Early the next morning, Mrs. Dresel’s telephone rang. It was Professor von Laue, calling for Szilard. “Your manuscript has been accepted as your thesis for the Ph.D. degree,” von Laue said.13
Both Einstein and von Laue were surprised and pleased with Szilard’s thesis, for it refuted a scientific concept that had puzzled physicists for half a century. He had “exorcised” Maxwell’s demon and done it in a way that united both classical and modern physics.
Thermodynamics is the study of heat and its conversion to mechanical, chemical, and electrical energy. Certain principles, or laws, of thermodynamics describe how heat behaves, and of these the second law asserts that it is impossible by any continuous self-sustaining process for heat to be transferred spontaneously from a colder to a hotter body. The energy lost, or unavailable, was called entropy by the German mathematical physicist Rudolf Clausius in 1850, when he formulated the second law. In all natural systems, entropy (disorder) increases over time. Clausius even assumed that as entropy increased the universe would eventually “die” by cooling, a notion that Szilard had first encountered at age ten in the epic Hungarian poem The Tragedy of Man by Madách, years before he studied physics. For the rest of Szilard’s life, he remembered Madách’s scene in which starving Eskimos are the last survivors of the human race as the earth steadily cools. The entropy concept had momentous personal meaning for Szilard, quite apart from its significance in science, and this concern may explain why he gave the subject so much thought.
In 1871, fifty years before Szilard wrote his thesis, the Scottish physicist James Clerk Maxwell published Theory of Heat. In it he posed a way to defy the second law of thermodynamics with an impish creation. Maxwell conceded that the second law “is undoubtedly true as long as we can deal with bodies only in mass, and have no power of perceiving or handling the separate molecules of which they are made up.” But he postulated that a “being” small enough to manipulate molecules—his demon—should be able to defy the second law and use all available heat energy without expending any in the process, in effect creating a perpetual-motion machine.14 To prove his point, Maxwell described a vessel with two chambers, A and B, which were connected by a tiny hole. Then he proposed that his demon “opens and closes the hole, so as to allow only the swifter [hotter] molecules to pass from A to B, and only the slower [cooler] ones to pass from B to A. He will thus, without expenditure of work, raise the temperature of B and lower that of A, in contradiction to the second law of thermodynamics.”15
At the time Szilard encountered Maxwell’s demon, physicists explained the second law in two ways: One was phenomenological; the other, statistical, or atomistic. The phenomenological theory started from the principle that heat is energy and always flows spontaneously from hot to cold regions. Laboratory experiments could demonstrate this, and using various ingenious arguments, many diverse phenomena could be explained by this principle. Clausius had formulated an abstract concept of entropy this way when he wrote that “the energy of an isolated system remains constant, and its entropy always increases.”16 With this, a theory that first explained the nature of heat was extended to include all forms of energy.
This phenomenological argument was simple and elegant, but necessarily abstract, and by the turn of the twentieth century, some physicists sought a more concrete formulation of the same idea. In doing so, they turned to the frontier of physics at the time, to the study of atoms, and within this field they described various physical events in terms of the random motion that atoms were known to perform. Atoms could not be observed in a laboratory, however, so physicists had to resort to models of atomic behavior by using statistics and probability. It was (and still is) impossible to describe the nature and position of each atom at a given time; the best physicists could do was describe the probability that certain events and conditions are occurring on the atomic level, making their method statistical. Around the turn of the century, Austrian physicist Ludwig Boltzmann was the first to quantify heat and entropy as statistical probabilities that he related to the randomness found in atomic movement. 17
With this, two different explanations were available to describe thermodynamic equilibrium: In a phenomenological explanation equilibrium is static, whereas in a statistical explanation it is dynamic. Szilard had considered both approaches to entropy and in his thesis demonstrated that the atomic fluctuations that are part of a detailed statistical equilibrium can be included within the elegant but abstract phenomenological theory as well. And he did this without making any reference to probability or other mathematical models of atomic behavior. As he explained it later, he “showed that the second law of thermodynamics covers not only the mean values, as was up to then believed, but also determines the general form of the law that governs the fluctuations of the values.”18
In his calculations, Szilard also demonstrated that entropy must increase for Maxwell’s demon, using proofs from both the “old” and the “new” physics and forging a link between classical and quantum mechanics. The second law, he showed, does not become inexact when demonstrated statistically but “evolves in some higher harmony” to explain not only thermodynamics but also its fluctuations—and other changes as well. “On the Extension of Phenomenological Thermodynamics to Fluctuation Phenomena” was accepted as his doctoral thesis in 1922 and in 1925 appeared as his first published paper, in Zeitschrift für Physik, Europe’s leading physics journal. The thesis was noted as “eximia,” the highest honor.19
Historians of science have found other achievements in Szilard’s thesis as well. To give a mathematical expression of “thermal equilibrium,” Szilard coinvented the concept of sufficiency (a statistic that summarizes all the information in a sample) at about the same time as the English mathematician Ronald Aylmer Fisher did, but entirely independently.20
While Szilard struggled with these abstract mathematical concepts, he was forced each day to confront a more practical numerical problem: inflation. By 1922 it had risen to undermine even the lives of the wealthy, and the cost of meeting League of Nations reparation payments for the world war further eroded the German mark’s value. To survive, both Leo and Bela collected food coupons at their schools and redeemed them for sugar, flour, and other commodities, which they gave to Mrs. Dresel. The economy in Hungary was almost as weak, and the Szilards could only rarely send food packages to their sons in Berlin. “I remember,” Szilard told a friend years later, “walking around Berlin, looking at the food in store windows, looking at the people in restaurants, and not being able to afford a thing. To satisfy my appetite, I didn’t eat. I just looked.”21
It is a mystery to Bela how Leo survived as a student once his roll of 100-pound notes was spent. Bela earned money tutoring fellow students in engineering drawing and as a part-time draftsman for engineering companies. Except for the occasional help he gave to students needing tutoring with their math, Leo appeared to have no income at all. Yet somehow both Bela and Leo managed to send small sums of money to their parents in Budapest. From their first days together in Berlin, Bela did most of the letter writing home; Leo would only sign “Gruss, Leo” (Greetings, Leo) at the bottom of the last page. After a while, as Leo became involved in his lectures and thesis, even this became too demanding, and he scrawled only “Gr. Leo.”
Within months of submitting his doctoral thesis, in the summer of 1922, Szilard wrote a second paper on thermodynamic equilibrium: “On the Decrease of Entropy in a Thermodynamic System by the Intervention of Intelligent Beings.”22 This work extended the calculations in his thesis from physical phenomena, such as heat and gases, to “information” by paying more attention to the activities that Maxwell’s demon might perform. This work is now considered to be the earliest known paper in what became the field of “information theory” in the 1950s and 1960s. “In eliciting any physical effect by action of the sensory as well as the motor nervous systems a degradation of energy is always involved, quite apart from the fact that the very existence of a nervous system is depend
ent on continual dissipation of energy,” Szilard wrote.23 Or as Szilard’s friend in Berlin physicist Carl Eckart later summarized: ‘Thinking generates entropy.”
Here Szilard addressed Maxwell’s challenge directly, seeking the essential interaction that might allow the demon to decrease his system’s entropy. Szilard found that the interaction is “a kind of memory” inherent in the “measurement” that the demon must perform when he decides to let one molecule through the hole but to block another. To measure, he argued, is to establish and memorize. Szilard assigned a value of y for the demon’s memory/measurement, then identified this activity according to the time (t) it occurs. “If we are not willing to admit that the second law [of thermodynamics] is violated,” he wrote, “we have to concede that the action which couples y and t—i.e., establishes the ‘memory’—is indissolubly connected with production of entropy.”24 Szilard then postulated that any decrease of entropy in other parts of the system would be compensated by an increase in that of the memory/measurement process itself. Therefore, Maxwell’s demon could not decrease entropy in the system and thus could not violate the second law of thermodynamics.
“In this paper,” Eckart noted, “Szilard had eradicated the ancient dichotomy of mind and matter, just as Einstein had already eradicated the less ancient dichotomy of energy and matter.”25 When von Laue and Planck reviewed Szilard’s work on entropy and information, they found it an example of independent thought and recommended “warmly” to the faculty that he be admitted. The two reviewers did note, however, that Szilard “obviously chose some of the experiments not very carefully . . . but the way he did it is correct.”
While Szilard saw the key elements of information theory some three decades before it became popular, there is no evidence that the theory’s early developers were ever aware of his pioneering work. For although he first wrote about his insights in 1922, he did not present them publicly until he gave a “habilitation” lecture in 1926 to qualify for a teaching post at the university—and this Szilard did not publish in Zeitschrift für Physik until three years later.26 If any link did exist, it may have come through the extraordinary mind of John von Neumann, the mathematical genius whom Szilard knew and taught seminars with in Berlin during the late 1920s. He may have recalled Szilard’s bridge between statistical definitions of motion and the interchange of ideas as von Neumann designed and built the world’s first computers in the 1940s. In 1951 the information theorist Leon Brillouin reviewed Szilard’s 1929 paper; he apparently heard about it from Warren Weaver at the Rockefeller Foundation. Brillouin then met and chatted with Szilard around Columbia University and after these conversations restated the idea: An intelligent being, whatever its size, has to cause an increase of entropy before it can effect a reduction by a smaller amount. Claude E. Shannon, who spelled out detailed relationships between information and entropy in the 1950s, also later acknowledged that Szilard’s paper had proposed the basis for his new field of study.27
The way that Szilard set aside his insightful paper on information and entropy shows the impatience—even audacity—of his restless mind. He rarely followed an idea from beginning to end, taking his intellectual discovery to its practical application; had he done so, Szilard might have tried to design a computer in the 1920s—a Bride-o-Mat for thoughts rather than emotions. Thinking that some of his ideas had practical value, he did apply for patents now and then, hoping revenue from his inventions would finance free time to continue brainstorming. But most of Szilard’s thoughts were never even scribbled in his hasty hand, and he rarely kept a notebook or journal, as many scientists do. Instead, he freed his ideas in conversation and wondered on.
In addition, Szilard seems to have sought something even broader than what we know as information theory. Influenced by Einstein’s quest for unifying principles, Szilard was after a more general concept for understanding life itself—and on the grandest possible scale. Szilard was fascinated with kinetics, the science of objects in motion, and for him the “equilibrium” that any activity reaches—whether molecules in water, people in a railway station, or stars in a galaxy—tended in some way toward order and away from chaos. He seemed to crave universal laws that would explain equilibrium and define order and no doubt enjoyed discovering that the second law “evolves in some higher harmony” beyond classical non-statistical principles. In this pursuit, the dynamics of information were just one of many activities that gave mystery to the world.
Szilard may have even seen entropy as a concept to explain and unify other scientific and personal understandings. What we call disorder or chaos might actually be order, if order is seen as a random distribution and not as a static, idealized condition. Often he spoke to colleagues in Berlin about freie Weglänge, the free path of molecules as they move between collisions, suggesting that at this moment of their escape a kind of universal order occurs.28
Colleagues such as Eckart have even suggested that Szilard could be so brilliantly original because on his own free path of thought he was able to personify abstract theoretical concepts. In a sense, his analysis of the problems facing Maxwell’s demon became an exercise in psychophysics, just as years later he would use a personalized approach to try to trick mammalian cells into dividing with a kind of psychobiology.29
He received his doctorate in physics on August 14, 1922, and wondered what to do next. At first, he “thought it would be interesting” to earn a second doctorate, this time in economics. But when he applied at the university, he was referred to one official after another, each doubting that it could be done. As Szilard persisted, he eventually was shown into the office of the rector.
“We would like to oblige you,” said the rector, “but I don’t see how we can do it. When we gave you the degree of doctor of philosophy, we certified that you are a man who is able to acquire any kind of knowledge that he desires, is capable of independent judgment, and has the maturity of a scientist and scholar. I don’t quite see how we can certify the same thing twice.”30
Still, Szilard enjoyed the atmosphere around the university and relished talking and arguing with his colleagues. Although shy in most social situations, he could be glib and entertaining among intellectual peers, posing impossibly simple questions or improbably complex answers in the chatter of academic discourse. One colleague with an esoteric sense of humor called Szilard the university’s Katholisator, a medieval title bestowed on the academic official charged with making sure that students and visiting scholars met all the right people. And with informal relations already begun among Planck, Einstein, and other great men of science, Szilard seemed at ease in this role.31 He would play it for the rest of his life.
CHAPTER 5
Just Friends
1920–1932
Women bored and befuddled Leo Szilard. They were, for him, both weird and wondrous creatures; weird because they didn’t think logically, as men did; wondrous because they lived in a seemingly fanciful and sensuous realm that he could only begin to fathom. Szilard became infatuated with several women in his life, especially when he could match wits and banter—his closest approach to flirting. But for most of his life the intimate honesty he first shared with his mother was never captured in another relationship—never, it seems, even seriously pursued—until years after he came to know the woman who would be his wife.
This meant that Szilard’s friendships with both men and women were practical, candid affairs based on certain shared interests. When those interests waned, so did the friendships as Szilard’s mind chased on to new curiosities. “Leo would pick up people, suck them dry of ideas, and like an empty orange peel, toss them aside,” his brother, Bela, recalled of their years together in Berlin in the early 1920s. For Leo, friendships were mostly extensions of his mind, not of his heart.
Shy and introverted except in situations he could clearly control, Szilard behaved formally with most of his friends. As a teenager in Budapest and as a young man in Berlin, he seemed awkward at the few social gatherings he bothered
to attend, by turns withdrawn, aloof, gregarious, or distracted. His giddy and brooding adolescent infatuation with Mizzi Freund, a coquettish woman who was older than he and married, left Szilard reluctant to open his heart. His teenage companion from across the Fasor, Alice Eppinger, was more a fixture in his family life than a personal sweetheart—first his sister Rose’s best friend and only rarely the object of his own attentions. At the time of Leo’s first acquaintance with Alice, Bela and Rose Szilard, their cousins the Scheiber boys, and Alice took hikes in the Buda hills every week. But Leo never joined them, and his own excursions with Alice seemed strained, almost furtive.
Alice admired Leo in high school, and she thought him especially handsome in uniform during the war. Sometimes directly but more often through Bela, Alice wrote to Leo in Berlin. She seldom received a direct reply. “I missed him terribly,” she recalled years later, “and decided to do something bold.”1 When her high school studies ended with a baccalaureate degree in mathematics in the summer of 1921, Alice boarded a train in Budapest and headed for Berlin, seeking a way—somehow—to be closer to Leo. A gifted math student, Alice was accepted at the University of Berlin for the winter semester of 1921–22, the same time that Leo was struggling unsuccessfully with von Laue’s assigned thesis topic for a doctorate in physics. Her father’s business contacts brought him to Berlin so often that he owned a house there and knew the city well. He arranged a room for her in an elegant dormitory for university women on the Kurfürstendamm, the lively and broad boulevard near the zoo and the Tiergarten—Berlin’s central park. Mr. Eppinger liked Leo and thought, as Alice did, that if she studied in Berlin, Leo might see more of her and perhaps consider marriage. Mrs. Eppinger had no such expectations but, to satisfy her husband and daughter, made the trip to Berlin, inspected the dormitory, and grudgingly approved Alice’s move.
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