“If the sick man meditates deeply about what awaits him after death, that means that the dead have touched him: he will die.” (From an ancient Akkadian medical treatise.)
Walter Reed Hospital, May 1956. John von Neumann is lying on his bed, dying of bone cancer, contracted in the service of America while testing the hydrogen bomb. Co-founder of the modern computer and of the theory of games, one of the greatest mathematician of the twentieth century, the Secretary of Defense and the Pentagon brass would sit around his bed to listen to the genius’ last drops of advice. Kurt Gödel, the famous logician who was a colleague of von Neumann's at the Institute for Advanced Study, comes to visit. What follows is the dialogue between them, not from records but through an engagement of the imagination with what is recorded and generally known about the two men.
“Gödel, what a good surprise! Come in, sit down. So, you haven’t forgotten you old friend. Another proof, as if another proof were needed, of the deep originality of your mind. Tell me, how are things at the Institute? How about our colleagues up there? And how about yourself? And your work? From what I can see and judge, at least on the surface, your health’s not bad. You are lucky!”
“Just on the surface, my friend, just on the surface. My morning rectal temperature has been erratic. I thought there would be a mildly negative correlation between my morning rectal temperature and the duration of my night sleep, but I couldn’t find any. There is no clear pattern to the duration of my night sleep either. It seems to depend, to some extent, on whether I leave the toilet’s cover open or closed in the bathroom next door, which I do, on alternating days. As a consequence, I have become convinced that noxious vapors rise from the toilet. They also affect the pattern of my bowel movements. It is remarkable that over the last two months my consumption of milk of magnesia has gone up by roughly a hundred and sixty-five per cent. Someone must be poisoning the Princeton sewer system or some part thereof, to what purpose one can only conjecture.”
“Have you called the police, the fire department?”
“Yes, of course, several times. But you know how sloppy they are. They come in with a measuring instrument, hold it above the toilet, the needle doesn’t move, so they say there’s nothing to worry about. You don’t have to be Sir Arthur Eddington to understand that a single instrument cannot possibly detect all noxious molecules. I’ve pointed this out to them, and I quickly realized that the only noxious vapors they have ever heard of or will be held responsible for, are carburetted hydrogen and carbon monoxide. Think about it, you who worry so much about this country’s preparedness against atomic attack. Think about it. An enemy doesn’t have to bother with big, expensive nuclear weapons. Enough to insert a relatively rare but very toxic substance into the sewer systems, and wait. I suspect Princeton was chosen on account of the number of top scientists living there. It would be interesting to find out if the same or a similar phenomenon is occurring in Cambridge, Massachusetts. I thought of contacting Quine at Harvard.”
“Well, I wish you good luck with your investigations. I must say I am very happy that you are here, because I wanted to ask your opinion about a very old question which of late has been very much on my mind.”
“Coincidentally, what brings me here is that I want to ask your opinion about a very fundamental question which has occupied me for the last few weeks. Suppose that A is a recursively enumerable set, and—”
“Kurt, please, no logic, not now. First, I have a very important and urgent question—”
“Johannes, what could possibly be more important than the possibility or impossibility of an algorithmic solution of all Diophantine equations—”
“Kurt, my question is one of life and death, and I am now, believe me, considerably closer to death than you are.”
“How can you be sure of that, I wonder— But okay, go ahead. What’s your question?”
“In your opinion, Gödel, is this it? Or will we have another shot at it? I mean, is there a significant probability that there will be another life after this one?”
“I think so. I consider it very likely that there is something at work like metempsychosis or transmigration of the souls. It stands to reason.”
“Explain what do you mean by ‘it stands to reason’.”
“Reason, or logic in the widest sense, whatever else it might be, is that which enables us to put some order into the otherwise chaotic flux of our experiences of the world. Isn’t that so?”
“Let’s suppose that’s true.”
“Do you agree, too, that the order we humans find in, or impose on, the manifold of our experiences is not something static, always essentially the same, but gets more interesting, more intricate and more beautiful the more we learn about the world and about ourselves in it?”
“Granted.”
“Learning, therefore, is—what’s that American expression?—the name of the game. I mean, learning or mathesis is the purpose of life, if life has any purpose at all.”
“That’s a big if, my friend, that’s the big if.”
“True. But I take the urgency of your questioning as a strong sign that you want another chance at life. That would be unworthy of you, of the Hans von Neumann I know, if you were not already convinced that life has meaning and purpose. So we may proceed on the assumption that life does have a purpose, even if we don’t know yet what it is, and even if that purpose turns out to be no more than to inquire, as we are doing now, into whether life has a purpose or not.”
“Yes, we can assume that.”
“Well then, consider our capacity for learning. Learning which is the name of the game, since life, as we agreed, has a purpose. But what sort of game is this? Of the millions and millions of possibilities open to any intelligent individual when it comes to his development by means of learning, we, as it happens, are able to realize one or two in this life, because of lack of time. A given brain can only realize about one-millionth of the total number of its possibilities. I, for just a single instance, have not had the necessary time to develop my mind in the direction of theology, although I have glimpses of astounding connections between Cantor’s theory of the ordinals and the Neoplatonist doctrines of emanations. Or take Einstein. I know how much he would have liked to be able to play Beethoven’s Rassumovsky quartets on his violin, but he never found the time. How can we reconcile the notion of life having meaning and purpose with such evident, egregious waste? What could be the point of a process which produces human brains in big numbers, but forever denies each individual brain the possibility of a fuller or wider development? The only way out of this dilemma is to admit that this life is only one act in a play consisting of many acts. That we, or some of us at any rate, will be able to remember what we learned in previous lives, and hold on to it, and keep adding to it.”
“What you say reminds me very strongly of the remarkable story of Er in Plato’s Republic. The moral of the story is that the more we learn in this life, the better prepared we will be, when we arrive after death at Lethe’s plain, to dominate our thirst, our desire for drinking the waters of forgetfulness. And so the more will we be able to remember from previous lives and the wiser will we become on each incarnation. I would put it briefly and poetically like this: the Greek root for learning, math, is opposed by Plato to the Greek root for forgetting, lath. You know, Gödel, some scholars refer this myth of Er to the Orphics mysteries, but I am convinced that the origin of all such stories and doctrines is Pythagoras.”
“Nothing happens by accident, my friend. Plato was a reincarnation of Pythagoras. And so am I.”
“Kurt, are you serious?”
“Why, of course I am serious. Many people, including Aristotle, have laughed at Pythagoras’ famous idea that all is number. I believe I was the first one to implement that idea, by assigning a number to every proposition, to every statement about the world. This would hardly have occurred to anyone who is not Pythagoras redivivus.”
“Well, I’ll be doggoned. But as long as we’re on the subject, let me say that often, and especially in my dreams, I am under the very definite impression that I am a reincarnation of Archimedes.”
“I am definitely inclined to think that you are.”
“So, Gödel, is it your opinion that you and me, with our enormously superior brains, stand a much better chance of being reincarnated as human beings than the riff-raff, the hoi polloi?”
“Absolutely. You see, among living beings, only those who are able to learn have any chance of being granted further lives. Otherwise, what would be the point of it? But even among human beings, the capacity for learning varies widely. Men such as you and I, with our extraordinary mental capabilities, are virtually assured another life.”
“That’s encouraging. Listen: let’s try to keep in touch in our next life. Perhaps you and I will be able to collaborate again on some momentuous work, and have both our names affixed to some immortal theory.”
“It would be a real pleasure.”
“There is one crucial point in your argument, however, which fails to convince me. You speak of an evident, egregious waste, which you hold incompatible with reason and with any reasonable purpose of life. Yet of the energy produced by our sun only a minuscule amount, of the order of let’s say ten to the minus fourteen, can be remotely related to the sustenance of life on this planet. Wouldn’t you call that evident and egregious waste? To make my point more forcefully, look outside that window, if you please. What do you see?”
“Not much. There’s some kind of white dust everywhere. It looks like it’s raining ashes, or tiny white feathers, or cotton. There’s a prodigious number of rotating helices or aeorofoils slowly descending to the ground.”
“My excellent Gödel, that white dust, that cotton rain, those aerofoils slowly coming down, that is the annual, noiseless rite of spring in Washington, D.C. It is the genetic assault of poplars, willows, maples, sycamores, dandelions, and god knows what else, out to conquer the world. It constitutes an evident and egregious waste of energy, don’t you think? Your principle of natural parsimony smacks of Leibniz’s Theodicy and of the Cosmology of Maupertuis, but I am afraid that in reality individuals count for nothing, and even entire species for not much. Nature’s attitude seemes to be just as unsentimental and devoid of feeling as Napoleon’s. Remember? When, after the battle of Eylau, Napoleon and his aide-de-camp surveyed the field strewn with the bodies of French soldiers, the warlord reportedly said, ‘Bah, just one night of Paris will replace all that.’ There you are, my dear Gödel: Tout ça—bah—une nuit de Paris.”
“I don’t dispute that there is much egregious waste in nature. But I make an exception when it comes to consciousness, and a stronger exception when it comes to fully developed consciousness. One thing is a dandelion, and another thing is a grenadier or a dragoon. And still another thing are you and I.”
“But there is another difficulty with your, or Pythagoras’, idea of transmigration of souls. What could be roughly balanced twenty-five centuries ago is no longer possible today. The human population of the world has been increasing at such a rate that there are, at any given moment, more bodies than available souls. All those, plus other difficulties, make the likelihood of the preservation of my consciousness after death, at least in my view, rather low. I am thinking that a more prudent course of action would be not to wait till death comes but to tackle the problem while I am alive, and while I still have my wits intact.”
“Do you believe you will be able to find a cure for your cancer?”
“No, I don’t believe I’ll be able to do that in the usual medical sense. But I may find a way to go back in time. You see, according to some expert opinion, the cancer in my bones may have been caused by the strong doses of ionizing radiation my body absorbed at the nuclear tests where I was present, especially the ones at the Bikini atoll. If I succeed in going back in time and skip those tests, I may be able to skip the cancer as well.”
“That stands to reason. Don’t forget that some years ago I found a new type of solutions to Einstein’s equations which allows going back in time by the simple expedient of making a round trip in a rocket ship along a sufficiently wide curve.”
“Yes, your solutions to Einstein’s equations are very much in my mind. But I feel tired. These days I tire easily. When will you be back in Washington? You don’t know? Well, let me point out that this may well be the last time we see each other. At least, in this world. Give my regards to Adele and to your mother.”
“And give mine to Klara. In any case, I will send you a letter with my questions regarding representations of recursively enumerable sets. We didn’t have the opportunity to discuss that today, and I mean to have your opinion. I really do. Auf Wiedersehen.”
John Von Neumann with President Eisenhower and Kurt Goedel with Albert Einstein.
