It seems to me evident that the system of prizes, honors and awards in physics has run completely amok, absorbing far too much of the time and energy of the community in proportion to the benefits conferred. Yet nobody complains. Every month Physics Today routinely announces the latest crop of winners, all the major American Physical Society meetings have sessions to bestow prizes, the APS directory continues to distinguish the asterisked from the unasterisked, and nobody ever complains. Why?

To ask the question is to answer it. Indeed, merely by publishing the above paragraph I have probably already irreparably blemished my reputation in the profession, and if Physics Today has actually printed this column I imagine it can only have been after heated and prolonged editorial debate. Much of this essay, in fact, sat aging in my computer in a directory with highly restricted access for almost two years. It was finally sprung loose by the 1988 Presidential campaign, which filled me with so intense a loathing for those who hesitate to speak provocative truths that I can no longer restrain myself. Here I go.

Why does nobody ever complain? Nobody complains because there are two categories of physicists: those who have won prizes and those who have not. Winners cannot criticize the system. It would be rude to the donors of their prizes. It would be offensive to the committee that selected them and the people who wrote letters on their behalf. It would be a vulgar display of bad taste.

These are volumes II and III of Sir Karl Popper's hitherto unpublished Postscript to the Logic of Scientific Discovery. In addition to the Postscript itself, which was largely completed twenty years after L.S.D. in 1954, about a third of each volume is devoted to more recent writings. Volume II, The Open Universe, subtitled “An argument for Indeterminism”, has three “addenda”: a reprint of Popper's 1973 essay, “Indeterminism is not enough”, a revised version of his 1974 “Scientific Reduction and the essential incompleteness of all science”, and a brief essay, “Further remarks on reduction”, written in 1981. Volume III, Quantum Theory and the Schism in Physics, has a lengthy 1982 preface, and contains a revised and expanded version of Popper's 1967 “Quantum mechanics without the observer”.

It was not Popper's original intent that the work should appear in separate volumes. Volume II, though primarily about classical physics, bears importantly on his views of the quantum theory, and further discussions of classical concepts (notably entropy and irreversibility) are in Volume III. I shall therefore discuss the two books as a single coherent work. (Volume I, Realism and the Aim of Science, was unavailable at the time this review was written.)

Popper argues with wit, ingenuity, and passion, that the prevailing “Copenhagen” interpretation of the quantum theory is a mistake. Heisenberg, he says, “led a generation of physicists to accept the absurd view that one can learn from quantum mechanics that ‘objective reality has evaporated’” (III p. 9). According to Popper, there really are particles out there, not “wavicles”, and each particle has both a position and a momentum.

I write bleary eyed and disheartened, after a long proofreading session mainly devoted to inserting into the galleys calls for the restoration of what was capriciously and destructively altered in the editorial offices of Physical Review. I proofread simply by reading the galleys, without reference to the original manuscript. My writing is a process that does not converge; I cannot read a page of my own prose without wanting to improve it. Therefore when I read proofs I entirely ignore the manuscript except to check purely technical points. Proofreading offers one more shot at elusive perfection. Proceeding in this way, I come to the end of a paragraph with a lurching sensation. The last sentence seems to be a non sequitur. Can I be failing to get my own point? Turning to the copy edited manuscript, I find a marginal message: “Author: Please note that we discourage single-sentence paragraphs.” As an application of this principle, one short emphatic paragraph has been attached to the end of another, to which it is entirely unrelated. If you set asunder what Physical Review has joined, it makes sense again.

What is the justification for such a rule? Excessive use of single-sentence paragraphs blurs the distinction between the sentence and the paragraph, makes for a visually unattractive page, and becomes boring. But the occasional single sentence paragraph is a valuable device. It gives a pause in the rush of thought, it focuses attention, and it can contribute powerfully to the rhythm of the prose.

Introduction: the quantum theory

The quantum theory was born in 1900, with the twentieth century, and future centuries will list it among our own's most remarkable achievements. Designed to account for the puzzling behavior of matter at the submicroscopic scale of individual atoms, the theory has enjoyed phenomenal success. It has accounted in a quantitative way for atomic phenomena with a numerical precision never before achieved in any field of science. When it was subsequently applied within the atom to the atomic nucleus – an object some hundred thousand times smaller – no further modification in the theory was needed. More recently, when applied within the particles making up the nucleus to describe their own internal structure – an investigation on a scale as much smaller than atoms as atoms are smaller than us – the quantum theory still shows no signs of requiring extension or revision.

When I suggested to Simon Capelin that Cambridge University Press think about publishing a collection of my non-technical and pedagogical writings in and about physics, he responded politely, but expressed his concern that “a major problem is going to be trying to invent some sort of theme to the book.”

“No need for invention,” I thought. I have always felt that these essays and the aspect of my career as a physicist they embody have a greater unity and coherence than the rather diffuse and opportunistic conglomeration of my more technical efforts. But spelling this out has been a painful process. By putting my finger on the common thread of excitement and concern that led me to write them, I can't help feeling that I'm killing the magic some of these articles had (and still have) for me. I'd rather leave it to the reader to find (or fail to find) what I'm up to (or think I'm up to). But editors must be served, so here I go.

What the essays have in common is a concern with the problem of scientific communication. Some are addressed to a general audience, some to students, and some to other physicists; some are about physics, some about the tools of physics, and some about the practice of physics. But all share a preoccupation with both the substance and the style of written scientific communication.

Over the past fifty years or so, scientists have allowed the conventions of expression available to them to become entirely too confining.

I know the exact moment when I decided to make the word “boojum” an internationally accepted scientific term. I was just back from a symposium at the University of Sussex near Brighton, honoring the discovery of the superfluid phases of liquid helium-3, by my Cornell colleagues Doug Osheroff, Bob Richardson, and Dave Lee. The Sussex Symposium took place during the drought of 1976. The Sussex downs looked like brown Southern California hills. For five of the hottest days England has endured, physicists from all over the world met in Sussex to talk about what happens at the very lowest temperatures ever attained.

Superfluid helium-3 is an anisotropic liquid. The anisotropy is particularly pronounced in the phase known as He-A. A family of lines weaves through the liquid He-A which can be twisted, bent or splayed, but never obliterated by stirring or otherwise disturbing the liquid.

Several of us at the Sussex Symposium had been thinking about how the lines in He-A would arrange themselves in a spherical drop of the liquid. The most symmetrical pattern might appear to have lines radiating outward from the center of the drop, like the quills of a (spherical) hedgehog (Fig. 1). There is an elegant topological argument, however, that such a pattern cannot be produced without at the same time producing a pair of vortex lines connecting the point of convergence of the anisotropy lines to points on the surface of the drop (Fig. 2).

Introduction

Among other things, this is indeed a paper about Logarithms! I hope the difference between Logarithms! and logarithms will be clear at the end. Evidently Logarithms! are the nicer kind, but if that is not enough to entice you to read on, let me at once answer three questions:

1. (1) For whom am I writing?

2. (2) What about?

3. (3) Why?

1. (1) I am writing for physicists who teach the one-year course in “liberal arts physics” for students with absolutely no trace of professional interest in the subject. Although the paper itself simply presents the contents of the lectures on Logarithms! that I have given such students for several years, the presentation here is aimed at a more sophisticated audience of colleagues, to reveal to them briefly and efficiently how the techniques can be used. The paper might be of some interest to the students themselves, but if they can follow the argument without help they probably don't belong in the course for which it is intended.

2. (2) I am writing about three different things:

3. (a) An efficient and entertaining way to review arithmetic skills in manipulating powers, which, for typical students in the “liberal arts” physics course, may have lain unused for as many as four years. Without restoring such skills to them it is virtually impossible to teach any physics whatever.

4. […]

Pauli and Einstein were both wrong. The questions with which Einstein attacked the quantum theory do have answers; but they are not the answers Einstein expected them to have. We now know that the moon is demonstrably not there when nobody looks.

The impact of this discovery on philosophy may have been blunted by the way in which it is conventionally stated, which leaves it fully accessible only to those with a working knowledge of quantum mechanics. I hope to remove that barrier by describing this remarkable aspect of nature in a way that presupposes no background whatever in the quantum theory or, for that matter, in classical physics either. I shall describe a piece of machinery that presents without any distortion one of the most strikingly peculiar features of the atomic world. No formal training in physics or mathematics is needed to grasp and ponder the extraordinary behavior of the device; it is only necessary to follow a simple counting argument on the level of a newspaper braintwister.

I first heard this joke from Rudolph Peierls in 1961. Since then the size of Physical Review has doubled, doubled again, and is on the verge of completing its third doubling. Physical Review Letters is nearly as big as Physical Review was in 1961. The journals of other physical societies have undergone comparable expansions, as have the numbers and sizes of the commercially published physics journals.

I was recently asked to address a group of Cornell alumni and librarians on how the library is used by a typical physical scientist. I did point out that they had selected a distinctly oddball specimen, but they persisted. So to give them a sense of the calamitous conditions we have created, I went systematically through the current periodicals section of the Cornell Physical Sciences Library to count how many journals I felt I ought to look at but didn't. My criterion was stringent. A journal made my list only if it would be downright embarrassing to admit that I never looked. I had to be able to imagine a colleague responding to my confession with amazement: “You never look at X?!.” Counting only once those with multiple versions (A, B, C, …) I still found 32.

A few months ago I found myself living one of my milder versions of hell, trapped on a flight to Los Angeles, having forgotten to bring along anything to read but Physical Review Letters. Finishing the two articles that had inspired me to stuff it in my briefcase before we even reached the Mississippi, I decided to make the best of a bad thing by taking the opportunity to expand my horizons. Scanning the table of contents, I was arrested by a title containing the word “Lagrangean.”

Funny, I thought, it's not often you see misprints so blatantly displayed. But when I turned to the article, there it was again, “Lagrangean,” in the title and scattered through the text. Well, I thought, an uncharacteristic failure of the copy editing process. The authors were foreign and apparently didn't know how to spell. Copy editors aren't physicists, the word is surely in few if any dictionaries, and so it slipped through.

But I had nagging doubts. Easily resolved, I thought: You can't write an article in theoretical particle physics without a Lagrangian, so I can check it right now. Well, it turns out to be not quite that easy. To be sure, you can't do particle physics without a Lagrangian, but you don't have to call it anything more than L, and many don't. Nevertheless, I found a Lagrangian, fully denominated, in one more article, and there it was, shimmering derisively before my eyes again: “Lagrangean.”

Now I am not a man of great self-confidence, and my secretary will testify that I am a rotten speller.

the picture of the fluxional calculus that one can derive from the textbooks written for teaching purposes is not completely representative of the level and methodology of the research carried out by British mathematicians. It was not the kinematical method of fluxions but rather another tool, labelled vaguely as ‘analytics’, which was adopted by some of the most active fluxionists. Among them the most notable were: Thomas Simpson (1710–61), John Landen (1719–90) and Edward Waring (1736–98). ‘Analytics’ had a different meaning for each of the three: however, a general idea can be inferred from their works.

‘Analytics’ was a calculus not immediately interpretable in terms of geometrical or kinematical concepts. The use of symbolism was free from the constraints of interpretability: imaginary numbers, logarithms of negatives and so on were considered admissible. This freedom was not usual in eighteenth-century Great Britain. The limits imposed by the kinematical conception of mathematical quantities were ignored because it was thought that the progress of the fluxional calculus was directly connected with the development of analytical methods. For instance, a formal use of series was considered fundamental: the analytical fluxionists were hoping to attain results by working algebraically on infinite series.

The research on the continent was thought of very highly by the analytical fluxionists, and a genuine attempt was made to import continental methods. This early attempt of reforming the calculus was largely a failure.