in Guadalajara. 1946-1950 With Arturo Rosenblueth received a five-year Rockefeller Foundation grant that allowed them to collaborate in Mexico and at MIT on alternating years. 1946 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. 1947 Visited England and France, and gave lectures on in Nancy, France. 1948 Spoke at the AMS's Second Symposium on Applied Mathematics. 1949 Received the Lord & Taylor American Design Award. Delivered the AMS's Lecture at the annual meeting. 1950 Attended the seventh Macy conference. Lectured at the International Congress of Mathematicians at . 1951 Lectured at the University of Paris, College de France, under a Ful• bright Teaching Fellowship, and also lectured in Madrid. Received an honorary Sc.D. degree from the University of Mexico. 1952 Received the Alvarega Prize from the College of Physicians III Philadelphia. Delivered the Forbes-Hawks Lectures at the University of Miami. 1953 Lectured on the theory of prediction at the University of California at Los Angeles. Taught a summer school course with and Robert Fano on the mathematical problems of communications theory. 1953~1954 Lectured at the Tata Institute of Fundamental Research, Bombay, attended the All- Science Congress, and visited research centers. 1955~1956 Visiting professor at the Indian Statistical Institute in Calcutta. 1956 Lectured in Japan and gave a summer school course at UCLA. 1957 Received an honorary Sc.D. degree from Grinnell College. Awarded the Virchow Medal from the RudolfVirchow Medical Soci• ety. 1959 Gave a summer school course at UCLA. Appointed institute professor at MIT. 1960 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 , 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 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 Docu• ments 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.) 377 Bibliography of Norbert Wiener

[13a] On a method of rearranging the positive integers in a IA of ordinal numbers greater than that of any given funda• mental sequence of omegas, Messenger of Math. 43 (1913), 97-105. [l4a] A simplification of the logic of relations, Proc. Cambridge Philos. IA Soc. 17 (1914), 387-390. [14b] A contribution to the theory of relative position, Proc. Cambridge IA Philos. Soc. 17 (1914), 441-449. [l4c] The highest good, J. Phil. Psych. and Sci. Method 11 (1914), IIA 512-520. [14d] Relativism, J. Phil. Psych. and Sci. Method 11 (1914), 561-577. IIA [15a] Studies in synthetic logic, Proc. Cambridge Philos. Soc. 18 (1915), ,IA 14-2S. [15b] Is mathematical certainty absolute?, J. Phil. Psych. and Sci. Method 12 (1915), 568-574.IA [16a] Mr. Lewis and implication, J. Phil. Psych. and Sci. Method 13 IA (1916),656-662. [16b] The shortest line dividing an area in a given ratio, Proc. Cambridge I, I Philos. Soc. 18 (1916), 56-58. [16c] Review of Cassius J. Keyser, Science and Region: the Rational and IVA the Superrational, J. Phil. Psych. and Sci. Method 13 (1916), 273-277. [16d] Review of A.A. Robb, A Theory of Time and Space, J. Phil. Psych. IVA and Sci. Method 13 (1916), 611-613. [l7a] Certain formal invariances in Boolean algebras, Trans. Amer. lA Math. Soc. 18 (1917), 65-72. [17b] Review of C.J. Keyser, The Human Worth of Rigorous Thinking, IVA J. Phil. Psych. and Sci. Method 14 (1917), 356-361. [ISa] Review of Edward V. Huntington, The Continuum and Other IVA Types of Serial Order, J. Phil. Psych. and Sci. Method 15 (1918), 7S-S0. [ISb] Aesthetics, in Encyclopedia Americana, 1915-20 edition, vol. I, IIA 19S-203. [ISc] Algebra, definitions and fundamental concepts, in Encyclopedia I, I Americana, 1918-20 edition, vol. I, 3S1-385. [lSd] Alphabet, in Encyclopedia Americana, 1918-20 edition, vol. I, IIA 435-43S. [lSe] Animals, chemical sense, in, in Encyclopedia Americana, 1918-20 ITA edition, vol. I, 704. I Sf] Apperception, in Encyclopedia Americana, 1918-20 edition, IIA vol. II, 82-S3. 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. Bibliography of Norbert Wiener 379

[2Ie] A new vector method in integral equations (with F.L. Hitchcock), I, I J. Math. and Phys. I (1921), 1-20. [22a] The of space and geometry to experience, Monist 32 IA (1922), 12-60, 200-247, 364-394. [22b] The group of the linear continuum, Proc. London Math. Soc. 20 IA (1922), 329-346. [22c] Limit in terms of continuous transformation, Bull. Soc. Math. IA France 50 (1922), 119-134. [22d] The equivalence of expansions in terms of orthogonal functions IE (with J.L. Walsh), J. Math. and Phys. I (1922), 103-122. [22e] A new type of integral expansion, J. Math. and Phys. 1 (1922), I, I 167-176. [23a] On the nature of mathematical thinking, Austral. J. Psych. and IA Phil. 1 (1923), 268-272. [23b] Nets and the Dirichlet problem (with H.B. Phillips), J. Math. and IB Phys. 2 (1923), 105-124. (Reprinted in [64f].) [23c] Discontinuous boundary conditions and the Dirichlet problem, IB Trans. Amer. Math. Soc. 25 (1923), 307-314. [23d] Differential-space, J. Math. and Phys. 2 (1923), 131-174. IC (Reprinted in [64f].) [23e] o szeregach L~(± Iln}-Note on the series L~(± lin), Bull. IC Acad. Polon. Ser. A, 13 (1923), 87-90. [23f] Note on a new type of summability, Amer. J. Math. 45 (1923), ID 83-86. [23g] Note on a paper of M. Banach, Fund. Math. 4 (1923), 136-143. I, I [24a] Certain notions in potential theory, J. Math. and Phys. 3 (1924), IB 24-51. [24b] The Dirichlet problem, J. Math. and Phys. 3 (1924), 127-146. IB (Reprinted in [64f].) [24c] Une condition necessaire et suffisante de possibilite pour Ie problt'!me IB de Dirichlet, C.R. Acad. Sci. Paris 178 (1924),1050-1054. [24d] The average value of a functional, Proc. London Math. Soc. 22 IC (1924), 454-467. [24e] Un probleme de probabilites dfmombrables, Bull. Soc. Math. IC France II (1924), 569-578. [24f] The quadratic variation of afunction and its Fourier coefficients, J. ID Math. and Phys. 3 (1924), 72-94. [24g] Review of four books on space, Rudolf Carnap's Der Raum: Ein IVA Beitrag zur Wissenschaftslehre, E. Study's Mathematik und Phy• sik: 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. [24h] Review of E. Study, Denken und Darstellung: Logik und Werte; IVA Dingliches und Menschliches in Mathematik und Naturwissenschaf• ten, Bull. Amer. Math. Soc. 30 (1924), 277. [24i] In memory of Joseph Lipka, J. Math. and Phys. 3 (1924), 63-65. IVB [25a] Note on a paper of o. Perron, J. Math. and Phys. 4 (1925), IB 21-32. [25b] The solution ofa difference equation by trigonometrical integrals, J. ID Math. and Phys. 4 (1925), 153-163. 380 Bibliography of Norbert Wiener

[25c] On the representation of functions by trigonometrical integrals, ID Math. Z. 24 (1925), 575-616. [25d] Verallgemeinerte trigonometrische Entwicklungen, Goltingen ID Nachr. (1925), 151-158. [25e] Note on quasi-analytic function, J. Math. and Phys. 4 (1925), IE 193-199. [25f] A contribution to the theory of interpolation, Ann. of Math. (2) 26 I, I (1925),212-216. [26a] The harmonic analysis of irregular motion, J. Math. and Phys. 5 ID (1926),99-121. [26b] The harmonic analysis of irregular motion (Second Paper), J. ID Math. and Phys. 5 (1926), 158-189. [26c] The operational calculus, Math. Ann. 95 (1926), 557-584. ID [26d] A new formulation of the laws of quantization of periodic and IH aperiodic phenomena (with M. Born), J. Math. and Phys. 5 (1926), 84-98. [26e] Eine neue Formulierung der Quantengesetze fur periodische und IH nichtperiodische Vorgiinge (with M. Born), Z. Physik 36 (1926), 174-187. [26f] Analytic approximations to topological transformations (with P. I, I Franklin), Trans. Arner. Math. Soc. 28 (1926), 762-785. [27a] The spectrum of an array and its application to the study of the ID 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). [27b] A new definition of almost periodic functions, Ann. of Math. (2) 28 ID (1927), 365-367. [27c] On a theorem of Bochner and Hardy, J. London Math. Soc. 2 ID (1927), 118-123. [27d] Une methode nouvelle pour la demonstration des tMoremes de M. ID Tauber, C.R. Acad. Sci. Paris 184 (1927), 793-795. [27e] On the closure of certain assemblages of trigonometrical functions, IE Proc. Nat. Acad. Sci. U.S.A. 13 (1927), 27-29. [27f] Quantum theory and gravitational relativity (with D.J. Struik), IH Nature 119 (1927), 853-854. [27g] A relativistic theory of quanta (with D.J. Struik), J. Math. and IH Phys. 7 (1927), 1-23. [27h] Sur fa tMorie relativiste des quanta (with D.J. Struik), C.R. Acad. IH Sci. Paris 185 (1927) 42--44. [27i] Sur la tMorie relativiste des quanta (Nate), C. R. Acad. Sci. Paris IH 185 (1927), 184-185. [27j] Laplacians and continuous linear functionals, Acta Sci. Math. I, T (Szeged) 3 (1927), 7-16. [27k] Une generalisation des fonctions a variation bornee, C.R. Acad. I, T Sci. Paris 185 (1927), 65-67. [28a] The spectrum of an arbitrary function, Proc. London Math. Soc. ID (2) 27 (1928), 483--496. [28b] A new method in Tauberian theorems, J. Math. and Phys. 7 (1928), ID 161-184. [28c] The fifth dimension in relativistic quantum theory (with D.J. IH Struik), Proc. Nat. Acad. Sci. U.S.A. 14 (1928), 262-268. Bibliography of Norbert Wiener 381

[28d] Coherency matrices and quantum theory, J, Math, and Phys, 7 IH (1928), 109-125. [29a] Harmonic analysis and , J. Math. and Phys. 8 (1929), ID 148-154. [29b] A type of Tauberian theorem applying to Fourier series, Proc. ID London Math. Soc. (20) 30 (1929), 1-8. [29c] Fourier analysis and asymptotic series. Appendix to V. Bush, ID Operational Circuit Analysis, New York, John Wiley, 1929, 366-379. [29d] Hermitian polynomials and Fourier analysis, J. Math. and Phys. 8 IE (1929), 70-73. [2ge] Harmonic analysis and the quantum theory, J. Franklin Inst. 207 IH (1929), 525-534. [29f] On the spherically symmetrical statical field in Einstein's unified IH theory of electricity and gravitation (with M.S. Vallarta), Proc. Nat. Acad. Sci. U.S.A. 15 (1929), 353-356. [29g] On the spherically symmetrical statical field in Einstein's unified IH theory: A correction (with M. S. Vallarta), Proc. Nat. Acad. Sci. U.S.A. 15 (1929), 802-804. [29h] Mathematics and art (Fundamental identities in the emotional IIA aspects of each) , Tech. Rev. 32 (1929),129-132,160,162. [29i] Einsteiniana (Facts and fancies about Dr. Einstein's famous IIIE theory), Tech. Rev. 32 (1929), 403-404. [29j] Murder and mathematics, Tech. Rev. 32 (1929), 271-272. IVA [30a] Generalized harmonic analysis, Acta Math. 55 (1930), 117-258. ID (Reprinted in [64f] and [66b].) [30b] Review of A. Eddington's Science and the Unseen World, Tech. IVA Rev. 33 (1930), 150. [31a] Ober eine Klasse singuliirer Integralgleichungen (with E. Hopt), IF Sitzber. Preuss. Akad. Wiss. Berlin, KI. Math. Phys. Tech., 1931, pp. 696-706. (Reprinted in [64f].) [31b] A new deduction of the Gaussian distribution, J. Math. and Phys. I, I 10 (1931), 284-288. [31c] Reportsfrom Cambridge-1931, Tech. Rev. 34(1931), 82-83,131, IIIE 218, 220. [32a] Tauberian theorems, Ann. of Math. 33 (1932),1-100 (Reprinted in ID [64f] and [66b].) [32b] A note on Tauberian theorems, Ann. of Math. 33 (1932), 787. ID [32c] Back to Leibniz! (Physics reoccupies an abandoned position), Tech. IIA Rev. 34 (1932), 201-203, 222, 224. [32d] Reports from Cambridge-1932, Tech. Rev. 34 (1932), 62, 74. IIIE [32e] Review of A.S. Besicovitch, Almost Periodic Functions, Math. IVA Gaz. 16 (1932), 275-277. [32f] Analytic properties of the characters of infinite Abelian groups (with V R.E.A.C. Paley), Abstract, Int'1. Math. Congr., Ziirich, 1932,95. [33a] Notes on random functions (with R.E.A.C. Paley and A. Zyg• IC mund), Math. Z. 37 (1933), 647-668. [33b] A one-sided Tauberian theorem, Math. Z. 36 (1933), 787-789. ID [33c] Characters of Abelian groups (with R.E.A.C. Paley), Proc. Nat. ID Acad. Sci. U.S.A. 19 (1933), 253-257. [33d] The total variation of g(x + h) - g(x) (with R. C. Young, Trans. ID Amer. Math. Soc. 35 (1933), 327-340. 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 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 (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. Bibliography of Norbert Wiener 383

[38a] The homogeneous chaos, Amer. J. Math. 60 (1938), 897-936. IC (Reprinted in [64t].) [38b] On absolutely convergent Fourier-Stieltjes transforms (with H. R. ID Pitt), Duke Math. J. 4 (1938), 420-440. [38c] Fourier-Stieltjes transforms and singular infinite convolutions (with ID A. Wintner), Amer. J. Math. 60 (1938), 513-522. [38d] Taylor's series offunctions of smooth growth in the unit circle (with ID W.T. Martin), Duke Math. J. 4 (1938),384-392. [38e] The historical background of harmonic analysis, Amer. Math. Soc. ID Semicentennial Publications Vol. II, Semicentennial Addresses, Amer. Math. Soc., Providence, R.I., 1938, 513-522. [38t] Remarks on the classical inversion formula for the Laplace IE integral (with D. V. Widder), Bull. Amer. Math. Soc. 44 (1938), 573-575. [38g] The decline of cookbook , Tech. Rev. 40 (1938), 23. IIIE [38h] Review of L. Hogben, Science for the Citizen, Tech. Rev. 40 IVA (1938), 66--67. [39a] The ergodic theorem, Duke Math. J. 5 (1939), 1-18. (Reprinted in IC [64t].) [39b] The use of statistical theory in the study of turbulence, Proc. 5th IC Int'l. Congr. of Applied Mechanics, Sept. 12-16, 1938, Wiley, New York, 1939, 356--358. [39c] On singular distributions (with A. Wintner), J. Math. and Phys. 17 ID (1939), 233-246. [39d] Convergence properties of analytic functions of Fourier-Stieltjes IE transforms (with R. H. Cameron), Trans. Amer. Math. Soc. 46 (1939), 97-109; Math. Rev. 1 (1940), 13; rev. 400. [3ge] A generalization of Ikehara's theorem (with H.R. Pitt), J. Math. ID and Phys. 17 (1939), 247-258. [39t] Review of Roger Burlingame, March of the Iron Men, Tech. Rev. IVA 41 (1939), 115. [39g] Review of W. George, The in Action, Tech. Rev. 41 IVA (1939), 202. [39h] A new method in statistical mechanics, Abstract 133 (with B. V McMillan), Bull. Amer. Math. Soc. 45 (1939), 234; Science 90 (1939), 410-411. [40a] Review of M. Fukamiya, On dominated ergodic theorems in IVA Lp(p~l), Math. Rev. 1 (1940), 148. [40b] Review ofM. Fukamiya, The Lipschitz condition ofrandomfunc• IVA tion, Math. Rev. I (1940), 149. [40c] Review of Th. De Donder, L'imergetique deduite de la mixanique IVA statistique generale, Math. Rev. 1 (1940), 192. [40d] A canonical series for symmetric functions in statistical mechanics, V Abstract 133, Bull. Amer. Math. Soc. 46 (1940), 57. [41a] Harmonic analysis and ergodic theory (with A. Wintner), Amer. J. IC Math. 63 (1941), 415-426; Math. Rev. 2 (1941), 319. [41b] On the ergodic dynamics of almost periodic systems (with A. Wint• IC ner), Amer. J. Math. 63 (1941), 794-824; Math. Rev. 4 (1943),15. [42a] On the oscillation of the derivatives of a periodic function (with IE G. P6Iya), Trans. Amer. Math. Soc. 52 (1942), 249-256. [43a] The discrete chaos (with A. Wintner), Amer. J. Math. 65 (1943), IC 279-298; Math. Rev. 4 (1943), 220. 384 Bibliography of Norbert Wiener

[43b) Behavior, purpose, and (with A. Rosenblueth and J. IIA Bigelow), Philos. Sci. 10 (1943), 18-24. [44a) Review of Hugh Gray Lieber and Lillian R. Lieber, The Education IVA of T. C. Mils; What Modern Methematics Means to You, Tech. Rev. 46 (1944), 390, 392. [45a) La teoria de la estrapolacibn estadistica, Bol. Soc. Mat. Mexicana IG 2 (1945), 37--45; Math. Rev. 7 (1946), 461. [45b) The role ofmodels in science (with A. Rosenblueth), Philos. Sci. 12 IIA (1945),316-322. [46a) A generalization of the Wiener-Hopf integral equation (with A. E. IF Heins), Proc. Nat. Acad. Sci. U.S.A. 32 (1946), 98-101; Math. Rev. 8 (1947), 29. [46b) The mathematical formulation of the problem of conduction of im• IIB pulses 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. [47a) Sur les fonctions inde{iniment derivables sur une demi-droite (with IE S. Mande1brojt), C. R. Acad. Sci. Paris 225 (1947), 978-980; Math. Rev. 9 (1948), 230. [47b) A scientist rebels, Atlantic Monthly 179 (1946), 46; Bill. Atomic IIIB Scientist 3 (1947), 31. [48a) Time, communication and the nervous , Ann. New York IIB Acad. Sci. 50 (1948), 197-220; Math. Rev. 10 (1949), 133. [48 b) , Scientific American 179 (1948),14-18. IIB [48c) An account of the spike potential ofaxons (with A. Rosenblueth, IIB W. Pitts, J. Garcia Ramos, and the assistance of F. Webster), J. of Cellular and Comparative Physiol. 32 (1948), 275-318. [48d) A rebellious scientist after two years, Bull. Atomic Scientists 4 IIIB (1948), 338-339. [48e) Review of L. Infeld, Whom the Gods Love. The Story of Evariste IVA Galois, Scripta Math. 14 (1948), 273-274. [48f] Cybernetics, or Control and Communication in the Animal and the VI 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 learn• ing: ants and men, in Classics in Biology (A Course of Selected Reading by Authorities), Philosophical Library, New York, 1960, pp. 205-213. [49a) Sur la tMorie de la prevision statistique et du filtrage des ondes, IG Analyse Harmonique, Colloques Internationaux du CNRS, No. 15, pp. 67-74. Centre National de la Recherche Scientifique, Paris, 1949; Math. Rev. 11 (1950), 376. [49b) A statistical analysis of synaptic excitation (with A. Rosenblueth, IIB W. Pitts, and J. Garcia Ramos), J. of Cellular and Comparative Physiol. 34 (1949), 173-205. [49c) A new concept of communication engineering, Electronics 22 IIB (1949), 74-77. [49d) Sound communication with the deaf, Philos. Sci. 16 (1949), IIB 260-262. [4ge) Some problems in sensory prosynthesis (with J. Wiesner and L. IIB Levine), Science 110 (1949), 512. 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 , 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 ofprediction 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] 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 ofstochastic processes, J. Opt. Soc. Amer. 43 IG (1953), 225-228; Math. Rev. 17 (1956), 33. 386 Bibliography of Norbert Wiener

[53b] A new form for the statistical postulate of quantum mechanics (with IH A. Siegel), Phys. Rev. 9 (1953),1551-1560; Math. Rev. 15 (1954), 273. [53c] Distributions quantiques dans l'espace differentiel pour lesfonctions IH d'ondes dependant du spin (with A. Siegel), C.R. Acad. Sci. Paris 237 (1953), 1640-1642; Math. Rev. 15 (1954), 490. [53d] Les machines a calculer et la forme (Gestalt), Les machines a lIB calculer et la pensee humaine, Colloques Internationaux du Centre National de la Recherche Scientifique, Paris, 1953, pp. 461-463; Math. Rev. 16 (1955), 529. [53e] The concept of homeostasis in medicine, Transactions and Studies IlB of the College of Physicians of Philadelphia (4) 20 (1953), No.3, 87-93. [53f] Problems of organization, Bull. Menninger Clinic 17 (1953), lIB 130-138. [53g] The future of automatic machinery, Mech. Engrg. 75 (1953), lIB 130-132. [53h] Ex-prodigy: My Childhood and Youth, Simon and Schuster, New VI York, 1953; The MIT Press, Cambridge, Mass., 1965 (paperback edition, The MIT Press); Math Rev. 15 (1954), 277. [53i] The electronic brain and the next industrial revolution, Cleveland IlIA Athletic Club Journal (January, 1953). [53j] The machine as threat and promise, St. Louis Post-Dispatch IlIA (December, 1953). [53k] We can't attain truth without risk of (from This I Believe IlIA radio show), Minneapolis Tribune (November, 1953). [54a] Men, machines, abd the world about, in Medicine and Science, lIB New York Academy of Medicine and Science, ed. I. Galderston, International Universities Press, New York, 1954, pp. 13-28. [54b] Conspiracy of conformists, Nation 178 (1954), 375. I1IE [54c] Automatization (with Donald Campbell), St. Louis Post-Dispatch IlIA (December, 1954). [55a] Nonlinear prediction and dynamics, Proc. Third Berkeley Sym• IG posium on Mathematical Statistics and Probability, University of California Press, Berkeley, Calif., 1954/5, pp. 247-252; Math. Rev. 18 (1957), 949. [55b] On the factorization of matrices, Comment. Math. Helv. 29 (1955), IG 97-111; Math. Rev. 16 (1955), 921. [55c] The differential-space theory of quantum systems (with A. Siegel), IH Nuovo Cimento (10) 2 (1955), 982-1003, No.4, Supp!. [55d] Thermodynamics of the message, in Neurochemistry, ed. K.E.C. lIB Elliott, Thomas, Springfield, 1955, pp. 844-849. [55e] Time and organization, Second Fawley Foundation Lecture, Uni• lIB versity of Southampton, 1955, pp. 1-16. [56a] On a local L 2-variant of lkehara's theorem (with A. Wintner), Rev. ID Math. Cuyana 2 (1956), 53-59. [56b] The theory ofprediction, in Modern Mathematicsfor the Engineer, IG ed. E.F. Beckenbach, McGraw-Hill, New York, 1956, pp. 165-187. [56c] "Theory of Measurement" in differential-space quantum theory IH (with A. Siegel), Phys. Rev. 101 (1956),429-432. 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 , 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 388 Bibliography of Norbert Wiener

[58i] Nonlinear Problems in Random Theory, The MIT Press, Cam• VI bridge, Mass., and Wiley, New York, 1958; paperback edition, The MIT Press, 1966. [59a] A factorization of positive Hermitian matrices (with E.J. Akuto• IG wicz), J. Math. Mech. 8 (1959),111-120. [59b] Nonlinear prediction (with P. Masani), in Probability and Statis• IG tics, The Harald Cramer Volume, ed. U. Grenander, Stockholm, 1959, 190-212. [59c] On bivariate stationary processes and the factorization of matrix• IG valuedfunctions (with P. Masani), Teor, Verojatnost, i Primenen. 4 (1959), 322-331. (English trans I. Theor. Probability App. 4 (1959), 300-308). [59d] Man and the machine (Interview with N. Wiener), Challenge (The IIIA Magazine of Economic Affairs) 7 (1959), 36-41. [5ge] The Tempter (novel), Random House, New York, 1959. VI [60a] The application of physics to medicine, in Medicine and Other IIB Disciplines, New York Academy of Medicine, ed. 1. Galderston, International Universities Press, 1960, pp. 41-57. [60b] The brain and the machine (Summary of an address), in Dimensions IIB 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. [60c] Kybernetik, Contribution to Worterbuch der Soziologie, F. Enke lIB Verlag, Stuttgart, 1960, pp. 620-622. [60d] Some moral and technical consequences of , Science 131 IlIA (1960), 1355-1358. [60e] The duty of the intellectual, Tech. Rev. 62 (1960), 26-27; reprinted IIIB 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." [60f] Preface to Cybernetics of Natural Systems, by D. Stanley-Jones, IVA Pergamon Press, London, 1960, pp. v-viii. [60g] Possibilities of the use of the interferometer in investigating IIB macromolecular interactions, in Fast Fundamental Transfer Pro• cesses in Aqueous Biomolecular Systems, ed. F. O. Schmitt, Department of Biology, MIT, Cambridge, Mass., June 1960, pp.52-53. [61a] Uber Informationstheoreie, Naturwissenschaften 48 (1961), JIB 174-176. [61b] Science and society, Voprosy Filosofii (1961), No.7, 117-122; JIB reprinted in Estratto Rivista Methodos 13 (1961), 1-8, and in Tech. Rev. 63 (1961), 49-52. Excerpts in Science 138 (1962), 651. [61c] Cybernetics, Second edition of [48f] (revisions and two additional VI chapters), The MIT Press and Wiley, New York, 1961; paperpack edition, The MIT Press, 1965. [62a] A verbal Contribution to Proc. of the International Symposium IIB on the Application of Automatic Control in Prosthetics Design, August 27-31, 1962, Opatija, Yugoslavia, pp. 132-133. [62b] The mathematics of self-organizing systems, in Recent Develop• IIB ments in Information and Decision Processes, Macmillan, New York, 1962, pp. 1-21. 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 , 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. , 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 posi• tion 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 References

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WI Walter, W. Grey, Neurocybernetics, pp. 93-108, in Survey of Cybernetics, Edited by J. Rose, Gordon & Breach, New York, 1969. W2 Watson, J.D., The Double Helix, Penguin Books, Middlesex England, 1971. W3 Watts, A.W., The Two Hands of God, Colliers, New York, 1972. W4 Weyl, H., The Theory of Groups and Quantum Mechanics, Dover Publica• tions, New York, 1931. W5 Weyl, H., Philosophy of Mathematics and Natural Science, Princeton Uni• versity Press, Princeton, New Jersey, 1949. W6 Weyl, H., Symmetry, Princeton University Press, Princeton, New Jersey, 1952. W7 Whitehead, AN., Introduction to Mathematics, (1919), Home University Library, London, 1945. W8 Whitehead, A.N., Science and the Modern World, (1928), Cambridge Uni• versity Press, Cambridge, 1933. W9 Whitehead, A.N., Religion in the Making (1928), Meridian, New York, 1960. WIO Whitehead, AN., Mathematics and the good, pp. 660-687, in The Philo• sophy of A.N. Whitehead, Edited by P.A. Schilpp, Tudor, New York, 1951. WI I Whitehead, A.N. and B. Russell, Principia Mathematica, Vol. I, II, III (1910-1913), Cambridge University Press, Cambridge, 1925-1927. W12 Whittaker, Sir Edmund, A History of the Theories of Aether and Electricity. Vol. II, Harper, New York, 1953. WI3 Wigner, E.P., The unreasonable effectiveness of mathematics in the natural sciences, Commun. Pure Appl. Math. 13 (1960), 1-14. WI4 Wittgenstein, L., Tractatus Logico-Philosophicus, Routledge & Kegan Paul, New York, 1961.

Yl Yaglom, A M., An Introduction to the Theory of Stationary Random Func• tions, Prentice-Hall, Englewood Cliffs, N.J., 1962. Y2 Yaglom, A.M., Einstein's 1940 paper on the theory of irregularly fluctuating sums of observations, Problemy Peredachi Informatsii (Problems ofInforma• tion Transmission), 1985, Vol. 21, No.4, pp. 101-107. English translation: IEEE ASSP Magazine, October 1987 (Vol. 4, no. 4). 400

Name Index

Acheson, George 197 Bergman, Stefan (1898-1978): 232, 393 Aeschylus (525-456 B.C.): 370 Bergson, Hcnri (1859-1941): 42,57,60, Aiken, H.H. (1900-1973): 239 152, 254, 255, 277, 366 Alaric (3707-410): 332 Bernal, J.D. (1901-1971): 261,359,393 Albertson, Ralph A. (I RR6-1951): 30, Bernard, Claude (1813-1878): 253 392 Bernstein, Felix (1878-1956): 60 Alexander, J. W. (1888-1971): 63, 68 Bernstein, J. (b. 1924): IS, 393 Ambartsumian, V. (b. 1908): 337 Besicovitch, A.S. (1891-1970): 104,117, Ampere, Andre Maric (1775-1836): 252, 141 253, 392 Bessell, F.W. (1784-1846): 104,107 Anaxagoras (5007-428 B.C.): 62 Bigelow, Julian 182-186, 188, 194, 20 I, Anderson. Clinton (1895-1975): 312 211,218,239,373,391 Aquinas, Saint Thomas Birkhoff, G. D. (18841944): 64, 85, 93, (l225?-12747): 41,62,277,344 126,127,132,139,141,145,241,254, Archimedes (287-212 B.c'): 345 326, 341, 360, 361, 363, 393 Aristotle (384 322 B.c'): 203, 277, 327, Blair, C. 297,311,314,393 368 Blaschke, Wilhelm (1885-1902): 136 Ashby, W. Ross (1903-1972): 212,250, Bliss, G.A. (1876-1951): 68 255, 256, 258-260, 262, 292, 293, 333, Bloch, Andre (1893-1948): 352 367, 392 Bloy, Reverend Myron 370 AtanasofT, V.J. (b. 1903): 172 Bocher, Maxime (1867-1918): 34,108 Augustine, Saint (354-430): 318-321, Bochner, S. (1899-1982): 101, 112, 195 324, 329, 331, 344, 392 Bode, IIendrik W. (19067-1982): 182, A vogadro, Count Amedeo 189 (1776-1856): 82, 148 Bohm, D. 129, 130,393 Bohr, Harald (1887-1951): 104,105, Babbage, Charles (1791-1871): 162,171, 251,372 219, 220, 254 Bohr, Niels (1885-1962): 55, 123, 128, Bach, Johann Sebastian 393 (1685-1750): 293 Boltzmann, Ludwig (1844-1906): 54,81, Bacon, Francis (1561-1616): 41, 62 122,143,146,148,149,155,158,159, Bacon, Roger (l214?-12947): 41, 62, 254 259, 277, 368 Bolyai, J. (1802-1860): 73 Baker, H.F. (1866-1956): 47 Bonaventura, Saint (1221-1274): 343, Banach, Stefan (1892-1945): 76 346, 393 Barlow, John Sulton (b. 1925): 235,250 Boole, G. (1815-1864): 22 Barnes, John L. (1906-1976): 159,392 Borel, E. (lR71-1956): 90,354 Barnett, 1. Albert (1894-1975): 77,167 Born, Max (1882-1970): 111,115, Bartlett, Sir Francis C. (1886-1969): 56 117-119,132,155,157,241,366,393 Bass, J. 151,392 Bouligand, C. D. 92 Beethoven, Ludwig van (1770-1827): 18, Boyce, J.c. 192,391 200 Bourbaki, N. 348 Behrend, B.A. (1875-1942): 340 Bradley, F.H. (1846-1924): 56,60 Bell, Daniel (b. 1919): 287,392 Bray, Hubert (1889 0 -1978): 68 Bell, E. T. (18831960): 59, 392 Brazier, Mary A. B. 235 Benedetto. J.J. (b. 1939): 114,392 Brelot, Marcel (1903-1987): 86, 393 Benke, G. 114 Bridgman, P.W. (1882-1961): 121,393 Berger, Hans (1873-1941): 233 Brillouin, L. 155 Name Index 401

Broad, C.D. (1877-1971): 72 Democritus (b ab 460 B.c.): 143 Broglie de, L.V. (1892-1987): 26,119, Descartes, Rene (1596-1650): 277 122, 123, 125, 129, 130,241,345 Deutsch. Karl (b. 1912): 288,289,330, Brown, G.S. (b. 1907): 163,396 336, 394 Brown, Robert (1773-1858): 81, 82 Dewey, John (1859-1952): 61,62, Browning, Robert (1812-1889): 30 277-279, 371, 394 Buchdahl, H.A. 157,393 Dickens, Charles (1812-1870): 287 Bush, Vannevar (1890--1974): 96, 101, Dirac, Paul A.M. (1902-1984): 119,260, 160--162,165,166,170-172,174,175, 345, 368 179, 239, 241, 264, 295, 296, 366, 393 Doob, J. L. (b. 1910): 83, 394 Butler, Nicholas Murray Draganescu, M. 253, 394 (1862-1947): 61 Duns Scotus, John (1265'1-1308): 62 Butler, Samuel (1835-1902): 35 Eckhart, Meister J. (l260?-1327): 343 Cairns, T. 205 Eddington, Sir Arthur (1882-1944): 26, Caldwell, Samuel H. (1904-1960): 181, 57, 152, 345, 394 184,373,391 Edwards, C. B. 71 Cameron, R. H. (1908-1989): 151, 266, Ehrenfest, P. (1880--1903): 147 271,393 Ehrenfest, T. 147 Cannon, J.W. 85,393 Einstein, Albert (1879-1955): 19,25,26, Cannon, Walter B. (1871-1945): 34,168, 47, 53, 55, 72, 79, 80-83, 85, 90, 102, 197, 198,203, 361 113, 115, 120, 121, 129, 130, 136, 143, Cantor, Georg (1845-1918): 48,50, 59, 241, 258, 267, 268, 292, 296, 324, 325, 76,93 330-334, 344-346, 369, 394 Caratheodory, C. (1873-1950): 94, 157 Eisenhower, Dwight D. Carnap, R. (l87l-l970): 49,54,72,218, (1890-1969): 295,299,310,312 223, 393, 394 Eliot, T.S. (1888-1965): 60,61,279,331, Carnot, Sadi (1837-1894): 147, 148,254 366, 394 Carroll, Lewis (1840-1921): 335 Ellis, H. Havelock (1859-1939): 342 Cartwright, Mary (b. 1900): 136 Emerson, Ralph Waldo (1803-1882): 93 Cassirer, E. (1874-1945): 25,326,394 Engels, Friedrich (1820--1895): 260,277, Caton, R. 233 293,314,395 Chafetz, Morris E. 339 Engemann, Marguerite (see Margaret Chase, M. W. (b. 1905): 248 Wiener) Chiang Kai-shek (1887-1975): 302 Euclid (3651-275? B.C.): 326, 368 Christopherson, D.G. 180 Euler, Leonhard (1707-1783): 62, 97, Church, A. (b. 1903): 220 345 Clausewitz, Karl von (1780-1831): 298, Euripides (480?-406? B.C.): 370 302-303,307,308,313,314,316,394 Evans, W. 114 Cockcroft, Sir John D. (1897-1967): 367 Compton, Karl T. (1887-1945): 92, 192, Fano, Robert (b. 1917): 373 391 Faraday, Michael (1791-1867): 24,99, Conant, James Bryant (1893-1978): 361 176 Coomaraswamy, A.K. (1887-1947): 329, Faramelli, N.J. 333, 395 343, 346, 394 Ferry, D. K. (b. 1940): 173, 174 Courant, Richard (1888-1972): 105 Feynman, R.P. (b. 1918): 84,128 Cousins, Norman (b. 1912): 311 Fisher, Sir Ronald A. (1890-1962): 153, Cramer, Harald (1893-1985): 194 254, 395 Croce, Benedetto (1866-1952): 136 Fisk, James B. (b. 1910): 312 Fock, V. (1898-1974): 121, 125,271 Daniell, P.J. (1889-1946): 78,79,90, Foias, C. 193 394 Folin, Otto (1867-1934): 34 Dante, Alighieri (1265-1321): 293,343 Forrester, Jay W. (b. 1914): 175 Darwin, Charles Robert Forsyth, G. E. (b. 1917): 296 (1809-1882): 249 Foures, Y. 182,395 Davenport, H. (1907-1969): 47 Fourier, Jean-Baptiste Baron de Dean, Gordon 310 (1768-1830): 97-99,104,144,163,177 Dedekind, J.W.R. (1831-1916): 50 Fowler, Henry Watson (1858-1933): 70 Deem, G. 151 Francis of Assisi, Saint (1182-1226): 318 De Kruif, Paul (1890--1971): 340,341 Frank, Philipp (1884-1966): 115, 136, Delbruck, Max (1906-1981): 245,248 395 402 Name Index

Frankel-Conrat, H.L. (b. 1910): 248 Hardy, G.H. (1877-1947): 22,47,55, Frankfurter, Felix (1882-1965): 362 78, 94, 105-107, 135, 136, 335, 344, Franklin, Philip (1898-1965): 68,71 345,353,371,396 Frechet, Maurice (1878-1973): 74-77 Haug, E. 233 Fredholm, I. (1866-1927): 163 Hausdorff, F. (1868-1942): 84 Freudenthal, Hans (b. 1905): 349, 353, Hazen, H.L. (1901-1980): 163,396 355, 395 Healy, Sister E. T. 343, 393 Frege, G. (1848-1925): 49-50,59 Heaviside, Sir Oliver Freundlich, E.F. (1884-1964): 133 (1850-1925): 100-103,336,340,346 Freyman, M. 251 Hegel, G.W. (1770-1831): 60 Friedrichs, K. (1901-1983): 101 Heims, S. (b. 1926): 20, 242, 248, 293, Fuller. H.J. 280, 395 308,314,333,334,396 Heine, Heindrich (1797-1856): 335,341 Heins, A. E. 134 Gabor, Sir Dennis (1900-1979): 111 Heisenberg, Werner (1901-1976): 117, Gage, F.D. 393 118,121,184,241 Galileo (1564-1642): 315,368 Helmholtz von, H.L.F. Gallie, W.B. (b. 1912): 314,317,395 (1821-1894): 148 Galois, E. (1811-1832): 345 Heraclitus (6th-5th cent. B.C.): 268 Garno, Hideya (b. 1924): 111 Hermite, C. (1822-1905): 270 Gandhi, M.K., Matatma Heron of Alexandria (c. 100 A.D.): 256 (1869-1948): 318, 351, 395 Hershey, Alfred D. (b. 1908): 249 Garcia Ramos, J. 197,205-208,248, Hertz, H. (1857-1894): 24, 25 395 Hewitt, E. (b. 1920): 108, 114,396 Gauss, Karl F. (1777-1855): 59,87 Hilbert, D. (1862-1943): 26,59,60,94, Gelfand, I.M. (b. 1913): 108 240, 371 Getting, Ivan A. (b. 1912): 349 Hill, G. W. (1838-1914): 207 Gibbs, Josiah Willard (1839-1903): 55, Hille, Einar (1894-1980): 108 79, 122, 139, 143, 145, 146, 254, 354 Hitchcock, Alfred (1899-1980): 94, Gilbreth, Frank (1868-1914): 254 338-340 Gilbreth, Lillian (1878-1972): 254 Hocking, William E. (1873-1966): 66 Giuculescu, A. 256, 395 Hodgkin, Sir Alan Lloyd (b. 1914): 208 Gleason, A.M. (b. 1921): 128,395 Homer (c. 850 B.C.): 293, 335 Glimcher, Melvin J. (b. 1925): 230 Hopf, Eberhard (1902-1983): 132-135, Glushkov, Y.M. (b. 1923): 260,261,395 139, 186, 196,396 Giidel, Kurt (1906-1978): 50,51,52,56, Horace (65-8 B.c'): 335 136,219,220,261,346, 395, 396 Huntington, E.Y. (1874-1952): 43,46, Goethe, J.W. (1749-1832): 32,316,341 73-75, 89, 371 Golden, Reverend 370 Hurewitz, Witho1d (1904-1956): 349 Goldstine, H.H. (b. 1913): 175,232, Husser!, Edmond (1859-1938): 59, 371 239, 396 Huxley, A.F. (b. 1918): 208 Gordon, W. 120 Huygens, C. (1629-1695): 125 Gould, K.E. 162,396 Goursat, E. (1858-1936): 353 Grattan-Guiness, I. (h. 1941): 43, 64, Ikehara, Shikao (l904?-1984): 107, 168, 396 Gray, T.S. (b. 1906): 162, 163,396 375 Green, G.F. (1793-1841): 87 Inge, W.R. (1860-1954): 369 Green, Gabriel Marcus (1891-1919): 77, Ingham, A. E. (1900-1967): 105 Ito, K. (b. 1915): 83,86 363 Greenberg, D. S. 361, 396 Jackson, Dougald C. (1865-1951): 96 Hadamard, Jacques (1865-1963): 169, Jacobs, W.W. (1863-1943): 316 170, 325, 396 Jacquard, J.M. (1752-1834): 219,220 Haldane, J.B.S. (1892-1964): 121-127, James, William (1842-1910): 39,62 136, 168, 248, 251, 254, 260, 293, 366, Jesperson, Otto (1860-1943): 280 396 Jewett, Frank (1879-1949): 18,356,360, Halmos, P.R. (b. 1914): 345-347,396 361 Hamilton, Sir William R. Johnson, Lyndon B. (1908-1973): 15, (1805-1865): 142, 147, 345 364, 374 Hantschius 127 Jones, Rufus (1863-1948): 218 Name Index 403

Kac, Mark (1914~1984): 83,84,86,128, Lemaitre, Cannon G.H. 396 (l894~1966): 170 Kahn, Henry 30 Lenard, P.E.A. (l862~1947): 315 Kailath, T. (b. 1935): 135 Lenin, V.1. (1870~ 1924): 122, 260, 275, Kakutani, S. (b. 1911): 88,130,151, 397 266,271,397 Leontovich, M. 86 Kaluza, Th. (1885~1954): 119,121 Leray, J. (b. 1906): 101 Kant, Immanuel (1724-1804): 41,59, Lettvin, Jerome (b. 1920): 218 71,72, 120,277,316,341 Levinson, Norman (l912?~1975): 92, Karamata, J. 108 172, 349, 350, 353, 355, 375, 397 Kellogg, O.D. (1878~1932): 86,87,91, Levy, Hyman (l889~1975): 59,261 361 Levy, Paul (1886-1971): 86, 194 Kelvin, Lord (Sir William Thompson) Lewis, Albert C. 18 (1824-1907): 102,103,161,254 Lewis, T. 204 Kennedy, Peggy (see Peggy Wiener) Lichenstein, Leon (1878~1933): 136, 167 Kepler, Johannes (1571~1630): 19,25, Liddell Hart, Sir Basil H. 345 (1895~1970): 298, 398 Kerensky, A.F. (1881~1970): 32 Lilienthal, D.E. (b. 1899): 311 Ketner, K.L. 221 Lindsley, D.B. (b. 1907): 236 Kettering, C.F. (l876~1958): 340 Liouville, J. (l809~1882): 147 Keynes, Lord J.W. (1883~1946): 284, Littlewood, J.E. (l885~1977): 47, 397 105~1O7, 135, 136,368,371 Keyserling, Leon (b. 1908): 274 L1ull, R. (1225~1316): 254 Khinchine, A.L. (1894-1959): 86,113, Lobatchevsky, N.1. (1793~ 1856): 73 149,194 Locke, John (l632~1704): 368 Kipling, Rudyard (1865~1936): 335, 336 Lorente de No, R. (b. 1902): 239 Kirchoff, G.R. (1824~1887): 176 Lovelace, Lady (Ada Byron) Kleene, S. C. (b. 1909): 220 (l815~?): 219 Klein, Felix (l849~ 1925): 225 Lovell, C.A. 182, 189, 192 Klein, O. 120, 121, 125 Lowell, Abbot Lawrence Kline, J. R. 167 (l856~ 1943): 32, 66, 362 Koebe, P. (l882~1945): 18 Lucretius (9?~55 B.C.): 122 Kolmogorov, A.N. (1903~1987): 86,90, Lynd, Albert 280, 398 149, 193~195, 241, 261, 397 Konoye, Prince (1891 ~ 1945): 298 Mach, E. (1838~1916): 54,277 Kosambi, D.D. (1907~1966): 363,397 Mackey, G. W. (b. 1916): 128, 398 Kronecker, L. (1823~1891): 59 Maimonides, Rabbi Moses (1842~lnl): Kropotkin, Prince P.L. 34 (1135~1204): 41,43,398 Malliavan, P. 114 Lafargue, Paul (1842~1911): 292,397 Mandelbrojt, Szolem (l899~ 1983): 170, Lagrange, J.L. (1736-1813): 87,99,345 251 Laguerre, E. (l834~ 1886): 164, 165, 270 Mandelbrot, Benoit (b. 1924): 85,291, Lambert, J.H. (l728~1777): 107 368, 398 Landau, Edmund (1877~1938): 17,59, Mann, Robert W. (b. 1924): 230, 231 60,371 Marcinkiweicz, J. (1910-1940): 114 Langmuir, Irving (1881~1957): 245 Marquand, A. 221 Laplace, P.S. (1748~1827): 87 Marshall, George C. (1880-1959): 296 Laski, Harold (l893~ 1950): 362 Martin, K. 362, 398 Lau, K-S. (b. 1948): 114,397 Martin, W. T. (b. 1911): 151,266,271, Lazarsfeld, P.F. (b. 1901): 290 393 Leahy, William D. (1875~1959): 296, Marx, Karl (1818~ 1883): 260, 277, 284, 298 292, 314, 322, 398 Lebesgue, H. (1875~1941): 77,78,83, Masani, P.R. (b. 1919): 112,265,333, 92, 139, 145, 147, 354 398 Lee, Yuk Wing (b. 1904): 165~168, 178, Masaryk, Thomas (1850-1937): 31, 136 187, 195,212,235,239,240,372,397 Maupertius, P.L. (l698~1759): 121 Legendre, A.M. (1752~1833): 163 Maxwell, James Clerk Leibniz, G.W. (1646-1716): 19,39,76, (1831~1879): 23~25, 81, 99,109,116, 121,122,125,126,161,162,171, 143, 146, 155,254,258,334,345 219~222, 239, 254, 277, 319, 363, 366, McCulloch, Warren S. (l898~1969): 200, 368 205, 218, 219, 222, 223, 225, 227, 232, 404 Name Index

236, 238, 239, 243, 248, 346, 366, 367, Paley, R.E.A.C. (1907-1933): 84, 398, 399 136-138,140,166,169,177,197,372 McMillan, Brockway (b. 1915): 151,375 Palmer, G.H. (1842-1913): 43,46,371 McTaggart, 1.M.E. (1866-1925): 56,60, Parkinson, C. Northcote (b. 1909): 286, 371 287, 399 Mehra,l. 118,398 Pascal, B. (1623-1662): 19,161, 171, Mendel, Gregor (1822-1844): 249 239, 254 Menger, Karl (b. 1902): 136, 167 Pauling, L. (b. 1901): 312 Mercer, J. (?-1932): 47 Peano, Giuseppe (1858-1932): 53,59, Meyer, Ella J. (Mrs. J. Franklin) 353 147 Michaelangelo, B. (1475-1564): 293, 347 Pearl, Raymond 65 Michaelson, A.A. (1852-1931): 110 Peirce, Charles Sanders Mill, John Stuart (1806-1873): 35 (1839-1914): 15-17,22,39,55,62,74, Millikan, Robert Andrew 93,221,255,277,369,399 (1868-1953): 366 Perrin, J.B. (1870-1942): 79,81,82,84, Milton, lohn (1608-1674): 293 293, 366, 399 Milyukov, P.N. (1859-1943): 32 Perry, Ralph Barton (1876-1957): 43. Minkowski, H. (1864-1909): 346 46,66 Mobius, A.F. (1790-1868): 63 Phelan, G.B. (b. 1892): 367,399 Moliere (1. B. Poqug1in) Phillips, H.B. 71,88,171, 180 (1622-1673): 342 Phillips, Ralph S. (b, 1-913): 349,391 Monod, 1. (1910-1971): 249,398 Pierce, J.R. (b. 1910): 155,257,399 Moore, E.H. (1862-1932): 77 Pincus, 1. 135 Moore, G.E. (1873-1958): 56,371 Pitt, Harry Ray (b. 1914): 108,372 Moore, O.K. 191 Pitts, Walter (1923-1969): 201,207,208, Moore, R.L. (1882-1974): 75 218,219,223-225,227,232,236,239, Mordell, L.l. (1888-1972): 47 243, 248, 398, 399 More, Saint Thomas (1478 1535): 335 Planche rei, M. (1885-1967): 98, 147 Morgenstern, O. (1902-1977): 268, 290, Planck, Max (1858-1947): 117,130,156 296, 303,401 Plato (427-347 B.C.): 15,24,43, 122, Morishima, M. (b. 1923): 314,399 124, 252, 253, 255, 259, 260, 297, 327, Morris, William (1834-1896): 277 335, 344, 363, 368 Morse, Marston (1892-1977): 108 Poincare, H. (1854-1912): 59,62,207, Mozart, W.A. (1756-1791): 93,259 315 Muller, H.J. (1890-1967): 312 Poisson, S.D. (1781-1840): 87 Mumford, Lewis (b. 1895): 284, 336, Pollack, Rabbi Herman 370 337, 369, 399 P6lya, George (1887-1985): 47 Munsterberg, H. (1863-1916): 46 Pope, Alexander (1688-1744): 342 Post, E.L. (1897-1954): 220 Potra, F. 232 Nagy, B. Sz. (b. 1913): 193, 399 Prokhorov, Yu. (b. 1929): 86 Napoleon, B. (1769-1821): 300,304 Pupin, M.1. (1858-1935): 336 Nelson, Edward (b. 1932): 83, 128, 130, Pythagoras (572-501 B.C.): 24, 345, 368 241, 399 Nelson, Lord Horatio (1758-1805): 304 Quevedo, Tores y 304 Neurath, O. (1882-1945): 336,399 Quine, W.V. (b. 1908): 52,54,55,399 Newton, Sir Isaac (1642-1727): 19,76, 87, 122, 342, 345 Rabi, I. (b. 1894): 312 Nordhoff, C. (1830-1901): 29,399 Raisbeck, Barbara (see Barbara Wiener) Ramanujan, S. (1887-1920): 345,350 Randell, Brian 173, 175, 180, 399 Odob1eja, Stefan (1902-1976): 253,399 Rashevsky, N. (b. 1899): 218 Ogden, C. K. (1889-1957): 56 Rayleigh, Lord 1.W.S. (1842-1919): 102, Ohm, G.S. (1787-1854): 176 103, 111 Oppenheimer, J. Robert Rechenberg, H. 118,398 (1904-1967): 311, 313, 363 Reuther, Walter (1907-1970): 16,62, Orey, S. (b. 1928): 91 273-275,299,300,302, 303, 314 Osgood, W.F. (1864-1943): 71, 77, 353, Riccia, 1. Della 128 361 Richards, LA. (b. 1893): 56 Osher, W.l. 205 Rickover, Hyman (1900-1986): 281,299 Ostwald, W. (1853-1932): 54 Riemann, B. (1826-1866): 107,346 Name Index 405

Riesz, F. (1880-I 956): 75 Socrates (470-399 B.C.): 93 Robinson, E.A. (b. 1930): 297 Sophocles (496-406 B.C.): 370 Roosevelt, Franklin D. Southwell, R. V. 180 (1882-I 945): 296, 298 Speiser, Andreas (1885-1970): 341 Rosenblith, W.A. (b. 1913): 235 Spinoza, Baruch (1632-1677): 39,43, Rosenblueth, Arturo (\ 900-I 970): 34, 277, 366, 370 197-205,207,208,210,21 1,218,225, Stalin, Joseph (\ 879-1953): 325 233, 239, 240, 243, 248, 249, 25 I, 36 I, Stewart, Duncan 192 366, 367, 373, 399 Stewart, H. R. 393 Rosenthal, A. 147 Stibitz, G.R. (b. 1904): 172,187,190, Ross, K. A. (b. 1936): 108, I 14, 396 391 Rousseau, J.J. (1712-1778): 277 Stieltjes, TJ. (\856--1894): 84, 107 Royce, Josiah (1855-1915): 43,46,361, Stimson, H. L. (1867-1950): 296 371 Stirling, J. (1696--1770): 159 Rudin, W. (b. 1921): 137,399 Stokes, G.G. (1819-1903): 23 Runge, C. 180 Stone, M.H. (1903-1989): 241 Ruskin, John (\819-1900): 335 Stoughton, T R. 296 Russell, Bertrand (1872-1970): 18, 22, Strauss, Lewis, J. (1896--1974): 312,313 45,47-52, 55, 56, 59, 60-64, 72, 79, 93, Struik, Dirk Jan (b. 1894): 120, 293, 199, 220, 239, 277, 297, 303, 335, 346, 349-351,353,368,400 366, 371,400, 402 Swift, Jonathan (1667-1745): 335,342 Russell, H.N. (1877-1957): 243 Szasz, Otto (1884-1952): 60,167 Rutherford, Lord Ernest Szilard, Leo (1899-1964): 155,296 (1871-1937): 123,322 Tamakrin, J.D. (1888-1945): 108 Saeks, R.E. (b. 1941): 173,174,400 Tasaki, I. 208 Samuel, A. L. (b. 1901): 306,400 Taub, Abraham H. (b. 191 I): 120,3\3, Santayana, George (1863-1952): 43,61, 400 371 Tawney, R.H. (1880-1962): 284,400 Santillana, George de 18 Taylor, Frederick (1856-1915): 254 Sarvagatananda, Swami 370 Taylor, Sir Geoffrey I. (1886-1975): 79, Schetzen, M. (b. 1928): 271,400 102, 103, 113, 400 Schickard, W. (1592-1635): 254 Teller, Edward (b. 1908): 311 Schiller, J.C.F. (1759-1805): 341 Tennyson, Alfred (1809-1892): 299 Schmidt, K. 43, 46, 371 Tesla, Nicola (1856--1943): 340 Schmidt, Robert 105-106 Thackeray, W. M. (1811-1863): 335 Schopenhauer, A. (1788-1860): 341 Thilly, Frank (1865-1934): 41,371 Schottky, W. 85 Thompson, Kenneth (b. 1943): 305 Schrodinger, E. (1887-1961): 120, 122, Tillich, P.J. (1886-1965): 324,400 123, 130, 241, 249, 345, 400 Tinbergen, Jan (b. 1903): 285 Schroeder, F. (1841-1902): 43,48 Titchmarsh, E. C. (1899-1963): 47 Schuster, Sir Arthur R. Tolstoy, Count L. (1828- 1910): 31 (1851-1934): 102-104, 11 I-I 13,400 Toynbee, Sir Arnold J. (1889-1975): Schwartz, Laurent (b. 1915): 100, 251 3 \3, 401 Schweitzer, Albert (1875-1965): 318 Tran, L. T. 91, 401 Scimone, Frank J. 352-353 Trentowski, S. 252 Segal, I.E. (b. 1918): 241,395 Truman, Harry S. (1884-1972): 273, Shakespeare, William (1564-I 616): 347 295,296,298-300,310,311 Shannon, Claude E. (b. 1916): 50, I I I, Turing, A.M. (1912-1954): 50,219,220, 153-155, 159, 182,221,224,253,262, 243,246,251,401 356, 373, 400 Sheffer, Henry Morris (1883-1864): 55, Ulam, Stanislaw (1909-1984): 51,295, 74 311,314,401 Siegel, Armand (b. 1914): 128, 129, 131 Simeone, S.A. 198 Vallarta, M. S. (b. 1899): 120, 203 Sinclair, Upton (1878-1968): 362 Van de Graaff, Robert J. 367 Singleton, H. E. (b. 1916): 211 Veblen, Oswald (1880-1960): 63,68,75, Smith, Adam (1723-1790): 281 85,95, 167,363 Smoluchowski, M.V. 55,79,241 Verne, Jules (1828-1905): 37,335 Snow, Sir C. P. (b. 1905): 359,400 Vico, Giambattista (1668-1744): 62, 255, Sobolev, S. L. (b. 1908): 101 277, 325 406 Name Index

Vigier, J.P. 129 Wiener, Bertha Kahn (mother) 30, 371 Vinci da, Leonardo (1452-1519): 18,343 Wiener, Constance (sister) (b. 1898): 30, Voltaire, F.M. (1694--1778): 122 35 Volterra, Vito (1860-1940): 77,163,264, Wiener, Fritz (brother) (b. 1906): 30 266, 271 Wiener, Leo (father) Von Foerster, Heinz 248 (1862-1939): 29-47,67,94,335,361, Von Laue, Max (1879-1960): 111 371 Von Mises, R. (1883-1953): 86 Wiener, Margaret (wife) (b. 1894): 38, Von Neumann, John (1903-1957): 50, 94, 95, 372 51-52,109,119,129,131,140,141, Wiener, Peggy (Margaret) (daughter) 184, 225, 232, 237, 239-242, 247, 248, (b. 1929): 94, 339 268,290,295,297,303,310-315,335, Wiener, Philip P. (b. 1905): 369 345, 373, 396, 400, 401 Wiener, Solomon (grandfather) 29 Wiesner, J. (b. 1915): 211,212,228 Walsh, J. L. (1895-1973): 360 Wigner, E.P. (b. 1902): 367,402 Walter, W. Grey (1910-1977): 212,234, Wilder, R.L. (b. 1896): 77 237,240,251,401 Wilhelm II, Emperor (1871-1918): 32 Walton, E. T. S. (b. 1903): 367 William of Ockham (c. 1200-1259): 62 Watson, J.D. (b. 1928): 20,401 Wilson, Woodrow (1856-1924): 67 Watt, James (1736-1819): 252 Witner, A. (1903-1958): 141, 151,204 Watts, A.W. (1915-1973): 25,401 Wittgenstein, Ludwig (1889-1951): 52, Weaver, Warren (1894--1978): 183, 192, 53, 57,402 207, 391 Wold, H. 193 Weiss, P.R. 391 Wolf, J. 111, 393 Wells, H.G. (1866-1946): 37,335 Wolfson, Harry A. (1887-1974): 69 Weyl, Hermann (1885-1955): 53, 115, Womack, J. Printise 275-276 120, 151,200,225, 345, 368, 369, 401 Wrinch, Dorothy 245 Whitehead, Alfred North (1861-1947): 21,25,43,45,50,56,59, Yaglom, A.M. 113,193,401 72,93, 199,220,259,277,324,334, Young, L. C. (b. 1905): 136 346, 361, 367, 368, 369, 402 Young, R. C. 136 Whittaker, Sir Edmund Young, W.H. (1863-1942): 136 (1873-1956): 118,402 Wiener, Barbara (daughter) Zangwill, Israel (1864--1926): 34 (b. 1928): 94 Zermelo, E. (1871-1953): 51 Wiener, Bertha (sister) (b. 1902): 30, 35 Zygmund, A. (b. 1900): 84 407

Subject Index

Aberdeen Proving Grounds 61, 63, 68, Automatic factory 272-273 372 Automatization 15,25,51,272,273 Abduction 62 Avogadro's Law 148 Academie Francaise 358, 359 Avogadro's number 82 Accademia dei Lincei 358 Ayer High School 37, 371 Active and passive mechanisms 202 Axons 207, 213 Albany, New York 67 Algorithm 219,220 Alice in Wonderland 93, 152 American Mathematical Society Banach algebras 108, 241 1934 Colloquium Lectures 137, 372 Banach space 76, 114 1940 Dartmouth meeting 172 Ballistics 68, 187 1949 J.W. Gibbs Lecture 373 Bangor, Maine 65 American Society of Mechanical Bell Telephone Laboratories 228, 305 Engineers 277 Bergsonian philosophy 57, 58 Analysis situs 63 Bergsonian time 151-153 Angelos 251 Bertrand Russell Editorial Project 18 Animal feedback (homeostatic, postural, Bessell identity 104-105, 107 voluntary) 210-211 Binary scale 172 Anti-aircraft fire control 181 Birkhoff's ergodic theorem 110, 132, cranking 189 139, 140, 141, 149, 150 error of performance 186, 187 Bocher Prize 108, 372 predictor 187 Bochner's theorem 113 transient errors 189 Boolean algebra 73, 74, 89, 221 Arabian Nights 316 Borel measurability 83, 90 Art Boston 362 Dante's view of 343 Boston Arm (and Elbow) 229-231 Eckhart's view of 343 Boston Herald 71, 372 presentative aspect of 344 Boston police strike 362 representative aspect of 344 Brain 214 Arthasastra 287 Brain-mind dualism 198, 306 Artist and Artisan 343, 346 Brain-wave encephalography 227, 233, Atomic diplomacy 295, 311 234, 235-236 Atomic energy Bridge on the River Kwai 338 and Oakridge National Brownian motion 55,79-86,88,90,91, Laboratory 312 102 and Price-Anderson Act 312 and heat equation 84 Atomic warfare and potential theory 88 atomic bomb 301,310 and quantum mechanics 128-131 atomic bombing of Japan 296, 298 and random 130-131 civil defense 301 and shot effect 85 Litianthal Report 311 as input 264-266 Attica prison 351-353 as noise 143 Einstein's theory of 81-83 game-playing automata 304, 305, 306, flow of 140-141 355-356 idealized 83-86 type-classification in 52, 306 Bureaucracy 92-93, 170, 286-287, 338 Automatic control 272 Bush differential analyzer 160, 181 408 Subject Index

Bush integraph 160, 161 Controlled experiment 152 Bush network analyzer 160 Convex bodies 72 Convolution filters 10 I, 107, 163-164, Calculi (logical) 54 177-179 Calculus of variations 186 Convolution integrals 101, 106, 107, 264 Calculus ratiocinator 219, 221 Copyright 338 Cambridge University 45,66, 122, 136, Curl 23 Cybernetics (defined) 256 372 Causal operators 101 cybernetical attitude 239-240, 253-256 Causality and analyticity 101, 134-135 Cybernetical Circle 239 Cell, complexity of 244-245 origin of idea of 56, 57, 58 Chaotic integrals 265 origin of name of 251-252 Chess-playing automata 304-305, Soviet attitudes toward 260-261 355-356 Child training, Leo Wiener's views Deterministic 141-142 on 35 Diagonalization procedure 48 Clonus (see Muscle clonus) Dialectic duality 25-26 Coherence of light 110--111 Dialetic materialism 293 Coherency matrix 110--111 Dirichlet problem 87-88, 171, 180 Cold War 313 Docent Lectures 62-64 Columbia Medical School 218 Dual nature of light 25-26, 116 Columbia University 61, 371 Duty 66, 125, 327 Communication 152 (see also Dynamical system Information) coefficients of inertia 157 and time scales 307-308 conservative 142 as social cement 288 deterministic 141-142 channels of 288-289 Hamiltonian 142, 157 communal information and Hamilton's canonical equations 142 cohesiveness 288 kinetic energy 157 communications engineering 101-102, phase space 142 206 potential (energy) 87, 157 Communism 332 state space 142 Communists 293, 294 Complementarity 116-117 Complex number field C 89 Econometrics 291 Computer (see also Turing machine) Economic planning 285-286, 329 abacus 171 (U.S.) 281-283 all-purpose 219 acquisitiveness in 283, 284 analogue 110, 160-161 alienation in 284 as prosthesis for the brain 232, 233 and hard-work ethic 283 data-storage by tape 172, 173, 174 credit-card hedonism in 283-284 digital 171 entrepreneurship in 282 electronic 15, 172, 224 investments in 282-283 ENIAC 174, 239, 244 irreligious aspect of 284 exchangeability of time and market as n-person game in 281 space 226-227 promotion in 283 necessity for high speed 171-172, 173 volatility of 283 program 220, 238 Education 277-281 special purpose 171 and Parent Teachers Association special purpose digital 219 (PTA) 281 solution of PDE's by scanning and teachers' colleges 280 179-180 and teachers' trade unions 281 transistorized 174 damage from harshness in 35 use of vacuum tubes in 172, 174 decline of in U.S. 281 Computing machines (see Computer) John Dewey's ideas on 277-280 Conditional Banach spaces 114 quackery in public schools 280 Consonance 253 Electric engineering 10 I-I 02 Contest 268 Electric filters Control (see Anti-aircraft fire control; amplitude response function 165 Automatic control; Homeostasis; causality (physical realizability) 101, Animal feedback) 138, 163-164 Subject Index 409

frequency response function 164, 165 non-differentiable 79, 84 linearity 101 periodic 97 lumped-passive 164, 176 84 phase-response function 165 weighting function 163 Electric networks (see Electric filters) Gadget-worship 171 Electrodynamometer 160 Game theory 268-269, 286, 287, 290, Electroencephalogram (EEG) 233 (see 303, 306, 309 also Brain-wave encephalography) Gating mechanism 236 Electromagnetic theory of light 24, 109 Gauge theory 120 Electron microscopy 245, 246 Gene-reproduction 124 Electronic computer 15, 172, 224 General Electric 67 Electronic Age 25 Generalized Harmonic Analysis Encvclopedia Americana 67 372 (GHA) 102, 104--105, 184 Energy 87, 148, 157 ' almost periodic functions 104, 141 ENIAC 174, 239, 244 (auto-)covariance (or correlation) Entrainment of frequency 237 function 102, 110, 113, 186 Entropy (see Thermodynamics) cross-covariance 110 Ergodic hypotheses 146-147 Einstein's contributions to 112-113 Ethics 58, 125, 311, 327 Generalized Bessel identity 104--105 altruism 125, 327 generalized Fourier coefficients 141 conscience 58 generalized 104 duty 66, 125, 327, 328 periodogram 104 vocation 327 spectral distribution and densitv 104, 112, 113 ' Evil analogy of, with entropy 319 total mean-power 109 as corruption 319 (see also Fall of Geometry man) Einstein's views on 53, 72 moral 319, 322 Euclidean 73, 342 natural 319 Greek conception of 73 non-eradicability of 319 Kant's views on 71-72 phylogenetic origins of 319, 320 non-Euclidean 73 St. Augustine's views on 318,319 321 German intellectual tradition 32-33 Explication 72 ' German romantic movement 341, 342 Extensive abstraction 56 Gestalt (see Pattern) Glasnost 293 Gleason's theorem 128 God (Logos) 25, 292, 330, 332-334 Jehovah 333 Fall of man 321,323-324 of Spinoza 25, 292, 333, 345 Feedback 169,201,202 (see also Animal personal 333 feedback) Giidel number 346 anticipationary 191 Giidel incompleteness double 210 metatheorem 52-53 negative 202 Gorgias 252 Feedback circuit, in muscular Giittingen University 56, 59-60, 105, clonus 206 117, 371 Field 99, 208 Gravitational force 23 Final cause 203 Guggenheim Fellowship 105, 372 Flight prediction, statistical aspect 184, Gulliver's Travels 335 190 Foreign policy (U,S,) Eisenhower-Dulles 311 Harmonic (Fourier) Analysis 96--100, Truman-Acheson 295,311 245-246 Fourier's series; Fourier transform' characters 97-98, 100 Fourier-Stieltjes transform (sce ' Fourier coefficients 97-98. 100 Harmonic analysis) Fourier series 97-98, 107, 135 Fractals 85, 291 Fourier-Stieltjes transform 98-99, 104. Function 112, 195 Borel measurable 90 Fourier (and Planche reI) Hermite 270 transforms 98, 101, 104-105, 107, Laguerre 164--165 112,114,115,134.136-137,177 410 Subject Index

pure tone 96 Inquiry 268 sin usoidal curve 97 Instruments 186, 187 Harmonic analyzer 161 limitations of 143, 146 Harvard Lampoon 362 response time (or latency) 109 Harvard reserve regiment 66--67, 371 Instrumentation theory 186, 187, 195, Harvard University 39-41, 43-44, 196 63-64, 361-362 Integraph 160,161,162,175-176 Hausdorff dimension 83, 85, 90, 91 International Copyright Convention 337 Heart, human 204 International Mathematical Congresses auricles 204 1920 Strasbourg 75, 372 dis tole 204 1932 Zurich 136, 166,372 fibrillation 204 1936 Oslo 170,231,372 flutter 204 1950 Cambridge, Mass. 373 sistole 204 Iron lung 229 tonic-clonic cortical Isomorphism 200 responses 204-205 Heat equation 84 Jacquard loom 219 Heaviside operational calculus 100, 160 Japan, atomic bombing of 296, 298, 323 Hebraiche Melodien 335 Jewish Numeras Clausus 32,361-362, Helices (spirals) 108, 114, 195 363 Hidden parameters 129 Jewish question 30-32,41-43, 59 Hidden periodicities 104, 112-113 John Thornton Kirkland Fellow 44, 371 Highest good 58 Josiah Macy Foundation 205, 373 Hilbert space 26, 108, 114, 118-119, Judaism 42 128-129, 131, 193, 195,241 Juniata College 94 Hilbert transform 165-166 History, episodic view of 297-298, 302 Kinesthetic organs (proprioceptors) 213 Hitopedesa 287 Klein-Gordon equation 120 Holography III Kolmogorov-Wiener prediction Homeostasis 34 theory 193 breakdown of 331 Korean War 273, 299, 300 homeostatic diseases 211 homeostatic feedback 210 Labor, American 212 migrant 275-277 Hominids 322, 323 retraining of 277 Homogeneous chaos 149 Lag mechanisms 19 I Homogeneous random fields 141 Laguerre functions 164-165, 177 Homo peccator 322 Laplace's equation 87 Homo sapiens 322 Latency 191 Hopf-Wiener integral equation 133-134, Lead mechanisms 191 186,241 Learning 152-153,262-264 (see also Hunting 201 Education) Learning mechanisms (machines) 58, Idealization 72, 116, 122, 184,258-259, 262 326 Lebesgue integral and measure 78, 83, Incoherent signals 110-111 99, 104, 140 Indeterminism 146, 253, 254-255, 290, Lee-Wiener network 163-165,177-179, 291,318 (see also Uncertainty 195, 264, 270 principle) Leibnizian philosophy 121-122, Indian Statistical Institute 193, 285, 351, 125-128,219 373 calculus ratiocinator 219,220 Industrial revolutions (First, Second, machina ratiocinatrix 219, 220 Third) 249,272,273,281,346 monads 121, 125-126 Infinite (actual) 59 principle of identity of 153-156 indiscernibles 121 communal 288 principle of sufficient reason 121-122, informative value of a 126 message 153-154 Leukemia 211 loss of 228, 229 Libertinism 47 misuse of 288-289 Linear operator 99-100 optical III, 228 Linear partial differential equations 99 Subject Index 411

Little Doritt 287 Molecular biology 248-250 Logic 22, 48---49 Monads 121, 125-126 (see also Logical empiricism 53, 54 Leibnizian philosophy) Logos (see God) Monkey's Paw, The 316 Monogenism 321,323-324 Machine 256 Monte Carlo method 151 Multivariate prediction 193, 297 Machine intelligence, creativity, tropism 212, 346--348 (see also Muscle clonus 205-207 Computers) Music, musical notation 116 Homeostat (machina sopora) 212 Mutualistic Societies in America 29-30 machina ratiocinatrix 219-222 Myopia 37 machina speculatrix ("tortoise") 212 Myths 324-325 "moth-bedbug" 211 Mythic mode of perception 25, 324-326 reproducing machines (see Self- Mythology 325-326 reproducing mechanism) Machine-man concatenation 188-189, Name and object 325 310 National Academy of Sciences "Mad Tea Party" of Trinity 56 (U.S.) 356--358,360-361,373 Project 310 National Defense Research Committee Marxism 292, 293, 294 (NDRC) 181-182,373 Massachusetts General Hospital 234 Project DJ.C. 5980 182 Massachusetts Institute of Technology National Institute of Cardiology, (MIT) 71,92,96, 181,207,218,234, Mexico 197,207 372 National Medical of Science 15,364 MIT Autocorrelator 234, 235 National University of Mexico 373 MIT Radiation Laboratory 349 Negentropy 155 Masters, The 359 Nerves 215 Mathematician's credo 341 , human 213,243 Mathematics action potential 213 aesthetical aspects of 22-25, 54 afferen t nerves 215 as fine art 341-343, 344, 345 autonomic 215 Halmos's views on 345 center of nerve 215 of 54 central 202,213 role of in the empirical realm 23-28, efferent nerves 215 53-54, 258, 259 gating 236 Mathology 345, 346 gray matter 213 Mathophysics 345, 346 mixed nerves 215 Maximal ideal 114 parasympathetic 215 Maxwell's demon 155-156,325 peripheral 214 Maxwell's equations 24, 119 physiological clock 236 McMaster University 18 reflex action 208 Memory 152 spatial summation 214 Mengenlehre 368 sympathetic 215 Merton College, Oxford 60 synapse 213 Message 19,239,251,256-257 synaptic delay 214 Metalanguage 50, 57 synaptic excitation 208 Metamathematics 50, 55, 56-57 temporal summation 214 Metric space 76 white matter 213 Mexican Mathematical Society 203, 373 Neuron 213 Mexico 203 association 214 Michelson interferometer 110 axons 207, 213 Military mind 296 cytoplasm 213 Military science (see also War) dendrites 213 continual reconnaissance 307-308, excitatory 214 310, 354-355 firing of 213,214 type classification in 303-305, 309 inhibitory 214 Mind, human irritability of 213 computing abilities of 223, 224 motor 214 pattern recognizing abilities nucleus of 213 of 225-226 quiet 214 Misinformation 289 refractory period of 214 412 Subject Index

resting state of axon 2 \3 Plattsburg, New York 66 sensory 214 Poetry 25 Neurophysiology 249, 250 Polarization of light III analogical aspects of 244, 262-263 Polynomial chaos 150 New England (democracy of) 34, 38, Postulate systems 73-79 289 Potential theory 86-88 New York Times 15,229 capacity 88 Newtonian mechanics (see Dynamical Dirichlet problem 87-88 system) the potential 87 Noise 19,143 Potentiometer 160 Non-linear filters (networks, Power engineering 102 transducers) 264-267,270--271 Pragmaticism 62 Nucleic acid complexes 249 Pragmatism 39, 57, 62 Prediction theory 193 Observation, photometic nature of 119 Prime number theorem 107 Observer-observed coupling 127-128, Principia Mathematica 45, 48, 50, 52, 53, 289, 290, 291 54, 55, 93, 220, 240 On a Balcony 30 Principle of least action 121 Ontogenetic learning 262-263 Probability distribution 86 Operationalism 121 Probability theory 86 Operator Project D.LC. 5980 182 linear 99-100 Prometheus 325, 332 non-linear 264 Proprioceptors (kinesthetic organs) 213 Optics 109-112 Prosthesis (muscular-skeletal and brightness 109 sensory) 227-231 coherence 110-111 Boston Arm 229-231 Michelson interferometer 110 Iron lung 229 photometer 109 sound communication with the polarized light III deaf 228-229 Optical depth 132 Protein molecule 124 (couple) 55 Psychic signs 325 Organization 96 Pure tone 96, 115 Purpose (see Teleology) Paley-Wiener criterion 138 Purpose tremor 20 I Paradise Lost 93 Purposive action 124 Paradoxes 48-50, 52 Parkinsonianism 210 Quantum mechanics 26,115-131 Partial differential equations 99 degeneracy 123 parobolic 174 hidden parameters 129, 131 Particle-wave dichotomy 26, 27, 121 potential barrier 123 Pa th integral 128 pure state 128, 131 Pattern (Gestalt) 96, 244 role of Brownian motion in 128-131 as group-invariant 225 self-repair in 123 Pattern recognition 15, 225-226 state 128 apparition 225 Quasi-analytic functions 169 limitations of theory of 244 Quasi-ergodic hypothesis 147 Peabody School 35,37,371 Quickening 191 Peano's postulates 53, 65, 73 Perception Radiative equilibrium 132 logical mode of 25 Ramakrishna Vedanta Society of mythic mode of 25, 325 Boston 370 sensory 199-200 Recursion 50, 53 Philosophies of mathematics 54 Reflex action 208-209 Philosophy of Science Club 197 Refugee scientists 167-168 Photometer 109 Relation structure 199, 200 Photosynthesis 156 Relation theory 50, 55, 63-64 Phylogenetic corruption 321,323-324 Relativism 57, 58, 60 Phylogenetic learning 263-264 Relativity theory 26, 120 Physiological clock 236-237 Religion (see also Evil; Fall of man; God) Planning 285, 329 "acts of God" 330 Platonism 258-260 "acts of Grace" 330, 332 Subject Index 413

Adam and Eve 321 Shot effect 85 and science 324, 330, 333-334 Signal 19, 102 (see also Information Black Mass 315-316 theory) Grace 321 Signal detection 257 role of death 319 Simony 316 self-alienation 322 Sin 322 (see also Evil) simony 316 Sinusoidal curve 97 sin 322 Social cohesiveness 289 Republic 43, 67 Society for the Advancement of Retrospective operator 101 Management 276, 277 Riemann zeta function 107 , observer-observed coupling Ritual 324 in 289 Robot arm 232-233 Sorcerer's Apprentice 316 Rockefeller Foundation 205, 207 Sorcery 316 Royal Society 358, 359 South Tamworth, New Hampshire 38 Russell's antinomy ("paradox") 48-50, Soviet attitudes 229,251,260-261,314 52 Space-time continuum 26 Spectral distribution and density 104, Sage School of Philosophy 40, 41, 371 112, 113 Spectral synthesis 108, 114 Scannmg 171, 173, 179-180,226-227 Schwartz distribution 100 Spectral theory of operators 193 Spike potential 207,215-217 Science fiction 335-336 differential equation of 217 Science and human welfare 285,291, Hermann model 216 292,311,314-315,329-330 Spinal cord 208, 209 Scientific methodology Spinoza's God 25, 292, 333, 345 centrality of relation-structure 198, Spirals (helices) 108, 114, 195 199,200 State, the 328, 329 complementarity 116-117,127-128 Stationary random measure 149 195 cybernetical augmentation of 253-255, Stationary sequences 193, 195 ' 257 Statistical mechanics explication 72 and communications engineering 102, faith as a part of 24-25, 326 154-155 function of science 358 Boltzmann's H-theorem 149 idealization as a part of 258-260, 326 incomplete orderliness of the complexion of a gas 159 ergodic hypothesis 146 world 146 ergodic theorem for homogeneous instrumental limitation 143, 146 chaos 150 logical empiricist theses 53-54 Maxwell's demon 155-156 325 mythic perception as a part of 25, microstate of a gas 158 ' 324-326 quasi-ergodic hypothesis 147 nature of inquiry 268-269 statistical entropy 148 nature of logic 53-54, 222-223 Statistical thermodynamics 148 observer-observed coupling 127, 289, Stochastic integration 84, 150 290, 291 Stokes's theorem 23 organization of empirical data 41, 72 Stratagem 267-269, 286-287, 303-306, place of electronic computer in 232 233 ' 307,309,316-317 Strategic evaluations 306 propaedeutic role of mathematics in 22-28, 367, 368 Strategic learning 268 Switching networks 221 Secrecy 191, 192, 299 Symbolism, mathematical 21-28 Self-alienation 322 Synthetic a priori 71,72 Self-organizing systems 236, 237, 246 Synthetic logic 63 Self-reproducing mechanisms 246, Synapse 213 263-264, 266-267, 269 Semi-exact sciences 290 Sensory prosthesis (see Prosthesis) Servomechanisms 189,202,210 Tala Institute of Fundamental Set, concept of 48 Research 373 Shannon-Wiener information theory (see Tauberian theory 105-108 Information theory) Tchestnost 293 Sheffer's connective 74 Teleological Society 239 414 Subject Index

Teleology 57, 124, 152-153,201-202, Universal Turing machine (see Turing 253, 368 machine) purposive mechanism 202, 262, 268 University of London 94 teleological mechanism 202, 226 University of Maine 65 Television scanning 171, 173 94 Templer, The 336 University of Missouri 30 Tensor 26 University of Nancago 251 Terry Lectures 306, 331, 374 USSR 313,314 (see also Soviet Theory of messages 251 (see also attitudes) Message) Thermodynamics Values (see Ethics) absolute temperature 148, 157 Vector 23, 75-76 adiabatic transformation 147, 157 Vector space (metric, normed) 75-76,78 Caratheodory's principle 157 Virus 244-245, 248 empirical temperature 157 Vocation 327 entropy 147, 157 Vocoder 228 Helmholtz free energy 148 Voluntary activity 188-189 internal energy 157 state space J 47 War (see also Military science) Time absolute 303, 313, 316-317 anistropic 57. 152 effects of on scientific morale 298-299 Bergsonian 58, 152 military and political phases of 302, Newtonian 58 313,316-317 Time Series· real 302, 313, 316-317 Topological transformation 75 war games 306-307 Topology 62-63,74-75 Wave equation 24 Traclatus logico-philosphicus 53, 54 Wavicle 26 Trade union consciousness 275 Wiener class S 102-104, 184 Tragedy and catharsis 331-332 Wiener integraph 162,175-176 Transducers 256, 308 Wiener measure 83 Transfinite induction 48 Wiener process (see Brownian motion, Transformation (see Operator) idealized) Tsing Hua University 168, 372 Wiener-Hermite representation 271 Tufts College 39, 371 Wiener Tauberian theorem 107 Turbulence 79, 151 Wiener, Norbert Turing machine 173,219,220,221,222, absentmindedness of 349 223, 238, 346, 348 analogical mind of 366, 367 Type theory 47, 50-52 as lecturer 353-355 doctoral dissertation of 43-44 Uncertainty principle 115-117, 119, 129 early suffering of 16, 35, 41-43 Unified field theory 120 ideas on historical continuity United Automobile Workers of America of 368-369 (UA W) 273-275 literary style of 354 marriage of 94 military thought of 300-302,309-310 premature writings of 18, 358 • This term, occurring in Wiener's lexi• quirkishness of 349, 350 con, and meaning a function on the temperament of 16, 19,20,349,350, time-domain the values of which are 351 empirical data, is replaced in the book vegetarianism of 59 by terms such as input signal, output signal, signaL "Yellow peril" 182 415

Photograph Index and Credits

Norbert Wiener. 1945 (Frontispiece, p.2). Sir Arthur Schuster (p. 103). Courtesy of Courtesy of Mrs. Margaret Wiener. The Royal Society, London. America's first Leibniz (p. 17). Courtesy of Sir Geoffrey Taylor (p. 103), Reprinted Dr. William A. Stanley, National Ocean• from: The Scientific Papers of G.1. Tay• ic and Atmospheric Administration, lor, Vol. 4, ed. by G.K. Batchelor, New Washington, D.C. York 1971. Courtesy of Cambridge Uni• Figure 1 (Chalice or face profiles?) and Fig• versi ty Press. ure 2 (The wave-particle or "wavicle") G.H. Hardy (p. 106): Courtesy of Birk• (p. 27). Reprinted from: James Jeans: hiiuser Boston Inc. New Background of Science, New York 1933, Frontispiece. Wiener with Max Born (p. 118). Courtesy of The MIT Museum (Photo NW I). Bertha and Leo Wiener, parents of Norbert Wiener (p.31). Courtesy of The MIT Gofffried Wilhelm Leibniz (p. 126). Cour• Museum (Photo NW 81). tesy of Dr. E. A. Fellmann, Euler Archiv Norbert Wiener at age seven (p. 36). Cour• Basel. tesy of The MIT Museum (Photo NW J.B.S. Haldane (p. 127). Reprinted from: 39). Living Philosophers, New York 1931, Norbert Wiener in 1912 just before he re• p. 324. Courtesy of Harper and Row ceived his doctorate from Havard (p. 44). Publishers Inc. Courtesy of the MIT Museum (Photo (p. 133). Courtesy of The NW 60). MIT Museum (Photo EH I). Bertrand Russell (p.51). Reprinted from: R.E.A. C. Paley (p. 137). Copyright Elwin Autobiography of Bertrand Russell, Lit• Neame. Reprinted from: Fourier Trans• tie, Brown & Co., Boston 1968, p. 277. forms in the Complex Domain, Norbert Wiener in army uniform (p. 69). R.E.A.C. Paley and N. Wiener, Ameri• Courtesy of The MIT Museum (Photo can Mathematical Society Colloquium NW 46). Publications (1934), Vol. 19, by permis• sion of the American Mathematical Soci• Albert Einstein (p. 80). Reprinted from: ety. G. Kuznecov: Einstein. Leben-Tod-Un• sterblichkeit, Birkhiiuser Verlag, Basel J.-B. Fourier (p. 144). Reprinted from: 1977, Abb. 5. I. Grattan-Guinness: Joseph Fourier 1768-1830, MIT Press, Cambridge MA J.B. Perrin (p. 81). Courtesy of Dr. Francis 1972 (Plate 4). Courtesy of Archives de Perrin. l'Academie des Sciences de Paris. Marguerite Engemann in 1926 (p.95). Courtesy of The MIT Museum (Photo H. Lebesgue (p. 144). Courtesy of Birk• NW 89). hiiuser Boston Inc. Lord Kelvin (p. 103). Courtesy of The Royal J. W. Gibbs (p. 145). Courtesy of AlP Niels Society, London. Bohr Library. Lord Rayleigh (p. 103). Courtesy of The G.D. Birkhoff (p. 145). Reprinted from: Royal Society, London. G.D. Birkhoff: Collected Mathematical Papers (1950), by permission of the Sir (p. 103). Reprinted American Mathematical Society. from: O.K. McClerey: Introduction to Transients, New York 1961, Frontis• C. E. Shannon (p. 155). Courtesy of The piece. Courtesy of Wiley & Sons Inc. MIT Museum (Photo CES 1). 416 Photograph Index

Vannevar Bush (p. 166). Courtesy of The zigsten Jahrhunderts. Heinz Moos Ver• MIT Museum (Photo VB 2). lag, Heidelberg 1966. Y. W. Lee (p. 167). Courtesy of The MIT William Ross Ashby (p. 259). Courtesy of Museum (Photo YWL 2). Professor N. N. Rao, Electrical & Com• Wiener with colleagues (p. 169). Courtesy of puter Engineering Department, Uni• The MIT Museum (Photo NW 67). versity of Illinois. Julian Bigelow (p. 183). Courtesy of Mr. Walter Reuther (p. 274). Courtesy of Mrs. Julian Bigelow. Norma Bogovich, UA W Public Rela• tions and Publications Department De• Academician Andre Kolmogorov (p. 194). troit, MI. Photo by Alexander Archer, Courtesy of Birkhiiuser Boston Inc. UAW Solidarity Magazine. Arturo Rosenblueth (p. 199). Courtesy of John Dewey (p. 278). Reprinted from: Mrs. Virginia Rosenblueth. Living Philosophers, New York 1931, Norbert Wiener with Drs. J. Weisner and p. 21. Courtesy of Simon & Schuster. Y.K. Lee (p. 212). Courtesy of The MIT Chess playing automaton, built by Tores y Museum (Photo NW 26). Quevedo in 1890: (p.304). Courtesy of Warren McCulloch (p.222). Courtesy of The MIT Museum (Photo NW 55). The MIT Museum (Photo WSM 4). Chess pla,ring automaton, the Belle (p. 305). Walter Pills (p. 224). Courtesy of The MIT Courtesy of Dr. Kenneth Thompson, Museum (Photo WHP I). Belle Telephone Laboraties.

The Boston Arm (p. 230). Courtesy of Mr. St. Augustine in His Stu,~v (p. 320). Cour• T. Walley Williams, Liberty Mutual In• tesy of Scala Istituto Fo\ografico Edito• surance Company, Boston. riale S.p.A., Firenze. The Boston Elbow (p. 231). Courtesy of Mr. Homo peccator (p. 323). Courtesy of Rin• T. Walley Williams, Liberty Mutual In• gier Dokumentationszentrum Ziirich. surance Company, Boston. (Photo WK 2 Japan II Dukas, Hiro• W. Grey Walter (p. 235). Courtesy of Bur• shima (G 0136232)). den Neurological Institute. Norbert Wiener in the (p. 364). John von Neumann (p. 247). Courtesy of the Courtesy of The MIT Museum (Photo Niels Bohr Institut. NW 14). Henri Bergson (p. 255). Reprinted from: Norbert Wiener at the White House (p. 364). Willy Haas: Nobelpreistrager der Litera• Courtesy of The MIT Museum (Photo tur. Ein Kapitel Weltliteratur des zwan- NW 51).