Edge 83— April 2, 2001

(6,648 words)



Ten years ago at the AAAS, Dennis Overbye, author of the classic Lonely Hearts of the Cosmos, found himself on a rainy Sunday afternoon in an auditorium watching a handful of historians and physicists arguing about whether Einstein's first wife Mileva had actually invented relativity. This was an eye opener to him, to put it mildly. He was astounded that there could be any mystery about either the origin of relativity or about Einstein's life. He had just assumed that he was so famous and so recent that everything that could be known about him was known.

What followed was a 10-year investigation in which Overbye immersed himself in Einstein's life and wrote his recently published book, Einstein In Love.

"Romantically speaking, Einstein always felt — and always told his girlfriends — that Paradise was just around the corner," he says," but as soon as he got there, it started looking a little shabby and something better appeared. I've known a lot of people like Albert in my time. During this project I have felt lots of shocks of recognition. I feel like I got to know Albert as a person, and I have more respect for him as a physicist than I did when I started, simply because I have more a sense of what he actually did — and how hard it was — than before. If he was around now, I'd love to buy him a beer ..... but I don't know if I'd introduce him to my sister."

— JB

DENNIS OVERBYE is Deputy Science Editor of The New York Times and author of the critically acclaimed Lonely Hearts of the Cosmos and the recently published Einstein in Love.


A Talk with Dennis Overbye

A Talk with Dennis Overbye

"What else is there? Sex and physics."


John Baez and Terry Sejnowski on Freeman Dyson's "Is Life Analog or Digital?"

Response to the responders, from Freeman Dyson
Chris Westbury on Yossi Vardi's "The Economics of Dreams"
Leon Ledeman and Jeremy Bernstein on "Sex and Physics"


A Talk with Dennis Overbye

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Edge: What was Einstein's big question?

DENNIS OVERBYE: Did God had any choice in creating the universe? This question, Einstein's favorite, was at the root of all of his science. I take the question to mean whether the universe, the laws of physics as we are finding and uncovering them, are logically necessary. Or can you imagine consistent alternative universes, not just with different values for constants like the speed of light and Planck's constant, but maybe with a whole different set of fundamental forces and particles. Is quantum mechanics really necessary? Is there an alternative to what we have now, or, if you really understood everything, would you know that it had to be the way it is? Einstein obviously felt very strongly that it had to be this way.

EDGE: Did Einstein stop asking questions later in his life? Did something happen to him later in his life where he turned inward and stopped listening to other people?

OVERBYE: Einstein never stopped talking to other people and asking questions, but after a certain time he increasingly steered an independent course of thought. One turning point came in the fall of 1915 when Einstein got the final version of general relativity into shape and he used it to calculate the perihelion shift of mercury — a minute discrepancy in the planet's motion that had puzzled astronomers for decades. This was a calculation which had no fudge factors at all. It was either right or wrong, and it came out right on the nose. Einstein had developed this theory basically from pure thought and logic.

It was almost like a conversion experience. Later he said he had heart palpitations when the answer came out. And it probably made him a little too cocky about the power of pure thought. He was so impressed that he started being guided more and more by mathematical elegance, and probably less and less by experimental fact as he went on through the succeeding years searching for his so-called unified field theory and he became divorced from the main body of physics that was going on.. And of course what was going on mainly was nuclear physics, which was all quantum mechanics, and he wasn't very happy with the direction that that was going, so he basically reserved his right to step aside from it.

EDGE: If he were alive today, how would he feel about the way things are?

OVERBYE: That 's an interesting question. I think he'd be very puzzled. Today there is a candidate for a unified theory, namely string theory, and it certainly is mathematically challenging, to say the least. Would Einstein be a string theorist? Strings seem to have taken physics departments by storm and they are almost the only game in town, but Einstein had this deep-seated need to be an outsider. So I don't know.

He would be disappointed with the current vogue for multiple universes, I think, and of course that quantum mechanics is still at the center of physics. There is a small minority of physicists, I am told, who think that string theory may ultimately wind up resolving some of the paradoxes of quantum mechanics. But I think most physicists believe that the main principles of quantum mechanics are here to stay, and that general relativity won't be modified. But there certainly is a big schism in physics.

There is a saying in the newspaper business that some stories are too good to check, and the legend of the humble patent clerk who overturned the universe was certainly such a story for most of my life. Not ever having done any investigation, I didn't realize that there was a lot of mystery about Einstein. He'd been very secretive about his family life, and the secrecy had prevailed after his death. He left behind some 40,000 documents in Princeton, and they had been locked up like the Dead Sea Scrolls until the late 1980s when the Hebrew University (which owns Einstein's copyright) and the Princeton University Press began to publish them. In the course of their investigation the scholars on the Einstein Papers project found love letters that he had written to Mileva when they were both students in Zurich in the late 1890s, and the years just after the turn of the century. It was clear from these letters that Einstein had talked about the issues of relativity, and atomic theory and everything else, but especially relativity, with Mileva. There were statements in these letters such as "how happy and proud I will be when our work on the relative motion is complete." It sounded provocative to some renegade historians and they made a fuss about Mileva having been deprived of her share of credit. I walked into one of those debates by accident.

Actually if you read these letters in full and in context, that statement has more emotional content than intellectual content. He was reassuring her about the state of their relationship. At the time they were separated and their parents were both violently opposed to the union. She was Serbian, he was a Jew from southern Germany. This was just not done as far as his mother was concerned. Plus Mileva was older, and that was a no-no. So I began looking into it. I discovered that these love letters were just the tip of the iceberg. Nobody had really tried to tell the story of where general relativity had come from, and the very winding path that he had taken to it, for a popular audience.

EDGE: I like this idea of combining love and the universe.

OVERBYE: What else is there? Sex and physics.

EDGE: To what extent is our view of the universe, nature, ourselves, affected by ideas of love, or specifically the subject of your book, Einstein in Love?

OVERBYE: That's a big question. Of course, your view of the world is affected by your emotions, your hormones, every instant of the day. If there were a way to keep very precise track of your attitudes — and they would probably shift all over the place depending on how you are feeling — you might have a hard time defining exactly what the normal John Brockman is. People feel differently in the morning when they wake up than in the evening than when they go to bed. You may feel better after lunch. You certainly feel better if you're involved in some sort of a relationship and you have that kind of tingle, and there's a kind of promissory glow to the world.

I don't think you have to be a scientist to understand that. What it has to do with scientific creativity is what everyone wants to know. John Wheeler told me recently that I should do an experiment in which I get two groups of physicists and give one group Viagra and the other a placebo for a year, and then have a committee evaluate their scientific output during the time. He was basically joking, and I don't know if Viagra actually enhances desire or just ability. An evolutionary psychologist would say the whole point Einstein inventing general relativity was in order to get laid.

Mathematical theory is just another form of peacock feathers. That may leave women out of the equation, evolutionarily speaking, so I'm not happy with such a simpleminded explanation but I don't know the answer. It is generally thought that Einstein's last real scientific contribution was in the 1920s, when he invented Bose-Einstein statistics. At that point he was 45 or so, so he was at the point where theoretical physicists consider their creative lives over. But he certainly maintained a vigorous romantic life, with various affairs and so forth through the rest of his life in Berlin, which went on in 1933, and he seemed to have had a girlfriend in Princeton — the wife of a Russian sculptor — in the late 40s. If he was being less creative at that time, I don't think it was because he was necessarily feeling less sexy; he might have run out of ideas, or he might have been pursuing his mathematical dreams, a little too far from contemporary physics, or there was some evidence, And, in his biography of Einstein, Abraham Pais made the point that after about 1920, Einstein, who was a very driven man, was willing to relax and enjoy life a little bit more.

EDGE: What was the impact of Einstein's love life on his work?

OVERBYE: In some ways I don't think he would have gotten off the ground without Mileva around to bolster him and believe in him during his college years and right afterward. It very difficult time for him: his man professor hated him, he couldn't find a job. Einstein, however, knew he was smart. Mileva understood physics, and she was no slouch, she had spent her whole life being the only girl in boys' science classes. He could talk about physics with her, and get feedback, something that was enormously important to him his whole life long. She believed in him and she was not a frivolous person, so her opinion counted. That was very important at the time. There is no good evidence that she actually contributed substantially to the ideas behind relativity. But he was somebody who always needed somebody to talk to, and she was that person, for several years. He needed people to argue with specifically, he needed people to attack him intellectually, and he could fight back, and he loved it. It was his favorite thing to do.

EDGE: Probably hard to find people at that mental level that you'd also want to speak to.

OVERBYE: When babies enter the picture it gets more complicated. He needed better and better sparring partners as he went along. Mileva was okay for awhile, but he progressed into having better and better physicists as his sparring partners, until he finally got to Niels Bohr. But Mileva was very important in his earlier years, when he was perhaps not as cocky and secure as he was a few years later. And it was certainly exciting for him to come across a woman who was interested in physics and could talk about it with him, because up until that point this was not something he had experienced. In fact, when he met Mileva, he dumped his girlfriend Marie, who he had gone to high school with and who was still doing his laundry for him. But I don't believe he ever quite got over Marie.

EDGE: Tell me more about Marie.

OVERBYE: It's a complicated story Something that we didn't appreciate about Einstein is that he grew up in a family who were making gadgets and electromagnetic gizmos When Einstein was about 15 or 16 his family was in the electrical business in Munich, which was like being in the Internet business today. His uncle had patents on dynamos and electrical meters. The Einstein Brothers company sold power and lighting systems around southern Europe. He was very familiar with this technology, which was the leading edge technology of the day, like computers are today.

The family moved to Italy, leaving Albert back in Munich where he was in school, and he he seemed to have some sort of nervous breakdown. He dropped out of school, and went back to Italy, where he found himself with nothing to do, so he told his parents that he was going to go to the Polytechnic in Zurich and study engineering. They took him there, but he was too young to go to college. He took the entrance exam, and he impressed them with most of his scores, except in languages, so they sent him off to a prep school for a year, for a season.

He lived with a family, the Wintelers, a big, boisterous intellectual family, who were always arguing and bird watching and hiking and seems to have had a wonderful time. And he got involved with one of the Winteler daughters, Marie. Later on, his sister married one of the Winteler brothers, and his best friend, Michele Besso married another one of the Winteler sisters. So the Einsteins, Bessos, and Wintelers became very intertwined. Albert's parents liked Marie a lot, and everyone was very unhappy when Albert dumped her for Mileva. And, in fact, Marie went into a depression was hospitalized for a while. But eventually she led a normal life and married a manager of a watch factory. Albert kept talking about her his whole life, about how he would be consumed in flames if he even saw her again. He would even tell this to Mileva. He was greatly relieved when Marie finally married, either because that put finally her out of reach or he felt very guilty about dumping her and what had happened to her.

EDGE: What was he doing in terms of science when he was with Marie?

OVERBYE: Well nothing, He was in the Ararau cantonal school which was like being in the senior year of high school. We learn later that even then he was thinking was about light waves and the ether, and about the issues that relativity would eventually resolve. He had done his first thought experiment when he was about 16: he tried to imagine what it would be like if he could travel along with a light ray, if he could surf on an electromagnetic light wave like a surfer surfing on an ocean wave. What would he see? But the question didn't make any sense, because Maxwell's equations, which describe electromagnetism, say that a light wave appears to move at a particular speed, roughly 300,000 kilometers per second. They don' say anything about how fast you are going, so it seemed that even if he were traveling along with a light wave, the light wave would still look like it was zipping past him at the speed of light. That was a paradox that bothered him, a lot.

Of course, the answer turns out to be that you can't go that fast; it takes an infinite amount of energy to get to the speed of light. But he was thinking about these things, and writing little essays to his uncles about them, even as young as 15 or so. But mostly he was just having a good time. He underwent a personality change, because back in Munich he was the class nerd. He had familiarized himself with the entire high school math curriculum by the age of 12. His image was that of a solitary youth, reading his math books. In Switzerland he presented himself as a man of the world. He was a very attractive looking guy, and seemed to have a lot of charisma and personality, and people remembered him as a force to be reckoned with.

EDGE: After Marie there 's Mileva?

OVERBYE: Mileva was his classmate at the Polytechnic in Zurich; he started chasing her around the lab table their first year there. She was so upset by this that she actually dropped out of school for half a year and went off to Heidelberg to try and get her mind clear. She knew that this could be nothing but trouble. She went through a lot of hard work to get to college. For a woman, studying physics in Europe in 1896 was an amazing accomplishment, and she knew that pursuing a scientific career going to get any easier from there.

So this young dude chasing her around the lab table could only derail her concentration, and she decided that getting involved with Einstein was not the best thing for her career. But he won her over in the end.

Einstein was not in the habit of going to classes. He spent most of his time reading books that weren't on the curriculum, about electromagnetic theory, for example, and keeping Mileva up all night talking about those same issues that he'd been wondering about, like what happens to a light wave if you're traveling along with it, and what 's the ether that's 's supposed to be vibrating and moving these light waves along? Why didn't it show up in the equations? It had been presumed since the time of Aristotle that space was filled with this kind of this ether, this substance, and that this was what vibrated when light waves traveled.

He graduated, she did not, partly because she was behind from being away for half a year; partly because he probably kept her up too late pursuing his own interests rather than doing the homework that they were supposed to be doing. He barely got away with it; she couldn't quite hack it. Her math grades particularly were the lowest of the six people in their class.

After graduation he couldn't get a job, so he kept getting yanked back to his parents' house outside Milan. And she kept getting yanked back to her parents' house in Novi Sad, in what is now Serbia. So they spent a lot of time apart, which is great for historians, because they wrote lots of letters. We have better accounts of the times they were apart than we do of the times when they were together.

He finally got a part-time teaching job, and they had a reunion in Lake Como and went on a trip across the Alps. She got pregnant. This was pretty much the disastrous turning point for her, because she wound up having the baby and she went back to Serbia. This was the nightmare that Albert's mother had been worrying about, that Mileva would get pregnant, and this would be the end of Albert's life. In fact, he offered to get some sort of menial job to support her; she turned him down. By the time she was ready to give birth, the famous patent office job in Bern became available, so he moved to there to take it, and she went to Serbia to have the baby.

We don't know what happened to the baby, she probably left it there to be adopted. It 's pretty clear that she didn't bring Lieserl, as they called her, back because it would have been a horrible scandal for Albert to show up in Bern to take this civil service job with an illegitimate baby. Swiss society was very conservative, and Swiss physics was a very small world. Einstein was already viewed as a weirdo, because he had a Serbian girl friend; his manners in some way were more Italian than Swiss, he wasn't in the kind of emotional lockup that was associated with Germans and Swiss.

So she made the supreme sacrifice, giving away the child to preserve Einstein's career. At that point the die was cast, but it took another ten years for their relationship to run its course. Eventually they married; he later said that he had married with a sense of unease. If the pregnancy had never happened, they probably would have drifted apart and never married, but at this point he owed her. She never did get her degree, so she moved to Bern and became a housewife, waiting hungrily for him to come home every day so they could talk about physics. That worked for a few years, and they were very productive years, especially 1905, which has been called his annus mirabilis in which he published his relativity paper as well as another very important paper on the quantum theory of light, among others. After 1905 he was on his way to becoming a big deal in physics, and he was more and more involved with physicists outside the home. People started coming to see him and he started going to visit them. He eventually left the patent office, and got a university job, and Mileva tagged along for several more years, but he pretty much forced her out of the vital center of his life, that is to say, physics.

Having said, all this, I should say that many women, including scientists who have no particular ax to grind about who invented relativity, have told me that they find Mileva's story chilling. The fact that she never got her degree, never got to do science, was shunted aside into housework and eventually forgotten by history — her grave in Zurich is even unmarked. They take it as an object lesson, an all too-familiar story.

EDGE: Let's move on to Elsa? Or was there a period in between?

OVERBYE: In 1912 Einstein took a trip to Berlin, during which he had a reunion with his cousin Elsa, whom he had known as a child. Elsa was related to him in two different ways. She was a first cousin through his mother and a second cousin through his father. In fact, Albert might have had something going with Elsa's sister Paula when they were kids; there 's some reference in his letters to Elsa about Paula:, "Whoever she has not lied to has not known bliss. You can't blame me; we were young and she was willing." But that 's all I know about Paula.

Albert struck up a relationship with Elsa on that trip. He was still married to Mileva; at the time I believe they were living in Prague. There was an intense correspondence for a few months and then Albert broke it off, and about a year later on his birthday Elsa wrote again and there was evidence that there was some sort of fracas between them. Maybe Mileva intercepted the correspondence. Shortly after that Albert was recruited by Max Planck. Basically the Germans decided that this quantum theory that Einstein had been pushing for the last ten years was really hot stuff and could help German industry rule the world, and they were ready to put a lot of money into it, and they made him an offer he couldn't refuse to go to Berlin. Einstein was sick of teaching. This was a job for more money and no students. It was everything he wanted except he had to move back to Germany. But Elsa was there, and there's even some evidence that she helped things along on the German end.

Einstein moved to Berlin in the spring of 1914, and things got very nasty between him and Mileva as soon as she arrived as he was running around with Elsa. By then Einstein started working on his general theory of relativity. He had a germ of an idea in 1907, but it started consuming him in 1911 or 1912, and once he moved to Berlin, that was pretty much all he did for the next couple of years. He lived in a bachelor pad downtown which was described as a place just littered with papers. One of his friends described his working habits as follows: he works until you drag him away, then you give him some food, he eats until it's gone, you put him in bed, he sleeps until you wake him up, and then it all starts all over again. He was completely obsessed.

EDGE: Obsessed with work?

OVERBYE: Elsa was there too.

EDGE: How did their relationship play out?

OVERBYE: Just before Mileva left, Albert and Mileva and one of Albert's friends and lawyer met, and they arranged a separation agreement. Elsa, who didn't want to be around, had left town during this period, but he went home to her house after that meeting and slept in her bed. Then Elsa started putting the screws on him to get married and to finalize his divorce with Mileva. Of course he had told Mileva when they split up that he would never marry again and he wasn't going to marry Elsa. But he eventually got dragged into it. It took Mileva a long time to agree to a divorce, and there were many stormy scenes. The war was dragging on; Einstein finished general relativity, towards the end of 1915. Mileva had a physical breakdown in the spring of 1916 right after Easter, probably after Albert had been there and told her he wanted a divorce.

That winter Albert got sick, he thought he had cancer, then he seemed to have had some sort of gall bladder problem, but he was on his back for months. They moved him into an apartment across the hall from Elsa; at this point he was effectively living with Elsa and her two daughters, who were around 18 and 20. It was clear that they were eventually going to get married.

They did get married, in 1919, but not before Albert had temporarily decided that he would rather marry one of Elsa's daughters, Ilse. All we know about this is that Ilse wrote a letter to her friend Georg Nicolai and said, help, what do I do here? She was not attracted to Albert she loved him as a father, and she had the good sense not to get involved. But it was Albert's Woody Allen moment.

He did marry Elsa, in 1919, and the marriage went on until 1936 when Elsa died. During the 1920s Albert had lots of affairs in Berlin — he was carrying on with a number of different women. Elsa was not happy with this, but she more or less decided she had made her deal. After she died Albert once made some comment about how his wife didn't know anything about physics. Unfortunately this had not been the case with his first wife.

EDGE: Do you have any notions about how these relationships with women affected his world view or changed his temperament?

OVERBYE: I know lots of people like Albert. I might be like him myself. He was a hopeless romantic, he lived on anticipation. He was always yearning for the next thing. He was always envisioning some wonderful life with somebody else, while grimly enduring life with the woman he was with. If I think about it, I would say that that was kind of the key to his psychology, that he had the lure of the perfect situation, the perfect person. Of course if you're Einstein, you want everything that you want your way and then you want to be left alone. So you want love, and you want affection, you want a good meal, but then you don't want any interference outside of that, so you don't want any obligations interfering with your life, with your work. Which is a difficult stance to maintain in an adult relationship; it doesn't work. Everything has to be a give and take.

Einstein always felt Paradise was just around the corner, but as soon as he got there, it started looking a little shabby and something better appeared. I've known a lot of people like Albert in my time, I have felt lots of shocks of recognition. I feel like I got to know Albert as a person in the course of this, and I have more respect for him as a physicist than I did when I started, I have more a sense of what he accomplished and how hard it really was to be Einstein than I did before. It's a great relief to be able to think of him as a real person. If he was around I'd love to buy him a beer ..... but I don't know if I'd introduce him to my sister.


John Baez and Terry Sejnowski on Freeman Dyson's "Is Life Analog or Digital?"

Response to the responders, from Freeman Dyson

(Most recent — top)

From: Freeman Dyson
Date: March 21, 2001

Thanks to all nineteen of you who responded, some of you twice, with thoughtful objections and disagreements. As I said in my opening statement, it is much more fun to be contradicted than to be ignored. I learned a lot from your contradictions.

The following two statements are my attempt to condense a rich assortment of opinions into two sentences. (1) Any real computer operating in the real world is partly digital and partly analog, and any living organism is an even more inextricable mixture of digital and analog components. (2) The concepts of digital and analog were invented to describe idealized models of human-designed machines, and are far too narrow to encompass the subtleties of living creatures. In other words, when I asked whether life is analog or digital, (1) the answer is ``both'', and (2) I asked the wrong question. There seems to be a consensus among the respondents for both these statements. Beyond that, each of you had interesting things to say about details. I comment now on only three of your comments. Sorry it would take too long to give equal time to all of you.

Lee Smolin gave the longest and most substantial response. He describes a third possible form of information processing which is neither analog (because it is based on discrete rather than continuous components) nor digital (because it cannot be simulated by a digital computer algorithm). His information storage is based on the topological structure of finite graphs in three-dimensional space. This illustrates the general statement that the categories of analog and digital are too narrow to cover the range of possible machines and organisms. It is possible that Smolin's topological information processing may actually exist, both in living cells and in the fine-structure of space-time.

Steve Grand reformulates my question in an interesting way. He asks whether the signals carrying information are similar or dissimilar to the objects that they represent. If the signals are similar we may call them analog, and if they are dissimilar we may call them digital. When the question is put in this way, it becomes clear that living creatures are usually neither analog nor digital, because life does not usually represent anything. Life is not a symbol for something else. Life just is. On the other hand, brains do represent external objects, and the question whether a brain uses analog or digital symbols is meaningful.

Two respondents, Joseph Traub and John Baez, criticize my mention of the Pour-El-Richards theorem on technical grounds. The theorem says that an analog computer is more powerful than any digital computer for performing certain abstractly defined tasks. Traub and Baez correctly point out that the theorem only applies to an ideal mathematical universe and not to the physical universe that we inhabit. I never said that the theorem applies directly to the real world. I only said that it makes the superiority of analog devices in a cold universe less surprising. I challenge any mathematicians among you to find out whether some version of the theorem might hold under conditions closer to the real world. John Baez has already answered this question in the negative for one particular set of assumptions.

In conclusion, I thank you all for raising a lot of new questions which I hope we will continue to think about. Science thrives on mysteries, and the nature of life remains as mysterious as ever. I hope and believe we will never run out of good questions.

Yours sincerely,

Freeman Dyson

From: Terrence Sejnowski
Date: March 20, 2001

Freeman Dyson raises several intriguing questions about life and computation. These questions are closely related to two different styles of error correction, which is needed to preserve information and prevent catastrophic failure.

Digital computer memories use error correction coding schemes, such as block codes, to achieve extremely low error rates; this allows logical calculations to be carried out to great depth. Cells use an error correction scheme to achieve DNA replication error rates of less than one base error in 100 million. Modern error correcting codes in communication are within a few percent of the Shannon limit.

Vertebrate brains depend on statistical redundancy for reliable operation, which has the advantage of robustness to errors and damage, but the logical depth of computation is limited. However, brains are not general purpose computing devices, but special purpose systems with adaptive abilities.

Redundancy is a better strategy when the signal to noise ratio becomes extremely low and the power available for coding and decoding becomes scarce. Although it might be possible to build a general purpose computer with this strategy, a special purpose system, along the lines of brains, might be best adapted to the conditions that Dyson has explored.

From: John Baez
Date: March 14, 2001

Freeman Dyson mentioned a theorem due to Pour-El and Richards, and reads it as saying that "analog computers are more powerful than digital computers". I've worked a bit on this stuff and disagree with this assessment. As usual, the devil is in the details.

Pour-El and Richards' result goes roughly like this. They consider the "wave equation", but let me talk about Maxwell's equations in a vacuum, since that would work too, and it sounds nicer. They show there are solutions with the following property: at time zero, the electric and magnetic fields are computable functions, but at some later time, there is one point in space at which the electric or magnetic field is not computable. The trick is to set up a lot of waves coming in, which all crash together at a single point at some moment.

As for "computable": here they're using a more or less standard definition of "computable" functions of several real variables, taking real values. The idea behind this definition is that you can write a computer program that can compute f(x) to any given accuracy if you specify x to sufficiently high accuracy.

Pour-El and Richards' result is interesting, but notice the catch: to use this setup in a practical device, you'd have to be able to measure the electric or magnetic field at a single point in spacetime. In practice we never do this: we measure smeared-out averages of the electric and magnetic fields, in a manner limited by the size of our probe.

In fact, it's crucial to Pour-El and Richard's argument that they are working with solutions where the electric and magnetic field are continuous and have continuous first derivatives. Mathematicians know that these details can make or break an argument. If instead we work with solutions that merely have finite energy (a weaker condition), their argument no longer works, because finite-energy solutions need not have a well-defined value at a single point in spacetime: only smeared averages are well-defined!

And in fact, one can show that in the context of finite-energy solutions, if the electric and magnetic fields are computable at time zero, they will remain computable for all time. I believe this is more relevant to physics than the theorem Pour-El and Richards proved.

Of course, in this other theorem, we need a slightly different definition of "computable", since we're dealing with solutions where only the smeared-out averages of fields make sense, not their values at specific points. But I came up with this definition when I was an undergrad at a school near where Dyson hangs out. At the time I was interested in Schrodinger's equation rather than Maxwell's equation or the wave equation, and I proved that time evolution for Schrodinger's equation takes computable wavefunctions to computable wavefunctions. But later I realized that the same techniques work for these other equations. So these days I doubt that realistic analog computers can compute nonrecursive functions.

Chris Westbury on Yossi Vardi's "The Economics of Dreams"

From: Chris Westbury
Date: March 14, 2001

With respect to Joseph Vardi's question: Asking "How long will it be until the stock market begins to go up?" makes about as much sense as asking "How long will it be until people are happy?".

Some of us are happy right now, and some of us will never be happy. There is no "stock market' that can move as a whole; there are just individual stocks and a variety of different yardsticks for trying to understand them in different ways. Solemnly-proclaimed rhetoric to the contrary notwithstanding, the DJI and the Nasdaq averages are no more representative of "the stock market" than the serotonin levels of Newfoundlanders are representative of how happy the human race is. The notion that "the stock market" has crashed in recent months is a myth based on the category error that confuses one operational measure of a thing with the thing itself.

What has in actual fact happened is that some stocks are selling for much less than they were selling for a few months ago. Other stocks are selling for much more. Anyone who bought a Yahoo or an Amazon at 250 times earnings (or a VA Linux with no earnings at all!) expecting the stock prices to rise was a little over-optimistic, to put it gently. Many investors were not at all surprised to see those stock prices come down. Insofar as most of them are still clearly over-priced by good old-fashioned value-based measures, I feel safe in predicting for Mr. Vardi that "the stock market" will not begin to go up, but will come down still further.

However, while Yahoo and Amazon were selling at such absurd multiples, I picked up an oil stock (CYZa.TO) sitting at about 4 times earnings in a time of huge oil price hikes, and a liquidator (LQW.TO) with an unbroken 8-year earnings growth record selling for less than the company's book value! These kinds of under-priced stocks have behaved just as rationally as over-priced stocks like Amazon and Yahoo: they've gone up. Using the yardstick of value based investors, the stock market never came down: it just became more comprehensible.

Leon Lederman and Jeremy Bernstein on "Sex and Phyiscs"

From: Leon Lederman
Date: April 2, 2001

Brockman is now really over the edge but in consideration of all his past service, I try a serious answer. Both sex and physics fill our daily existence with the expectation of enthrallment from the fantasy of an exchange of miniglances when walking on a crowded street to the working out of an ugly integral or the squooshing of the last bug in the data acquisition software. The physics parallel to the culmination in the act of sex as best I can remember, is the moment of discovery...when you alone come into important new knowledge, usually at three AM in the quiet time. If heavy breathing and sweaty palms are common indicators....well, I have three stories off the top to illustrate the essay:

(1) "What", asked Professor Schmidt, "comes between Fear and Sex? Give up? Funf, dumkopf!"

(2) "Is it better to have a wife or a mistress?" asked Pierre. "Both", said the physicist. When your wife thinks you are with the mistress and the mistress believes you are with the wife, you can be happily in the lab, doing physics.

(3) 'Meet me in one hour.", said the CERN physicist's wife at the door of the hairdresser. So the physicist strolls the streets of Geneva and sees a lovely blond staring helplessly under the hood of a green Porche. "Can I help?", he offers. He fixes it but the need to wash his greasy hands leads to a cup of tea and a romp in bed, terminated by a "Oh, my God!". He dresses, grabs his jacket, borrows chalk from his new friend, rubs it in the coat and runs to the hairdresser...an hour late! He explains: "there was this cute blond with a Porche and I fixed it but had to wash my hands and so we went up and one thing lead to another and...". "Just a minute", the wife interrupts, "turn around. You liar you went to CERNB and did physics!"

From Jeremy Bernstein
Date: April 2, 2001

I won't comment on the central point; i.e. sex and physics, except to say I found the overall tone a little flippant. But here are three points:

1. "Of course the answer turns out to be that you can't go that fast..." Of course that is not the answer. The answer is that the speed of light in vacuum is the same for every observer in relative uniform motion. If this were not true and you could only go say half the speed of light you would still have similar paradoxes.

2. Actutally Einstein's grades in both highschool and at the ETH were quite good. Rabi once told me that at a New Years Eve party in Princeton Einstein brought out his old report cards and Rabi was surprised by the good marks.

3. The notion that Planck and "the Germans" had decided that the "quantum stuff" Einstein had been pushing for the last ten years was really hot stuff" — note the tone — is total nonsense. In fact in his letter of recommendation to the Prussian academy Planck urged that Einstein's quantum hypothesis not be held against him! and that he receive the appointment despite it. See Folsing, eg, p.328.

John Brockman, Editor and Publisher

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