What Is Real?

 

1. On the night of 25 March 1938, at 22:30, Ettore Majorana, who was regarded as one of the most talented physicists of his generation, boarded a Tirrenia steamer in Naples—where he had held the chair of theoretical physics for a year—heading for Palermo. In the words of the announcement published on 17 April in the “Chi l’ha visto?” column of the Domenica del Corriere, from that moment, except for unconfirmed reports and conjectures, every trace of “the thirty-one year old professor, 170 cm tall, lean, dark hair and eyes, with a long scar on the back of his hand” was lost. In spite of searches involving the police authorities and, under pressure from Enrico Fermi, the head of government in person, Ettore Majorana had disappeared forever. His relatives never accepted the possibility of suicide, which in itself seemed to convince the police that he had killed himself, and did not apply for a declaration of presumed death, as is usual in these circumstances. Unverifiable legends then circulated about the scientist’s escape to Argentina or Nazi Germany, his retreat to a monastery, and reappearance as a tramp in Sicily and Rome in the 1970s.

Every reflection on his disappearance should start from the letters Majorana wrote on the very day of his departure and the next as the only indisputable documents. A careful analysis of the texts shows that, at the very moment when he decides to disappear, Majorana seems to suggest divergent explanations for his gesture, as if he wanted to cover his tracks, intentionally leaving it open to contrasting interpretations.

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4. In the early months of 1941, one year before the publication of Majorana’s article, Simone Weil began to write in Marseille an essay titled “La science et nous,” which is essentially a critique of quantum physics. The heterogeneity of the latter with respect to classical physics is placed in stark relief in the introduction: “To us, people of the West, a very strange thing happened at the turn of the century; without noticing it, we lost science, or at least the thing that had been called by that name for the last four centuries. What we now have under this name is something different, radically different, and we do not know what it is.”4

According to Weil, classical science was constituted by considering every natural phenomenon in the light of a single notion, derived from that of work: the notion of energy. If I want to carry out work, for instance, moving a body from one place to another, I need to use a certain amount of energy; while, on the other side, the body in question will necessarily have to go through all the intermediate states between the initial and the final one. “Building upon the discoveries of Bernoulli and D’Alembert, Lagrange came to define by a single formula every possible state of equilibrium and motion of any system of bodies subjected to any force; this formula refers only to distances and forces or, what amounts to the same thing, to masses and velocities.”5 Classical physics added to the notion of energy thus defined an equally necessary principle of entropy. “This necessity derives from time itself and consists in the fact that it has a direction, in that the orientation of a transformation is never indifferent, whatever happens. We experience this necessity, not only through the aging that holds us ever more firmly in its grasp and never abandons us, but also through everyday events. A minimal moment or effort is sufficient to throw a book off the table, mix up a pile of papers, stain some clothing, crumple some linen, burn a field of wheat, or kill a man. But it takes considerable effort and time to put a book up on the table, put papers in order, clean clothing, and iron linen; a year of toil and care is necessary to produce a new harvest from the field, and one cannot make a dead man come back to life.”6This means that, in every phenomenon in which a transformation of energy is produced, it is not possible exactly to reestablish the initial state once the phenomenon has been accomplished. The second law of thermodynamics, formulated by Clausius, gave mathematical form to this reality through the fiction of a notion—entropy—that necessarily increases in every system in which a change occurs, so that, if external factors do not intervene, energy is dispersed and moves from order to disorder. “Such was the crowning achievement of classical science, which therefore claimed that it would be possible by calculations, measurements, and numerical equivalents to read across all phenomena that are produced in the universe simple variations of energy and entropy conforming to a simple law.”7 These variations amounted to necessary and continuous processes, and therefore one could say that classical science was based on the same necessity and continuity with which we are confronted every time we carry out work.

Quantum theory radically calls into question this correspondence between physical laws and the image of the world founded on the experience of work. “Twentieth-century science is classical science after something has been taken away from it. Taken away, not added. . . . We have subtracted from it the analogy between the laws of nature and the conditions of work, which is to say, its very principle; it is this that the quantum hypothesis has decapitated.”8 In classical physics, “energy is a function of space, and space is continuous; it is continuity itself; it is the world considered from the standpoint of continuity; it is things insofar as their juxtaposition implies something continuous.”9 Planck’s formula and constant introduced discontinuity into energy at the precise point at which, according to Weil, it cannot take place. In fact the appearance of discontinuity in physics is connected with the investigation of atomic systems, which thus reveal themselves to be subject to laws that are completely different from those of macroscopic systems. Moreover, according to Weil, the introduction of discontinuity entailed the emergence of probability: “Discontinuity, number, smallness; this is enough to make the atom appear, and the atom has come back to us along with its inseparable entourage, that is, chance and probability. The appearance of chance in science has been seen as scandalous; we asked where it came from and did not realize that the atom brought it; we forgot that, already in the ancient world, chance went along with the atom, and failed to realize that it could not have been otherwise.”10In the pages that immediately follow, the decisive factor that has led to quantum physics is not so much discontinuity as the calculation of probabilities. In a curious reversal, probability is not a function of the discontinuity of atomic systems, but rather the latter is derived from the former. Examining Planck’s writings—which Weil quotes repeatedly—“it clearly appears that what introduced discontinuity is not experience . . . but only the usage of the notion of probability.”11 In an article published in Cahiers du Sud in December 1942, this genealogical primacy of probability is stated once again: “One wonders whether it is not the very nature of the calculation of probabilities, which originates from the game of dice, and consequently from numerical relations, that led Planck to introduce whole numbers into his formula.”12 A few pages later, Weil adds: “When scientists came across discontinuity, they still went on reducing everything to variations of energy; they simply located discontinuity within energy, depriving it of all meaning. . . . The difficulty of establishing through the notion of probability a bridge between the world we are given and the hypothetical and purely mechanical world of atoms did not embarrass them; the consequences of quantum theory, which originates from the study of probability, prompted them to locate probability within the atoms themselves.”13 At this point, Simone Weil focuses on an examination of this concept.

5. Weil begins by referring the concept of chance [caso] back to that of necessity:14 “We are often mistaken about chance [hasard]. Chance is not the opposite of necessity and is not incompatible with it. On the contrary, chance always and only appears in relation to necessity. If we suppose a certain number of different causes producing effects according to a rigorous necessity, and if there appears in these effects a set that has a certain structure, we will obtain chance if we cannot group the causes in a set of the same structure. Due to its shape, a dice can only land in six ways; while, on the other hand, there is an unlimited variety of ways of throwing it. If I throw a dice one thousand times, its landings can be distributed into six classes that have numerical relations between them; the throws cannot be distributed in the same way. Moreover, I cannot presume the least deficiency in the texture of the mechanical necessity that determines at each turn the movement of the dice. If I throw the dice once, I ignore what the result will be, not because of an indetermination of the phenomenon, but because this is a problem where in part I do not know the givens. . . . In these games, the set of causes has the power of continuity, which means that the causes are like the points of a line; the set of the effects is instead defined by a small number of different possibilities.”15If chance is, in this sense, inseparable from necessity, then probability is in turn inseparable from chance, and thanks to probability chance becomes a quantity that may be controlled in experiments. “When, in games of chance, I consider the continuous set of causes and the small number of categories into which their effects can be distributed, I affirm that, although each effect proceeds rigorously from a cause, there is absolutely nothing in the set of causes that corresponds to these categories; that is what it means to say that there is chance. Hence these categories all have an identical relation to the set of causes that, at the same time, is indifferent to them. That is what it means to say that they are equally probable. The notion of probability always implies a distribution into equal probabilities. . . . With respect to the relation of probability to experience, it is analogous to the relation of necessity to experience. Experience presents an image of necessity when, by varying a cause, one obtains effects that vary according to a function; it presents an image of probability when the distribution of effects into categories gets closer and closer to the proportions indicated by calculation as the effects accumulate.”16At this point, Weil reconstructs the way in which Planck was led to introduce probability and discontinuity into the theory of physics through his constant, and how this principle was generalized in quantum mechanics: “There is a natural transition between the notion of entropy and that of probability, for the fact that if a system, isolated from external disturbance, can pass from state A to state B by means of any chain of intermediaries, but not the other way round, then state B is more probable than state A.”17 At the precise moment Planck was elaborating these ideas, chance appeared in the sphere of the atom. The observation of Brownian motion in fact showed that a fluid that appears to be in a state of equilibrium at the macroscopic level is not so at all at a microscopic level, and that, in general, a system defined in a certain necessary way on the first level corresponds on the molecular level to a plurality of possible combinations. “If we try to transfer necessity into the atomic sphere, the relation between two states of a system defined at a macroscopic level is no longer a necessity but a probability. This is not because of any flaw in causality, but only because of an effect of the oscillation of thought between the two levels, through a process analogous to that of a game of dice. A natural movement of thought led us to bring together the two probabilities simultaneously arising in our minds—the one linked to entropy and the other linked to atoms—and to consider them as one and the same probability. . . . However, since the calculation of probabilities is a numerical calculus, it was stipulated that the combinations of atoms are, so to speak, discrete and that their quantity is a number; this is the point of rupture with classical science.”18It is evident that Simone Weil is here making a decisive criticism of the idea that the statistical laws of quantum physics are not the consequence of an incomplete knowledge of the data concerning the state of a given system, but refer back—in Majorana’s words—to a deficiency of determinism in reality. The paradigm of necessity and of the cause-effect relation remains valid for quantum physics, and the superiority of classical physics is based precisely on this: “Some splendid verses of Lucretius suffice to give us a sense of what is purifying in the sight and experience of necessity; well-endured affliction is a purification of this kind, as is classical science also a purification, if one makes good use of it, for it tries to read through all appearances this inexorable necessity that makes of the world a world where we do not count, a world where we work, a world indifferent to desire, aspirations, and the good; it is the study of the sun that shines indifferently on the just and the unjust.”19

According to Weil, renouncing necessity and determinism in the name of probability, quantum mechanics has purely and simply renounced science. If the cause of the rupture with the continuous model of classical physics was the numerical character of the calculation of probabilities, Weil wonders at this point why scientists did not choose to work on the very notion of probability in order to elaborate a model of calculation that is not founded on discontinuity but on continuity—instead of changing the theory of physics from top to bottom.206. The same scientists who had contributed to laying the foundations of quantum physics themselves advanced criticisms of its probabilistic character. For instance, Louis De Broglie, who developed the theory of the simultaneously corpuscular and wavelike character of quantum particles, attempted to provide a non-probabilistic interpretation of this duality, which was by and large more compatible with the notions of classical physics. But the prevalent interpretation promoted by Niels Bohr, Max Born, Werner Heisenberg, and Paul Dirac rejected it. De Broglie claimed that this interpretation “considered both waves and particles, but in a way which relegated both to a sort of phantom existence and without any attempt to connect the two in a clear spatio-temporal model. The particle itself no longer had a fixed position, velocity, or trajectory—it could mark its presence only by revealing a given position, energy, and momentum at the moment of measurement. At any given moment, the particle may therefore be said to have a host of possible positions and momenta, each of which has a given probability of being found on measurement. Side by side with this evanescent particle which had ceased to be a definite object in space and time, there now existed a regular wave that had lost all the physical properties of the classical wave. The wave had become a purely mathematical function representing the probability of obtaining certain results from measurements of the particle.”21Even Einstein, who decisively contributed to quantum theory, had until the end reservations about an exclusively probabilistic interpretation of it. In May 1935, he published with Boris Podolsky and Nathan Rosen an article in Physical Review titled “Can Quantum-Mechanical Description of Physical Reality Be Considered Complete?,” in which he argued that, insofar as it is the case that when two physical quantities are given in quantum mechanics, the knowledge of the one precludes the knowledge of the other (following Bohr’s complementarity principle), either the description of reality provided by the wave function is not complete or the two quantities exist simultaneously. The article, which ended by affirming the possibility of a complete physical theory, produced an immediate reaction from Bohr in the same journal. Bohr founded the complementarity principle—according to which it is impossible to assign defined values to two regularly combined variables, such as the velocity and the position of a particle—on the quantum principle that the interaction between the measuring instruments and the object under examination necessarily implies the abandonment of the classical idea of causality. In quantum mechanics, natural laws never lead to a complete determination of what occurs in space and time, and every event depends on chance and probability. At the end of his article, somehow maliciously but not unreasonably, Bohr recalls that what Einstein intended to criticize in the probabilistic character of quantum physics was nothing other than a consequence of his general theory of relativity: “This new feature of natural philosophy means a radical revision of our attitude as regards physical reality, which may be paralleled with the fundamental modification of all ideas regarding the absolute character of physical phenomena, brought about by the general theory of relativity.”22 But this modification of reality in a statistical sense was precisely the difficulty Einstein could not resolve throughout his life—and his reasoning was not without contradictions.

A few months after the polemic between Einstein and Bohr, Erwin Schrödinger—who, among the founders of quantum mechanics, had arguably the strongest philosophical background—intervened and proposed an experiment that became known as “the cat paradox.” He starts off by restating that, according to the prevailing interpretation, it is impossible to describe objects as one does in classical physics, and we therefore need to provide a purely probabilistic representation of them. Before the observer intervenes and measures the variables of a physical system, they have no definite value, and measuring them does not mean verifying the value they objectively have. The measurement irrevocably modifies the system, but prior to it, in probabilistic representation, the observable particle can be, so to speak, found simultaneously in every position it can assume, or, in the case of two distinct states, in any of their combinations.

Here Schrödinger introduces the “ridiculous case” of a cat that we are compelled to suppose is both alive and dead at the same time: “One can even set up quite ridiculous cases. A cat is penned up in a steel chamber, along with the following device (which must be secured against direct interference by the cat): in a Geiger counter there is a tiny bit of radioactive substance, so small, that perhaps in the course of the hour one of the atoms decays, but also, with equal probability, perhaps none; if it happens, the counter tube discharges and through a relay releases a hammer which shatters a small flask of hydrocyanic acid. If one has left this entire system to itself for an hour, one would say that the cat still lives if meanwhile no atom has decayed. The first atomic decay would have poisoned it. The psi-function of the entire system [i.e., the function that expresses its probabilistic state] would express this by having in it the living and dead cat (pardon the expression) mixed or smeared out in equal parts.”23 It is only by opening the box that the observer forces the system (the cat) definitively to pass into one of the two states (alive or dead).

It is evident that, as was suggested by Simone Weil, the paradoxes in question in quantum mechanics derive from the unconditional assumption of probabilistic conceptions, which are not matched by an adequate reflection on the very nature of the notion of probability. For both the supporters of the orthodox theory and their critics, the state of the system before and after observation is not a real but a probabilistic state; however, they seem to produce a representation of this state and argue as if probability were a very special kind of reality, which one can think only in a paradoxical way (for example, as if a particle were at the same time in both state A and state B). But is it correct to represent the probable as if it were something that exists? In other words, what is at stake is a problem concerning the ontology of the probable—or the possible, since probability is nothing other than a possibility qualified in a certain way. Following Weil’s suggestion, at this point it is therefore necessary to focus on the very notion of probability.

7. The calculation of probabilities was elaborated in the context of a consideration of dice games. The treatise De ludo aleae, written by Gerolamo Cardano in 1575 but published only after his death, in 1663, enunciates its foundations for the first time. Cardano starts by distinguishing between games of dexterity—such as ball games—games of strength—such as wrestling and discus throwing—and games of chance—including cards and dice games. Cardano was a compulsive gambler and, in his autobiography, he confesses to playing dice every day for twenty-five years, “with the loss at once of reputation, time, and money.” However, he suggests that experience showed him that dice games are useful remedies against grief and death: “In times of great anxiety and grief, gambling is not only permissible, but even beneficial. . . . When it seemed to me after a long illness that death was close at hand, I found no little solace in playing constantly at dice.”

The “fundamental principle” (principale fundamentum) of dice games is the equality (aequalitas) of conditions, not only among players, who should not be too dissimilar in terms of power, money, and fortune, but first and foremost in the dice themselves, which should not be loaded. In Chapter IX, “De unius aleae iactu” (On throwing one dice), Cardano approaches a definition of probability. “The dice has six faces; in six casts (in sex revolutionibus) every single point should take place (evenire deberent).”24 This means that, if the dice is not loaded and the condition of aequalitas respected, the probability of each point is 1/6; but Cardano writes “should,” since he knows that as a matter of fact it may happen that the same number presents itself more often than others (this led some scholars to claim that he somehow intuited the law of large numbers, on which every statistical calculation is based). Chapter XIV thus articulates what could be regarded as a more explicit definition of probability: “There is one general rule, namely, that we should consider the whole circuit [for Cardano, the circuit is the set of possible results] and the number of those casts that represents in how many ways the favorable result can occur, and compare that number to the remainder of the circuit, and according to that proportion should the mutual wagers be laid.”25 Once he has established that, in the case of two dice, the number of the circuit is 36 (and 216 in the case of three), Cardano can calculate in specific tables the probabilities of the various points—for instance, given that the point three can be obtained only in one way (2+1) and the point ten in two ways (5+5 and 6+4), the probabilities are different in the two cases.

8. After elaborating these tables, Cardano claims that it is impossible to eliminate luck from the dice, “which makes some people benefit from unexpected cases and impoverishes others because of what they were expecting,”26 but a careful reading of his short treatise allows us to extrapolate the first features of a theory of probability. First of all, as Simone Weil sensed, the notion of probability presupposes a distribution among equal probabilities (that is, the principle of aequalitas, which Cardano enunciates in a still vague way). If we acknowledge chance, that is, the fact that the relationship between the events under examination (the landing of the dice) and their cause (the throw) is absolutely indifferent, this can be expressed by saying that such events are all equally probable. As Poincaré observed, from this it follows that the definition of probability is circular, since it contains the term that needs to be defined: “The probability of an event is the ratio of the number of cases favorable to the event to the total number of possible cases, provided that these are all equally probable.”27This circularity implies that the notion of probability never refers to a certain real event (a given throw of the dice as actual) but only to the event as considered in its pure possibility. In other words, probability presupposes that the human mind is capable of considering an event as possible and, moreover, as equally possible with respect to the class of events in question. This is the convention without which the calculation of probabilities is unthinkable. However, the fact remains that this calculation cannot concern an individual case, but only an imaginary being [ente di ragione] we call the “probable case.”

Let us consider the case of the roulette wheel evoked by Poincaré; a small ball is thrown onto a board divided into a large number of sections of equal size, painted alternately red and black. The probability that the ball stops on the red is 1/2. But this does not at all allow us to assume that the result of a given throw will be red even after six, ten, or twenty consecutive results of black. Only after a great number of throws shall we be able to ascertain that the average of the results is distributed according to the expected probability of 1/2. This is the meaning of the law of large numbers Bernoulli enunciated in his 1713 Ars coniectandi, which forms a system with the law of the equality of probabilities and confirms the principle that probability does not concern a real given event but only the tendency to infinity of the number of examined samples.

In other words, the principle that supports the calculation is the replacement of the realm of reality with that of probability, or the superimposition of the one upon the other. Those who act with probability in mind abide by this superimposition and are compelled to acknowledge, more or less tacitly, that although it never determines an individual real case, it can nonetheless influence to some extent their decisions with respect to reality, in spite of the evident paralogism. Modern science—and every single human being with it—directs its decisions according to a criterion that cannot directly refer to the case in question, but only to a “probable case” that can coincide with the former only “randomly” [casualmente].

If the probability of the plane I have to take crashing is 1/1000, then the crashing of that precise plane is an “unlikely case,” which remains such even after the plane has actually crashed. In Wittgenstein’s words, the world is only “all that is the case” and probability can therefore never exist as such, since it is nothing other than that very world, a world whose reality is suspended in order for us to be able to govern it and take decisions about it. What we call “case” is the fiction according to which the probable and the possible “fall” into reality, while the opposite is true; when considered in a certain way, it is the real that suspends its reality and can thus fall into itself as merely probable.

9. Perhaps there is no other text in which the aim and nature of the calculation of probabilities appear more clearly than in the 1654 correspondence between Pascal and Fermat. Antoine Gombault, Chevalier De Méré, proposed to Pascal the problem of the so-called interrupted game: if a dice game is interrupted before the final victory of one of the two players, how should the stake be fairly divided? Pascal’s solution is founded on the possibility of finding, by means of a calculation of risk (Pascal uses the term hasard and not probabilité, which he reserves for theology), the “proper value of each game” (la juste valeur des parties).

“This is the way I go about it to know the value of each of the games when two gamblers play, for example, in three games, and when each has put 32 pistoles at stake. Let us suppose that the first has won two games and the other one. They now play one game of which the chances are such that if the first wins, he will win the entire wager that is at stake, that is to say, 64 pistoles. If the other wins, they will be two to two and in consequence, if they wish to separate, it follows that each will take back his wager, that is to say, 32 pistoles.

Consider then, Monsieur, that if the first wins, 64 will belong to him. If he loses, 32 will belong to him. Then if they do not wish to risk this game, and put themselves at risk without playing it (s’ils ne veulent point hasarder cette partie et se hasarder sans la jouer), the first should say, ‘I am sure of 32 pistoles, for even a loss gives them to me. As for the 32 others, perhaps I will have them and perhaps you will have them; the risk is equal (le hasard est égal). Therefore let us divide the 32 pistoles in half, and give me the 32 of which I am certain besides.’ He will then have 48 pistoles and the other will have 16.”28

Commentators have often dwelt on the increasingly complex examples of calculation that Pascal examines in the course of the correspondence, which certainly influenced later treatises on probability. But we have thus lost sight of what Pascal aimed at with the solution of the problem, namely, to enable a decision about reality through an exact probabilistic assessment of possibilities. As suggested by the very phrase “interrupted game,” it was a matter of suspending the real game in order to replace it with a calculation of risks, which made it possible to decide the division of the stake that was most equitable and useful in this perspective. The expression se hasarder sans jouer is particularly significant; the one who calculates probability relies on risk without actually taking a risk, that is to say, he leaves reality and at the same time transforms chance—l’hasard—into a principle allowing him to decide on reality. This means that probability is never punctually realized as such, nor does it concern a single real event, but, as Majorana understood, it allows us to intervene in reality, as considered from a special perspective, in order to govern it.

The concept of hasard developed in the letter to Fermat reappears in Pascal precisely where we would least expect it, that is, in the well-known passage about the wager (pari) with which the believer wagers on the existence or inexistence of God, and on the uncertainty of eternal life as opposed to earthly pleasures. Let us suppose that heads corresponds to the existence of God and eternal life and tails to his inexistence, and that the gamblers are obliged to wager. The disparity between the infinity of possible gains and the finitude of the equally possible loss requires that we do not take account of a probability that could be calculated but decide only on the basis of the stakes. The uncertainty of the gain is in fact consubstantial with the game, and the calculation is used precisely in order to decide in a situation of uncertainty and not to ensure an impossible certainty. “It is no good saying that it is uncertain whether you will win, that it is certain that you are taking a risk (il est certain qu’on hasarde), and that the infinite distance between the certainty of what you are risking and the uncertainty of what you may gain makes the finite good you are certainly risking equal to the infinite good that you are not certain to gain. This is not the case. Every gambler takes a certain risk (hasarde) for an uncertain gain, and yet he is taking a certain finite risk for an uncertain finite gain without sinning against reason.”29 If the risk of winning is equal to that of losing, but what is at stake is, on the one hand, something infinite and, on the other, something finite, it is clear that the gambler cannot but take this into account. The same calculation that in the “interrupted game” recommended us to divide the stakes of the last game into two equal parts, suggests us here—given that the stake is not divisible—to bet on what would be a decidedly higher gain. The wager with which I decide upon my life depends on the stakes and not on verification of its probability of winning—which is, moreover, impossible.

10. Modern statistics takes for granted the idea that probability is independent of its empirical verification. The recurrent tendency ingenuously to consider the distribution of frequencies of a given value as an objective property of the system under examination is therefore stigmatized as a “naturalistic fallacy.”30 It is in fact important not to confuse the calculation of probability with its experimental verification. If in flipping a coin the observed frequency of heads and tails is not 0.5 but 0.7, or that of a dice throw is not 1/6 but 3/6, this does not mean that the probabilistic theorem is wrong, but that it is probable that the coin or dice is unbalanced and needs to be replaced.

Statistics is not a science that aims at an experimental knowledge of the real; rather, it is the science that enables us to take decisions in uncertain conditions. For this reason, as was evident in its origins in dice games, the concept that underlies probability is not so much frequency over a long period of time as the “critical odds for a bet,”31 in which frequency is used not to infer a supposedly real property of the system, but—precisely as happens in quantum mechanics—to corroborate or refute a previous conjecture (which is fully comparable to a wager).

11. The idea that potency or possibility (dynamis) should be considered as a way of being along with actuality (energeia) dates back to Aristotle. Against the Megarians, who claimed—not without good reason—that potency exists only in the act, that is, in the occurrence of its exercise, Aristotle objects that if this were the case we could not consider an architect to be an architect when he is not building or call a doctor who is not exercising his art, “doctor.”32 In other words, potency (which Aristotle attributes especially to human techniques and knowledge) is constitutively defined by the possibility of its exercise, its power to be or not to be and to pass or not to pass to the act. According to all the evidence, what is here in question is the way of being of possibility, which indeed exists in the form of not yet being in act, that is, of existing independently of its actual realization. For this reason Aristotle can affirm that “every potency is the impotency [that is, the potency not to be] with respect to the same [thing] of which it is the potency.” The possibility of suspending its own realization is inherent to the very concept of potency.

Although he affirms without reservation the existence of potency, not without contradiction, Aristotle decidedly subordinates the sphere of dynamis to that of reality and energeia. Energeia precedes possibility according to both concept and substance, not only because the adult necessarily precedes the child and man precedes his seed, but also because everything that is potential tends toward the act as its own end. Living beings thus have the possibility of seeing in order to actually see, and not vice versa, and mankind has the possibility of knowing in order to know, and not just to have the faculty of knowing. For this reason, Aristotle can state that, on the one hand, if there are no impediments, what is possible will naturally pass to the act, and, on the other, it does not make sense to speak of possibility with regard to things that necessarily exist.33Aristotle was not familiar with the concept of probability, but he addressed chance (which he called automaton and tuche) in relation to his doctrine of the four causes (material, formal, efficient, and final). Chance is a non-cause, or an accidental cause, which we refer to when events that seem to have been produced because of a given final cause are instead produced accidentally and unexpectedly. If a man who goes to a certain place but without the intention of collecting a debt accidently meets his debtor, who is himself there by chance and pays his debt, we will say that the collection of the debt occurred apo tuches, because of chance.34

It goes without saying that Aristotle rules out that there can be a science of chance and what is accidental: “There can be no science of the accidental, because every science has as its object that which is so always or usually, and the accidental falls under neither of these descriptions. . . . Chance [or fortune, tuche] is the accidental cause of things that happen because of a decision in view of an end. Hence chance and thought have the same sphere of action, for there is no decision without thought. There are infinite causes from which fortuitous accidents may come about; for this reason, fortune is inscrutable to human reason and is a cause only accidentally, but in an absolute sense is a cause of nothing.”35If we try to define probability in Aristotle’s terms, we may say that it is a potency emancipated from its hierarchical subjection to the act. Insofar as it has secured an existence that is independent of its actual realization, such a possibility tends to replace reality and thus to become the object of a science of the accidental—unthinkable for Aristotle—that considers possibility as such, not as a means of knowing the real, but as a way of intervening in it in order to govern it. The analogy with Aristotelian dynamis is all the stronger here since the latter was indeed the specific dimension of human techniques and knowledge. In De Anima, Aristotle thus comes to define the intellect as “a being whose nature is potential being” and compares it to a writing tablet on which nothing has yet been actually written. What happened in modern statistics and quantum physics is that the writing tablet—pure possibility—replaced reality, and knowledge now knows only knowledge itself. Following the beautiful image given by a medieval philosopher, what does not stop being written on the tabula rasa of the intellect is not reality but the very potency of thought, “as if the letters wrote themselves on the tablet.”

12. If we now return to the motivation for Majorana’s disappearance, we may argue that the article we examined earlier shows beyond doubt that he had clearly seen the consequences of the introduction of probability into physics. If we need to rule out every psychological interpretation—as he never tires of repeating that we should—then the meaning of his decision to disappear must somehow refer to this problematic context. The limit of Sciascia’s interpretation, however subtle, is that, if we suppose that Majorana abandoned physics because he had grasped that it led to the atomic bomb, then his decision to disappear and retreat to a monastery appears to be a consequence of the dismay (Sciascia speaks of “disquiet” and “fear”) caused by the disastrous path science had taken. This means locating the decision in that psychological dimension that Majorana wanted to dismiss; just like the “Ibsen heroine” evoked in the letter to Cardelli (probably the character of Nora in A Doll’s House, who abandons her husband because she has lost her moral certainties), Majorana renounced physics because he had lost faith in science.

If we instead accept that his case is intentionally “different”—as Majorana insistently demands, and against the biased testimonies of his colleagues from the Institute of Physics regarding the “eccentricity” and “abnormality” of the “Saracen” (as Amaldi defines him, in a friendly spirit)—then his disappearance must contain in itself, along with its motivations and meaning, a decisive objection to the probabilistic nature of quantum mechanics. It is worth recalling that when Majorana met Fermi, the latter was well known for the statistical model that is still named after him (depending on the statistical model they follow, all particles are divided into bosons, which accord with the statistics of Bose and Einstein, and fermions, which accord with the statistics of Fermi and Dirac). As Simone Weil sensed a few years later, Majorana immediately realized that, as soon as we assume that the real state of a system is in itself unknowable, statistical models become essential and cannot but replace reality (as he wrote in the article we have cited, “the result of any measurement seems, therefore, to be concerned with the state the system is led to during the experiment rather than with the unknowable state of the system before being perturbed”).

The hypothesis I intend to put forward is that, if quantum mechanics relies on the convention that reality must be eclipsed by probability, then disappearance is the only way in which the real can peremptorily be affirmed as such and avoid the grasp of calculation. Majorana turned his very person into the exemplary cipher of the status of the real in the probabilistic universe of contemporary physics, and produced in this way an event that is at the same time absolutely real and absolutely improbable. When, on that evening in March 1938, Majorana decided to vanish into thin air and render ambiguous every experimentally detectable trace of his disappearance, he asked science the question that still awaits its unrequestable [inesigibile] and yet ineluctable answer: What is real?

What Is Real?

Giorgio Agamben