Writing a book on controversial questions without visibly making judgments on the controversies is not as easy as you may think. You have to go out of your way to avoid using the language in which these matters are usually discussed, because any choice of familiar words calls to mind its familiar context and therefore tends to align the author, in the reader’s mind, with the side of the controversy that uses these words. (Think of the debates over government spending and taxes in US politics.) Often no alternative language is at hand, however; to avoid the appearance of leaning to the side associated with the vocabulary you therefore need to add cues that show that you do not necessarily adhere to the values habitually expressed by that vocabulary. Scare quotes will work, but you don’t want to litter your manuscript with them, so you are stuck with irony. Heavy-handed irony is even worse than scare quotes, so you try to be subtle, but then you run the risk of being perceived as unclear, and some readers will be tempted to guess at what the author was really trying to say.
Ernest Davis’s review of the book for SIAM News largely consists of four guesses of this type. In each case the reviewer guessed wrong; in one case, admittedly the most delicate of the four, very badly wrong. The reviewer’s errors offer the unexpected advantage of providing an opportunity to set the record straight. And I have the obligation to do so: as the author I am fully responsible for failing to write a text that makes my intentions, or absence thereof, absolutely unambiguous, especially when ambiguity was my intention.
(All reviews, good, bad, and indifferent, will be visible on this page.)
1. To exemplify the book’s “general spirit” that is “‘unapologetically’ self-satisfied and self-congratulatory,” the reviewer chooses an anecdote from chapter 6, an authentic quotation by Reine Graves, the co-director of Edward Frenkel’s film Rites of Love and Math. Bad choice. Much of the book is not about how and what mathematics really is (whatever that may mean) but rather about how mathematics is perceived. Chapter 6 is almost entirely about the image of mathematics and mathematicians (a secondary theme is the historical search for a “love formula”). The frame is established in the first sentence with the word “mirror,” which (not coincidentally) is also the last word in the chapter. I write that Reine Graves “gave the best possible answer” (to the question: why did she make a film about mathematics?), not because I agree with the answer — how could one either agree or disagree? — nor because it is flattering, as Davis supposes. No, it is “the best possible answer” because it fits beautifully with (to quote one of the pivotal sentences of Chapter 6) “the image of the mathematician as romantic hero, the stereotype that, for [historian Amir] Alexander, has represented mathematics ‘in the popular imagination'” for over 150 years. But the answer was even better than that, from my authorial point of view: not only did Graves (unwittingly?) exemplify “the popular imagination” but her reference to “the eye that gleams” provides a perfect lead to the following paragraph, in which Amir Alexander focuses on — what else? — gleaming eyes in portraits of 19th century mathematicians, and the marked contrast with the eyes in portraits of physicists of the same era.
The reviewer writes:
Creative artists and adoring sophisticated women with a worshipful attitude toward mathematics and mathematicians are a recurring presence in Harris’s book.
I’m pretty sure they only “recur” in Chapter 6, which is precisely about attitudes, worshipful or otherwise. (Attitudes of musicians toward mathematics are quoted in Chapter 8; they range from respectful to extremely hostile.) I was tempted to include in the chapter a picture of this memorial to Pierre Fermat (literally on a pedestal) in the city hall of his home city of Toulouse, but refrained from doing so.
(And an apology is in order: if the quotation about the Wranglers in Chapter 6 is meant to be an —admittedly fairly silly—secret joke, like other tidbits scattered through the text, then the reviewer’s revelation of the secret counts as a spoiler, in keeping with the chapter’s cinematic frame.)
2. Chapter 2’s title — How I Acquired Charisma — was meant to be provocative. To avoid the impression of arrogant self-promotion in the segment in which I apparently “recite [my] CV” I wrote, explicitly, no fewer than three times — once in the preface and twice in the chapter itself — that the account of my own progress toward “charisma” was, to quote, “little more than a convenient focal point around which to organize the text.” In this chapter I limited myself to the chronology I call (following Weber) “ideal-typical”: an inspiring high-school teacher, an interview with the undergraduate advisor, a choice of thesis director, the steps to tenure (the concrete meaning of “routinized charisma”), and the privileges that come along with that status. Most professors in a scientific discipline have presumably followed a similar career path. There’s nothing “somewhat tongue-in-cheek” about that; that’s the point. The chapter is not about any individual following this ideal-typical path, least of all about me, but about the community values that are assimilated along the way. What is “tongue-in-cheek” are two allusions to the book: one on p. 39 to the convention of listing the author’s credentials on the inside flap of the jacket, and this one in the last paragraph of Chapter 2:
even my modest level of charisma entitles me, not only to say in public whatever nonsense comes into my head…but even to get it published.
May I suggest that it would have been more generous (and more in keeping with the book’s “general spirit”) to have reproduced this quotation rather than the mock recitation of my CV?
3. The reviewer accuses me of “pat[ting] myself on the back vigorously for being too pure of soul to grok anything so vulgar and grasping as finance.” This case seems less a wrong guess than a deliberate misreading, because the main point of the passage is contained in the part omitted from the reviewer’s selective quotation (restored in boldface below):
It’s not the equations that make it difficult for a mathematician like me to grasp quantitative finance. My problem is with adopting the psychology, the motivations, the persona of Investor… invariable protagonist of the allegory through which politicians, the mainstream press and the finance math textbooks ram the moral lessons of public economic policy into popular consciousness. Someone who . . . has never aspired to playing Investor, a figure whose cardinal virtue is maximizing returns, is at a distinct disadvantage.
This chapter has three themes: the use of mathematics to provide a facade of objectivity for economic policy decisions disguised as science; a brief account of causal explanation in mathematics, illustrated by the use of simple difference equations; and the growing dependence of mathematical research on private philanthropy. The passage in question is an illustration of the first of these themes. There are of course neither pure souls nor vulgarity in my text, but the reader is always free to find whatever he or she expects to see.
There is a back story behind this passage. The gradual elimination of defined-benefit pension schemes (such as the one my father enjoyed as a schoolteacher in Philadelphia) in favor of the obligation, disguised as freedom, to play the role of Investor and bet one’s retirement on market performance, all to the benefit of the investment houses that are “too big to fail,” has been one of the great calamities of our time. Mathematical finance helped make it possible. But that’s a long story and it has been told much better by professional economists. What they can’t say is how mathematicians can acknowledge our partial responsibility for the situation.
4. The main topic of the review is one I have been preparing for this blog: if mathematics can’t be justified as useful, or true, or beautiful, then how can it be justified? Specifically, why should anyone pay for mathematicians to enjoy ourselves? The reviewer thinks I have an answer to this question, and he thinks he knows what it is:
Harris is disgusted with the philistines in government who dare question that mathematical research should be funded at taxpayer expense.
If only it were so simple. The question is really important and I really wish I knew the answer, and that’s certainly one of the reasons I wrote the book. But I don’t know the answer, and I never pretend that I do. I do go as far as to put into the mouth of a fictional character that
It’s easy to argue that … mathematics is one of the few remaining human activities not driven by commercial considerations.
The reviewer quotes the last part of the sentence — failing to mention that it’s excerpted from a dialogue — but not the part in boldface. He therefore transforms what is a claim by a fictional character of what is hypothetically possible into a positive affirmation by the author. This is about as far from my intentions as is logically possible, especially because the sentence is excerpted from a dialogue between two purely fictional characters, who (here and elsewhere) represent two horns of my own dilemma!
I have to assume (reluctantly, I admit) that this was an honest mistake. Admittedly, other sentences in the book could be read in the same way, but I made an effort to keep all such assertions ambiguous. This is because — I repeat — I don’t have a satisfactory answer to the question. What I can say is that, when pure mathematicians claim that our research deserves to be funded because of potential future applications, we are being disingenous, not to say hypocritical, about our true motivations. Maybe the reviewer is OK with that; I’m not.
The question — if “not merely good, true, and beautiful,” then what? — will repeatedly be addressed in this blog. The book does not pretend there is a simple answer. I therefore ask future reviewers to refrain from looking for one and to focus on what the book actually says. There’s plenty to criticize!
For those who want authors to make unambiguous statements, here’s a statement that (almost) meets that description. If you believe the world is corrupt, then you have to believe that those who (like university professors) benefit from privileged positions in that world are complicit in that corruption; there are no “bastions of purity.” But that’s just empty moralizing; close description is much more interesting.