Monthly Archives: August 2007

A World Without Time: The Forgotten Legacy of Godel and Einstein – Palle Yourgrau

What Godel Means by Time
At issue is the leitmotif of Godel’s lifework, the dialectic of the formal and the intuitive, here, of formal versus intuitive time, between what remains of time in the theory of relativity and the time of everyday life. The difference between these two conceptions is crucial. It can be illuminated by considering what the early-twentieth-century philosopher J.M.E. McTaggart called the A-series and B-series. The B-series is founded on the characterization of dates and times in terms of the fixed relationship of “before” and “after.” It is a structurally or “geometrically” defined series, analogous to a space. It is the temporal series captured by calendars and by history books. The year 1865, for example, comes-now and forever-before 1965 and after 1765, and these structural, “geometric” facts are fixed and unchangeable. The A-series, in contrast, is essentially fluid or dynamic. It contains the “moving now,” i.e., the present moment, which is always in flux. That your dentist appointment is at 3 p.m. on May 19 is a B-series fact that has been marked on your calendar for months. It will remain a fact after the appointment is long forgotten. That now, however, is the very date and time of the appointment is a scary A-series fact that has not obtained until this very moment, and will happily no longer obtain tomorrow. (It is no accident that a famous philosophical essay on the A-series is entitled “Thank Goodness That’s Over.”)
Though the A-series represents, intuitively, the most fundamental aspect of time-indeed, what distinguishes time from space-it is marked by several concomitants, each one difficult to capture in the formal language of mathematics. First is the fact that one time-now-is privileged over all others. This privilege passes from time to time. What is now will soon be then. Second, according to this conception, time passes, or flows, or lapses, and in a certain “direction”: what is future becomes present, then past. Third, unlike both space and the B-series, “position” in the A-series is not ontologically neutral. Whereas to exist in New Jersey is to exist no less than in New York (protests by New Yorkers notwithstanding), to “exist in the past” is no longer to exist at all. Socrates had his time on stage, but it passed, he died, and his name has been removed from the rolls. (It follows that there is nothing subjective or mind-bound about the A-series, i.e., about what is happening now. If there is such a thing as “inner time”-the subject, it would appear, of Husserl’s investigations-then this must be distinguished from the A-series.) Fourth, while the past has passed and is now forever fixed and determinate, the future remains, as of now, open. Simultaneity, finally, since it determines what really exists at the same time as other things exist, is absolute and nonrelative. We cannot, merely by choosing a frame of reference, determine what really exists at this moment. Either my friend in Paris is speaking on the phone at very same time at which I am writing this, or she isn’t, regardless of how I try to determine, via synchronized clocks, whether her speaking is occurring at the same moment as my writing.
Intuitively, time is characterized by both the A- and the B-series. If time as we experience it in everyday life, however, is to be identified with formal time-time as it is studied in physics-a problem arises. What we call “t,” the temporal component of relativistic space-time, can be consistently interpreted as representing the B-series. The problem lies with the A-series. Since, as Einstein put it, in special relativity “‘now’ loses for the spatially extended world its objective meaning” that is, there is no objective, worldwide “now”-it appears that “t” cannot represent the A-series, in which there is a single worldwide “now” whose “flux” constitutes the change in what exists that characterizes temporal, but not spatial, reality. This should come as no surprise. One of the most striking characteristics of relativistic space-time is that space and time are no longer to be considered independent beings but rather two inextricably intertwined components of a single new kind of being, not space or time but rather space-time.
The A-series cannot be made to resemble space. What keeps this seemingly obvious fact hidden from many formal thinkers, whether physicists or logicians, is that in special relativity, “t” is formally distinguished from the three spatial dimensions. In the definition, for example, of the space-time “interval”-the unique relationship between any two space-time events that is frame-invariant, hence agreed upon by all observers, no matter their state of motion-the temporal variable, “t,” is distinguished from the three spatial variables by being preceded by a negative sign. All this demonstrates, however, is that time in special relativity has a different “geometry” from the spatial dimensions, not that it is a qualitatively different kind of being, namely something that “flows.” To be blind to this fact is to confuse the formal with the intuitive.

It is not for nothing that with the theory of relativity Einstein is said to have accomplished the geometrization of physics (an achievement for which, as we have seen, he owed a great debt to the mathematician Minkowski, his long-suffering teacher at the Technical Institute in Zurich, who took the bold step of re-creating special relativity in a four-dimensional geometric framework). It is not just that Einstein reconceived the geometry of the universe. Rather, in special relativity, he made the defining characteristic of time not its qualitative distinction from space, as Kant and Newton had done, but rather its contribution to the geometry of four-dimensional space-time. Similarly, in general relativity, he not only provided a new geometry for the laws of gravity, he defined gravity itself geometrically, as space-time curvature. One of Einstein’s claims to fame, after all, is his uncanny ability not only to provide new descriptions of old phenomena but new definitions as well. In this, as in many other aspects of his discoveries, he is as much philosopher as physicist. The coup de grace came when he replaced Newton’s intuitively evident Euclidean mathematics with unintuitive non-Euclidean geometry.

Time as it appears in relativity theory, then, was ripe for consideration in the “Godel program” of assessing the extent to which intuitive ideas can be captured by formal concepts. This is what Godel had in mind when he titled his contribution to the Schilpp volume, “A Remark About the Relationship Between Relativity Theory and Idealistic Philosophy.” The “idealistic philosophers” he was referring to were thinkers like Parmenides, Plato and Kant, who questioned whether our subjective experience of the flow of time has an objective correlative. To such thinkers, time was always an ontological suspect. As before, when he examined the relationship of intuitive arithmetic truth, or big “T,” to its representation as formal mathematical proof in Russell’s Principia Mathematica, Godel would begin by clarifying the distinction between intuitive time and little “t,” its formal representation in Einstein’s theory of relativity as the temporal component of four-dimensional Einstein-Minkowski space-time. Drawing from his contribution to the Schilpp volume as well as the longer versions of this essay that have now been published, we can say that Godel characterized intuitive time-“what everyone understood by time before relativity theory”-as “Kantian,” or, “prerelativistic.” Time in this intuitive sense, he said, is “a one-dimensional manifold that provides a complete linear ordering of all events in nature.” This “objective lapse of time” is “directly experienced” and “involves a change in the existing [i.e., in what actually exists].” Time in the intuitive sense, for Godel, is something “whose essence is that only the present really exists.” In particular, it “means (or is equivalent to the fact) that reality consists of an infinity of layers of ‘now’ which come into existence successively.” These features Godel took to be essential properties of time in the intuitive sense, since “something without these properties can hardly be called time.” Clearly, time so characterized is reflected in the A-series, and indeed Godel refers to McTaggart by name in his essay. The question that remains is whether this intuitive concept can be captured by the formal methods of relativity.
Godel’s Dialectical Dance with Time

As he had previously done in his incompleteness theorem, Godel demonstrated that those who fail to grasp the distinction between the intuitive and the formal concept are not in a position to make a proper assessment of their relationship. Having made that distinction with remarkable clarity, he was able to establish, by an ingenious and entirely unsuspected formal argument-which in itself, as Einstein pointed out, was a major contribution to relativity theory-the inability of the formal representation to capture the intuitive concept. Godel’s dialectical dance with intuitive and formal time in the theory of relativity contained an intricate series of steps. We begin with a large-scale view of the structure of Godel’s argument, then move on to a closer examination. First the forest, then the trees.
The opening move concerns the more limited special theory of relativity. Given that the A-series contains the flux of “now,” the absence of an objective, worldwide “now” in special relativity rules out its existence. But absent the A-series there is no intuitive time. What remains, formal time as represented by the little “t” of Einstein-Minkowski space-time, cannot be identified with the intuitive time of everyday experience. The conclusion, for Godel, is inescapable: if relativity theory is valid, intuitive time disappears.
Step two takes place when Godel reminds us that special relativity is “special” in that it recognizes only inertial frames in constant velocity relative to each other. It does not include an account of gravity. Einstein’s general theory of relativity, in contrast, of which the special is a special case, does. In general relativity, as we have seen, gravity itself is defined as space-time curvature, determined, in turn, by the distribution of matter in motion. It follows that whereas in special relativity no frames of reference or systems in motion are privileged, in the general theory some are distinguished, namely those that, in Godel’s words, “follow the mean motion of matter” in the universe. In the actual world, it turns out, these privileged frames of reference can be coordinated so that they determine an objective remnant of time: the “cosmic time” we encountered earlier. In general relativity, then, time (of a sort) reappears.
But no sooner has time reentered the scene than Godel proceeds to step three, where he exploits the fact that Einstein has fully geometrized space-time. The equations of general relativity permit alternative solutions, each of which determines a possible universe, a relativistically possible world. Solutions to these complex equations are rare, but in no time at all Godel discovers a relativistically possible universe {actually, a set of them)-now known as the Godel universe in which the geometry of the world is so extreme that it contains space-time paths unthinkable in more familiar universes like our own. In one such Godel universe, it is provable that there exist closed timelike curves such that if you travel fast enough, you can, though always heading toward your local future, arrive in the past. These closed loops or circular paths have a more familiar name: time travel. But if it is possible in such worlds, Godel argues, to return to one’s past, then what was past never passed at all. But a time that never truly passes cannot pass for real, intuitive time. The reality of time travel in the Godel universe signals the unreality of time. Once again, time disappears.
But the dance is not over. For the Godel universe, after all, is not the actual world, only a possible one. Can we really infer the nonexistence of time in this world from its absence from a merely possible universe? In a word, yes. Or so Godel argues. Here he makes his final, his most subtle and elusive step, the one from the possible to the actual. This is a mode of reasoning close to Godel’s heart. His mathematical Platonism, which committed him to the existence of a realm of objects that are not accidental like you and me-who exist, but might not have-but necessary, implied immediately that if a mathematical object is so much as possible, it is necessary, hence actual. This is so because what necessarily exists cannot exist at all unless it exists in all possible worlds.
This same mode of reasoning, from the possible to the actual, occurs in the “ontological argument” for the existence of God employed by Saint Anselm, Descartes and Leibniz. According to this argument, one cannot consider God to be an accidental being-one that merely happens to exist-but rather a necessary one that, if it exists at all, exists in every possible world. It follows that if God is so much as possible, He is actual. This means that one cannot be an atheist unless one is a “superatheist,” i.e., someone who denies not just that God exists but that He is possible. Experience teaches us that ordinary, garden-variety atheists are not always willing to go further and embrace superatheism. Following in the footsteps of Leibniz, Godel, too, constructed an ontological argument for God. Then, concerned that he would be taken for a theist in an atheistic age, he never allowed it to be published.
In arguing from the mere possibility of the Godel universe, in which time disappears, to the nonexistence of time in the actual world, Godel was employing a mode of reasoning in which he had more confidence than most of his philosophical colleagues. In the case of the Godel universe, he reasoned that since this possible world is governed by the same physical laws that obtain in the actual world-differing from our world only in the large-scale distribution of matter and motion-it cannot be that whereas time fails to exist in that possible world, it is present in our own. To deny this, Godel reasoned, would be to assert that “whether or not an objective lapse of time exists (i.e., whether or not a time in the ordinary sense exists) depends on the particular way in which matter and its motion are arranged in this world.” Even though this would not lead to an outright contradiction, he argued, “nevertheless, a philosophical view leading to such consequences can hardly be considered as satisfactory.” But it is provable that time fails to exist in the Godel universe. It cannot, therefore, exist in our own. The final step is taken; the curtain comes down: time really does disappear.

Why Nations Go to War – John G. Stoessinger

Perhaps the essential truth about Lyndon Johnson and the men who made Vietnam policy during his presidency was that they had never experienced the kind of pain or tragedy that is the source of empathy. These men had only been successful, and their vision was limited to the American experience. None knew, until it was too late, that nations, like people, can die. None knew that intelligence alone, without wisdom and empathy for suffering, is hollow.
Myths are heady stuff and will not be easily dispelled by even the most conscientious historians. These legends tend to develop a life of their own and those who pass them on from one generation to another stubbornly refuse to be confused by historical facts.
Why does the human species learn so slowly and at such terrible cost? I keep wondering. What I do know is that, in the last analysis, the answer to war must be sought in humanity’s capacity to learn from its self-inflicted catastrophes. Why did the Germans and the French make war between them well nigh impossible after a century that had witnessed three horrendous wars and the Holocaust? And why have the Serbs learned nothing after six hundred years? Perhaps because Germany and France came up with visionary postwar leaders like Konrad Adenauer and Jean Monnet, who said No to war once and for all while Serbia produced a Slobodan Milosevic. Perhaps it is like with ordinary people, some of whom learn and grow from tragedy while others just get older-and more stupid.
How was it possible for Hitler to inflict himself on the German people, to mesmerize them, and to take them with him to disaster in the wastes of Russia?

I am convinced that Hitler’s charismatic grip on Germany can best be explained by the authoritarian structure of the German family. Erik Erikson paints a convincing portrait of the typical German father, whose frequent remoteness and tyranny over his children make their maturation process excessively difficult:

When the father comes home from work, even the walls seem to pull themselves together. . . . The children hold their breath, for the father does not approve of “nonsense”-that is, neither of the mother’s feminine moods nor of the children’s playfulness. . . .

Later, when the boy comes to observe the father in company, when he notices his father’s subservience to superiors, and when he observes his excessive sentimentality when he drinks and sings with his equals, the boy acquires the first ingredient of Weltschmerz: a deep doubt of the dignity of man-or at any rate of the “old man.”. . .

The average German father’s dominance and harshness was not blended with the tenderness and dignity which come from participation in an integrating cause. Rather, the average father, either habitually or in decisive moments, came to represent the habits and ethics of the German top sergeant and petty official who-“dressed in a little brief authority” -would never be more but was in constant danger of becoming less; and who had sold the birthright of a free man for an official title or a life pension.

This kind of father, of course, makes the son’s adolescence an unusually difficult period of “storm and stress” that becomes a strange mixture of open rebellion and submissive obedience, of romanticism and despondency. For each act of rebellion the boy suffers profound guilt, but for each act of submission he is punished by self-disgust. Hence, the search for identity frequently ends in stunned exhaustion, with the boy “reverting to type” and, despite everything, identifying with his father. The excessively severe superego implanted by the father in his son during childhood has entrenched itself like a garrison in a conquered city. The boy now becomes a “bourgeois” after all, but he suffers eternal shame for having succumbed.

During the 1930s the catalytic agent that offered the possibility of escape from this vicious cycle was Adolf Hitler. In the Fuhrer’s world the adolescent could feel emancipated. The motto of the Hitler Youth, “Youth shapes its own destiny,” was profoundly appealing to a youth whose psychological quest for identity was often thwarted. Erikson points out that Hitler did not fill the role of the father image. Had he done so, he would have elicited great ambivalence in German youth. Rather, he became the symbol of a glorified older brother, a rebel whose will could never be crushed, an unbroken adolescent who could lead others into self-sufficiency-in short, a leader. Since he had become their conscience, he made it possible for the young to rebel against authority without incurring guilt. Hermann Goering echoed the sentiments of the Hitler Youth when he stated categorically that his conscience was Adolf Hitler. It was this complete official absolution from guilt that made the German pattern of authoritarianism unique.

Parents were to be silenced if their views conflicted with the official doctrines of the Third Reich: “All those who from the perspective of their experience and from that alone combat our method of letting youth lead youth, must be silenced.” The young Nazi was taught that he was destined by Providence to bring a new order to the world. Young Nazi women too felt a surge of pride to learn that childbirth, legitimate or illegitimate, was a meaningful act because “German women must give children to the Fuhrer.” I recall how, on numerous occasions, large groups of young women would march through the streets chanting in chorus: “We want to beget children for the Fuhrer!” National socialism made it possible for the young to rid themselves of their deep-seated personal insecurities by merging their identities with the image of a superior and glorious German nation. This image of a common future was well expressed in the famous Nazi marching song sung by the German soldiers as they advanced into Russia: “Let everything go to pieces, we shall march on. For today Germany is ours; tomorrow the whole world!”

Gregor Strasser summed up Hitler’s appeal concisely:

Hitler responds to the vibrations of the human heart with the delicacy of a seismograph. . . enabling him, with a certainty with which no conscious gift could endow him, to act as a loudspeaker proclaiming the most secret desires, the least permissible instincts, the sufferings, and personal revolts of a whole nation.


A few weeks before an earthquake devastated Kobe, I was in the Japanese port city as the keynote speaker to the World Congress of Junior Chamber International. The Jaycees were celebrating their fiftieth anniversary year. It was a festive event with a huge gathering of delegates from every continent.

I was seated on the stage about to be introduced by the JCI’s world president, a charming man from the island nation of Mauritius. As I looked over my audience, I noticed a large group of Japanese VIPs in the gallery. They stood out from the glittering assemblage by their dark, solemn-looking suits. A sudden flash of memory came back to me. I had been in Kobe before, under very different circumstances. It was in April 1941 and I was then a boy of thirteen, en route from Prague, Czechoslovakia, to Shanghai, China, fleeing for my life from the Nazi Holocaust.

The story of my family was not unusual for those unusual times. I was growing up in Vienna, Austria, in a middle-class Jewish family when Hitler annexed Austria in 1938.

My parents divorced when my father emigrated to Palestine, where my mother refused to follow him. She did not want to leave her parents behind in Prague. She and my grandparents were convinced that matters would not get worse for the Jews; hence my mother and I moved to Prague to join them.

Shortly after Hitler entered Prague in 1939, my mother learned that my father had died in Palestine, and a year later, lonely and frightened, she remarried. By late 1940, terrible fights erupted between my stepfather and my grandparents, with my mother caught in the middle. My stepfather, who seemed to understand Hitler, insisted upon leaving Europe immediately.

“You are an adventurer,” my grandparents shouted. “This is after all the twentieth century. It can’t get any worse.”

However, the evidence to the contrary was mounting steadily. Hitler had conquered most of Western Europe and the war against the Jews was beginning in earnest. By January 1941, my stepfather dragged my mother and me to dozens of consulates in Prague, begging for visas.

Finally, an official at the Chinese Embassy, in a gesture of compassion, granted us a visa to Shanghai in exchange for “landing money,” which cost us most of our belongings. This visa, however, was useless unless we could procure a transit visa across the Soviet Union, and that, in turn, was unavailable unless we could prove that we could leave the Soviet Union and somehow get to Shanghai. This meant yet another transit visa, this time via Japan.

But it was well known in the Prague Jewish community that the Japanese were sympathetic to the Germans and therefore reluctant to help the Jews. Thus without this indispensable Japanese link in the chain of flight, the Shanghai visa was worthless. In February 1941, however, long lines suddenly formed in front of the Japanese Consulate in Prague. The news had spread like wildfire that a new consul was issuing Japanese transit visas via Kobe to hundreds of desperate Jews.

After several days in line, we were ushered into the office of an elegant, kindly-looking man who, after patting me on the head, issued us three visas without the slightest difficulty. “Good luck,” he said to us in German as the next applicants were already being ushered in. Three days later, my stepfather procured the transit visa across Russia, the final link in the chain. Departure date was set for March 4, 1941, my mother’s birthday.

Pain has etched the memory of that night into my mind forever. My grandparents had come to the station to say goodbye. We were taking the train to Moscow, where we were to connect to the TransSiberian “Express” to Vladivostok on the Soviet Pacific coast. My mother was frantic with grief, my stepfather icy and determined. The train was to leave at 8 P.M.

“I don’t want to go, I want to stay with you,” I screamed, leaping from the train into my grandparents’ arms.

“No,” my grandfather admonished. “You must go.”

He gently lifted me back onto the train, and a few minutes later the train left the station. My grandparents waved a flashlight, the light flickering up and down in the darkness. Up and down. A few weeks later, they were deported to Theresienstadt, the way station to Auschwitz, where they perished in 1944.

The journey through Siberia seemed endless. Most of the time, I stared out at the vast expanses of the Russian landscape, infinitely patient in its snow-covered silence. We shared a compartment with a Japanese diplomat who introduced himself as Dr. Ryoichi Manabe. He was being transferred from Berlin to Shanghai to a new diplomatic post, he explained to us in fluent German. He seemed quite young, perhaps in his early thirties, and had a courtly, gentle manner about him.

We shared our meals with him and I played chess with him occasionally. After the first week of the long journey, my mother mentioned to him that we too were headed for Shanghai, as refugees. After all, the Japanese consul in Prague had helped us, and she saw no reason to fear this nice young man, so well versed in German literature. Before we parted, he handed us his card and invited my mother, quite matter-of-factly, to call him in Shanghai if we should ever need his help.

We then crossed on a small fishing vessel from Vladivostok to Kobe, Japan, where we were allowed to await passage to Shanghai. The three weeks of waiting were tinged with trepidation since we knew absolutely no one in Shanghai. Finally, we were able to book passage and arrived in the Chinese port city in April 1941.

My stepfather, a resourceful man, was able to land a job as a teller in a small bank in the international settlement. My mother developed a talent for millinery, and I was enrolled in a British public school with excellent teachers who thrived on Shakespeare. We lived in two little rooms in the French concession of the city, and my mother prepared modest Chinese culinary miracles. Things were looking up. But this brief interlude came to an abrupt end.

In June 1941 Hitler invaded the Soviet Union, and in December the Japanese, in another surprise assault, attacked Pearl Harbor. Germany and Japan were now military allies in a war for world domination. Not surprisingly, the Germans now instructed the Japanese what to do with the Jews under their control.

There were approximately 15,000 European Jews living in Shanghai at the time of Pearl Harbor. In early 1943 all Jews were ordered to move into a ghetto in Hongkew, an impoverished and neglected section of the city. Within a few weeks, most of Shanghai’s Jews were herded into large, overcrowded communal centers, or tiny, equally overcrowded dwelling places. Food was scarce, sanitation terrible, and education for the ghetto children sporadic and disorganized at best. The ghetto was placed under the direct control of the Japanese military, complete with barbed wire and police dogs. Then, with eviction from our little apartment in the French concession only a week or so away, my mother remembered Dr. Manabe.

I recall my mother agonizing over whether she should take up Dr. Manabe’s invitation to call him. After all, the political situation had deteriorated drastically since that long trek across Siberia. We knew nothing about Dr. Manabe except that he was assigned to Shanghai as part of the Japanese Diplomatic Corps.

Finally, with the move to the ghetto only three days away, my mother decided to take the chance and see him. My stepfather had developed a heart ailment and was afraid to accompany her. He and I spent the day anxiously awaiting her return. She came back at 6 P.M., her eyes shining-Dr. Manabe had been as kind as ever.

Not only had he remembered us, but when my mother asked him to allow us to remain outside the ghetto, he immediately issued a one year extension of stay so that my stepfather could be near a good hospital and I could continue my education in the British public school where the teachers protested against the Japanese occupation of the city by continuing to teach us Shakespeare.

Thus it came about that, in the midst of war and devastation, I received a first-class education. My mother went back in 1944 and again in 1945 to ask Dr. Manabe for another extension, and both times he complied. We eked out a living from my mother’s millinery work; my stepfather had become too ill to hold a job.

I learned excellent English, good French, and passable Chinese and Japanese at a school which, despite the noise of war all around, somehow maintained superior standards. When I graduated in the spring of 1945, I knew the part of Hamlet by heart. Then, after V-J Day, I became a shoeshine boy because that was the best way to meet one of the American demigods who had liberated us and might help me build a future.

Luck smiled on me. In September 1946 a young lieutenant from Iowa, Peter Delamater, wrote a letter on my behalf to his alma mater, Grinnell College, and that fine Midwestern school admitted me with a scholarship in 1947.

My mother and stepfather followed me to America in 1949. In 1950, incredibly enough, I was admitted to Harvard, where I earned a Ph.D. in International Relations in 1954. Thus I became one of the lucky few who had survived the Holocaust and was able to fashion a life in the New World.

After the war, my mother tried to track down Dr. Manabe, to thank him for what he had done for us. She finally received a letter from him in 1952 from an address in Tokyo, thanking her for thanking him for the “small favor” he had extended us. He was living in obscurity now, he wrote. He added that he was happy, though, that in our case, “Humanity had triumphed over evil.” Then he simply disappeared.

Despite repeated efforts to contact him again we failed, and, finally, we assumed that he had died. Yet two questions never ceased to haunt me: Who was the mysterious consul in Prague who gave us that transit visa via Kobe, and why did Dr. Manabe put himself at risk to help us?

I was nearing the end of my speech in Kobe. Then, I briefly told the story of my stay in Kobe over half a century ago and asked the press corps if they could help me find any information they could about the two Japanese diplomats who had saved my life during the Holocaust years. Since I had to return to the United States the following evening, I begged the reporters to give the search priority.

That night the phone rang in my hotel room. It was Mr. Toshinori Masuno of the Kobe Shimbun, a leading Japanese newspaper.

“We found out how you got your visas,” the reporter said. “It was Consul Chiune Sugihara who issued thousands of visas to Jewish refugees against the express orders of his superiors in Tokyo.”

I began to tremble. Was this a Japanese Oskar Schindler or Raoul Wallenberg? I wondered. “Sugihara issued most of these visas in Lithuania until they posted him to Prague in early 1941,”
Masuno continued. “And the three of you were on the list. You were among the last before they shut down his consulate.”

“How did he do it?” I inquired.

“He saw this as a conflict between his government and his conscience,” the reporter replied, “and he followed his conscience.” “When did he die?” I asked.

“In 1986, in disgrace for not having followed orders,” Masuno said sadly. “But he was a moral hero in Israel. They planted a tree in his honor in Jerusalem.”

“And what about Dr. Manabe?” I queried.

“We are still searching,” the reporter replied. “But he’s probably deceased.”

That night I returned to the United States to teach my classes at Trinity University in San Antonio, Texas. My emotions were in turmoil. Too late, I thought. I cannot thank either one of them; it’s too late.

The next morning, the phone woke me from a troubled sleep. It was Mr. Masuno.

“We’ve found Dr. Manabe,” he exclaimed. “He is eighty-seven years old and quite frail, but he remembers everything. He lives alone and has an unlisted phone number. We managed to get it for you, though. Here it is.”

I thought of little else that day, November 16, 1994. And then, in the middle of the night-the middle of his day-I dialed the number.

He did indeed remember everything. We were not the only ones he had helped more than fifty years ago. Other desperate Jews had benefited from his selfless generosity. A music lover, he had come to the rescue of the Shanghai Philharmonic Orchestra by saving its Jewish members from the ghetto. We both tried not to weep as we recalled those far-gone events that seemed to have taken place on another planet. I sent him one of my books that would never have been written without him, and a picture of my mother taken in 1991, a year before her death.

Yet letters and phone calls were not enough. Thinking of his age, I flew to Tokyo and went to see him in the small apartment where he lived, surrounded by his books. I found a man with a beautiful, deeply spiritual face, and a natural grace and dignity. Bridging half a century proved surprisingly easy. He, like myself, had chosen an academic life after the war and had served as a professor of German literature at Tokai University in Tokyo.

We saw each other every day for a week and I quickly grew to love him. On my last day in Tokyo I finally asked the question that had always haunted me: “Weren’t you ever afraid to help us?” I asked. “After all, you could have lost your job, or worse, they could have killed you.”

He looked at me in amazement. “That thought never occurred to me,” he answered. “Besides, people should not be forced to live in ghettos. “

I hugged him goodbye, and by so doing, embraced my long-dead father and my murdered grandparents who had been wrenched out of my childhood during the Hitler years. An old wound, open for more than fifty years, had begun to heal.

Dr. Manabe died in April 1996.

I had the privilege to express my gratitude to one of the true moral heroes of our time and to do so while he was still alive. Most of us who carry such unredeemable debts must somehow try to honor them after our benefactor’s death. I was given the chance to do so in the here and now.

As a teacher of young college students, I see now that I must teach a most important truth: that there is no such thing as collective guilt, and that, in dark times, there are always men and women who will confront evil, even in its most absolute form, and reaffirm our humanity. In the depths of the abyss, moral courage still survives, and at times even prevails.

My life was saved that way not once, but twice.

Beware of Pity – Stefan Zweig

I listened in astonishment, my interest particularly aroused by the vehemence with which he now went on: ‘Don’t let us deceive ourselves. If in any country whatever a recruiting campaign were to be launched today for some utterly preposterous war, a war in Polynesia or in some corner of Africa, thousands and hundreds of thousands would rush to the colours without really knowing why, perhaps merely out of a desire to run away from themselves or from disagreeable circumstances. But as for any effective opposition to a war – I wouldn’t care to put it above zero. It always demands a far greater degree of courage for an individual to oppose an organized movement than to let himself be carried along with the stream – individual courage, that is, a variety of courage that is dying out in these times of progressive organization and mechanization. During the war practically the only courage I came across was mass courage, the courage that comes of being one of a herd, and anyone who examines this phenomenon more closely will find it to be compounded of some very strange elements: a great deal of vanity, a great deal of recklessness and even boredom, but, above all, a great deal of fear – yes, fear of staying behind, fear of being sneered at, fear of independent action, and fear, above all, of taking a stand against the mass enthusiasm of one’s fellows. It was not until later on in civil life that I personally realized that most of those reputed to be the bravest at the front were very questionable heroes – oh, please don’t misunderstand me!’ he said, turning politely to our host, who was pulling a wry face. ‘I do not by any means except myself. ‘
This was how it came about that during the next few weeks I spent the latter part of the afternoons, and as a rule the evenings as well, at the Kekesfalvas‘ . Very soon these friendly chats became a habit and, what is more, a form of indulgence that was not without its dangers. What a temptation for a young man who from childhood up had been buffeted about from one military institution to another unexpectedly to find a home, a home after his heart, instead of bleak barrack-rooms and smoke-filled mess-rooms! When, at half-past four or five, my duties finished, I strolled out there, my hand would no sooner lift the knocker than Josef would delightedly throw open the door as though he had seen me coming through a magic spy-hole. In all sorts of delightful, obvious ways I was made to realize that I was regarded as one of the family. Every one of my little weaknesses and predilections was anticipated and encouraged; my favourite brand of cigarettes was always laid out ready for me, the book that on my last visit I had happened to say I should like to read I would find lying, as though by chance, the pages carefully cut, on the little stool; one particular arm-chair opposite Edith’s chaise-longue was regarded incontestably as ‘my’ chair – trifles, mere nothings, all these, to be sure, but such things as imperceptibly cast a homely warmth over a strange room and, without one’s being aware of it, cheer and lighten the spirit. There I would sit, feeling more at ease than ever I did among my comrades, chatting and joking away as the mood took me, realizing for the first time that any form of constraint fetters the true forces of the spirit and that the real measure of a man is only revealed when he feels entirely at his ease.

But yet another, far more mysterious, factor was responsible for the fact that I found the daily company of the two girls so exhilarating. Ever since I had been sent, at an early age, to the military academy, that is to say, for the last ten or fifteen years, I had lived continuously in a masculine, a male environment. From morning till night, from night till morning, in the dormitory at the military academy, in camp, in barracks, in the mess and on the march, in the riding-school and in the class-room, always and always I had breathed an air that reeked of the male, first of boys, then of grown lads, but always of men, men; I had grown used to their virile gestures, their firm, noisy tread, their guttural voices, their tobacco-y smell, their free and easy ways and sometimes coarseness. To be sure, I was extremely fond of most of my fellow-officers, and could not really complain that my feelings were not reciprocated. But there was one exhilarating element that this male atmosphere lacked; it contained, as it were, insufficient ozone, insufficient power to rouse, invigorate, stimulate, quicken, electrify; and just as our excellent military band despite its exemplary rhythm and swing, nevertheless remained a brass band, its music therefore harsh, blaring, depending solely for its effect on rhythm, because it lacked the delicately sensuous tones of stringed instruments, so did even our jolliest times in barracks lack that element of subtlety which the presence or even the mere proximity of women invisibly adds to all social intercourse. Even when, as fourteen-year-old cadets, we had promenaded two by two through the town in our smart gold laced uniforms and had come across other lads flirting or chatting idly with girls, we had felt regretfully that because of our monastic incarceration our young lives had been violently robbed of something that was every day permitted to our contemporaries as a matter of course, in the streets, in the parks, in railway trains and in dance-halls: the untrammelled enjoyment of the society of young girls. We, segregated, imprisoned behind iron bars, stared at these short-skirted imps as though at enchanted beings, dreaming of even a single conversation with a girl as of something unattainable. Deprivation of that kind is not easily forgotten. The fact that, later on, swift and, for the most part, cheap adventures with all kinds of accommodating wenches came our way, by no means compensated for those sentimental boyish dreams, and I could tell by the gauche and clumsy way in which I stammered and stuttered whenever I happened to be introduced to a young girl in society (although I had by this time slept with a dozen women) that long years of deprivation had impaired, robbed me of, my naive and natural ease of manner.

‘Odd!’ murmured Condor. ‘Odd! I always thought he was exaggerating when describing you. And I may as well tell you frankly – it’s obviously my day for making false diagnoses I was a little suspicious of his enthusiasm. . . I couldn’t really believe that you only went to the house because of that first little mishap, and then went again and again simply out of sympathy, out of friendliness. You’ve no idea how the old man is exploited, and I had made up my mind (why shouldn’t I tell you?) to find out what it actually is that takes you to the house. I thought to myself, either he’s a – how shall I put it politely? – a designing young fellow, who is trying to feather his nest, or, if he does go there in good faith, he must be very young emotionally, for it is only on the young that the tragic and dangerous exerts so curious an attraction. Incidentally, the instinct of really young people in that respect is nearly always right, and you were absolutely on the right track. . . Kekesfalva is really quite an exceptional person. I know perfectly well all the things that can be said against him, and it seemed to me, if you’ll forgive my saying so, somewhat funny your referring to him as a nobleman. But, if you will believe someone who knows him better than anyone else here, there’s no need for you to feel ashamed of having shown him and that poor child so much friendliness. You needn’t let whatever anyone says bother you; it really doesn’t apply to the touching, pathetic, moving person that Kekesfalva is today.’

To think that I had been going about the world at the age of twenty-five with such unseeing eyes! During all these weeks I had been a daily visitor to the house, and, befogged by my own pity, I had refrained, out of a stupid feeling of delicacy, from ever asking either about Edith’s illness or about the mother who was so obviously missed in the house, had never asked how this curious old man had come by his wealth. How could I have failed to see that those veiled, almond-shaped, melancholy eyes were not those of a Hungarian aristocrat, but that their keen yet weary gaze reflected the age-long tragic struggle of the Jewish race? How had I failed to perceive that in Edith yet other elements were mingled, how failed to realize that over this house hung the spectral shadow of a strange past? In a flash I now called to mind a whole series of minor incidents, remembered with what a frosty stare our Colonel had on one occasion dismissed Herr Kekesfalva’s greeting, merely raising two fingers half-way to his cap, and how my friends had talked of the ‘old Manichaean‘. I felt as one does when the curtains in a dark room are suddenly drawn aside, and the sunlight is so blinding that everything swims purple before one’s eyes and one reels in the dazzling glare of the almost inconceivable flood of light.

But, as though he had guessed what was going on in my mind, Condor leaned over me with almost professional solicitude, and his small, soft hand patted mine reassuringly.
‘You couldn’t possibly have known, Herr Leutnant how could you? You have been brought up, after all, in a secluded world, a world apart, and you are, moreover, at the fortunate age when one has not yet learned to regard anything out-of the-ordinary with immediate suspicion. Believe me, as an older man, I know there is no need to be ashamed of being taken in by life now and again; it is, if anything, a blessing not yet to have acquired that over-keen, diagnostic, misanthropic eye, and to be able to look at people and things trustfully when one first sees them. You could not otherwise have helped the old man and his poor sick child so splendidly. No, don’t be astonished, and, above all, don’t be ashamed – you have instinctively behaved in the best possible way!’ Hurling his cigar-stump into a corner, he stretched himself and pushed back his chair. ‘But now I think it’s about time for me to be going.”
Why was the old retainer looking at me so ecstatically? I asked myself in amazement. Why was he so fond of me? Were people really made so kind and happy by seeing others display kindness and pity? If that were so, Condor was right; if that were so, anyone who made a single person happy had fulfilled the purpose of his existence; it was really worth while to devote oneself to others to the very limit of one’s strength, and even beyond. If that were so, every sacrifice was justified, and even a lie that made others happy was more important than truth itself. Of a sudden I felt my step grow firm, for a man who knows that he is bringing happiness with him has a new lightness in his tread.
A man of limited vision is hard to bear with in any sphere in which he is invested with power, but in the army is intolerable. Since service in the army consists of the carrying out of a conglomeration of a thousand-and-one over-meticulous, for the most part outmoded and fossilized regulations, which only an out-and-out martinet knows by heart, and the literal carrying out of which only a fanatic demands, none of us ever felt safe from this worshipper of the sacrosanct army code. As he sat in the saddle his corpulent figure was the very embodiment of military precision, he presided at mess with eyes as sharp as needles, he was the terror of the canteens and the regimental offices. A cold wind of fear invariably heralded his coming, and when the regiment was drawn up for inspection and Bubencic came riding slowly along on his stocky chestnut gelding, his head lowered slightly like that of a charging bull, every movement was stilled in the ranks as though enemy artillery had been brought into action and were already unlimbering and taking aim. At any moment, we knew, the first shot would be fired, and no one could be sure that he himself would not be the target. Even the horses stood as though frozen to the spot; not an ear twitched, not a spur jingled, not a breath stirred. Obviously enjoying the terror that he struck into everyone’s heart, the tyrant would ride forward at a leisurely pace, spearing one after another of us, as it were, with his accurate eye, which let nothing escape it. It took in everything, that steely military eye, it spotted the cap that was pulled down a finger’s-breadth too low, detected the button that was badly polished, spied out the slightest speck of rust on a sword, or a badly groomed horse; and no sooner had the most trifling irregularity come to light than the culprit was for it. Beneath his close-fitting uniform the Colonel’s Adam’s-apple would swell up apoplectically like a tumour, the forehead under the closely cropped hair would turn the colour of beetroot, thick blue veins would stand out on his temples. And then, in his raucous, hoarse voice, he would burst out into a storm, or rather a muddy torrent, of abuse; floods of foul invective would be poured upon the head of the guiltily innocent victim, and sometimes the coarseness of the Colonel’s epithets was so embarrassing that we officers would gaze in discomfiture at the ground for very shame in the presence of the men.
The men feared him as though he were the Devil incarnate, for he would shower fatigues and punishments on them, and sometimes, in his fury, would even punch a man full in the face with his great fist. I myself had on one occasion in the stables seen a Ruthenian Uhlan make the sign of the Cross and tremblingly mutter a short prayer when the ‘old bull-frog’ – we called him that because his fat throat swelled to bursting-point in his fury – was rampaging away in an adjoining box. Bubencic chivvied the wretched lads to the point of exhaustion, cuffed them, made them do rifle drill until their arms almost broke, and compelled them to ride the most restive horses until their legs were chafed and bleeding. Surprisingly enough, however, in their obtuse and frightened way these good peasant lads were fonder of their tyrant than of more lenient and yet more aloof officers. It was as though some instinct told them that this severity of the Colonel’s had its origin in an obstinate and narrow desire for a divinely ordained state of order. The poor devils, moreover, were consoled by the knowledge that we officers did not come off very much more lightly, for a human being will accept the strictest disciplinary measures with a better grace if he knows that they will fall with equal severity on his neighbour. Justice in some mysterious way makes up for violence. Again and again the soldiers were cheered by the story of young Prince W.; related to the Imperial family, he had imagined that he could claim all sorts of special privileges, but Bubencic had sentenced him to fourteen days’ detention just as ruthlessly as though he had been a peasant’s son; in vain distinguished personages had rung up from Vienna to intervene; Bubencic had refused to remit a single day of the young aristocrat’s sentence – a piece of defiance, incidentally, that cost him his promotion.
But what was odder still, even we officers could not help feeling a certain affection for him. We too were impressed by his blunt, implacable honesty, and above all by his feeling of absolute solidarity with officers and men. Just as he would not tolerate a speck of dust on a tunic, a splash of mud on the saddle of a single horse, so he could not endure the slightest injustice; he felt that any breath of scandal in the regiment was a slur on his own honour. We belonged to him and knew perfectly well that if ever one of us got into a scrape the wisest thing to do was to go straight to him. At first he might abuse us roundly, but in the end he would do his utmost to get us out of it. When there was any question of obtaining promotion or of securing an advance from the special officers’ fund for any of us who was in a tight corner, he always took a firm line, went straight to the War Ministry, and forced the matter through with his bullet head. No matter how he might annoy and plague us, we all felt deep down in our hearts that this peasant from the Banat upheld more loyally and honestly than all the sprigs of the aristocracy the spirit and tradition of the army, that invisible glory on which we poorly-paid subalterns subsisted far more than on our pay.
This, then, was Colonel Svetozar Bubencic, the arch-slavedriver of our regiment, in whose wake I now climbed the stairs. During the Great War he was to call himself to account in the same manly, blinkered, naively honest and honourable way in which he was for ever coming down upon us. During the Serbian campaign, after Potiorek’s disastrous defeat, when exactly forty-nine men out of our whole regiment, the Colonel’s pride, retreated safely across the Save, he stayed behind to the last on the opposite bank; then, feeling that the panic-stricken retreat was a slur on the honour of the army, he did something that only a very few commanders and senior officers did after a defeat: he took out his service revolver and put a bullet through his own head, so as not to be obliged to witness the downfall of his country which, with his limited perception, he had prophetically foreseen in that terrible moment when he had watched the retreat of his regiment.
Our decisions are to a much greater extent dependent on our desire to conform to the standards of our class and environment than we are inclined to admit. A considerable proportion of our reasoning is merely an automatic function, so to speak, of influences and impressions which have become part of us, and anyone who has been brought up from childhood in the stern school of military discipline is particularly apt to succumb to the hypnotic and compulsive force exercised by an order or word of command; a force which is logically entirely incomprehensible and which irresistibly undermines his will. In the strait-jacket of a uniform, an officer will carry out his instructions, even though fully aware of their absurdity, like a sleep-walker, unresistingly and almost unconsciously.
I bent down and kissed her hand. When I looked up, I could not understand how this woman with the grey hair, the harsh mouth, and that bitter look in her blind eyes had at first seemed ugly to me. For her countenance now shone with love and human sympathy. I felt as though those eyes that mirrored nothing but eternal darkness knew more of the reality of life than all those that gazed out, clear and radiant, upon the world.
Like a man cured of an illness I took my leave. The fact that at this moment I had pledged myself anew and for ever to another helpless outcast no longer seemed to me to entail a sacrifice. No, it was not the healthy, the confident, the proud, the joyous, the happy that one must love – they had no need of one’s love! Arrogant and indifferent, they accepted love only as homage that was theirs to command, as their due. The devotion of another was to them a mere embellishment, an ornament for the hair, a bracelet on the arm, not the whole meaning and bliss of their lives. Only those with whom life had dealt hardly, the wretched, the slighted, the uncertain, the unlovely, the humiliated, could really be helped by love. He who devoted his life to them atoned to them for what life had taken from them. They alone knew how to love and be loved as one should love and be loved – gratefully and humbly.

Are Quanta Real?: A Galilean Dialogue – J.M. Jauch

Third Day
SIMPLICIO’S DREAM I was in a vast, dimly lit hall, like a church, and there were very many people around. Someone was officiating as at a religious service,(¹) but I could not see him at first because the crowd barred the view. The people were all very solemn and they seemed to know what was going on,(²) but I was completely in the dark as to the meaning of it all. Finally I asked somebody next to me what this was all about. He looked at me rather surprised and then he said in a low voice, “Don’t you know that we are here to await our fate?”(3)

This did not make much sense to me, but because of the solemnity of the occasion I did not have the courage to ask further.

Then I noticed that the crowd was slowly moving toward the center of the sanctuary. I moved along with it, and when I finally arrived close enough to see, I perceived a very old man(4) with a silvery beard wearing a long white dress. He was standing near a roulette table throwing a ball made of luminous stone.(5) Many players stood around the table. Each one had only one chance to play. After the play a little Maxwell demon (6) handed each player an envelope containing his fate and escorted him from the room.

When it was my turn I was frightened and wanted to run away. But one of the Maxwell demons had put his crooked hand around my wrist and croaked with a fantastic little giggle: “Come on, buddy, you can’t escape your fate.”

Seeing that there was nothing else to do, I took my chip and put it on number three. A woman who was standing next to me whispered in my ear (7): “You are a fool, you will never unify the opposites on three. You should have chosen four.”

I felt terribly foolish at not having noticed that myself (8) but at this very moment the old man said sharply: “Les jeux sont faits, rien ne va plus.”

The luminous ball was circling around in an erratic manner, tumbling from one number to another, until it finally came to rest on number three. I had won! (9)

A muffled exclamation of wonder broke the silence and everybody looked at me with astonishment and envy. The mean little Maxwell demon became excessively polite, and the croupier handed me a golden(10) envelope, which contained a card with the following inscription:

The Green Man will see you in his chambers; follow your guide.(11)

Immediately my little demon took me gently by the hand and led me through the crowd, which cleared the way respectfully to let us pass. We came to a door and then descended a spiral staircase into a long, dark passage. At its end we entered a chamber lighted with a pleasant, pale green light. At the wall opposite the entrance was a throne, on which sat the “Green Man,” who immediately addressed me with these words: “I have expected you for a long time and you never came, but now that you are here, it is time to begin. You must find the unknown road to truth.”

I was deeply impressed and did not know what to say. Before I could collect my thoughts the “Green Man” continued: “Tell us what you need in your search for truth, it shall be granted. But remember, you can have only one wish, the rest is up to you.”

I was so startled by this sudden revelation that I could scarcely think. Then the meaning of the statement became clear to me, and I said quickly: “Give me a library containing the books with all the wisdom, all the truth, and all the beauty of all time.” (12)

I had barely finished speaking when the light in the room dimmed and a strange transformation took place. When I began to discern the details of my surroundings I discovered that I was in a kind of open spaceship floating through an immense row of book stacks, which extended to infinity in all directions. The spaceship could be moved at any speed up to that of light and could be stopped in an instant without the least feeling of discomfort. Every hundred miles in each direction there was a small platform on which was installed a librarian working at a desk. I went to one of the stacks and opened a beautiful, leather-bound volume. To my astonishment I could not read it, since it seemed to contain only a random series of letters and spaces. Thinking that it might be written in a foreign language I went to the nearest librarian, about 30 miles away, and asked in what language it was. His answer startled me even more. He said:

“These books contain everything that ever was and ever will be written in any language of the past or the future. But together with all the meaningful statements, they also contain all the random sequences of letters up to the longest book that will ever be written. This is the only truly complete library in the world because it contains everything.” (13)

“But such a library must be infinitely large!” I exclaimed. “No,” he replied, “this library has a finite number of volumes. The exact number is unknown but it is finite.”

“But how can I ever find anything in this library?” I asked in despair.

“We have a most efficient electronic retrieval system,” he said, “and anything you want can be instantly commanded by composing on this command console a message to the central memory device.” To show me how it worked, he commanded for me in an instant a letter written by Galileo to his daughter, Sister Maria Celeste, in 1633.

I was deeply impressed, because I knew that this letter, hitherto lost,(14) contains the clue to the unsolved mystery of Galileo’s trial before the Inquisition in 1633.

But before I had time to open the book and read the letter the librarian continued, “Anything that you wish to see is here at your disposal. Try it for yourself.”

I thought quickly what I could command, and after some reflection said, “Let me see the theory of elementary particles which explains all known facts about them.”

“Which one?”

I was a bit surprised at this question and replied, “I did not know there are several. Of course I want the correct one, that is the one which agrees with all the facts known today.”

He smiled and explained, “There are 137 different theories available which satisfy this requirement. You must give me further specifications if I am to select one. Or do you wish to see them all?” (15)

Much surprised that there should be so many different, correct theories, unable to think of any other criterion for selecting one from all this wealth of theories, and lacking the inclination to study them all, I replied, “No, not just now, I just wanted to know what is available.”

As he turned away to resume his work, which no doubt was immense, he said courteously, but a bit dryly, “Any time you need anything, I am at your disposal.”

I left him, and a deep feeling of depression came over me as I moved aimlessly through my immense library in the three dimensions of never-ending space. . . . . .

1. The semi religious setting, the dim light, and the mystery are all symbols which underscore the ideological involvement in Simplicio’s psychic state.

2. Ideologies are in a sense also social adaptations, and the better they function the less is required of the individual to differentiate himself from the others in the crowd. The process of individuation begins with the awareness of the “other,” who usually seems to the beholder much better adapted than himself.

3. This is it! The fatal word has been pronounced. It is the source of Simplicio’s anxiety, and it represents the existential counterpart of determinism.

4. The “wise old man” is a well-known archetype discovered by C. G. Jung in countless dream sequences. The encounter with the “wise old man” means that the resources of collective racial wisdom are at the disposal of the dreamer if he learns to read and assimilate the symbolic message of the dream.

5. The luminous stone is the “lapis philosophorum” of the alchemists. It symbolizes the integration of the personality.

6. The Maxwell demon was invented by Maxwell in his famous discussion on the irreversibility of thermal systems. It is an imaginary creature (or device) which can control the movements of individual atoms. The demons cannot actually function in physical systems because they are subject to the same fluctuations as the atoms which they are to control. The fact that they can function in the dream means that they are creatures from another level of reality than the dreamer, and thus carry the message of the existence of deeper levels of consciousness which are essential for the psychic processes about to be initiated in Simplicio.

7. The mysterious woman whispering into Simplicio’s ear is the archetype of the “anima.” She is the harbinger of instinctive truths yet to be learned by Simplicio. The passage from the number three to four symbolizes a fundamental problem in individual psychology that is related to the acceptance and unification of opposites. In the context of the dialogue it represents the symbolic acceptance of the principle of complementarity, for which Simplicio is not yet ready.

8. The self-assured intellectual male looks foolish next to the instinctive female, who, with one simple gesture, can upset his entire value system.

9. This is the heart of the dream’s message: What is the good of winning the whole world if one loses one’s own soul? Evidently there are two ways of winning and losing. The first is the one to which the anima was referring just before the game started. The other is the one which we now see occurring. Simplicio is not yet capable of distinguishing the two, hence his surprise at
“winning” when just a moment before he believed the anima that he was going to lose.

10. The gold represents the material gain and also, on a symbolic level, the objective of alchemy.

11. The color green is the symbol of hope and of a new start. It often occurs in dream sequences at a decisive moment in the individual’s history, when options leading to new prospectives become available.

12. This is typical of the materialist’s psychic disposition. He believes that there is no problem which cannot be solved by more or bigger material things.

13. The idea of the “complete” library has been discussed many times before. It occurred to the author from reading “The Library of Babel” by J. L. Borges, in Labyrinths (New York: New Directions, 1961). It poses an interesting paradox. For instance, being complete the library must also contain all its catalogues, including the catalogue of all the catalogues and so on. Evidently such a library cannot be finite. This problem is closely related to Russell’s paradox.

14. We know that the letter referred to here was actually written by Galileo since the replies from his daughter in the convent at Arcetri are preserved. The letters from Galileo to his daughter are unfortunately lost. They would be the most important source of information on Galileo’s trial, since in them he gives a complete account of everything that happened to him when he was questioned by the inquisition in Rome.

15. This is the point where the naked truth is revealed to Simplicio. The ultimate wisdom is not to be found in quantity. There is the other side, so far completely overlooked by Simplicio. There are two criteria of truth as Einstein told us and, as the dream shows, the neglect of the second one leads to absurdity. Cf. A. Einstein, Autobiographical notes, in P.A. Schilpp, ed., Albert Einstein, Philosopher-Scientist (Evanston, Ill.: Library of Living Philosophers, 1949), p. 11.

Fourth Day

SAGREDO If this is so, may we not try to formulate axiomatically the essential properties of a measuring instrument by saying that such an instrument must permit the choice between classical alternatives and no others. This is the exact translation of your definition of unambiguous and of objective, and means, in the formalism of quantum mechanics, that the only observable quantities which can be measured with a particular apparatus are represented in this formalism by commuting projection operators.

SALVIATI I believe that such a characterization of the measuring instrument is possible, but I must express a warning concerning the absolute precision of such an axiomatic formulation. The word “classical” cannot single out such clear-cut properties as you imply with your axiomatic representation. It should be used only in an approximate sense. Indeed, any concrete model of the measuring process based on the essentially quantal nature of all material bodies shows only that the nonclassical features will be absent with an overwhelming probability in the sense of statistical physics. The axiomatic treatment of the measuring process would thus seem to idealize the situation more than it need be.

SAGREDO I understand exactly what you mean and I am convinced that you are right on this point. But in spite of this, it seemed to me of interest to bring out the ideal classical properties of a measuring apparatus with full precision and clarity which can be furnished only by the axiomatic characterization of such a system. The situation is similar to those which we have noticed several times, when an essential point can be made more easily with idealized elements and concepts in a theory. For instance, this is the case when we use irrational numbers. Strictly speaking, such numbers have no counterpart in reality, yet they are extremely useful.

Of course, I am no doubt presumptuous in trying to contradict you in a matter which you understand so much better than I could ever hope to.

SALVIATI I think your point of view offers no serious inconvenience so long as you keep in mind the limitation of your method. In particular, in such a process one must always remember that no formal rendering can ever be complete, that it must leave undefined a certain number of “primitive” concepts and take for granted, without further analysis, certain relationships between these concepts. The concrete meaning of these primitive concepts and axioms can only be formulated in a “meta language” which is outside the formal scheme of the theory. The particular difficulty in this situation is that the proper choice of these undefined concepts and of their interpretation presupposes a complete knowledge of the entire physical situation. Thus at the outset there is a mutual interdependence of the physical content and its conceptualization which can never result from a simple, logical process.

Once one has understood this point one is necessarily more reluctant to attach a great deal of importance to the axiomatic-deductive organization of a theory such as quantum mechanics, although on a superficial level or for didactic purposes such a procedure might be quite useful.

SAGREDO What you say is certainly most significant and lends credence to the belief that there is much more in science than the mere observation and recording of events and their integration into a conceptual structure.

There are also vision and creative imagination, qualities which alone enable us to abstract from the multitude of possible phenomena those which reveal the true nature of reality. Science reveals structures which are significant or meaningful in some sense and the more meaningful they are, the more real they are.

Is this not the answer to the unresolved task in Simplicio’s dream? Are they not the ingredients needed to bring to light the beauty and perfection of creation, all hidden away in Simplicio’s library, but inaccessible to him because he did not pay attention to what is essential in the search for truth?

Among those principles, that of complementarity is no doubt the sum and substance of our experience with the phenomena of microphysics. Instead of being a principle which expresses the limitation of our ability to know, it expresses the very essence of the objective rendering of the physical phenomena in the unambiguous language pertaining to factual evidence. Once its general character is recognized its operation is seen in many areas where objectivation of experience takes place. In particular, the behavior of quantal systems furnishes us with new points of view concerning the essential properties of composite systems, where it is recognized that the sum of the parts does not at all exhaust the properties of the whole.

SALVIATI I do agree, Sagredo, and I have on several occasions formulated similar ideas. I would go further and add that the understanding of the behavior of individuals interacting within a group is incomprehensible without new structural and dynamical categories which cannot be derived from individual behavior.

Just as the correlations between interacting quantal systems lead to many different kinds of mutations in the behavior of individual systems, which, for want of a better term, we call quantum jumps, so does the person integrated in a group produce spontaneous insights which would have been inaccessible to him in isolation.