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On the Meaning of Order (II) 235 frequency of the actually emitted light when the electron changed its orbit was connected only with the differences of energy in the electron’s transition between stationary states. By 1922Bohr knew that the problem wasone involving not only physicsbut also epistemology.Natural languages are simply inadequate to describe processes within an atom, to which human experience is connected in only very indirect ways. But, since understanding and discussion depend on available languages, this deficiency made any solution difficult for the time being. Bohr confessed to Heisenberg that originally he had not worked out his complex atomic models by classical mechanics; he reported ‘they had come to him intuitively ...as pictures’, representing events within atoms. Talking about electron paths in atoms was easy, but the imagery had really been borrowed from watching actual electron tracks in cloud chambers or other events of that sort on a scalebillionsof times larger than an atom itself. Similarly, the properties of light allowed one to talk about it by analogy either with water waves or, in other experiments,in terms of energetic bullets (quanta). But how could light, as such, be both? Visualizability had been of real help in the past; in this new realm it appeared to be a trap. Yet, how could onedo without it? In 1921-22 there began a long journey through the wildernessfor most physicists-even for Heisenberg,who has given a description of that period [2]. There were several years of ‘continuous discussion ....We actually reached a state of despair ....Out of this state of despair finallycame this change of mind. Allof a sudden [we said] well, we simply have to remember that ourusual language does not work any more, that we are in the realm of physics where our words don’t mean much.’ A key event in this transition from despair to euphoria was Heisenberg’s own work done in the spring of 1925. He worked out aformalisticapproachtothe understanding of light radiation, using a mathematics that later turned out to be known to more experiencedscientists as matrix algebra. Heisenberg had totally eliminated the concept of electron orbits or, indeed, of any ‘picture’ of an atom. (When Born later saw it, he found this at first ‘disconcerting ’.) In its place, Heisenberg put a mathematical schema based on the laws of quantum physics, adjusted by introducing the data (e.g., the frequencies and intensities of the spectral lines) that long ago had been established by observation. In his revealingarticle (31, he declared that the customary view-derived from ordinary space-time conceptions,which are in principle‘continuous’ -has to give way in the atomic realm to the ‘unvisualizability ’ of in-principle ‘discontinuous’ elements. He advised that the grasping of those elementsand of a ‘kind of reality’ appropriate to them was the real problem of atomic physics. After the initial consternation among physicists about this approach, it turned out to give results that fit splendidly with the work of others, among them Bohr, Pauli, Dirac and Schrodinger. The goalof a true quantum mechanics had been reached (although a small number of respected physicists rejected it as no more than a partial answer); even a new kind of visualizability was soon gained [4]-although a meaningfulversion of it hasyet to penetrate beyond science laboratories. REFERENCES 1. Physik und Realitat, J. Franklin Institute 221,315 (1936). I have provided (here and as necessary in the other quotations) a corrected translation from the original German. Discussion with Professor Heisenberg, in The Nature o f Scientific Discovery, 0.Gingerich, ed. (Washington, DC: Smithsonian Institution Press, 1975) pp. 556-573. W. Heisenberg,Quantenmechanik,Die Natunvissenschaften 14, 989 (1926). A. I. Miller, Visualization Lost and Regained:The Genesis of the Quantum Theory in the Period 1913-27, in On Aesthetics in Science, J. Wechsler, ed. (Cambridge, MA: M.I.T. Press, 1978) pp. 73-102. 2. 3. 4. (Received 14 Jan. 1981) Gerald Holton Dept o f Physics Harvard University Cambridge. MA 02138. U.S.A. ON SYMMETRY IN NATURE AND IN THE VISUAL ARTS It has long been known that various kinds of spatial order inthevisualartshavegiven humans aestheticsatisfaction. One can ask why this is so. Some recent considerations...

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