Leonard Adleman: Interview with Diane Krieger.

Q: They say the most creative and challenging part of research is finding the right question to ask. Do you agree with that?

LA: I wouldn't characterize it as the most challenging thing, but it's of critical importance. Sometimes it's not hard to find the 'right question'. For example the mathematics literature is full of very important unanswered questions. In this case, the real issue is: Has that question's time come? Have we reached a point where developments in the appropriate area of science give us some chance of breaking the problem? For example, I worked on a famous centuries old math problem called "Fermat's Last Theorem". I was not 'strong' enough to solve it, but I find some solace in the fact that my intuition that its 'time had come' was right. The problem was finally solved two years ago by Andrew Wiles of Princeton. It was one of the major events in the history of mathematics.

The other side is to generate new questions. That's a funny process. The way I seek to generate new questions is to start to look at whole new fields, like biology, immunology or physics. Since I come from a different field, mathematics, I bring an unusual point-of-view that sometimes allows me to generate questions different from the classical questions in those areas. Like the question of DNA computing.

For the young scientist, this question of choosing the right question to spend your valuable limited intellectual resources on is critical. I often sit for months and do no productive work that anybody can see, because I don't feel I have a good enough question to work on. Rather than take on some lesser question, I would prefer to read a mystery novel. The point is, sometimes it's important to lie fallow for a time waiting for the 'right question' to appear, rather than to engage in uninspiring work and miss the important opportunity when in comes.

But in the end, the real challenge of science is to make progress - to succeed, to contribute knowledge.

Q: Of course, in an academic setting, there's that drive to publish or perish…

LA: Yes, that's a problem, because you have to feed your family. But I always tell my students and junior faculty that they are better off following their inspiration and their hearts in what research they do, that they should always try to take on the most interesting and important problems, that they should not waste their time on little problems just to make another line on a vitae.

My philosophy is that it's important, in a curious way, for scientists to be courageous. Not physically courageous, but courageous in an intellectual way. I believe that by working on extremely hard problems, by being courageous, you may succeed. But even if you fail, you fail gloriously. And you will have learned immense amounts, you will have extended the envelope of what you can do. As a byproduct of failing on a great problem, I have always found that I could solve some lesser but still interesting problems - which then fill your vitae.

Jonathan Blow: Reply to a programmer seeking advice

I am 42-year-old very successful programmer who has been through a lot of situations in my career so far, many of them highly demotivating. And the best advice I have for you is to get out of what you are doing. Really. Even though you state that you are not in a position to do that, you really are. It is okay. You are free. Okay, you are helping your boyfriend's startup but what is the appropriate cost for this? Would he have you do it if he knew it was crushing your soul?

I don't use the phrase "crushing your soul" lightly. When it happens slowly, as it does in these cases, it is hard to see the scale of what is happening. But this is a very serious situation and if left unchecked it may damage the potential for you to do good work for the rest of your life. Reasons:

Cory Booker:

Metabolize your blessings.

Jorge Luis Borges:

Nothing is built on stone; all is built on sand, but we must build as if the sand were stone.

Warren Buffett on the importance of big decisions:

You'd get very rich if you thought of yourself as having a card with only twenty punches in a lifetime, and every financial decision used up one punch. You'd resist the temptation to dabble. You'd make more good decisions and you'd make more big decisions.

Lois Bujold:

All great human deeds both consume and transform their doers. Consider an athlete, or a scientist, or an artist, or an independent business creator. In service of their goals they lay down time and energy and many other choices and pleasures; in return, they become most truly themselves. A false destiny may be spotted by the fact that it consumes without transforming, without giving back the enlarged self.

Lois Bujold¹:

I'd rather blow up the rest of my life than look like a fool for five minutes.

Brian Eno on the conservatism of success

I'm afraid to say that admirers can be a tremendous force for conservatism, for consolidation. Of course it's really wonderful to be acclaimed for things you've done - in fact it's the only serious reward, because it makes you think "it worked! I'm not isolated!" or something like that, and it makes you feel gratefully connected to your own culture. But on the other hand, there's a tremendously strong pressure to repeat yourself, to do more of that thing we all liked so much. I can't do that - I don't have the enthusiasm to push through projects that seem familiar to me ( - this isn't so much a question of artistic nobility or high ideals: I just get too bloody bored), but at the same time I do feel guilt for 'deserting my audience' by not doing the things they apparently wanted. I'd rather not feel this guilt, actually, so I avoid finding out about situations that could cause it. The problem is that people nearly always prefer what I was doing a few years earlier - this has always been true. The other problem is that so, often, do I! Discovering things is clumsy and sporadic, and the results don't at first compare well with the glossy and lauded works of the past. You have to keep reminding yourself that they went through that as well, otherwise they become frighteningly accomplished. That's another problem with being made to think about your own past - you forget its genesis and start to feel useless awe towards your earlier self: "How did I do it? Wherever did these ideas come from?". Now, the workaday everyday now, always looks relatively less glamorous than the rose-tinted then (except for those magic hours when your finger is right on the pulse, and those times only happen when you've abandoned the lifeline of your own history).

Brian Eno on process, not product:

I wanted to construct "machines"… that would make music for me. The whole idea was summarized in the famous saying… "Process not product!" The task of artists was to "imitate nature in its manner of operation" as John Cage put it - to think of ways of dealing with sound that were guided by an instinct for beautiful "processes" rather than by a taste for nice music.

Brian Eno:

[S]ystems and rules in music allow you to come up with things that your sense of taste would never have allowed you to do. But then your sense of taste expands to accommodate them! For instance, I'm sitting here now looking at something that my Stained Glass machine just made on my monitor. It has color combinations in it that are so weird. I would never dream of putting these things together. But, soon they start to look pretty good, and then they start to look really good.

Richard Feynman: Letter to a former student, reprinted in "Perfectly Reasonable Deviations from the Beaten Track"

Dear Koichi,

I was very happy to hear from you, and that you have such a position in the Research Laboratories. Unfortunately your letter made me unhappy for you seem to be truly sad. It seems that the influence of your teacher has been to give you a false idea of what are worthwhile problems. The worthwhile problems are the ones you can really solve or help solve, the ones you can really contribute something to. A problem is grand in science if it lies before us unsolved and we see some way for us to make some headway into it. I would advise you to take even simpler, or as you say, humbler, problems until you find some you can really solve easily, no matter how trivial. You will get the pleasure of success, and of helping your fellow man, even if it is only to answer a question in the mind of a colleague less able than you. You must not take away from yourself these pleasures because you have some erroneous idea of what is worthwhile.

You met me at the peak of my career when I seemed to you to be concerned with problems close to the gods. But at the same time I had another Ph.D. Student (Albert Hibbs) was on how it is that the winds build up waves blowing over water in the sea. I accepted him as a student because he came to me with the problem he wanted to solve. With you I made a mistake, I gave you the problem instead of letting you find your own; and left you with a wrong idea of what is interesting or pleasant or important to work on (namely those problems you see you may do something about). I am sorry, excuse me. I hope by this letter to correct it a little.

I have worked on innumerable problems that you would call humble, but which I enjoyed and felt very good about because I sometimes could partially succeed. For example, experiments on the coefficient of friction on highly polished surfaces, to try to learn something about how friction worked (failure). Or, how elastic properties of crystals depends on the forces between the atoms in them, or how to make electroplated metal stick to plastic objects (like radio knobs). Or, how neutrons diffuse out of Uranium. Or, the reflection of electromagnetic waves from films coating glass. The development of shock waves in explosions. The design of a neutron counter. Why some elements capture electrons from the L-orbits, but not the K-orbits. General theory of how to fold paper to make a certain type of child's toy (called flexagons). The energy levels in the light nuclei. The theory of turbulence (I have spent several years on it without success). Plus all the "grander" problems of quantum theory.

No problem is too small or too trivial if we can really do something about it.

You say you are a nameless man. You are not to your wife and to your child. You will not long remain so to your immediate colleagues if you can answer their simple questions when they come into your office. You are not nameless to me. Do not remain nameless to yourself – it is too sad a way to be. now your place in the world and evaluate yourself fairly, not in terms of your naïve ideals of your own youth, nor in terms of what you erroneously imagine your teacher's ideals are.

Best of luck and happiness.

Sincerely,

Richard P. Feynman.

Richard Feynman: letter to James Watson about his book The Double Helix, which I first saw reprinted in James Gleick's book "Genius" (and now reprinted in lots of places around the web):

Don't let anybody criticize that book who hasn't read it thru to the end. Its apparent minor faults and petty gossipy incidents fall into place as deeply meaningful and vitally necessary to your work (the book — the literary work I mean) as one comes to the end. From the irregular trivia of ordinary life mixed with a bit of scientific doodling and failure, to the intense dramatic concentration as one closes in on the truth and the final elation (plus with gradually decreasing frequency, the sudden sharp pangs of doubt) — that is how science is done. I recognize my own experiences with discovery beautifully (and perhaps for the first time!) described as the book nears its close. There it is utterly accurate.

And the entire 'novel' has a master plot and a deep unanswered human question at the end: Is the sudden transformation of all the relevant scientific characters from petty people to great and selfless men because they see together a beautiful corner of nature unveiled and forget themselves in the presence of the wonder? Or is it because our writer suddenly sees all his characters in a new and generous light because he has achieved success and confidence in his work, and himself? Don't try to resolve it. Leave it that way. Publish with as little change as possible. The people who say "that is not how science is done" are wrong. In the early parts you describe the impression by one nervous young man imputing motives (possibly entirely erroneous) on how the science is done by the men around him. (I myself have not had the kind of experiences with my colleagues to lead me to think their motives were often like those you describe — I think you may be wrong — but I don't know the individuals you knew — but no matter, you describe your impressions as a young man.) But when you describe what went on in your head as the truth haltingly staggers upon you and passes on, finally fully recognized, you are describing how science is done. I know, for I have had the same beautiful and frightening experience.

Galileo:

Philosophy [nature] is written in that great book which ever is before our eyes – I mean the universe – but we cannot understand it if we do not first learn the language and grasp the symbols in which it is written. The book is written in mathematical language, and the symbols are triangles, circles and other geometrical figures, without whose help it is impossible to comprehend a single word of it; without which one wanders in vain through a dark labyrinth.

James Gleick:

[Feynman] began dating his scientific notes as he worked, something he had never done before. [Historian Charles] Weiner once remarked casually that his new parton notes represented "a record of the day-to-day work," and Feynman reacted sharply.

"I actually did the work on the paper," he said.

"Well," Weiner said, "the work was done in your head, but the record of it is still there."

"No, it's not a record, not really. It's working. You have to work on paper, and this is the paper. Okay?" It was true that he wrote in astonishing volume as he worked—long trains of thought, almost suitable to serve immediately as lecture notes.

Murph Goldberger (on Fermi):

These discussions [with Fermi] showed us what it means to be a real physicist. You work everything out, you never delude yourself by saying that you probably could do something if you really wanted to. You do it and you write it down so that you can recover it when necessary. Fermi was religious about this. His notebooks were incredibly clear—he would work things out on the blackboard, get them absolutely right and then copy the essentials into those carefully indexed notebooks. He once flirted with the idea of taking Polaroid pictures of his blackboard to save time and effort, but he really didn't find that satisfactory. On countless occasions I tried to follow his example, but I never had the self-discipline necessary to index and crossindex my own notebooks. The basic lesson I, like all of Fermi's students learned was described by Frank Yang this way: "Physics is to be built from the ground up, brick by brick, layer by layer."

Murph Goldberger (on Fermi):

Another of Fermi's patterns was the development of what he called his Magic Memory or sometimes his Mechanical Memory. This was a collection of formulas for things Fermi felt he would need frequently in doing research, like the radiation from a charge moving at relativistic speeds, quantum-mechanical sum rules, vector-addition coefficients, solutions of the Dirac equation in a coulomb field, hydrodynamic phenomena, heat transfer, etc. (Non-experts need not be concerned about this jargon.) Only useful eternal truths made their way into this single-file drawer reserved for the Mechanical Memory and Fermi never questioned the validity of anything in there. If it was there at all, it was correct and ready to be used.

Grothendieck: Récoltes et Semailles

In those critical years I learned how to be alone. [But even] this formulation doesn't really capture my meaning. I didn't, in any literal sense, learn to be alone, for the simple reason that this knowledge had never been unlearned during my childhood. It is a basic capacity in all of us from the day of our birth. However these three years of work in isolation [1945-1948], when I was thrown onto my own resources, following guidelines which I myself had spontaneously invented, instilled in me a strong degree of confidence, unassuming yet enduring in my ability to do mathematics, which owes nothing to any consensus or to the fashions which pass as law. By this I mean to say: to reach out in my own way to the things I wished to learn, rather than relying on the notions of the consensus, overt or tacit, coming from a more or less extended clan of which I found myself a member, or which for any other reason laid claim to be taken as an authority. This silent consensus had informed me both at the lycee and at the university, that one shouldn't bother worrying about what was really meant when using a term like "volume" which was "obviously self-evident", "generally known," "in problematic" etc… it is in this gesture of "going beyond" to be in oneself rather than the pawn of a consensus, the refusal to stay within a rigid circle that others have drawn around one – it is in this solitary act that one finds true creativity. All others things follow as a matter of course.

Since then I've had the chance in the world of mathematics that bid me welcome, to meet quite a number of people, both among my "elders" and among young people in my general age group who were more brilliant, much more 'gifted' than I was. I admired the facility with which they picked up, as if at play, new ideas, juggling them as if familiar with them from the cradle – while for myself I felt clumsy, even oafish, wandering painfully up an arduous track, like a dumb ox faced with an amorphous mountain of things I had to learn (so I was assured) things I felt incapable of understanding the essentials or following through to the end. Indeed, there was little about me that identified the kind of bright student who wins at prestigious competitions or assimilates almost by sleight of hand, the most forbidding subjects.

In fact, most of these comrades who I gauged to be more brilliant than I have gone on to become distinguished mathematicians. Still from the perspective of thirty or thirty five years, I can state that their imprint upon the mathematics of our time has not been very profound. They've done all things, often beautiful things in a context that was already set out before them, which they had no inclination to disturb. Without being aware of it, they've remained prisoners of those invisible and despotic circles which delimit the universe of a certain milieu in a given era. To have broken these bounds they would have to rediscover in themselves that capability which was their birthright, as it was mine: The capacity to be alone.

Robin Jones Gunn:

If you want to go fast, go alone. If you want to go far, go together.

Marijn Haverbeke:

The art of programming is the skill of controlling complexity.

Marijn Haverbeke:

Be careful who you learn from.

Steve Jobs:

When you grow up you tend to get told that the world is the way it is and your life is just to live your life inside the world. Try not to bash into the walls too much. Try to have a nice family life, have fun, save a little money. That's a very limited life. Life can be much broader once you discover one simple fact: Everything around you that you call life was made up by people that were no smarter than you. And you can change it, you can influence it. Once you learn that, you'll never be the same again.

Alan Kay:

The real romance of management is nothing less than the creation of civilization itself.

Alan Kay (fuller quote):

I have always believed that of all the ways to approach the future, the vehicle that gets you to the most interesting places is Romance. The notion of tool has always been a romantic idea to humankind—from swords to musical instruments to personal computers, it has been easy to say: "The best way to predict the future is to invent it!" The romantic dream of "how nice it would be if…" often has the power to bring the vision to life. Though the notion of management of complex processes has less cachet than that of the hero singlehandedly wielding a sword, the real romance of management is nothing less than the creation of civilization itself. What a strange and interesting frontier to investigate. As always, the strongest weapon we have to explore this new world is the one between our ears—providing it's loaded!

Alan Kay (writing in 1989):

Everyone seems to want user interface but they are not sure whether they should order it by the yard or by the ton.

Alan Kay:

Where some people measure progress in answers-right/test or tests-passed/year, we are more interested in "Sistine-Chapel-Ceilings/Lifetime. This is not to say that skill achievement is de-emphasized."Sistine-Chapel-Ceilings are not gotten without healthy application of both dreaming and great skill at painting those dreams. As bystander L. d. Vinci remarked, "Where the spirit does not work with the hand, there is no art". Papert has pointed out that people will willingly and joyfully spend thousands of hours of highly physical and mental effort in order to perfect a sport (such as skiing) that they are involved in. Obviously school and learning have not been made interesting to children, nor has a way to get immediate enjoyment from practicing intellectual skills generally appeared.

Bruno Latour and Steve Woolgar ("Laboratory Life"):

We shall therefore attempt to make the activities of the laboratory seem as strange as possible in order not to take too much for granted.

Lawrence Lessig:

Q: How have your clerkships with Posner and Scalia, respectively, shaped your worldview? Posner was the most important person (after my dad) in my life. He showed me the life of someone not afraid to be hated.

C. S. Lewis:

Courage is not simply one of the virtues, but the form of every virtue at its testing point.

Christopher McCandless:

Happiness only real when shared.

Jacques Monod:

Any mingling of knowledge with values is unlawful, forbidden.

Haruki Murakami: Norwegian Wood

If you only read the books that everyone else is reading, you can only think what everyone else is thinking.

Seneca (as quoted by Carl Sagan):

The time will come when diligent research over long periods will bring to light things which now lie hidden. A single lifetime, even though entirely devoted to the sky, would not be enough for the investigation of so vast a subject… And so this knowledge will be unfolded only through long successive ages. There will come a time when our descendants will be amazed that we did not know things that are so plain to them… Many discoveries are reserved for ages still to come, when memory of us will have been effaced. Our universe is a sorry little affair unless it has in it something for every age to investigate… Nature does not reveal her mysteries once and for all.

Susan Sontag:

I need to care about and be touched by what I read. I can't care about a book that has nothing to contribute to the wisdom project.

Susan Sontag:

I want to read only what I'll want to reread — the definition of a book worth reading once.

Bill Thurston: The Mystery of 3-Manifolds, via Steven Wittens

I think a lot of mathematics is really about how you understand things in your head. It's people that did mathematics, we're not just general purpose machines, we're people. We see things, we feel things, we think of things. A lot of what I have done in my mathematical career has had to do with finding new ways to build models, to see things, do computations. Really get a feel for stuff.

It may seem unimportant, but when I started out people drew pictures of 3-manifolds one way and I started drawing them a different way. People drew pictures of surfaces one way and I started drawing them a different way. There's something significant about how the representation in your head profoundly changes how you think. It's very hard to do a brain dump. Very hard to do that. But I'm still going to try to do something to give a feel for 3-manifolds.

Words are one thing, we can talk about geometric structures, there are many precise mathematical words that could be used. But they don't automatically convey a feeling for it. I probably can't convey a feeling for it either, but I want to try.

Bill Thurston: Auto-biographical note on the question and answer site MathOverflow

Mathematics is a process of staring hard enough with enough perseverence at at the fog of muddle and confusion to eventually break through to improved clarity. I'm happy when I can admit, at least to myself, that my thinking is muddled, and I try to overcome the embarassment that I might reveal ignorance or confusion. Over the years, this has helped me develop clarity in some things, but I remain muddled in many others. I enjoy questions that seem honest, even when they admit or reveal confusion, in preference to questions that appear designed to project sophistication.

Bill Thurston: in response to a question on MathOverflow

It's not mathematics that you need to contribute to. It's deeper than that: how might you contribute to humanity, and even deeper, to the well-being of the world, by pursuing mathematics? Such a question is not possible to answer in a purely intellectual way, because the effects of our actions go far beyond our understanding. We are deeply social and deeply instinctual animals, so much that our well-being depends on many things we do that are hard to explain in an intellectual way. That is why you do well to follow your heart and your passion. Bare reason is likely to lead you astray. None of us are smart and wise enough to figure it out intellectually.

The product of mathematics is clarity and understanding. Not theorems, by themselves. Is there, for example any real reason that even such famous results as Fermat's Last Theorem, or the Poincaré conjecture, really matter? Their real importance is not in their specific statements, but their role in challenging our understanding, presenting challenges that led to mathematical developments that increased our understanding.

The world does not suffer from an oversupply of clarity and understanding (to put it mildly). How and whether specific mathematics might lead to improving the world (whatever that means) is usually impossible to tease out, but mathematics collectively is extremely important.

I think of mathematics as having a large component of psychology, because of its strong dependence on human minds. Dehumanized mathematics would be more like computer code, which is very different. Mathematical ideas, even simple ideas, are often hard to transplant from mind to mind. There are many ideas in mathematics that may be hard to get, but are easy once you get them. Because of this, mathematical understanding does not expand in a monotone direction. Our understanding frequently deteriorates as well. There are several obvious mechanisms of decay. The experts in a subject retire and die, or simply move on to other subjects and forget. Mathematics is commonly explained and recorded in symbolic and concrete forms that are easy to communicate, rather than in conceptual forms that are easy to understand once communicated. Translation in the direction conceptual -> concrete and symbolic is much easier than translation in the reverse direction, and symbolic forms often replaces the conceptual forms of understanding. And mathematical conventions and taken-for-granted knowledge change, so older texts may become hard to understand.

In short, mathematics only exists in a living community of mathematicians that spreads understanding and breaths life into ideas both old and new. The real satisfaction from mathematics is in learning from others and sharing with others. All of us have clear understanding of a few things and murky concepts of many more. There is no way to run out of ideas in need of clarification. The question of who is the first person to ever set foot on some square meter of land is really secondary. Revolutionary change does matter, but revolutions are few, and they are not self-sustaining — they depend very heavily on the community of mathematicians.

Vernor Vinge:

So high, so low, so many things to know

Steven Weinberg on plunging in

When I received my undergraduate degree — about a hundred years ago — the physics literature seemed to me a vast, unexplored ocean, every part of which I had to chart before beginning any research of my own. How could I do anything without knowing everything that had already been done? Fortunately, in my first year of graduate school, I had the good luck to fall into the hands of senior physicists who insisted, over my anxious objections, that I must start doing research, and pick up what I needed to know as I went along. It was sink or swim. To my surprise, I found that this works. I managed to get a quick PhD — though when I got it I knew almost nothing about physics. But I did learn one big thing: that no one knows everything, and you don't have to.

Steven Weinberg:

This is often the way it is in physics —our mistake is not that we take our theories too seriously, but that we do not take them seriously enough. It is always hard to realize that these numbers and equations we play with at our desks have something to do with the real world. Even worse, there often seems to be a general agreement that certain phenomena are just not fit subjects for respectable theoretical and experimental effort. Alpher, Herman and Gamow (1948) deserve tremendous credit above all for being willing to take the early universe seriously, for working out what known physical laws have to say about the first three minutes. Yet even they did not take the final step, to convince the radio astronomers that they ought to look for a microwave radiation background. The most important thing accomplished by the ultimate discovery of the 3K radiation background (Penzias and Wilson, 1965) was to force all of us to take seriously the idea that there was an early universe.

Robert Weisbrodt on Ed Witten's path to his calling:

How long will you need to find your truest, most productive niche? This I cannot predict, for, sadly, access to a podium confers no gift of prophecy. But I can say that however long it takes, it will be time well spent. I am reminded of a friend from the early 1970s, Edward Witten. I liked Ed, but felt sorry for him, too, because, for all his potential, he lacked focus. He had been a history major in college, and a linguistics minor. On graduating, though, he concluded that, as rewarding as these fields had been, he was not really cut out to make a living at them. He decided that what he was really meant to do was study economics. And so, he applied to graduate school, and was accepted at the University of Wisconsin. And, after only a semester, he dropped out of the program. Not for him. So, history was out; linguistics, out; economics, out. What to do? This was a time of widespread political activism, and Ed became an aide to Senator George McGovern, then running for the presidency on an anti-war platform. He also wrote articles for political journals like the Nation and the New Republic. After some months, Ed realized that politics was not for him, because, in his words, it demanded qualities he did not have, foremost among them common sense. All right, then: history, linguistics, economics, politics, were all out as career choices. What to do? Ed suddenly realized that he was really suited to study mathematics. So he applied to graduate school, and was accepted at Princeton. I met him midway through his first year there–just after he had dropped out of the mathematics department. He realized, he said, that what he was really meant to do was study physics; he applied to the physics department, and was accepted.

I was happy for him. But I lamented all the false starts he had made, and how his career opportunities appeared to be passing him by. Many years later, in 1987, I was reading the New York Times magazine and saw a full-page picture akin to a mug shot, of a thin man with a large head staring out of thick glasses. It was Ed Witten! I was stunned. What was he doing in the Times magazine? Well, he was being profiled as the Einstein of his age, a pioneer of a revolution in physics called "String Theory." Colleagues at Harvard and Princeton, who marvelled at his use of bizarre mathematics to solve physics problems, claimed that his ideas, popularly called a "theory of everything," might at last explain the origins and nature of the cosmos. Ed said modestly of his theories that it was really much easier to solve problems when you analyzed them in at least ten dimensions. Perhaps. Much clearer to me was an observation Ed made that appeared near the end of this article: every one of us has talent; the great challenge in life is finding an outlet to express it. I thought, he has truly earned the right to say that. And I realized that, for all my earlier concerns that he had squandered his time, in fact his entire career path–the ventures in history, linguistics, economics, politics, math, as well as physics–had been rewarding: a time of hard work, self-discovery, and new insight into his potential based on growing experience.