Things that are not wrong with MWA, I: reasoning by lipstick traces


Image credit: John Bartelstone, from

Greil Marcus was teaching the world how not to be wrong many years before Jordan Ellenberg published a book by that title.  That, at least, was the opinion expressed by John Lydon—better known as Johnny Rotten—when asked about Marcus’s book Lipstick Traces.  To quote from the book’s back cover (with my emphasis added):

John Lydon:  “It’s so mad, it’s so daft, it’s so off the wall—it’s thoroughly enjoyable…”

Interviewer:  “But you don’t think he’s completely wrong?”

John Lydon:  “No, he’s not wrong.”

A foolproof way not to be wrong is to avoid making assertions to which the tired opposition between right and wrong can be meaningfully applied.  Actually, that’s on the back cover as well:

Marcus offer[s] interpretations that are meant to excite the reader to further imagining and thought rather than mere agreement or disagreement… (Anthony DeCurtis, Rolling Stone)

The brief proposal I submitted to Princeton University Press, accompanied by early drafts of what were to become Chapters 5, 6, and 9, opened with a promise to write a book in the same vein.

The idea for this book can be traced back to my reading more than ten years ago of Lipstick Traces by Greil Marcus. Marcus’s book, which has nothing to do with mathematics, is hugely entertaining; it is also a profound work of cultural archeology, tracing the roots of a striking and apparently unprecedented cultural phenomenon — the emergence of punk rock in the 1970s — through echos of millenarian movements and the forgotten history of striving for transcendence. My immediate reaction was: mathematics has been around a lot longer than rock and roll, and is much more pervasive in our lives, in our popular culture, and in our very way of thinking. Why is there no book that presents mathematics in a historical and cultural context rich enough to reveal mathematics as a fully human experience, with all the pathos that entails?

For a long time it was my firm intention to recycle that paragraph in the preface of the book PUP quickly agreed to publish.  The preface was the last thing I wrote, though, and either because I was exhausted or because I was concerned my meaning would be misunderstood or because the main text was already overloaded with rock and roll, I decided to try to adopt a more conventional tone in the first pages a potential reader was likely to see upon opening the book.  After more than half a year of writing this blog and reading the occasional bad review of MWA — I’ll be turning my attention to one of those before I’m through with this post — I am now convinced this was a mistake.  Besides, one of the outside reviewers to whom PUP sent the proposal before agreeing to sign a publishing contract reacted to this very paragraph:

I strongly urge  PUP to acquire Michael Harris’s (untitled) book.  Let
me put it quite simply.  Harris proposes to write a book that will stand
in the relation to mathematics that Greil Marcus’s LIPSTICK TRACES does
to cultural theory and the academic study of popular music.  You have
sent the proposal to the right reviewer, because I am a huge admirer of
LIPSTICK TRACES and think that Marcus’s book is the exemplar of the role
an academic press (in this case Harvard) can play in getting important,
complicated ideas from the academy out to the public.

To appreciate what Marcus accomplished with Lipstick Traces it’s not necessary to share his feeling that “every good punk record made in London in 1976 or 1977” is “the greatest thing you’ve ever heard.” (Lipstick Traces, p. 80; all references to the 1990 Harvard University Press paperback edition).  It’s enough to be willing to respect  “…the pursuit of a non sequitur for the pleasures only a non sequitur can bring… (p. 20) and to agree not only that “Real mysteries cannot be solved, but they can be turned into better mysteries” (p. 24) but that this can be the motto of a legitimate form of intellectual exploration going by the name of cultural criticism.

The anonymous reviewer accepted my proposal’s claim that, by writing book reviews and occasional articles,

I began to learn how to dissimulate a tightly directed narrative beneath an apparent series of free associations;

the reviewer added that “I cannot say confidently what [Chapter 6] is ABOUT but it is clear that something real is happening.”  Last week, in the course of a wide-ranging discussion of his two most recent books at the French bookstore Albertine in New York (pictured above), Marcus alluded to the appearance of free association in his writing, and for several minutes he explained his methods and his motives with impeccably quotable clarity.   Unfortunately I was not taking notes and, although some of the events at the Cultural Services of the French Embassy are recorded and made available on line — check out this conversation with John Nash and Cédric Villani if you haven’t already done so — I fear that all that’s left of Marcus’s words are the scattered traces that my memory will not be able to reassemble.

It would have been useful to be able to channel Marcus in responding to Mark Hunacek’s review of MWA in the American Mathematical Monthly.  This particular negative review appeared nearly three months ago, but I have been putting off linking to it on this page because I really don’t know what to make of it.  The conclusion, though, is unambiguous:

Final verdict: a reader will have to make an individual determination as to whether the benefits of this book outweigh the author’s rhetorical excesses and heavy-handed writing style. Undoubtedly, some will say that they do, but I’m afraid that I can’t count myself in that group.

Hunacek dislikes three things about the book:  its “opaque writing style,” its “self-congratulatory tone,” and its

stream-of-consciousness feel…, with the author jumping from one idea to the next, following no particular narrative pattern that I could discern.

I thought I had explained what was behind the “self-congratulatory tone” the last time a reviewer missed the point, in point 2 of this post.  But Hunacek obviously decided his assignment was to read the book, the whole book, and nothing but the book; he found MWA “opaque” because it refers to authors he had not read.   (By the way, I don’t understand why it’s more acceptable to announce one’s ignorance of Max Weber in the pages of the American Mathematical Monthly than it would be to write that one doesn’t “really know[…] anything about” Darwin, say, in a hypothetical analogous journal of sociology — or rather, I do understand the reason, and it doesn’t reflect well on our profession.)

Lipstick Traces, like many of Marcus’s other writings, is relevant to Hunacek’s third complaint, the one about stream-of-consciousness — or, as Marcus put it, free association.  Now Marcus is a professional writer and I am not, and I am under no illusion that I can make use of his stylistic innovations in cultural criticism with anything like his skill or effectiveness, not to say brilliance.  But Hunacek’s third objection, as far as I can tell, is not to my lack of skill nor even to the style he calls “heavy-handed” but to the very notion that a non sequitur, even a merely apparent non sequitur, can bring pleasure; so that his lack of discernment is the author’s fault, not his.

Each chapter of MWA is in fact organized around a “tightly directed narrative” — with the possible exception of the last part of Chapter 8 — and I’m not going to spoil the reader’s pleasure, such as it is, in figuring out where the direction points.  But I do want to share what I understood while listening to Marcus at Albertine, about why I needed to write in that particular way.  I have long felt that writing about certain particularly sensitive topics in the practice of mathematics leads invariably to dead ends.  (A good example is the controversy over whether mathematics is invented or discovered; there are many others.)  I didn’t want to avoid sensitive topics; on the contrary, as far as possible I wanted to write only about sensitive topics.  Tackling them head-on — taking a right vs. wrong position one way or the other — would clearly lead me to the same dead ends.  So I chose to follow Marcus and to argue by the evidence of lipstick traces — by means of analogies, anecdotes, stories, digressions, and often incongruous or “daft … off the wall” juxtapositions “to excite the reader to further imagining and thought rather than mere agreement or disagreement.”  (Brendan Larvor referred to this, eloquently, as “disclosure through juxtaposition and paradox,” which he considers a “Parisian activity.”  Marcus is well-versed in critical theory of the Frankfurt as well as Parisian variety, though he belongs to no -ism.)  And accessorily, to incite professionally qualified readers — historians, for example — to investigate some of the more suggestive lipstick traces that may have been overlooked.

Marcus said it much better at Albertine, in connection with his own aims as a writer, but those words are no longer available to me.

I have to write about one more paragraph in Hunacek’s review, the most problematic as far as I’m concerned, before I’m ready to post quotations from the review prominently on this blog.  I’ll also consider the question of whether, on balance, the publication of this kind of negative review isn’t a blessing in disguise.  But that’s for another time.

P.S.  Lipstick Traces is also indirectly and implausibly responsible for the inclusion of Figure 6.4 in MWA, and more directly and plausibly responsible for the brief discussion of Isidore Isou in the same chapter.


9 thoughts on “Things that are not wrong with MWA, I: reasoning by lipstick traces

  1. JSE

    You should note that your PUP reviewer, in saying “something is really happening,” is intentionally if quietly echoing the refrain of Lipstick Traces — “THIS IS ACTUALLY HAPPENING” — as a kind of private communication of affinity between reviewer and author, sent along the procedural channel but not legible/digestible by that channel.


  2. Mike Shulman

    It never occurred to me before that “an apparent non sequitur can bring pleasure”. I won’t dispute it, of course, but I do not personally find it pleasurable to be forced to figure out what I’m reading about when the author could instead have made it clear.

    It seems to me that anyone writing a book has to choose their audience and then write to that audience. When you write a romance novel or a mathematics monograph, you automatically restrict your audience to people who enjoy reading that type of book; and if you write in a stream-of-consciousness style with apparent non sequiturs, then you likewise restrict your audience to people who enjoy reading that type of book. Hunacek may be wrong in not realizing that such people exist, but it’s equally wrong to assume that everyone is such a person. So while such writing may not be “wrong”, in the sense that it’s a choice that you as an author have the right to make, I would say it’s also a choice that excludes a substantial number of people from your audience.

    Similarly, you may wish that the readers of your book were as familiar with Weber as with Darwin; but the task of an author is to write for their audience, not for a hypothetical more-educated version of their audience. If you think your readers ought to be more familiar with Weber than they are, then I would say you should explain Weber to them and convince them of it; simply assuming such familiarity only serves to exclude potential readers.

    Liked by 1 person

    1. mathematicswithoutapologies Post author

      You make two points: one about the reviewer and one about the audience. I plan to address the question of exclusion of potential readers in a future post. As for the reviewer, I think I can state an unequivocal position for a change. When Hunacek was asked to review the book and when he saw that it referred to a literature with which he was unfamiliar, he had two legitimate choices. He could have declined to review the book on grounds of incompetence or he could have taken the time he needed to familiarize himself with the material. He chose a third option: to complain that the book refers to things he doesn’t understand. I don’t consider that legitimate.

      In 2002 I was asked by the Notices of the AMS to review “Mathematics and the Roots of Postmodern Thought” by Vladimir Tasic. It referred to some books I had read years earlier and to many books I had never read at all. I spent nearly three months rereading the former and immersing myself in the latter. I certainly didn’t find Heidegger and Derrida easy but I considered it my responsibility to have at least a general familiarity with the contents of the book I had agreed to review. I also learned the statements of the Zermelo-Fraenkel axioms for the first time, 25 years after my Ph.D. (and I was not surprised to learn that the three eminent number theorists quoted in the first paragraph of my review did not know the statements). It was a time-consuming but extremely enriching experience. My review was sympathetic but critical and I made a number of new friends along the way, including the author and the Notices editor who asked me to write the review.

      And I would not be having this exchange with you had I not taken the time to learn the material when the opportunity presented itself unexpectedly.

      If you want to know more about the pleasure to be procured from apparent non sequiturs, you should read Lipstick Traces. You don’t have to take my word for it; Johnny Rotten found it “highly enjoyable.”


      1. Mike Shulman

        I don’t think the two points can be separated. The job of a reviewer, after all (or, at least, part of it), is to offer the reader an opinion about whether they would enjoy reading the book. This opinion is valuable insofar as the reviewer is similar to the reader and thus likely to react to the book in a similar way. I don’t consider it illegitimate for a reviewer to complain that a book refers to things he doesn’t understand if it was reasonable for him to expect himself (as opposed to a hypothetical more-educated version of himself) to be in the book’s intended audience. Such a complaint supplies useful information to a reader (at least, a reader whose background is similar to the reviewer’s) about how they might feel upon trying to read the book. MWA has been marketed as a book for educated laypeople who are interested in mathematics; I think it is reasonable for a mathematician to expect to be able to understand such a book without having to immerse himself in the literature of some other discipline first.

        Would the review have been improved if Hunacek had also taken the time to become familiar with all the other stuff referred to in the book, so that he could also offer an opinion to the segment of readers who are familiar with it or willing to spend the time to become so? Probably. But even then, he might have chosen to comment that “for the average mathematician who doesn’t want to take the time to study X, Y, and Z, this book will be hard to understand”, and I think such a comment would have been equally legitimate.

        Liked by 1 person

      2. mathematicswithoutapologies Post author

        The future post I promised is going to take a very similar line in explaining the “blessing in disguise” mentioned at the end of the last post. But I still don’t think it’s legitimate. And Weber is hardly an obscure figure.

        As for marketing—don’t get me started.


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