The Devil's Mathematical Dictionary

Inspired by a comment in today's presentation, my new goal is to write a mathematics paper that uses the "Feeling" environment.

(This, in turn, inspired the present document. I decided to do this in a style akin to that of the Devil's Dictionary.) pic.twitter.com/UzpWKjQRRV

— Mason Porter (@masonporter) December 7, 2019

A Novel-Writing Algorithm

This also works for academic writing.

😅 @tomgauld and the novel writing algorithm 📚💻 pic.twitter.com/5WTk6XxTXt

— Dr Jess Wade 👩🏻‍🔬 (@jesswade) February 23, 2019

You Wouldn't Like These Functions When They're Angry

There is a family of special functions called Anger functions. You wouldn't like them when they're angry.

Here is the context: Physics Today has agreed to publish an obituary for Norman Zabusky, so I needed to find some information that they require to be part of it. This led me to Norman's PhD thesis, which I found online. It briefly mentions something called Lommel polynomials, with which I wasn't familiar. The definition in a thesis appendix was terse — it's not exactly an important part of the thesis — so I looked at Wikipedia, and I kept seeing links to special functions that weren't familiar to me, and I have followed a couple of them. Anger functions are one family.

These various special functions are closely related to Bessel functions.

"Title of a Paper"

I’ll soon be giving what amounts to a tutorial for my UCLA Ph.D. students, who will be embarking on writing papers, and — as I was thinking about what materials to prepare — my mind went to a dark, sarcastic place.

(Inspiration from "Title of the Song" by Da Vinci's Notebook.) pic.twitter.com/N1n3xSY6xr

— Mason Porter (@masonporter) March 15, 2018

Update: It turns out that I did this so quickly that I mixed my Oxford and UCLA affiliations. Oops.

How Not to Write a Mathematics Paper: Snarky Edition

Here are some brilliant tips for aspiring mathematics authors!

I don't think I've ever encountered this page before. It's hard to find a favorite. There's also lots of great snark in the explanatory notes.

Here is one bit of snark: "One practical criticism applies to this book as well as a large part of contemporary mathematical production: the various statements are called by different names, such as Lemma, Theorem, Proposition, Corollary; the first three are numbered independently of each other, while the numbers assigned to corollaries are functions of several variables; in addition, numbered formulae have their own separate numeration. The strain placed on the reader by this partial ordering is obvious, but apparently readers seek vengeance on other readers when they turn into authors."

(Tip of the cap to @mathematicsprof.)

"The Interested Reader"

I love how many mathematics papers refer "the interested reader" to various sources for more information.

It is a little-known—but not terribly surprising—fact that most mathematics papers have only a single reader, who may or may not actually be interested in further discussion.

The Acoustics of Breaking Chopsticks

In my latest post for the Improbable Research blog, I discuss the acoustics of breaking chopsticks.

The Complete Papers of Isaac Newton

For those of you who think we scientists can be a bit (or very) obsessive or even a bit nuts, keep in mind that we're just taking after our founding parents. For example, consider Isaac Newton.

And I bet that I'll leave more than 10 million words before I'm done. :)

(Tip of the cap to MoMath.)

Foaming at the Mouth: Academic Inbreeding

One of the nice things about having old issues of The California Tech available online is that I can occasionally look at articles I wrote as an undergrad and see how much I agree with what I wrote back in the day. In this issue from 1998 (the year I graduated), I have a commentary on p. 2 about academic inbreeding. In this case, I pretty much agree almost completely with what I wrote 16 years ago. My occasional feature column, by the way, was called "Foaming at the Mouth". I was a Tech Editor before then and, additionally, my articles from early in my Tech career were reporting more often than features. I made an active change during my time at Caltech. Now if only the Rivet were online so that I could post the blurb from the time (last week of senior year) that I was named "International Terrorist of the Week".

Academics Write Like Crap

Well, at least most of us write like crap for our academic writing. Additionally, most of us don't include humor in our scientific articles either.

I do the best I can to buck this trend, though others will be the judge of how well I do. I certainly attempt to put humor in some of my writing, and quite a few of my papers (e.g., this one) contain easter eggs. I do think that I am a good writer, and at minimum I am definitely very anal about my scholarly prose.

Although I don't agree with everything in the article about what we do that is bad --- for example, I think the paragraph with "The rest of this article is organized as follows." is genuinely useful for many readers, especially if the article is long --- but I agree with a lot of it. Also, I can't overemphasize how much my scientific career has benefited from my experience in journalism at Caltech. (Yes, being a Tech Editor has been amazingly beneficial. It's one of the best and most important things I did for my education.)

(Tip of the cap to Carlos Castillo Chavez.)

Long, Very Long, and ... What the Hell are You Doing?

Well, I guess I have a well-deserved reputation for writing very long papers.

Ernie Barreto wanted to make sure that I saw this article. I really like the terse commentary that likely ended a certain debate. It's key words are priceless. The others are excellent as well, though I had seen those before. In one of them, Michael Berry told me that his abstract of "Probably not." was "No." at some point but that he and his coauthors wanted to leave some possibility that their conclusions were wrong.

Fun Fact: Version 1 of my thesis was about 400 pages. My committee was (very understandably) not very happy with this --- among other things --- and demanded that I write version 2.0 (rather than 1.1) and that it be less than 200 pages. This was not fun at the time.

Fun Fact 2: One version of one of my papers --- the published version was much terser at 20 pages + 20 pages SOM (mostly a table) --- had a 100-page SOM at one reasonably final point, but then we decided the referees would kill us. So the version (which was desk-rejected, of course) that we sent to Nature had an SOM that was in the 60s or so, though that was regular typefacing and spacing rather than in journal-page format. [Acronym: SOM = Supplementary Online Material]

In progress now: a revision of a now 42-journal-page paper (though a review article), and new papers: a 40+ pager, a 35-pager, a pair of 32-pagers, and a few of them currently in the 20s.

(Tip of the cap to Ernie Barreto.)

Without Loss of Generality...

New Rule: If you say or write "without loss of generality" when you do lose generality, then I have the right to smack you.

Today's Rant: Passive Voice

The subject of today's rant is passive voice

Before going on, let me first acknowledge that passive voice is sometimes necessary. That said, what the fuck? It is used way too often in science. :)

Alright, so now that I've gotten that bit of irony out of the way, what's so bad about it? As far as I can see, there are basically three things wrong with passive voice. I'll illustrate them using an imaginary sentence in a scientific paper that might start with the phrase "An experiment was conducted..." You can fill in something from your favorite discipline to complete the sentence.

(1) It lessens clarity, and that's already a cardinal sin. Who conducted the damn experiment? Was it you? Was it the janitor? Was it done by the authors of the paper you cited a couple of sentences before this one? (D'oh... there goes clarity. Now we don't even know if the experiment was original or not.) Maybe it was done by a bunch of fluffy bunnies?

(2) It dehumanizes science. I suppose I can't make this argument in quite the same compelling manner as I can about clarity, but (seriously) it does do this. You put a human face on science by indicating your ownership of the work, and I think that science (and scientists!) needs all of the humanization it can get. So write it loudly and proudly: "I conducted the fucking experiment!" At least then we know who did the work! (As an exercise, see if you can make an appropriate change at the page proof stage of an article to try to get this exact phrasing in print.)

(3) It's bad writing. In most of its guises, passive voice is just an ugly use of language. Isn't that reason enough to try to minimize how much you use it? (Again, I want to acknowledge that sometimes passive voice really does provide the most parsimonious answer to your phrasing problems, but at least try to find another solution first.)



Here's another question: How in Hell did things get this way? Did a bunch of scientific gods get up one morning and decide that passive voice was somehow the right way to present scholarship? (Because it's really not...) Did the rampant use of passive voice in science just evolve slowly? Anyway, passive voice is bad writing and should be used sparingly. I go through great pains to try to get my students [and other coauthors... :) ] to unlearn such fallacies, and you should do that too. Scientific writing can also be good writing, so let's try doing that, ok?

Corollary: Just as annoying as the unnecessary preponderance of passive voice in science is the use of passive voice to avoid taking responsibility for mistakes. All too many times, I have seen a phrase along the lines of "A mistake was made" coming from the person who made the mistake in question. That's really a bunch of bullshit and a sleazy way to attempt to shirk responsibility. Just admit "I made a mistake." and be done with it---lose the sidestepping bullshit!

This rant was brought to you by the letters A, B, and C, and by the number ε > 0.

Why Science? (Revisiting My Essay From a Decade Ago)

When I was in graduate school (over a decade ago), I wrote an essay about becoming a scientist that was published in Beverly Hills Weekly. (I also posted a slightly modified version on my website.)

I just reread both of these documents. And, damn, I still agree with almost everything I wrote over a decade ago! I surprise myself sometimes. :) It also goes to show that---for all of my supposed cynicism---I still am an extremely idealistic person. I will do my best to stay that way!

The Importance of Being Anal

Collaborations are a form of marriage. They last differing amounts of time and can fail for all sorts of reasons.

I am a very anal person---absolutely through-the-roof anal---and one of the things about which I care very deeply is exposition. In my publications, I want to get my wording precisely right if at all possible, even though I will invariably change my mind about some things when looking back later after my memory of why I wanted a particular phrasing has faded away. (My writing goals for this blog are rather different, as you have probably noticed. Here my goal is to write in a stream-of-consciousness form whose intent is for you to imagine me ranting at you---or perhaps even to imagine me discussing things calmly with you, which does actually happen on occasion.)

So, in short, I believe that not only are scientific calculations critically important but that one also must be ultra-anal (one might even call it "OCD") about writing things both for clarity and for style. One can certainly argue endlessly about style, but let's just say that I have a style, and we can forego discussions of whether or not you or anyone else think it's crap. (I hope that's ok.) And because of this, I am generally a major pain in the ass for people like journal editors---possibly frustrating interactions with me have caused at least one reputable journal to change their editorial policies (or so I believe)---and, of course, my coauthors. Hashing out phrasing when I am on the author list can be a somewhat trying experience, and it usually lasts longer when working with me than it does when working with others. So if you can't handle that, than you shouldn't work with me. The marriage just won't work.

Anyway, I believe very strongly that scholarly work depends not just on the raw scholarship but that my personal scholarship is enhanced substantially by my anal writing. (I will speculate that this particular attitude meshes much better with my arts and humanities colleagues than it does with my scientific ones.) I spent time as a journalist in college, as I put in 4 years as a writer and 1 year as a co-editor for a vaunted (snicker) publication known as The California Tech, and I cannot overstate how important that has been for my scientific career.

But back to things closer to the point: I am presently dealing with the revision of a paper (for which a journal editor and referees keep moving the bar, which is massively annoying). I know that I tend to frustrate many of my coauthors with my keen insistence on language, but because of the circumstances with this revision---and there are some additional complicating factors that I am not telling you---perhaps things have boiled over a bit, and one of my coauthors (indeed, a soon-to-be-former coauthor) dismissed as trivial what I consider to be very important grammatical, stylistic, and spelling corrections (which I made crystal clear that I considered to be very important things to do to improve the paper). And it's fine for my coauthor to think things are trivial even when I think they're important. I can handle that, and we're all entitled to different opinions. Collaboration---like all marriages---requires compromise. But I will simply not accept something I consider as critically important being dismissed as trivial rather than hashed out (or my being allowed to have control of the file so that I can make the damn changes myself). If I make it clear that I feel something is important, then my coauthor damn well better either work with me on it or let me spend the time to make the changes I want and then iterate with me as necessary until we both like things. So when this paper is over and we get our final acceptance from this journal or some other one, we'll part ways---not because my coauthor thinks my comments were trivial but rather because the fact that I obviously considered them important wasn't construed as a sufficient reason to hash them out anyway. In these situations---namely, when my collaborator finds that something is important, regardless of whether I find it important---I do make time even when it doesn't exist, and I expect the same of others. (And, very importantly, I obviously deserve my share of the blame for our parting of ways. I can be difficult to work with at times, and it would be improper for me to deny that.)

Alright, I have now ranted a lot. Such is my nature. Let me end on a more positive note and bring things full circle (or perhaps the orbit has a different shape?). What are the fruits of being anal? To give one example, I am really proud of the introduction to this recent paper. It discusses different types of assumptions that people make when deriving approximate theories to study dynamical systems on networks, and it carefully distinguishes various assumptions (which are often implicit in many papers rather than discussed explicitly, let alone carefully) that are made when developing certain types of theories. I have been writing some lecture notes on dynamical systems on networks in preparation for my book (on which I am woefully far behind, by the way), and I have drawn one short section from the relevant part of this paper's introduction. I have looked through many sources while preparing my lecture notes, and I can't find a single other one that presents these assumptions so clearly, and here we have them all in the same place in one coherent discussion. This paper is a technical paper on a rather specific topic and it appears in Physical Review E, which is a very good but decidedly non-sexy journal. So it's readership isn't going to be very broad or include overwhelming numbers of people. And the discussion in the introduction to this paper is not the kind of 'impact' (shudder!) that concerns the UK government, University of Oxford, and (I believe) most researchers from most disciplines. But my coauthors and I did the best job I have ever seen of explaining this particular set of material, which is confusing to many people and is typically explained poorly (if at all) in other works that discuss analytical approximations for dynamical systems on networks. Granted, my coauthors and I hashed out this exposition after nontrivial referee prompting, but that's a story for another day. It was certainly worth it, though! (Hence, mad props go out to the referees as well.)

So if you take anything at all from this blog entry, let it be one thing: it's really important for a scientist to be anal not only in calculations and other forms of 'raw scholarship' but also in their writing (down to the last comma).

Version Numbers of Documents

I started numbering the initial drafts of my papers using 00 (instead of, say, 1) a long time ago, but today I sunk to a new low: I not only gave a paper a negative version number, which I have actually done before, but I gave it a negative and noninteger version number.

Of course, from a mathematical point of view, this isn't technically a new low, as it is version -0.5 and I have had a version -1 on other papers.

Also, the reason I use 00 instead of 0 is in anticipation of needing double digits and wanting the alphabetization to work correctly.

Update (5/25/12): Ernie Barreto challenged me in a comment in my Facebook post on this topic to use complex numbers in my version numbers. Challenge accepted. John Meacham reminded me of Knuth's up-arrow notation, and by looking that up, I learned for the first time that iterated exponentiation is called "tetration". That last fact alone is worth the entire Facebook post. (P.S. Now that it is 25 May, be it known that it is now Towel Day.)

It's not Wikipedia, bit it is a Start

I apparently have a wiki entry as a "writer" at BoardGameGeek because of an role-playing game article I wrote for Polyhedron in 1999. (I got the publication as a winning entry in a contest to design a character based on a picture published a couple of issues earlier in the magazine.) Somebody else wrote the page, and I just now added links to my blog and my Oxford home page.

I'd prefer an entry in Wikipedia, but I think I will need to become a bit more famous first. (And I'm not crass enough to write my own page.)

It is nice, however, to be have an entry on a gaming wiki. Ideally, the Legends of Caltech movie project will eventually land me with an IMDB entry.

Stranded Magazine

Stranded magazine is finally out. This is the magazine induced by ash clouds that was produced by stranded people. I have a couple of contributions in it.

"All proceeds go directly to the International Rescue Committee to help people stranded in a more permanent way."

Blast from the Past

I was doing some googling while the math department's e-mail server is down, and I found this old edition of "The California Tech". I need to get to a meeting with a student, so I haven't been able to check thoroughly if I can find a more interesting issue from the archives. I'll try later.

Update: Here is the directory of scanned issues in the archive for The California Tech. Awesome! (By the way, on page 7 of this issue is the 'strangle this cat' advertisement that tried to attract attention and get people to work for The Tech. The latter wasn't very successful, but we did attract some attention, and this led to a chain of events---including some stuff in future issues of The Tech that pissed off the Pasadena Humane Society and ultimately culminated in the special issue of The Rivet with an animal-oriented theme. Then the school year ended and everything blew over. Ah, memories.)

I think I want this on my tombstone.

Today I'd like to blog about the editorial by American Scientist Editor-in-Chief David Schoonmaker in the May-June issue of that magazine. This is the issue in which my article on the origin of the FPU problem appears, and David spent a lot of his editorial writing about our memorable in-person editing incident when I was visiting Peter Mucha, a collaborator at University of North Carolina at Chapel Hill. I had spent the entire day working on network science research with Peter and then we started our marathon meeting at 6pm. As David writes:

... Still, as someone who has lived through the advent of television and dial phones and the invention of fax and the Internet, I recognize that there also have been losses. A recent evening spent with the first author of "Fermi, Pasta, Ulam and the Birth of Experimental Mathematics" (pages 214--221) really brought that home (he visited here, much as I would have enjoyed visiting him in Oxford, England).

Mason Porter, contributing editor David Schneider and I sat for almost four hours fussing over the details of the text, captions and figures for the article. Refreshingly, Mason is a young scientists---indeed the recipient of the 2008 Sigma Xi Young Investigator Award---who cares deeply about language. He felt no compunction about challenging our choices in wording, yet was perfectly willing to be reasoned out of his own preferences. (Thank goodness there were two of us editors!)

The result could not have happened in an e-mail exchange. Together, the three of us found solutions that wouldn't have arisen without the spontaneity of human contact. It was not lost on me that Enrico Fermi, John Pasta and Stanislaw Ulam made their "little discovery" at a time (1955) when personal communications were rarely more electronically enhanced than the telephone. Would they have found what they did using e-mail?

In the aftermath of that stimulating but exhausting evening, I have reflected on my working relationship with other American Scientist authors. ...

After we were done, it was too late to get dinner and I had some other urgent work to do (and a talk to prepare from scratch for the next day). I spent about 3 more hours on various bits of urgent work that night before I needed to crash because my body was starting to shake somewhat uncontrollably. I didn't even have time to start preparing my slides, so I did that the next morning. (I somehow managed to give a really good talk on some results that I had never presented before, so I guess I am able to do a reasonable job under that kind of time crunch---though I don't want to do it again!)

In some ways, David's editorial would be appropriate for my tombstone---though there are other things I would actually prefer there; for example, I really like the one that says, "I told you I was sick."---though it's perhaps more accurate to say that I want to be remembered as someone who is really, really anal. Since this article came out, I have received a small number of compliments by e-mail both from people I know and from those I don't, and one of the ones I know even mentioned especially enjoying the editorial comments about that incident. I won't be surprised if others who know me bring it up as will, because I think it will ring rather familiar to them.

In closing, I must admit that I am pondering at the moment whether I should e-mail David to let him know that his editorial doesn't have any Oxford commas. Sadly, however, it is American Scientist policy not to include them.