Albert Einstein and Max Wertheimer: A Gestalt Psychologist's View of the Genesis of Special Relativity Theory

Cafe. Jones E. , The life and work of Sigmund Freud, ed. and abridged by Trilling L. Marcus S. , introduction by Trilling L. (Garden City, 1963), 493–4.

Private communication from Wertheimer's elder son Mr Valentin Wertheimer. Wertheimer discovered that sound travels to the brain at different speeds from the left and right ears. The left-right localization of sound is a function of the difference in time with which the sound wave strikes the two ears. Wertheimer designed a helmet with two protruding tubes at the location of the ears, which can be adjusted to ensure that both ears are stimulated simultaneously. For further discussion of Wertheimer's post-war researches on this problem see Koffka K. , Principles of gestalt psychology (New York, 1935), 219ff.

Köhler W. , Die physischen Gestalten in Ruhe und im stationären Zustand (Brunswick, 1920).

The kinship that the gestalt psychologists felt for the physicists surfaced many times in their writings: Köhler in his lectures delivered in 1966 at Princeton University took passages from Clerk Maxwell's Treatise on electricity and magnetism, published in 1873, and from a set of lectures given by Max Planck in 1909 to demonstrate that they were unknowingly working and expressing their thought along the guidelines of gestalt psychology—a subject not yet formulated until 1912. See Köhler W. , The task of gestalt psychology (Princeton, 1969), 58–62.

Wertheimer M. , “Relativity and gestalt: A note on Albert Einstein and Max Wertheimer”, Journal of the history of the behavioral sciences, i (1965), 86–87. Professor Michael Wertheimer is Max Wertheimer's younger son. I thank Professor Rand Evans for alerting me to this essay, and Mr V. Wertheimer for a copy of Einstein's original foreword in German. The volume was never published and hence this is, as far as I know, the only place where an English translation can be found. I have slightly corrected the translation.

Einstein's seminal paper on relativity is “Zur Elektrodynamik bewegter Körper”, Annalen der Physik, xvii (1905), 891–921. Reprinted in The principle of relativity: A collection of original memoirs on the special and general theory of relativity by Lorentz H. A. Einstein A. Minkowski H. Weyl H. , tr. by Perrett W. Jeffery G. B. (New York, n.d.), 37–65. This reprint volume will be referred to as PRC, and all references will be to PRC.

Wertheimer M. , Productive thinking (1st ed., New York, 1945; 2nd enlarged ed., 1959). The only changes from the first edition are the additions of three new chapters and six appendices, found among Wertheimer's notes by Professor Michael Wertheimer. However, the chapter on Einstein is unchanged in the two editions. All references will be to the more available enlarged edition of 1959, though my discussion does not need or make use of the added material.

Wertheimer , Productive thinking, xii.

Ibid., 213.

The gestalt theory of thinking c. 1943 was not as well developed as the gestalt theory of perception. Cf. Koffka , Principles (ref. 2), 615. Here Koffka expresses his hope “that Wertheimer will before long publish the results of the work which he did in this field [the gestalt theory of thinking] for many years”.

Wertheimer , Productive thinking, 212.

Ibid., 239.

Ibid., 245.

Ibid. , 205–12. Wertheimer presents in chap. 9, “A discovery of Galileo”, a gestalt reconstruction of Galileo's thought that supposedly led to his deduction of a law of inertia using a perfect sphere and an inclined plane, as presented in Dialogue concerning the two chief world systems , tr. Drake S. (Berkeley, 1967), 145–8. Wertheimer conjectures that Galileo was led by “the structural principle of the whole”, a gestalt law that borders on the quasi-aesthetic, to devise a crucial experiment. Yet another difference between Galileo's supposed crucial experiment and Einstein's supposed crucial experiment (i.e., the Michelson–Morley experiment), is that Galileo's is possible only in principle—one cannot observe forever the motion of a body rolling on a plane of infinite extent.

Wertheimer , Productive thinking, 212.

Loc. cit.

Ibid., 239. In analogy with vectors in physics, vectors in gestalt psychology possess “direction, quality and intensity” (p. 238).

Ibid., 212.

Ibid., 229.

Ibid., 212.

Ibid., 244.

Ibid., 239.

Ibid., 237.

Ibid., 11.

Ibid., xvi.

Ibid., 234.

Ibid., 3.

Shankland R. S. , “Conversations with Albert Einstein. ii”, American journal of physics, xli (1973), 895–901. Shankland writes (p. 898): “This writer finds the account of Wertheimer entirely consistent with his own notes and recollections of Einstein's attitude in 1952 toward the Michelson-Morley experiment”. However, they are entirely antithetical to Shankland's publication of 1963 (“Conversations with Albert Einstein”, American journal of physics, xxxi (1963), 47–57) of his discussions with Einstein in 1952, and in particular with every quotation of Einstein's words in 1950, 1952 and 1954 given in Shankland's 1963 article. The 1973 paper is consistent with Shankland's view of the matter which he had published in 1950 prior to his interviews with Einstein (“Michelson 1852–1931, Expérience de base la relativité”, in Les inventeurs célèbres—sciences physiques et applications (Paris, 1950), pp. 254–5.

Grünbaum A. , Philosophical problems of space and time (1st ed., New York, 1963; 2nd enlarged ed., Boston, 1973), esp. chaps 12, 21 and the Appendix to chap. 12 on pp. 834–9. All references will be to the second enlarged edition. Grünbaum writes that his “philosophical analysis” of the genesis of special relativity theory is “attested by the historical account that Einstein gave to Wertheimer as well as by his ‘Autobiographical Notes’” (p. 714).

Gutting G. , “Einstein's discovery of special relativity”, Philosophy of science, xlix (1972), 51–67. Gutting writes (p. 57): “By far the most thorough and explicit account of the discovery of special relativity is that given by Max Wertheimer, based on his own extensive conversations with Einstein in 1916”.

Schaffner K. , “Einstein versus Lorentz: Research programmes and the logic of comparative theory evaluation”, The British journal for the philosophy of science, xxv (1974), 45–78. Schaffner writes: “In the Einstein literature there seems to be only one source which explicitly touches on the crucial stage of Einstein's reasoning when he conjectured that the classical conceptions of time and simultaneity might require reanalysis. The source is Wertheimer's account” (p. 65). Schaffner continues: “… it may not be unimportant that, though the above [Wertheimer's] scenario was developed prior to the availability of Shankland's very recent and significant ‘Conversations with Albert Einstein, ii’ [1973] it would appear that this new evidence is in complete accord with the above [Schaffner's] reconstruction. Shankland finds the Wertheimer account completely reliable …” (p. 67).

Wertheimer , Productive thinking , 8. Thus, Gutting's assessment of Wertheimer's account of Einstein's thought is incorrect (op. cit. (ref. 30), 53): “There is no evidence that STR as a whole came to him [Einstein] as a flash of insight or a lucky guess. Rather, as Wertheimer points out, each step Einstein took was guided by the internal logic of his inquiry”.

Wertheimer (p. 227) quotes Einstein as saying: “‘I am not sure,’ Einstein said once in this context, ‘whether there can be a way of really understanding the miracle of thinking. Certainly you are right in trying to get a deeper understanding of what really goes on in a thinking process.’” This is consistent with Einstein's other comments on thinking. Cf. Einstein's “Autobiographical notes” in ref. 42 below. The gestaltists from the beginning disagreed with the positivistic viewpoint, as did Einstein explicitly in his published writings from 1933 on—cf. Koffka, Principles (ref. 2), esp. 684–5 and Holton G. , “Mach, Einstein, and the search for reality”, Daedalus (Spring 1968), 636–73; reprinted in Holton G. , Thematic origins of scientific thought: Kepler to Einstein (Cambridge, Mass., 1973), 219–59, esp. pp. 232ff. Henceforth, all references to Holton's essays will be to Thematic origins. For a positivist's critique of gestalt psychology see von Mises R. , Positivism: A study in human understanding (Cambridge, Mass., 1951; unabridged publication with minor corrections, New York, 1968), esp. pp. 280–6 of the 1968 edition. Von Mises reminds the reader that gestalt psychology is an outgrowth of Mach's researches (p. 281; italics in original): Gestalt psychology studies specific aspects of phenomena connected with sense impressions. It forms a special chapter, also discussed at length by Ernst Mach, of empirical natural science, of which elementary and structural psychology [ Mach E. , Popular scientific lectures , tr. by McCormack T. J. (La Salle, 1943), 214–35], are other chapters. It is completely unjustified to contrast with Gestalt psychology every other psychological approach as “physicalistic” or “empiricist”. Von Mises continues (pp. 281–2; italics in original): 5. The Whole and the Sum. The favorite formula by which the followers of the holistic doctrine like to assert their superiority over the lower level of empirical science is this: The whole is more than the sum of its parts. This can, indeed, be called the model of a pseudo sentence. It is indeed interesting that positivistically inclined philosophers circa 1975 have come full circle and use, when convenient, gestalt psychology in support of their viewpoint.

I have begun to discuss this topic in “On Lorentz's methodology”, The British journal for the philosophy of science, xxv (1974), 29–45.

With the generous assistance of Mr V. Wertheimer, I was able to arrange the manuscripts in the order in which they were written and edited (they are undated). All of the manuscripts are very similar. There are two originals—which I shall designate as 1 and 5—with carbons on which were made editorial changes. The changes on the carbons 2, 3 and 4 were then transferred back to the original copy 5. In the final stages (manuscripts 3 through 5) there appears almost exclusively the writing of Mr V. Wertheimer and Max Wertheimer's colleagues, Professors S. E. Asch, W. Köhler and C. W. Mayer. It is very likely that Wertheimer had already died by the time the final stylistic changes were transferred to manuscript 5, which was then sent to press.

Wertheimer , Productive thinking , 206. Wertheimer continues: “Besides the printed material would not be enough for the psychologist, who is interested in characteristics of the growing process of thought which is not usually put down in writing”. In Einstein's case Wertheimer did not claim to be basing his work on “printed” material, but on conversations with Einstein. Similarly, Frank E. Manuel in his adventurous foray into the psychology of discovery alerts his readers thus: “It will quickly become plain to the reader that on more than one occasion I steered my way between a Scylla of historians of science and a Charybdis of psychoanalysts” (A portrait of Isaac Newton (Cambridge, Mass., 1968), ix).

Wertheimer , Productive thinking, 213.

Ibid., 246ff.

Ibid., 214.

Ibid., 215.

Ibid., 216.

Einstein A. , “Autobiographical notes” in Albert Einstein: Philosopher-scientist, ed. Schilpp P. A. (Evanston, 1949).

Ibid., 53.

Loc. cit.

Shankland , “Conversations with Albert Einstein” (ref. 28), 49.

Wertheimer , Productive thinking, 216–18. Wertheimer refers to the Michelson–Morley experiment as “Michelson's experiment”.

For example, the letter of Einstein to F. G. Davenport written 9 February 1954 and quoted in Holton G. , “Einstein, Michelson, and the ‘crucial’ experiment”, Isis, lx (1969), 133–97; reprinted in Holton G. , Thematic origins (ref. 33), 261–352. The part of the letter relevant to the discussion here reads thus (pp. 325–6): In my own development Michelson's result has not had a considerable influence. I even do not remember if I knew of it at all when I wrote my first paper on the subject (1905). The explanation is that I was, for general reasons, firmly convinced how this could be reconciled with our knowledge of electro-dynamics. One can therefore understand why in my personal struggle Michelson's experiment played no role or at least no decisive role. Indeed, in this essay Holton warned that Wertheimer's “work has to be used cautiously” (p. 347).

Holton in Thematic origins, in a detailed historical study of the relationship of the Michelson–Morley experiment to Einstein's thought towards formulating the special relativity theory, found that one is forced to agree with the evidence for the veracity of Einstein's own comments, i.e. those written by Einstein himself or his words quoted or reported by physicists who interviewed him. See Thematic origins , 322, the letter of Einstein to Davenport quoted in ref. 47, and Shankland, “Conversations with Albert Einstein” (ref. 28), 48, 55. Holton is not denigrating the actual role of experiment in Einstein's thought. In fact, he concludes his essay by taking great care to explain that “experiments are essential for the progress of science”; however, the role of experiment in the scientific method and in the writing of the history of science must be carefully weighed, “the experimenticist fallacy of imposing a logical sequence must be resisted” (p. 329). To elevate the role of the Michelson–Morley experiment to a “crucial” one, as Einstein never did in any of his writings, is simply and demonstrably wrong, though the urge of pedagogues or experimenticist historians or philosophers to do so can be explained. Indeed, the majority of physics teachers c. 1943, and many even today, would probably present Einstein's relativity theory as explicitly motivated by the Michelson–Morley experiment (ibid., 272).

Wertheimer , Productive thinking, 218.

The first sentence of this passage is perplexing; for is it not the case that the formula for the Lorentz contraction is the mathematical statement of the contraction hypothesis? A discussion of Einstein's reported comments made to Wertheimer on the ‘ad hocness’ of the Lorentz contraction are of interest but go beyond the theme of this essay. For further discussion and references on the status of Lorentz's contraction see my essay in ref. 34.

Wertheimer , Productive thinking, 218–19.

Ibid., 218.

Ibid., 219.

Ibid., 218.

Loc. cit.

Ibid., 219.

Loc. cit.

Loc. cit.

Ibid., 219–22.

Einstein A. , Über die spezielle und die allgemeine Relativitätstheorie (Braunschweig, 1917), 21ff. All references will be to the translation by R. W. Lawson (London, 1929). Einstein wrote the preface in December 1916, which may account for Wertheimer's incorrectly dating the book's publication as 1916 (Productive thinking, 219). I shall continue to refer to this book, using Wertheimer's dating, as Einstein's popular book of 1916.

Ibid., v–vi.

Wertheimer , Productive thinking, 222–4.

Ibid., 222.

Loc. cit.

Ibid., 223.

Loc. cit.

Loc. cit.

Loc. cit.

Einstein , “Autobiographical notes” (ref. 42), 53.

Ibid., 53 and 57.

Wertheimer , Productive thinking, 223.

Ibid., 224.

Loc. cit.

Cf. Einstein , “On the method of theoretical physics”, The Herbert Spencer Lecture delivered at Oxford 10 June 1933: Reprinted in Essays in science (New York, 1934), 12–21, esp. p. 15.

Holton G. , “On the origins of the special theory of relativity”, American journal of physics, xxxviii (1960), 627–36; reprinted in Thematic origins, 165–83.

Klein M. J. , “Thermodynamics in Einstein's thought”, Science, clvii (1967), 509–16.

Further evidence in support of Holton's and Klein's arguments can be found in my essay “On Einstein, light quanta, radiation and relativity in 1905” (to be published in 1975 in the American journal of physics).

Einstein was aware of at least Max Abraham's theory of the electron (cf. my essays in refs 34 and 77 and my “A study of Henri Poincaré's ‘Sur la dynamique de l'électron’”, Archive for history of exact sciences, x (1973), 207–328). Furthermore, such a question as whether the velocity of light is the ultimate velocity had not been “unthought of before” Einstein. For example, Abraham in 1904 had pointed out this possibility—see my essay in ref. 77.

Wertheimer , Productive thinking, 225–6.

Ibid., 226.

Loc. cit.

Kaufmann's data was referenced in Abraham's papers of 1903 and 1904. It is true also of the other two papers which Einstein published in vol. xvii of the Annalen der Physik that in them he proposed tests at the very end, briefly and almost casually. I am not intimating that Einstein did not care about testability. That is not true. See his “Autobiographical notes” for further discussion.

Wertheimer , Productive thinking, 232.

Ibid., 229.

Loc. cit.

Ibid., 216.

Ibid., 229.

Loc. cit.

Loc. cit.

Ibid., 231.

Loc. cit.

Ibid., 229.

Ibid., 231.

Ibid., 230.

Loc. cit.

Loc. cit.

Loc. cit.

Loc. cit.

Koffka , op. cit. (ref. 2), 218.

Wertheimer , Productive thinking, 228.

Ibid., 230.

Ibid., 228.

Ibid., xi.

Ibid., 213.

Unpublished letter. I am grateful to the Estate of Max Wertheimer for permitting the use of this letter. The translation is mine.

I am grateful to Mr V. Wertheimer for pointing this out to me.

Such, for example, was clearly the intent of Einstein's letter to Freud of 21 April 1936, quoted in op. cit. (ref. 1), 493, and Freud's reply is on 494.

A copy of this letter is in the Einstein Archives at the Institute for Advanced Study. Except for the sentence, “You may be interested in this manuscript (not yet published)”, the letter appears in Hadamard J. , The psychology of invention in the mathematical field (Princeton, 1945; unaltered ed., New York, 1954), 142–3.

Op. cit. (ref. 42), 7.

Op. cit. (ref. 28), 48. This statement is from a conversation between Einstein and Shankland on 4 February 1950. Noteworthy is that Shankland reports Einstein as prefacing this statement with the words “only after 1905 had it [the Michelson–Morley experiment] come to my attention” (italics in original; p. 48).

Cf. Seelig C. , Albert Einstein: Eine dokumentarische Biographie (Zürich, 1954), 69. Indeed Einstein asserted in his “Autobiographical notes” that the “type of critical reasoning which was required” for resolving the “paradox” posed by the experiment from the Aarau period, and hence for discovering the relativity of simultaneity, “was decisively furthered, in my case, especially by the reading of David Hume's and Ernst Mach's philosophical writings” (op. cit. (ref. 42), 53).

Einstein , “The problem of space, ether and the field in physics”, in op. cit. (ref. 74), 61.

Miller A. I. , “Einstein and Poincaré revisited”, Lecture delivered 11 December 1973 at the Boston Colloquium for the Philosophy of Science. To be published in a forthcoming volume of Boston studies in the philosophy of science.

Op. cit. (ref. 42), 29.

Gestalt psychology plays an important role in certain recent studies in the history and philosophy of science. I mention in particular the works of Hanson N. R. , Patterns of discovery (Cambridge, 1958) and Kuhn T. S. , The structure of scientific revolutions (1st ed., Chicago, 1962; 2nd enlarged ed., 1970). Hanson and Kuhn found gestalt psychology to be useful to their views on the nature of scientific discovery and on the progress of science, which stress the discontinuous change from one theory, or paradigm, to another. According to Hanson it is possible for the relevant scientific data to be present, although unorganized, in the mind of the scientist. The scientist then conceives of a “pattern statement” (p. 88) that is the free creation of his mind. The pattern statement organizes the already existing knowledge into a pattern, enabling the scientist to perceive of the data as “seeing that”, rather than viewing an unstructured field of knowledge, which Hanson refers to as “seeing as” (pp. 19ff.). Hanson writes (p. 90): “Physical theories provide patterns within which data appear intelligible. They constitute a ‘conceptual Gestalt’ “. Like the gestaltists, Hanson uses frequently the analogy of the gestalt-switch in seeing figures and background in drawings. Kuhn writes (p. 174 of the 2nd enlarged edition in vol. ii of Foundations of the unity of science): “Therefore, at times of revolution, when the normal-scientific tradition changes, the scientist's perception of his environment must be re-educated—in some familiar situations he must learn to see a new gestalt”. Kuhn continues (p. 184): “crises … are terminated, not by deliberation and interpretation, but by a relatively sudden and unstructured event like the gestalt switch”. Kuhn does caution against overemphasis of the results of gestalt experiments for historical investigations, as does, he claims, Hanson (p. 175). “Yet”, Kuhn writes (p. 175), “though psychological experiments are suggestive, they cannot, in the nature of the case be more than that”. It is clear, however, that the key role played by discontinuities in gestalt psychology is congenial to Kuhn's view. I add that neither Hanson nor Kuhn differentiates between the gestalt theory of perception and the gestalt theory of thinking.

Cf. Arnheim R. , Visual thinking (Berkeley, 1971) for discussions of gestalt psychology towards the study of “visual perception as a cognitive activity” (p. v): And Gombrich E. H. , Art and illusion: A study in the psychology of pictorial representation (Princeton, 1956) who uses examples from art to illustrate the Prägnanz principle in action—Gombrich refers to the Prägnanz principle as the “simplicity hypothesis” (pp. 262ff.).

Op. cit. (ref. 75), 168.

PRC (ref. 6), 37.

The translation is that of Holton and appears in his essay “On trying to understand scientific genius”, in Thematic origins (ref. 33), 363–4. Here Holton once again warns that “Wertheimer's own remarks [in Productive thinking] on psychology are useful, but those on physics are far less soundly based” (p. 380).

Piaget J. , Genetic epistemology, tr. by Duckworth E. (New York, 1970), 13.

Piaget recognizes the importance of the fact that biological systems, and hence cognitive processes have a tendency towards organizations that possess simplicity, symmetry and regularity. He refers to this tendency, which to Wertheimer was the Prägnanz principle, as the “first law of good form” (Biology and knowledge, tr. by Walsh B. (Chicago, 1971), 246). Piaget asserts that the “Gestalt notion … is still perfectly viable once it is cut loose from its purely Gestalt chains” (p. 245).

Holton , Thematic origins (ref. 33), esp. “Introduction”.

Manuel, op. cit. (ref. 36).