But he did not suggest a return to determinism. Rather he defended the idea of chance in the universe as irreducible to hidden causes in principle. After a couple of centuries in which random distributions were regarded as deterministic, Landé invented a demon needed to achieve such deterministic pseudo-random distributions, to show that they were nonsense.

He used the example of a "Galton box," also known as a "quincunx," in which balls fall onto a knife edge - or small bins - and then bounce to the left or to the right at random.(David Little has programmed a Java applet demonstration)

Experience shows that between right- and left-hand aim there is always a small but finite range Δa of aim within which an experimentally adjusted angle a leads neither to all balls dropping to the right nor to all balls dropping to the left but rather to both r- and l-balls occurring at a certain frequency ratio. The latter varies from 100 : 0 to 0 : 100 when the aim is shifted from the right to the left of the small range Δa. Primitive persons and other indeterminists will interpret this as a sign of uncertainty, of blind fate, with one and the same cause capable of being followed by two different effects, r or l. Determinists will say, however: "The distribution of the r- and l-results only appears to be erratic. Actually each individual result has its particular deterministic cause, be it a small deviation of the angle of aim, or a small perturbation of the ball on its flight." (Similarly, although insurance companies count on their frequency tables, each individual "accident" is not an accident but has its particular cause.)

I submit, however, that the hypothesis of (concealed) individual causes behind individual effects r or 1 does not explain the essential point of the observed situation in a deterministic fashion. When the determinist ascribes the present final event r to an r-producing chain ... r r r reaching back into the infinite past, he merely shifts the problem r- and l-events to r- and l-chains and, further, to the beginning of those chains, if they have a beginning. We must ask him now for a deterministic explanation of the strange empirical observation that those chains, or initial conditions, occur again and again at a definite frequency ratio and, furthermore, why even the fluctuations away from the average occur at a rate conforming with the mathematical theory of random as though by a pre-established harmony between fact and theory. It is this pre-established harmony that calls for explanation. Referring to the infinite past, and saying that his harmony has always prevailed, is an evasion rather than a deterministic explanation. A stubborn determinist may defend his cause, however, by means of the following argument: "Once upon a time there was a demon who knew his mathematical random theory and who deliberately went out to deceive the observer. He first initiated two r-chains, then an l-chain, then four r-chains; then realizing that he had given too much preponderance to r-chains, he thereupon started five l-chains in a row, cleverly arranging the whole sequence with averages and fluctuations so that a present-day scientist might be lured away from the true deterministic faith."

There seems indeed to be only the following alternative: Either the observed random-like distributions of final events or chains or initial conditions in games of chance represent a basic and irreducible trait of nature. Or statistical distributions only feign an appearance of random, when in reality there is, or has been, concerted deterministic action. Either a deus ex machina or no deterministic explanation at all. Since deceitful demons have no place in scientific theories, I have reluctantly joined the party of indeterminacy pure and simple. But I concede, that it is a party of renunciation with a purely negative creed. Most of my partisans, including myself, suffer from a guilt complex that draws us toward our old infatuation, determinism. This infatuation may have its roots in a feeling of being ourselves demons who can deliberately start deterministic chains. In other words, it may be that we believe in strict determinism because we feel we have free will - a somewhat paradoxical psychological hypothesis. But as a scientist who observes games of chance, and who is unwilling to admit a deus ex machina (at the beginning of time, if there is a beginning, or a finite time ago), I must concede that the deterministic interpretation fails; and this applies not only to ordinary "games of chance" in which the statistical dispersion is obvious, but in general to those cases where a similar dispersion of effects is revealed only by microphysical instruments.

Empirically it is a most surprising fact, which could not have been foreseen a priori, that there are sequences of events in harmony with mathematical random theory. This empirical discovery was already made by cavemen when they gambled for the best pieces of a slain bear. But when irreducible random is once accepted, then it is a comparatively minor point of dispute whether (a) each new experiment constitutes a new game of chance (as quantum theory maintains), or (b) random was set up once, a long or an infinite time ago, and random distributions observed at present are but the deterministic effects of that one initial "shuffling of the cards" (as classical statistical mechanics maintains).

n

("The Case for Indeterminism," in Determinism and Freedom in the Age of Modern Science, ed. S. Hook, 1958, pp. 83-85.)