When he invited me to deliver a lecture in this series, Jonathan Monroe provided a long list of questions that might be addressed. Many of them were autobiographical. Physics offers you so few public opportunities to talk about yourself, that I found this impossible to resist. So I'll begin with his opening question: What first drew you to your discipline?

What first drew me to my discipline was magic. It came in two varieties: relativity and quantum mechanics.

I know that the magic of relativity had grabbed me before I was 16, because I remember the first day of high-school physics. The teacher was a tight lipped gentleman who, it was rumored, had risen to the rank of Colonel in World War I. He liked to throw hard rubber erasers at people he thought were dozing.

"Physics,'' the Colonel told us, "is about laws that govern the behavior of matter. There is the law of the Conservation of Mass.'' My hand shot up. "Doesn't relativity say that mass is not conserved?'' There was a long terrifying silence. "I don't know anything about relativity,'' snarled the Colonel at last. "Do you?'' I never again inquired about anything not in the textbook: Modern Physics by Charles E. Dull.

So I knew something about relativity when I was sixteen. The magic of it was this: If you could move at 99.98% of the speed of light, then in a little over four years you could go four light years, and get to the nearest star. But — here was the magic part — you would be only a month older when you got there.

Same thing on the way back. When you got home everybody would be eight years older, but you would have aged only two months. If you did it three or four times you could come back younger than your own kids!

Just as amazing, if on the way out in your spacious mile-long rocket, you passed another one- miler on the homebound run and measured its length as it flashed past, you would find it to be only one foot long, and everybody in it, flattened to the thickness of sheets of paper. And, most mysterious of all, the occupants of the home-bound rocket would find that you and your rocket were correspondingly squashed.

How could this be? How could each of two rockets be shorter than the other? I desperately wanted to understand.

Although I took a course in relativity in graduate school, I didn't understand until I arrived at Cornell as an Assistant Professor of Physics. I was given my first semester off from teaching, the better to prove my prowess as a hot-shot researcher. (A big mistake since I was looking forward to teaching and, in my new environment, feeling distinctly unhot.) In November, however, I was asked to give a substitute lecture in the big introductory physics course. I attended the lecture before mine. It was on relativistic length contraction and I didn't understand a word of it. Fortunately I had the weekend to think it over. I realized that the reason I didn't understand was that most of what the professor had said was wrong. So I figured out how to say it right, and began my lecture with a delicately worded "review'' of what he had said. From that time I was hooked on the teaching of relativity.

The following semester my Chair decided that besides teaching a hot-shot graduate course, I should teach a course for high-school teachers in a science-education program at the Ag School. The course was supposed to be about a new set of teaching experiments. "Here,'' he said, handing me a key. "They're all in a filing cabinet on the third floor of Rockefeller.''

I climbed to the third floor and opened the cabinet. It contained what looked to me like a pile of undifferentiated junk. What to do? Fortunately the Chair had put me on a committee to look into how to improve the teaching of high-school physics. So I came to the committee meeting with an agenda, inspired only in part by my run-in with the colonel. After due consideration, we concluded that the most effective way to improve high-school physics was to incorporate relativity into the curriculum.

Thus empowered, I announced to my dozen high-school teachers that I would provide keys to the cabinet for anybody who wanted to play with the experiments, but that I was going to teach them relativity. They were delighted. A month into the semester I received a letter from the Department of Science Education denouncing me for dereliction of duty; I sent them back a copy of our committee report and never heard from them again.

That was 34 years ago. My lecture notes for the high-school teachers became a book, from which I've sporadically taught relativity to nonscientists at Cornell until about ten years ago. At that point I realized I didn't like the book any more. Part of this stemmed from the increasing discomfort I felt in having to pretend that I was the same person as the owner of the brash narrative voice from the pre-revolutionary side of the 1960's. More important, though, was my discovery, since my class with the high school teachers, that writing relativity wasn't nearly as easy as I once thought, as successive generations of Cornell undergraduates were bringing vividly to my attention. Now I'm deep in the process of writing a competing book. I've learned a better way to do it.

As an indication of the challenge in writing relativity, consider this: A year and a half ago I wrote an article in Physics Today criticizing the way some scientists had attacked Bruno Latour, the famous authority on scientists and their ways, for writing nonsense about relativity. I pointed out (I thought uncontroversially) that at least some of what Latour had said was not only correct, but quite elegantly put: "Instead of considering instruments (rulers and clocks) as ways of representing abstract notions like space and time, Einstein takes the instruments to be what generates space and time. Instead of space and time being represented through the mediation of the instruments, it is space and time which have always been representing the humble and hidden practice of superimposing notches, hands, and coordinates.'' While Latour also seemed to say some rather silly things about relativity, this particular formulation is precisely to the point.

Yet Physics Today published three angry letters to the editor. Every one of them took up my quotation from Latour. The first said that statements like Latour's "are thick upon the ground.'' It took the phrases I praised to be banalities. The second said that Latour's phrases were mistranslations from Einstein's German. It took the phrases I praised to be wrong. The third said that "When Mermin praises Latour for asserting that in relativity 'Einstein takes the instruments to be what generate space and time,' the science wars have already been lost.'' It took my praise of Latour to be the end of civilization as we know it. What makes writing relativity so tricky is this: Built into ordinary language — in its use of tenses, for example — are many implicit assumptions about the nature of temporal relations that we now know to be false. Most importantly, we have known since 1905 that when you say that two events in different places happen at the same time you are not referring to anything inherent in the events themselves. You are merely adopting a conventional way of locating them that can differ from other equally valid conventional assignments of temporal order which do not have the events happening at the same time.

This error — the implicit assumption that the simultaneity of events has more than a conventional meaning — can infect statements that seem to have nothing to do with time. Detecting the hidden presence of time can be challenging. Suppose, for example, somebody who doesn't like to back up has a garage with doors at the front and the rear on a circular drive. Whether or not "the car is shut in the garage'' can be a matter of convention. For implicit in being "shut in the garage'' is that neither door is open. For the car to be shut in the garage, both doors must be closed at the same time. If "at the same time'' is a matter of convention, then under appropriate conditions it can be a matter of convention whether the car was ever shut in the garage.

Time also makes an implicit appearance in the correct assertion that the mile-long rocket is only a foot long when moving, because the length of a moving rocket is the distance between two places. The first place is where its front end happens to be at some moment; the second place is where its rear end is at the same time that its front end is in that first place. If "at the same time'' is problematic, then so is the length of anything that moves.

Language evolved under an implicit set of assumptions about the nature of time that was beautifully and explicitly articulated by Newton: "Absolute, true, and mathematical time, of itself, and from its own nature, flows equably without relation to anything external... '' Lovely as it sounds, this is complete nonsense. Because, however, the Newtonian view of time is implicit in everyday language where it can corrupt apparently atemporal statements, to deal with relativity one must either critically reexamine ordinary language, or abandon it altogether.

Physicists traditionally take the latter course, replacing talk about space and time by a mathematical formalism that gets it right by producing a state of compact nonverbal comprehension. Good physicists figure out how to modify everyday language to bring it into correspondence with that abstract structure. The rest of them never take that important step and, I would argue that like the professor I substituted for in 1964, they never really do understand what they are talking about.

The most fascinating part of writing relativity is searching for ways to go directly to the necessary modifications of ordinary language, without passing through the intermediate nonverbal mathematical structure. This is essential if you want to have any hope of explaining relativity to nonspecialists. And my own view, not shared by all my colleagues, is that it's essential if you want to understand the subject yourself.

The other magic that first drew me to my discipline was quantum mechanics. When I was fourteen or fifteen I read a book by George Gamow, which I learned about from an editorial in Astounding Science Fiction. I've never been so excited by a book. It was my first exposure to the amazing facts of relativity. It also taught me some remarkable mathematics that I could actually see for myself made sense, which gave me confidence that the author could be right about the other things too. And it talked about quantum mechanics.

There was a car in a garage again. This time all the doors were shut all the time, so there was no possible ambiguity about "the car was in the garage.'' And yet, Gamow said, it was possible, without opening any doors, or damaging the car or the garage, that the car might subsequently appear outside the garage. (He was using this as a metaphor for the kind of radioactivity in which the nucleus of a heavy atom can shoot out a small fragment of itself, even though there is not enough energy for the fragment to penetrate the confining walls of the nucleus that contains it.)

Quantum mechanics is stranger than relativity. The strangeness comes again from the incompatibility of ordinary language with the actual facts. But nobody has clearly identified the traps in ordinary language that make it so difficult to talk correctly about quantum phenomena, and nobody has come even close to finding a way to use ordinary language that eliminates the perplexities. As with relativity, physicists have discovered a mathematical formalism that gets it right, leading to a state of nonverbal comprehension. Nobody has figured out how do better than that, which makes trying to write about quantum mechanics without the mathematical formalism an exquisite challenge.

Suppose, for example, you have some stuff, and you put it into some kind of testing device that always responds, by signaling Yes or No. Suppose when you test some particular stuff the device says Yes. You might be tempted to conclude that this was the kind of stuff that produces the answer Yes when tested, but that, of course, is more than you are entitled to say, since the response of the device might have little or nothing to do with the character of the stuff you just tested.

But surely you are entitled to conclude that this was not a specimen of a kind of stuff that must test No. After all if the stuff did require the answer to be No, the answer couldn't have been Yes. But it was Yes.

So it was a kind of stuff that doesn't have to test No.

Now suppose you worry about other things that might have happened to that particular stuff if you hadn't actually done that test. Since you actually did the test, you might think you've learned something about the stuff which could help you think about the possible results of other tests you might have done. Remarkably, however, if you make the hypothesis that it was a kind of stuff that doesn't have to test No, then there are circumstances under which you can deduce that if you had instead chosen to do a different kind of test the stuff could have behaved in a way that never happens when that different kind of test is actually done. So even though the result was Yes when the stuff was tested, you have to conclude that if it hadn't actually been tested, it might have been the kind of stuff that has to test No.

There's an additional assumption you have to make to get to this peculiar position: You have to assume that whatever character the stuff has can't be altered by a decision made by a friend of yours, who is off in the next county, out of contact with you and the stuff. Some people conclude from this that the character of your stuff can indeed be altered by decisions made by your far away friend. This is called quantum nonlocality. Others, myself among them, conclude that it is treacherous to make judgments about the character of stuff, and extremely treacherous to reason from what actually happened to what might have happened but didn't.

It's fascinating to try to write about this. We've known ever since Bohr and Heisenberg, that you can get into trouble if you try to infer the existence of properties independent of the process by which those properties are actually ascertained. But it's only through decades of trying to simplify and refine that kind of argumentation that we've come up with examples where you get into trouble by insisting that stuff that has just tested Yes, prior to the test could not have been the kind of stuff that must test No.

The very beautiful and concise mathematical language of quantum mechanics is designed to make it impossible to say things like the naughty things I just said and, preferably, impossible even to think such thoughts. The mathematical language says that if you ask this particular question about that particular stuff then these are the possible answers and their likelihood. It refuses to talk about what actually happens, beyond giving you the odds for the various possibilities. And it is utterly incapable of formulating questions about what would have happened under altered conditions based on what actually did happen under actual conditions.

Language, on the other hand, is filled with talk about what might have happened but didn't. If only I hadn't turned left at Cayuga St rather than Geneva, I would not have been sideswiped by the car pulling out from the library. We've discovered that there are grave inadequacies built into such forms of expression. You can't deal with them until you've understood quantum mechanics. But you can't really have understood quantum mechanics until you are capable of dealing with them.

Many physicists would disagree, maintaining that the only legitimate questions are about the possible results of an experiment and the likelihood of getting each one of those results. Quantum mechanics unambiguously answers both kinds of questions, so there is no mystery about it. The puzzlement only arises when you try to combine what quantum mechanics tells you about the possible results of a group of mutually incompatible experiments. When you actually do any one such experiment you lose the ability to do any of the others. Why worry about what might have happened in the experiment you didn't do, if you no longer can do it? That's a problem for philosophers, not physicists.

I'm inclined to agree. The problem is that most philosophers who do worry about quantum mechanics differ from the physicists who refuse to worry only because they worry and the physicists don't. The philosophers have, by and large chosen to embrace nonlocality as a natural phenomenon, rather than homing in on what bad habits of thought and expression make so implausible an inference so hard to resist. Uncharacteristically for philosophers, they ought to be more worried about the nature of language, how it can trap us into formulating questions that have no sensible answers, and whether it is possible to restructure ordinary language in a way that liberates us from those built-in errors that make it so hard to think clearly about quantum physics. They ought, in short, to be worried about writing physics.

The challenge of expressing in ordinary language matters whose most natural representation is nonverbal operates on much less profound levels. At the insistence of the National Science Foundation, the Cornell Center for Materials Research has recently become interested in something called "outreach''. Outreach means it's not enough to do research; you should also delight and instruct the general public outside the university. I'm sure all the lecturers in this series enjoy doing that, but we scientists are the only ones who are now required to do it. That's fine in principle, but in practice the Federal Agencies have imposed so much paperwork on scientists for them to get so little research support that there is hardly time left for the research, let alone the outreach. Writing grant proposals and progress reports is the least edifying way of writing physics.

You may have noticed the "Ask a Scientist'' column that recently started up in the Ithaca Journal. That is an example of outreach. If you are a scientist outreach can strike at any time. It hit me in the following form: "Why is it that when I look at one side of a spoon I see my reflection right side up, and when I turn the spoon over I see my reflection upside down?'' Please answer by Wednesday in 250 words suitable for a ten-year old. This turned into an all-day challenge. It helped not knowing any conventional optics, because I first had to figure out for myself that the spoon behaved as advertised. Then I looked in a spoon to make sure. It did. Then I had to decide what I could take for granted. In this case, how flat mirrors behave. Then I had to find a concise way to express the simulation of a curved mirror by a collection of flat ones. Then I had to find a way to say this in a language of spoons, not mirrors, anticipating and thwarting every imaginable misreading. Here's the result:

"To make it easier to picture, think of an enormous spoon, about as big as your head, not counting the handle. You can understand how a curved mirror behaves by thinking of it as built up out of lots of little flat mirrors. So suppose the enormous spoon is a wooden one, made to reflect by gluing a lot of little flat mirrors to both its surfaces, like mosaic tiles on the inside and outside of a dome.

"Now imagine holding the spoon vertically some distance from your face, and looking directly into the bowl part of the spoon, with the middle of the bowl at the level of your eyes. As you lower your eyes toward the lower part of the bowl, the little mirrors that you see will tilt upwards, so you see in them the reflection of the upper part of your face. But as you raise your eyes toward the upper part of the bowl, the little mirrors that you see will tilt downwards, so you see in them the reflection of the lower part of your face. In other words you see yourself upside down.

"On the other hand, if you turn the spoon so you're looking at the outside of its bowl, then as you lower your eyes the little mirrors that you see tilt downwards and you see a reflection of the lower part of your face, and as you raise your eyes the mirrors that you see tilt upwards and you see a reflection of the upper part. So reflected in that side, you look right-side up.''

You may not think so, but that is serious writing. The agony of producing it was similar to what I endured trying to produce the disquisitions on relativistic and quantum physics in the earlier parts of this lecture.

But it's not just quantum mechanics, relativity, and spoons that get me writing physics. I'm convinced that you don't understand the real significance of the research you've been struggling with for the past year, until you begin to write about it. Only then do you realize that it is much more interesting (or, if you're unfortunate and uncommonly honest, much less interesting) than you'd thought. Only then do you really see how your work fits into or, if you are lucky, changes the character of the tradition out of which it grew.

All this requires time. You cannot go through such a ruminative process if you feel the urgent need to get your work out ahead of your competitors. Because my written physics has to be slow- aged before it's fit for consumption, I've always sought unexplored backwaters to work in, or obscure corners of otherwise fashionable enterprises. At my back I rarely hear the competition getting near.

I was talking to a younger colleague about this just a few weeks ago. He was worried that his most interesting work was peripheral to what most people were doing, and therefore failed to arouse their interest. I said that if he found it interesting that ought to be enough — that I'd managed to get through an entire career that way. "Ah,'' he said, " but you've survived by managing to write about it in a way that makes people think it's interesting, even though it isn't.'' (I took that as a compliment.) This may be an example of what Jonathan Monroe had in mind when he asked us whether we considered our writing to be at odds with our discipline.

There have also been times when my writing of physics has quite directly troubled the guardians of my discipline. I once sent a paper to Physical Review Letters, the world's top physics journal, with the title "Beware of two-dimensional lattices with 46-fold symmetry". On the form acknowledging receipt of the manuscript was added in handwriting: "We question the suitability of the title. It is catchy but doesn't convey much information.''

Notice two things about this response:

The title is characterized as "catchy.'' In the context of the table of contents of Physical Review Letters it might indeed arrest the eye, but the problem is not that the title tries to catch the attention of potential readers. What is disturbing is its invocation of raw human emotion. Beware! Titles of physics papers rarely address the feelings their contents ought to inspire in the reader. The dominant tradition in late 20th century scientific prose has been to produce something suitable for direct transmission from one computer to another, from which any trace of human origin has been purged, and in which any suggestion of the humanity of the author or the reader would be in bad taste.

Furthermore, the complaint that the title is uninformative is a lame excuse. Had it been (as it was in an earlier draft) "Uniqueness of two-dimensional lattices with n-fold symmetry for n < 46'' it would have triggered no alarms. The actual title — "Beware of two-dimensional lattices with 46-fold symmetry'' — is more informative. The acceptable one leaves open the question of whether we stopped at 46, because 45 is already quite large enough, because it just got too hard to press the frontier further at that point, or because 46 is truly exceptional. The word "beware'' aptly conveys both the complacency appropriate to cases less than 46, and the trouble this can land you in if you blithely assume that 46-fold symmetry will be no different.

I decided not to respond to this provocation until the paper had been reviewed. Neither referee even mentioned the title, but in due course I received from the editors an unusual letter of acceptance:

"We have decided to publish the paper provided you submit a appropriate informative title. We find that your title is catchy, but not informative. We don't mind catchy titles if they are also informative.''

I decided to call their bluff, and give them an indisputably informative title that continued to begin with "beware''.

To my surprise and to their credit, they gave up at that point. Until writing this lecture I had assumed that mine was the only title in the physics literature containing the word "beware''. But as a very minor instance of how you don't understand the physics until you start to write it, when I dialed in to INSPEC a few days ago I found 131 scientific titles containing the word "Beware''. It seems to be prevalent in the engineering literature, as in