The emperor was naked, and so is this.
December 8, 2015 9:24 PM   Subscribe

"Respected research math is dominated by men of a certain attitude. Even allowing for individual variation, there is still a tendency towards an oppressive atmosphere, which is carefully maintained and even championed by those who find it conducive to success." Recent Princeton graduate Piper Harron's PhD thesis isn't written for these men. It is very cool number theory, and it is art.
posted by bergamot and vetiver (72 comments total) 65 users marked this as a favorite
 
My lawn!
posted by Going To Maine at 9:26 PM on December 8, 2015 [2 favorites]


Well I was going to paste the formula on page 11 and make a self deprecating math joke, but I;ll just leave this as a self deprecating HTML comment. (yes yes, take "we need mathML" to the grey ;-)
posted by sammyo at 9:32 PM on December 8, 2015


BTW, one thing that doesn't really come through in the quote in the OP: it's funny. (And written with lay readers in mind, too! I don't know the first thing about advanced math but I was able to follow along.)
posted by asterix at 9:37 PM on December 8, 2015 [1 favorite]


Wow, good for her. This is definitely the most engaging number theory PhD thesis I've ever read.

I really hope she stays in mathematics. The field needs more people with her mindset, attitude, and writing ability.
posted by town of cats at 9:54 PM on December 8, 2015 [2 favorites]


This is great reading:

I like to imagine abstraction (abstractly ha ha ha) as pulling the strings on a marionette. The marionette, being “real life,” is easily accessible. Everyone understands the marionette whether it’s walking or dancing or fighting. We can see it and it makes sense. But watch instead the hands of the puppeteers. Can you look at the hand movements of the puppeteers and know what the marionette is doing? A puppeteer walks up to you and says “I’m really excited about figuring out Fermat’s Last Thumb Bend!” You say, “huh?” The puppeteer responds, “Oh, well, it’s simply a matter of realizing that the main thumb joint has several properties that distinguish it from...” You’re already starting to fantasize about the Zombie Apocalypse. Imagine it gets worse. Much, much worse. Imagine that the marionettes we see are controlled by marionettoids we don’t see which are in turn controlled by pre-puppeteers which are finally controlled by actual puppeteers. NEVER HAVE A CONVERSATION WITH THESE FICTIONAL ACTUAL PUPPETEERS ABOUT THEIR WORK!
posted by latkes at 9:58 PM on December 8, 2015 [16 favorites]




I clicked link, see 139 pages, all blank. Reloaded, 139 pages, all blank.

"Oh, I see. This is a great joke about the impenetrability of academic papers, and stuff. And everyone is playing along, and making up quotes." I start typing a witty comment.

Partner clicks link; it loads just fine.

Oh.
posted by you could feel the sky at 10:14 PM on December 8, 2015 [12 favorites]


Awesome
posted by Joseph Gurl at 10:22 PM on December 8, 2015


I haven't made it far enough to see if she really manages to "laysplain" the whole thing but if she does that's... really fucking ambitious. I hope she gets a teaching job.
posted by atoxyl at 10:29 PM on December 8, 2015


Very proud that I brought this to the attention of the Internet this morning by tweeting it! (I was also a reader on this thesis.)

For some instructive contrast, you can see the journal version of the result.
posted by escabeche at 10:30 PM on December 8, 2015 [23 favorites]


The abstract is pretty great too:

A fascinating tale of mayhem, mystery, and mathematics. Attached to each degree n number field is a rank n−1 lattice called its shape. This thesis shows that the shapes of Sn-number fields (of degree n = 3, 4, or 5) become equidistributed as the absolute discriminant of the number field goes to infinity. The result for n = 3 is due to David Terr. Here, we provide a unified proof for n = 3, 4, and 5 based on the parametrizations of low rank rings due to Bhargava and Delone–Faddeev. We do not assume any of those words make any kind of sense, though we do make certain assumptions about how much time the reader has on her hands and what kind of sense of humor she has.
posted by asterix at 10:30 PM on December 8, 2015 [6 favorites]


I don't know enough about higher math to evaluate her work, but I can tell she's absolutely brilliant. Because you have to be brilliant to get away with that amount of sheer attitude.
posted by mikeand1 at 10:54 PM on December 8, 2015 [2 favorites]


(I was also a reader on this thesis.)

I saw your name dropped in the acknowledgements and came back here to see if anyone'd done the Mefi's Own thing. =D TBH I'm gonna have to return your book to the library soon so I'll probably get to Harron before How Not To Be Wrong.
posted by carsonb at 11:12 PM on December 8, 2015


I was expecting a lot more pictures, I think I misunderstood the "it is art" line :(
posted by the agents of KAOS at 11:15 PM on December 8, 2015 [3 favorites]


As someone currently working on a PhD in mathematics/informatics, skimming this made me laugh out loud several times. So thanks for that.
posted by Alex404 at 11:19 PM on December 8, 2015


The hardest part about math is the level of abstraction required. We have innate logical abilities, but they are based in context. If you give people a scenario of university students drinking beverages at a bar and give them information either about the person's age or about the person's beverage, most people know instinctively which students' drinks or IDs need to be checked to avoid underaged drinking (i.e., if the person's 22 you don't care what they're drinking, but if the person has a vodka tonic, you need to know heir age). Take the logically equivalent situation of cards with a color on one side and a number on the other. Suddenly it takes some work to gure out which cards have to be turned over to satisfy a given condition (say, all even numbers have red on the back). Just one level of abstraction and the untrained, but educated, person will have a good amount of diculty even understanding the situation. Now try doing Number Theory.
Someone wrote a math phd dissertation for the layperson. I am in love.
posted by aniola at 11:28 PM on December 8, 2015 [6 favorites]


The Wason Selection task. Basically the founding text of evolutionary psychology.
posted by grobstein at 11:56 PM on December 8, 2015 [1 favorite]


So where are the sections, aside from the introduction, where the author actually speaks truth to power? The parts where it might make the committee or other representatives of the institution "uncomfortable"?

Because if the author doesn't accomplish that, then where does this kind of rhetoric - the tension between the claim and the textual performance - take us? Nowhere. Style over substance is the consequence.
posted by polymodus at 12:32 AM on December 9, 2015 [1 favorite]


—And in case my comment was too abstract, consider in juxtaposition this reference point, a different dissertation also mentioned on metafilter:

UBC student writes 149-page dissertation without punctuation

posted by polymodus at 1:13 AM on December 9, 2015 [1 favorite]


the agents of KAOS: I was expecting a lot more pictures, I think I misunderstood the "it is art" line :(

Nick Sousanis' thesis (Unflattening) is in the form of a graphic novel.

Saul Griffith's thesis begins with a cartoon, in the HowToons style.
posted by James Scott-Brown at 1:41 AM on December 9, 2015


So where are the sections, aside from the introduction, where the author actually speaks truth to power? The parts where it might make the committee or other representatives of the institution "uncomfortable"?


I mean, it seemed to me that she was taking on the bloodlessness, self-seriousness, and proud inaccessibility of math papers, more than anything else, and that she identified these as factors that turn diverse candidates away from the field. I cannot, I will say, vouch for the interestingness of the math itself.
posted by atoxyl at 1:53 AM on December 9, 2015 [6 favorites]


The editor's note at the end of the introduction indicates, to me, that the 'truth to power' that's being spoken here is the entire paper: it is possible to write a doctoral dissertation in Mathematics that is understandable to an interested layperson. The fact that it is possible to do so, as amply demonstrated by the dissertation itself, is a criticism of all dissertations that don't even make the attempt to be understandable to laypeople.

I'm tempted here to go on a poorly-thought-out rant about what the value of any academic discipline is when its results are not comprehensible to interested laypeople, how that relates to the societal value of patents, and the parallels between deeply arcane jargon some academics pride themselves on using and the horrible user interfaces some programmers pride themselves on using. If you're not going to help other people get into your field, at least stay out of the way of people who are
posted by Fraxas at 2:16 AM on December 9, 2015 [13 favorites]


I'm not in math and I haven't finished reading the thesis. But the fact that she has written a math dissertation in which she 1. talks frankly about gender, 2. abandons the usual terse style in favor of a casual, approachable tone [which I think is probably particularly brave as a woman in STEM, because women can be under increased pressure to prove their "seriousness" as colleagues], 3. sets demystifying and explaining as a first priority, to a level that I've never even seen attempted in a STEM thesis, despite being written at an R1 where teaching and outreach are often undervalued, and 4. includes a comic that depicts her going into labor and having a second child, not only in a field where women are still very under-represented, but in a career where women still suffer penalties for choosing to raise children and for choosing to be involved parents -- that all seems plenty revolutionary to me (and likely to make some people in her field feel uncomfortable).
posted by en forme de poire at 2:18 AM on December 9, 2015 [29 favorites]


Nick Sousanis' thesis (Unflattening) is in the form of a graphic novel.

I can't speak to the maths in the FPP but having dealt with my own fears going into a viva, and seen friends and now my own students dealing with their fear going into their vivas, I find it incredible that someone could have the courage to do something so disruptive of the usual, very conservative pathway - to bet years of their life on not getting examiners who just throw it out. I've seen many people with really good quality work still plagued by doubt that an error could bring the whole thing down and years of work be shown to be in vain. I have now seen people fail too, bringing home that fears are not entirely unfounded. Remarkable effort.
posted by biffa at 2:18 AM on December 9, 2015 [1 favorite]


I am also a little biased because I was lucky enough to overlap a bit with Piper in grad school and I think she's rad.
posted by en forme de poire at 2:20 AM on December 9, 2015 [1 favorite]


I understand pretty much none of the actual math, but this delightful to read anyway.
posted by dersins at 2:22 AM on December 9, 2015


Wait, she delivered a baby during her thesis? And didn't make it to the hospital because she didn't want to stop writing it?
posted by Nanukthedog at 4:40 AM on December 9, 2015


I understand pretty much none of the actual math, but this delightful to read anyway.

As someone also in math, I think this is the fundamental issue with this kind of project. As much as I admire her aims - especially the more political ones - I think the reality is that basically no one outside of the research math community is going to actually understand this. Math is hard, not primarily because of the inaccessibility of exposition, but because it's actually just something you really have to grapple with, often for years, to understand. Her points about abstraction are kind of just testaments to this.

The idea that, if we can juuust explain things the right way, actual-laypeople will be able to understand our specific work, is something that often tempts me, but is not ultimately possible. What might be realistic is: 1. Writing research papers that are accessible to other mathematicians outside your little sub-sub-field; and 2. Writing expository material on basic higher-level math (algebra, number theory, topology) that is accessible to math-inclined lay people. I think these are probably really important goals.
posted by goodnight to the rock n roll era at 5:10 AM on December 9, 2015 [13 favorites]


I love this. Papers should be fun to read, because they are so punishing to write. Congrats to Piper, and I hope she keeps writing and thinking about mathematics.
posted by George Malloy at 5:54 AM on December 9, 2015 [1 favorite]


I drafted a manual for setting up equipment at a previous job in this sort of whimsical style. It was received with the equivalent of crickets and someone else quietly drew up something in a more conventionally dry form.
Kudos to her supervisor and defense board for letting it get published. At the same time, some may find the style distracting, which over 120+ pages of concentrated reading may totes annoy the reader trying to extract the thinky bits. By its nature, the people who will find this the most entertaining are elite math geeks who read PhD theses for their entertainment value.
posted by cardboard at 5:58 AM on December 9, 2015 [2 favorites]


Um. In retrospect my dissertation was kind of boring.

Now I really wish I had included the acknowledgement addendum I considered writing - to wit, "...and to the bear that almost ate me when I was 5, better luck next time."
posted by caution live frogs at 6:44 AM on December 9, 2015 [5 favorites]


The nice thing about reading a thesis is that the author is in that transition phase from layperson to professional, and so she's more willing to explain topics, give examples, go on digressions, and so on. When I was in grad school, I would often try to read someone else's thesis instead of the latest academic articles. And now this one has humor plus comics? I can't wait to read it!
posted by math at 7:14 AM on December 9, 2015 [2 favorites]


So where are the sections, aside from the introduction, where the author actually speaks truth to power? The parts where it might make the committee or other representatives of the institution "uncomfortable"?

Because if the author doesn't accomplish that, then where does this kind of rhetoric - the tension between the claim and the textual performance - take us? Nowhere. Style over substance is the consequence.


Hahahahaha.

I consider myself a reasonably liberal mathematician, left academia because the atmosphere is awful, and haven't seriously considered academic mathematics in about 6 years.

And I am super angry at this dissertation!

Like, I understand its aims. And I appreciate that the author wants to make things accessible to people. But I would argue that there is a time and a place, and a dissertation is not it. That said, Dr. Harron is clearly a good mathematician (escabesche's recommendations carry weight, after all), and her results exist in a form which is more comprehensible to mathematicians (yes, I consider the journal article vastly more understandable than the dissertation itself).

In any case, what I'm trying to say is: where you see a dissertation full of pablum and consider it boringly ineffective, I see a dissertation full of pablum and consider it wildly transgressive.
posted by TypographicalError at 7:20 AM on December 9, 2015 [1 favorite]


I'm curious - for the folks critiquing this - what are your specific critiques? Are you having trouble actually following the math with her presentation? I'm not clear why a dissertation is not the time or place for clear writing? The author recommends that mathy people skim over the lay explanations (and that lay people skim over the mathiest bits). Following her direction, do you have trouble understanding her actual math arguments? If not, what is the critique?
posted by latkes at 8:22 AM on December 9, 2015 [2 favorites]


So is she going to include a preamble about the nature of abstraction before everything she writes, or assume future lay readers have already read her dissertation? Or maybe refer them to it?

I'd think a feminist would be painfully aware of the pitfalls of expecting everyone to preface everything they write with My Discipline 101 so lay readers can follow every conversation an academic wants to have.
posted by straight at 8:37 AM on December 9, 2015


The parts where it might make the committee or other representatives of the institution "uncomfortable"?

The style and the fact that it will be signed off on as a phD worthy dissertation is sure to make a lot of committee members uncomfortable.

The cutesy style grates on me, honestly. You don't have to write that way to make material accessible to the layperson. For me, the writing process is all about self-control: namely how to harness all the ideas and feelings in your head to something clear and functional. The style grates on me because it is so familiar to me among some people I knew as an undergraduate who were obviously intelligent but had an inner need to constantly turn every interaction into showing how creative and clever they were.

That said, science is about experimenting. I feel this thesis was a failed experiment, but an interesting attempt at doing something different.
posted by deanc at 9:00 AM on December 9, 2015 [1 favorite]


This is great, for all the reasons mentioned so far, and my god would my life be easier and more fun if there was more of this sort of thing.

However, there are reasons why PhD theses (and papers in general) in technical areas are dense, dry and bloodless, and it's not just to exclude anyone who may want to bring something new to the party. There is no correlation between being able to produce useful work and being able to communicate it to a general audience, nor should that be a requirement to do research. If you can, then please, please do - and there has always been pressure on people who can, to not do it. That's wrong and unhelpful, and in a more general form reflects the academic disdain for popularists among their ranks. (The psychology of that isn't limited to the sciences.)

But the primary purpose of research reporting is to make that research available in replicable form to others at a similar level in the field, many of whom will not have good colloquial English skills. Extraneous stuff, diversions, recapitulations of basic ideas and other embellishments, if they don't help that primary purpose, are going to hinder it. By all means, write a popular version of the paper or thesis, or get someone who does that well to do it, and if you have the exceptional skills to present your ideas succinctly and accurately in a way a non-expert can follow... well, you're Feynman. (His cartoons did rather more work than most, mind.)

However, if I'm doing a review of, say, the latest developments in high power high speed transistor architectures, and I'm faced with ten papers each determined to include jolly asides about electron mobility and lattice structures, and how solid state physics is deliberately obscurantist, I'm going to lose patience really rather fast.

I am all for more papers being written with wit and humanity; these are seasonings that go a very long way to add joy and pleasure to what can be a real grind, and I for one am no good at real grinds without added pleasures and unexpected joys. I love this thesis. There should be more like it. But it can't get in the way of the general, rather industrial, business of quotidian research communication.
posted by Devonian at 9:12 AM on December 9, 2015 [3 favorites]


I downloaded the 139 pages and started thumbing my way through it. I stopped to read here and there. Being a layperson I appreciated her explanations though I was still struggling. But her attitude helped to prop me up in the struggle. I appreciated that. And I loved the ending. One of my complaints about math books is that they just stop. Period. No summing up. No looking forward. Just stop.

To the math people here, is there a way to help non math but intelligent people to begin to understand and at least parse the notation in a qualitative way? Or will math remain a Masonic secret code that governs reality yet is barred from basic comprehension of the common folk?

Now to fully read her work.
posted by njohnson23 at 9:23 AM on December 9, 2015 [1 favorite]


So is she going to include a preamble about the nature of abstraction before everything she writes, or assume future lay readers have already read her dissertation? Or maybe refer them to it?

I'd think a feminist would be painfully aware of the pitfalls of expecting everyone to preface everything they write with My Discipline 101 so lay readers can follow every conversation an academic wants to have.
I see hidden assumptions in here:
1. That, because Dr. Harron went to some lengths to make her dissertation accessible to the layperson, she will do so for all her future mathematical papers.
2. That referring future lay readers to her dissertation is an unreasonable thing to do. I may be reading into your tone a bit overmuch here but it seems like this is what you're implying.
3. That she or anyone else expects all other mathematicians to do the same for all their papers.
4. That she is a feminist. Granted, this is the most reasonable of these assumptions.
posted by valrus at 9:34 AM on December 9, 2015


Or will math remain a Masonic secret code that governs reality yet is barred from basic comprehension of the common folk?

Feynmann on this topic

The basic principle here is: if you want to understand it, do the work. There isn't a shortcut to understanding number theory. This does not absolve mathematicians from generating interest, trying to communicate, but you have to meet mathematics where it lives, to some extent. That means learning (for example) what a general linear group is, if you want to really comprehend why people would talk about them so damn much.
posted by TypographicalError at 9:51 AM on December 9, 2015 [5 favorites]


2. That referring future lay readers to her dissertation is an unreasonable thing to do. I may be reading into your tone a bit overmuch here but it seems like this is what you're implying.

I'm just sayin' it's a slippery slope from a footnote that says, "btw, check out my dissertation for a little background about the different kinds of infinity" to the traditional terse academic math paper that assumes the reader is a member of the guild.
posted by straight at 10:05 AM on December 9, 2015 [1 favorite]


OnceUponATime: "I also am nearly always on the side of familiar language over jargon, in any context, including physics and mathematics. However, The result is that papers and reports (and e-mails!) I write have a tendency to be about 4x longer than those of most of my colleagues, with the result that a lot of my colleagues sigh heavily and roll their eyes discreetly when they get them. But I find that I think more clearly when I force myself to unpack the dense concepts I am arguing about, and things tend to get bigger when they stay just as weighty while getting less dense... So I go on writing super long comments and e-mails and reports, in the interests of inclusion and not making people feel stupid and making sure I understand my own underlying assumptions."

i always appreciate it anyway :P
posted by kliuless at 10:42 AM on December 9, 2015 [2 favorites]


The hardest part about math is the level of abstraction required. We have innate logical abilities, but they are based in context. If you give people a scenario of university students drinking beverages at a bar and give them information either about the person's age or about the person's beverage, most people know instinctively which students' drinks or IDs need to be checked to avoid underaged drinking (i.e., if the person's 22 you don't care what they're drinking, but if the person has a vodka tonic, you need to know heir age). Take the logically equivalent situation of cards with a color on one side and a number on the other. Suddenly it takes some work to gure out which cards have to be turned over to satisfy a given condition (say, all even numbers have red on the back). Just one level of abstraction and the untrained, but educated, person will have a good amount of diculty even understanding the situation. Now try doing Number Theory.


I've long suspected that math ability is mediated to some extent by taste for abstraction.

To put it crudely, how much of the difference between people who are good vs. bad at math is explained by "horse power" and how much is explained by your willingness to think about abstract stuff?

But I think, for most research areas, there's probably no way to map the mathematical terrain down into familiar concreta such that it can be understood by laypeople without long, hard work (or ever).

The Wason task example is kind of a party trick. Thing is, the underlying problem is very simple, whether posed as an abstract puzzle or a practical question about social rules. Increase the complexity a little and most people will find such puzzles difficult and stop working on them unless you force them to continue. This is exactly what the LSAT "logic games" section is about, for example. Make it 5 or 6 people at the bar, Amy doesn't want to sit next to Carl, etc., suddenly people's "instinctive" ability to do logic puzzles will not be much help.
posted by grobstein at 11:23 AM on December 9, 2015 [1 favorite]


You can understand the Wason task result in various ways.

One possibility (the one championed by Cosmides and Tooby) is that there's a specialized solver in the brain dedicated to detecting violations of social norms. When a puzzle is posed as one about social norms, it gets routed to this module, which looks at it and spits out the answer. General reasoning ability doesn't play a role, at least for simple problems that are answered quickly.

A more moderate view is that the concrete scenario serves as some kind of attentional cue that brings general reasoning resources to bear. We are generally lazy, because math is hard, but the accounting center of the brain is willing to spend a little on detecting social norm violations, because in the environment of evolutionary adaptedness that could lead to a payday.

Either way, you can get a boost on easy problems by posing them as social games vs. pure symbol manipulation. But for hard problems I'm not sure how much we can expect.
posted by grobstein at 11:32 AM on December 9, 2015


Mathematics used to be much less abstract. Until the 17th century, just about everything (in Europe anyway) was done with geometric arguments. Researchers thought that an argument based on abstract symbols was insecure (they had some good reasons for thinking this).

The big reason they stopped doing that is because it was too hard to do the math they wanted to do. Geometric arguments are generally much harder both to produce and to verify than symbolic arguments (although they sometimes seem to be easier to understand). By contrast, I think it was Leibniz who said that, with the symbolic resources of algebra, you can do math without thinking. An exaggeration, perhaps, but several important truths:

1. You can learn pure symbol-manipulation rules to do a lot.
2. You can make more arguments without committing to the details of an interpretation.

Point 1 is about the ease of calculating and of finding proofs. Point 2 is about the subject matter mathematics can cover. When you say x = ..., you avoid committing ahead of time to what x is. You're saying, no matter what x is, (maybe if it is any number or w/e,) as long as it satisfies the given constraint, some consequence will follow. The weaker and more general the proof language you use, the stronger and more broadly applicable the conclusions will be. Many mathematicians today work on subject matters of very high generality.

The proof language you use defines a set of transformations that preserve your conclusions (Tarski (1986), skip the introduction). The conclusions of c. 17 geometric proofs are preserved under scalar transformations (IIRC), which is quite a restrictive class. Proofs stated in algebraic language can be much more general.

My larger point is that abstraction is not just a needless barrier to entry, it is an important tool for mathematics.

Arguably a big part of learning math is getting to grips with higher abstracta so that they don't feel abstract to you. The first time you encounter the definition of an open set, say, it feels formalistic and abstract, like a section of the tax code. But by working the problems, you develop an "intuitive" sense, and eventually find that you don't have to rely on the definition at all. If everyone learns properly, in later classes you will be able to simply assert, based on intuition, something that you had to prove laboriously when you first encountered it.

So we might hypothesize that mathematicians are good at manipulating abstracta because they are no longer abstract to them. Abstraction isn't good after all! But you can't just un-abstract the abstract by fiat, most of the time. You have to get there by working, and it takes a lot of work -- probably for mathematicians, definitely for non-mathematicians. You have to build those neural connections.
posted by grobstein at 12:05 PM on December 9, 2015 [6 favorites]


God, I'm just jealous. I wish my PhD thesis were this awesome (I sort of tried, but I was working under a tight deadline). I mean yeah, there's good reasons for jargon to exist and abstraction is not inherently a bad thing and there's no royal road to learning yada yada yada. But those constraints that force people into using boring jargon are a BUMMER.

"People really like discriminants, like really. What's so great about discriminants? Sometimes they let you in on secrets..." "I tried vaguely and decided it must require 'math' as opposed to just kind of falling nicely out of explicit calculations." "Arithmetic is what most people think math is ("you must be great at calculating tip!") and it's certainly what people tend to assume number theory is ("what, did you like invent a new number or something?"). And, okay, number theorists will tell you what they do is arithmetic, but they aren't talking about the arithmetic you learned in school."
posted by OnceUponATime at 12:50 PM on December 9, 2015 [2 favorites]


I am all for being more informal when informal writing is more direct or succinct than formal writing. However, interleaving jokes in a thesis is a terrible idea. Terrence Tao, one of the greatest modern mathematicians writes:
Overly philosophical, witty, obscure or otherwise “clever” comments should generally be avoided; they may not seem so clever to you ten years from now, and can sometimes irritate the very readers you want to communicate your result to.

Other mathematicians have similar thoughts..

I'm surprised her advisor wasn't able to discourage her from making this mistake, a mistake she may regret years later, and one which she may one day blame him for. After all, he has the experience to know better. It's normal to want to shake things up when you're in your early twenties.

Every piece of writing has an audience. Who reads a thesis? Mainly it's her phd committee, people who want to find out about her topic, and people who are considering hiring her. Not one of those groups is helped by her digressions. The first two are hindered by them.
posted by esprit de l'escalier at 12:55 PM on December 9, 2015 [2 favorites]


To be fair, I do appreciate some of her informal tone. This is better than stilted, indirect language: "We’ve seen that in order to count number fields, we will need to count maximal orders…"

It's just things like this that are annoying: "NEVER HAVE A CONVERSATION WITH THESE FICTIONAL ACTUAL PUPPETEERS ABOUT THEIR WORK!"
posted by esprit de l'escalier at 1:03 PM on December 9, 2015 [1 favorite]


I think the most important audience for your PhD thesis is yourself. It's a record of your years of hard work, a document capturing the all most important lessons you've learned along the way to your final conclusion. You're the person most likely to (re)read and refer to it later in your career.

Even if you have some awesome result, people will be unlikely to read your whole thesis when trying to build on it. They'll read the relevant chapter, or maybe the actual journal article you presumably published summarizing your awesome result. Your thesis is more of a historical record of where that result came from. Writing it in a way that captures the actual thought process which led to its conclusions is genuinely helpful for anyone (probably you) trying to reconstruct that.

But this person is clearly trying to broaden her audience beyond just herself and her committee (whom she knows -- so she's in a better position than a stranger on the internet to know whether they will be irritated by her digressions).

She wants to be able to direct people who ask her about her work to this document, and to have some hope that they can actually understand some of what it is she's done. Why not? Lightening the heavy conceptual load with some playful language makes it less of a chore to keep reading. (Though the density of playful language is actually very low if you scroll through the whole thing. Unfortunately, in my view!)

I will reluctantly defend jargon when needed, but there is just zero reason I can see for the normal stick-in-the-mud formality of so much academic writing. Academics don't talk to each other that way! And formal writing is often SO much harder to read than a more conversational tone.

Here's my favorite paper I've read recently for my job, written by an eminent physicist: http://arxiv.org/abs/0904.0163

"This is the high-N00N state, a moniker bestowed by our group due to the happenstance of the notational convenience of choosing the letter N to represent the total photon number. The term “high” indicates that the photon number N is large — at least greater than two. (The competing names of “P00P” and “0NN0” states were summarily discarded at an early stage of the research.) ... (None of these things are particularly easy to implement in the lab, but at least it is a start.) ... We can see that at each end is the desired N00N-state component, but there is much POOP in the middle that is undesirable. ... One approach is a quantum pooper-scooper; something that removes the POOP after the fact. Another approach is make sure the POOP is not there to begin with, but this requires something besides an ordinary 50-50 beam splitter — something we call a “magic” beam splitter. Much of the discussion that follows is devoted to magic BS."

I read five other papers trying to understand high-NOON states before this one, but this was way more helpful to me, sophomoric poop jokes and all, than any of the more conventional papers that cite it.
posted by OnceUponATime at 1:32 PM on December 9, 2015 [2 favorites]


I'm surprised her advisor wasn't able to discourage her from making this mistake, a mistake she may regret years later, and one which she may one day blame him for. After all, he has the experience to know better. It's normal to want to shake things up when you're in your early twenties.

Dr. Harron is a grown woman and mother of two who I am pretty sure is in her early thirties, not a novice trainee, and she has also published a version of this thesis directed specifically at mathematicians in a drier style (the arXiv link above). Whether or not you agree with her having taken this approach to her dissertation, the above is a rather condescending and infantilizing way to refer to her.

You also talked about the audience of a PhD thesis being restricted to the thesis committee and other working academics. This is certainly true by convention, but conventions are not static, even in academia. Take, for example, thesis defenses: in my old department, thesis defenses were formal and strictly-business followed by academic Q&A, but the prospective PhD was basically guaranteed to "pass." At my current institution thesis defense talks are usually geared for a general, non-academic audience, because it is more common for students' family and friends to attend and the thesis defense is seen as more of a celebration. At yet another institution where a co-worker did his grad work, the thesis defense was treated as an oral exam and failing was a legitimate possibility. Particularly since the graduate thesis has become increasingly redundant with publications, at least in STEM (many graduate programs explicitly require publications as graduation requirements, and deposition in pre-print databases like the arXiv or bioRxiv allows work from thesis chapters to be widely disseminated at the time of graduation), I think this definitely leaves room for the graduate thesis to become a different type of document.
posted by en forme de poire at 1:49 PM on December 9, 2015 [5 favorites]


I'm just sayin' it's a slippery slope from a footnote ... to the traditional terse academic math paper
You say that like it would be a bad thing, straight.
I'm surprised her advisor wasn't able to discourage her from making this mistake a mistake she may regret years later, and one which she may one day blame him for. After all, he has the experience to know better. It's normal to want to shake things up when you're in your early twenties.
A PhD thesis is by definition a product of the student. The student owns every word, every formula, every figure, every comma, every ACTUAL PUPPETEER in their thesis. PhD students are adults, responsible for their own decisions. It's the advisor's job to spell out the consequences of those decisions, but that's just advice, like it says in the word "advisor". If she's willing to accept the consequences of a non-standard tone that annoys a few people on MetaFilter, that's entirely her decision. Her advisor does not "know better", and neither do you. Butt out.

Also, very few math PhD students finish in their early twenties.

(I am a mathematician with PhD students.)
posted by erniepan at 1:51 PM on December 9, 2015 [5 favorites]


I'd think a feminist would be painfully aware of the pitfalls of expecting everyone to preface everything they write with My Discipline 101 so lay readers can follow every conversation an academic wants to have.

This is a false equivalence, though. First of all, education and outreach are (sometimes neglected) parts of the academic mission and this thesis is an explicitly academic document, in a way that does not apply to, for example, two people merely having a discussion about feminism on Metafilter. Second, conversations about feminism and conversations about math operate differently in the wider social context. Repeated, skeptical demands for explanation and accusations of obscurantism are not routinely used to derail and devalue conversations about math; indeed, laypeople are more often too intimidated to enter into a specialist mathematical discussion at all, in a way that is certainly not true when the subject is feminism.
posted by en forme de poire at 1:59 PM on December 9, 2015 [1 favorite]


If one of her premises is that the level of abstraction in the presentation of math goes (deliberately?) far beyond what is necessary I'm not sure she's right. Or rather I think she's only a little bit right. Certainly I think she reaches a point beyond which the analogies fail to illuminate, and I think there's a good point made in that Feynman bit - that analogy risks conveying a false understanding. However it's interesting as a pedagogical experiment - even if she doesn't seem to claim that as her primary intent exactly. More than anything though I think what she wanted to do was to protest exactly this attitude:

Overly philosophical, witty, obscure or otherwise “clever” comments should generally be avoided; they may not seem so clever to you ten years from now, and can sometimes irritate the very readers you want to communicate your result to.

I am somewhat agnostic about this in general. I prefer academic writing to be relatively concise, but also to be good writing and a little bit of levity often wouldn't hurt.
posted by atoxyl at 2:50 PM on December 9, 2015


Wow, the hand wringing in this thread reads as classic concern trolling, ("It's not so much that I don't like it, I just don't want her to be misjudged by others.")

I mean, the most substantial critique I can find here is, "Cutesy writing is bad." No one is even claiming that they find this difficult to read themselves, or that the supposed "cutesy-ness" is a barrier to their own comprehension of the thesis! Further, as has been pointed out, there is a stripped down, math only version of this for those who hate humor and flourish! Geeze, the Get Off My Math Lawn effect here comes off as, well, exactly that.
posted by latkes at 2:52 PM on December 9, 2015 [2 favorites]


Also, how come all these Feynman fans are anti-clever math writing? Only dead math dudes get to be funny?
posted by latkes at 2:54 PM on December 9, 2015


Also, how come all these Feynman fans are anti-clever math writing? Only dead math dudes get to be funny?

Did you read the Feynman link? It's relevant to the "laysplanation" part, not her style or use of humor. I am largely on her side about not wanting or needing everybody's prose to be thoroughly, "professionally" dessicated, while questioning some of her (apparent) premises regarding abstraction.
posted by atoxyl at 3:31 PM on December 9, 2015


Until the 17th century, just about everything (in Europe anyway) was done with geometric arguments. Researchers thought that an argument based on abstract symbols was insecure (they had some good reasons for thinking this).

Wasn't that supposedly part of what started the feud between Newton and Leibniz over the invention of calculus? Newton invented calculus but thought it was an ugly hack for doing something he ought to be able to do just with geometry, so he didn't publish much about it, and just sat on this immensely valuable tool for years. Then Leibniz finally publishes his version, possibly based on some hints Newton had dropped in his publications about his method, and then Newton is all, "Wait, I invented that first!"

(One likes to hope most of the dudes who spent years arguing about this were third-rate mathematicians who wouldn't have accomplished much with the time they were wasting anyway.)

I think it was Leibniz who said that, with the symbolic resources of algebra, you can do math without thinking.


It seems that he was imagining that with algebra you could do math with a mechanized process, basically dreaming about the possibility of computers.
posted by straight at 3:45 PM on December 9, 2015 [1 favorite]


I mean, the most substantial critique I can find here is, "Cutesy writing is bad."

No, the most substantial critique is that laysplaining isn't a sustainable expectation for academic math papers and that terse mathematical jargon might have a useful reason for existing that's not mere patriarchal stuffiness.
posted by straight at 3:49 PM on December 9, 2015


No, the most substantial critique is that laysplaining isn't a sustainable expectation for academic math papers and that terse mathematical jargon might have a useful reason for existing that's not mere patriarchal stuffiness.

I am inclined to agree with that critique but to be fair to latkes there were some people here also saying fairly insulting stuff like her advisor should have dissuaded her from making the mistake of writing in this cutesy way blah blah.
posted by atoxyl at 3:59 PM on December 9, 2015


Did I miss the part where she said she expects this kind of writing from anyone else, or in other contexts? Or the part where she said there was anything wrong with jargon? (she uses lots of jargon, just makes an effort to explain some of it, in easily skipable separate sections!...)

She says: "My goal here is to write something that I can understand and remember and talk about with my non-puppeteer friends and family, which will allow me to speak my own language to the puppeteers."

That's not the same as "everyone should write their math papers to be understandable to laymen and should avoid jargon."

And here is what the "editor's note" says:
[Editor’s note: The author throws in many phrases that seem to indicate uncertainty; please know that this does not represent mathematical uncertainty, but is meant to relay the following to student readers: 1) you are not expected to understand every word as you read it, 2) you can successfully use math before you’ve successfully understood it, and 3) it has to be okay to be honest about your understanding. The author refused to sacrifice these messages or what she called her “integrity” for the sake of what we saw as very important mathematical credibility.]
And here is what she says in the prologue about what motivated her to write this way:
"But what about the others like me, who don’t do math the 'right way' but could still greatly contribute to the community? I combined those two thoughts and started from zero on my thesis. What resulted was a thesis written for those who do not feel that they are encouraged to be themselves. People who, for instance, try to read a math paper and think, “Oh my goodness what on earth does any of this mean why can’t they just say what they mean????” rather than, 'Ah, what lovely results!' (I can’t even pretend to know how 'normal' mathematicians feel when they read math, but I know it’s not how I feel.)
Right on sister!

Ahem. I think it's pretty clear that there are specific messages of support that she personally wants to send with this specific work (which has no page limits or co-authors or journal styles, and so is a unique opportunity), not that thinks everyone should write like this all the time. Clearly she doesn't write like this all the time either. It's not practical. But this is her frickin' thesis. This is her chance to say what she really wants to say, and good for her for making the most of it. (And yeah, I think more people should write this way when they can, even if it's not practical very often...)
posted by OnceUponATime at 4:09 PM on December 9, 2015 [5 favorites]


Wasn't that supposedly part of what started the feud between Newton and Leibniz over the invention of calculus? Newton invented calculus but thought it was an ugly hack for doing something he ought to be able to do just with geometry, so he didn't publish much about it, and just sat on this immensely valuable tool for years. Then Leibniz finally publishes his version, possibly based on some hints Newton had dropped in his publications about his method, and then Newton is all, "Wait, I invented that first!"

It's definitely true that Newton bent over backwards (by our standards anyway) to do everything via geometric argument, and if you work through the Principia there are tons of clever, beautiful, difficult geometric arguments for propositions that would be extremely easy to prove with analytical methods. The notebooks often have analytical arguments for propositions where the ultimately published proof is geometric, IIRC.

But Newton resorted to analytical arguments in several places in the Principia, when he couldn't find a good geometric argument. I don't remember the citations.

The relationship to the priority dispute is a little complicated. Calculus does not belong to one notation or another, and in particular geometric presentations of calculus are still calculus. A derivative is a ratio of lengths in an infinite limit, for example. So the Principia is the first(-ish) published exposition of calculus, even though it doesn't introduce the algebraic notation. But I think it's right that Leibniz's algebraic notation was published first. But I think we also know, from Newton's papers, that he was first. And I think we also have at least good circumstantial evidence that Leibniz was exposed to this work, so that his invention was not really independent. Leibniz's notation seems to have been the better one, and the subsequent important work on analysis takes Leibniz as a foundation I think.

(One likes to hope most of the dudes who spent years arguing about this were third-rate mathematicians who wouldn't have accomplished much with the time they were wasting anyway.)

Unfortunately(?), Newton himself seems to have been quite exercised over, and involved in, the controversy.
posted by grobstein at 4:40 PM on December 9, 2015 [1 favorite]


The editor's note at the end of the introduction indicates, to me, that the 'truth to power' that's being spoken here is the entire paper: it is possible to write a doctoral dissertation in Mathematics that is understandable to an interested layperson.

If something is possible, then it's not challenging anymore, whereas challenging the legitimacy of authority is what "truth to power" requires. That's the philosophical contradiction.

Further, I cannot speak for Mathematics, but in another department on the same campus, we are taught that our dissertations should indeed be broadly accessible; for example the requirement of having outside readers on your committee. Conceptually this is not revolutionary; the sticking point is how many students practice what the faculty has always preached.

The fact that it is possible to do so, as amply demonstrated by the dissertation itself, is a criticism of all dissertations that don't even make the attempt to be understandable to laypeople.

Except the prologue specifically mentions, it's not about criticizing those dissertation writers failing to making an attempt. Harron even explained why: "The problem was not individuals, but a system…" An alternative solution is not a criticism; anyone who's written a proof knows these are different tools.

But the fact that she has written a math dissertation in which she … that all seems plenty revolutionary to me (and likely to make some people in her field feel uncomfortable).

Honestly I think those people will barely be budged. (Just look at some of the traditionalist viewpoints here.)

Because Princeton is already a comparatively comfortably liberal intellectual environment. In such a context, "Was it not revolutionary enough?" is a fair question. "Brutal honesty" is not effectively brutal, if it just your untroubled colleagues just lol, and tweet, and think it's cute, or irreverent, or stunty. That's self-congratulation.

It is a legitimate question to ask that maybe this rhetoric was permitted to happen. I.e., Is this a rite, or is this a transgression? To answer that, you have to look outside. Did anyone in the faculty or administration oppose this dissertation, yes or no? From the vantage point of the UBC example previously, did Harron's advisors similarly have to fight for its acceptance? Was there controversy? Was there resistance? Tension? Yes or no?

And I guess what I'm saying is, that's why I struggled with the initial claims of this text. I guess what I'm thinking is, the author took the prudent path of not saying the choice things that really would have ruffled feathers, viz., the experiences of intellectual marginalization, the ways that some intellectuals are systemically privileged over other intellectuals to the detriment of a field of study.

Show me one person who has not, in the process of writing their dissertation, fantasized about doing some personally meaningful thing that unfortunately others might perceive as stunty. And obviously, occasionally some people do get away with it; grad student lore is full of such antics. So the question becomes, how do you distinguish rhetorical utterance that is already permitted and even expected, institutionally, versus that which really is brutal (but motivated by authenticity), for a given audience/community?

Rather, what Harron's dissertation does accomplish is totally different: a) to show a different way of talking technically, b) to lead by example, and finally, c) to make a gesture of outreach—solidarity is the better word—to the marginalized, and all done by way of a testament to the status quo of academic culture in America. That's meaningful too.
posted by polymodus at 4:41 PM on December 9, 2015 [3 favorites]


Who reads a thesis? Mainly it's her phd committee, people who want to find out about her topic, and people who are considering hiring her. Not one of those groups is helped by her digressions. The first two are hindered by them.

I was on her Ph.D. committee. I liked it.
posted by escabeche at 5:41 PM on December 9, 2015 [15 favorites]


I was on her Ph.D. committee. I liked it.

You know nothing of my work!
posted by asterix at 5:47 PM on December 9, 2015 [4 favorites]


there is a stripped down, math only version of this for those who hate humor and flourish!

I don't hate humor and flourish. It's just that humor is hard, and the odds are that when you try to do it, you will fail. (one of my college application essays was really embarrassing for this reason. They looked past it and accepted me.) And as I said, I have seen that style before, and it comes from people who really, really need to show how clever they are, even if being humorous/clever/flourishing isn't their core competency.

We're mostly content with the idea that "math is hard" and to understand it and be good at it, you have to "do the work." Meanwhile, everyone thinks they can write, much like everyone thinks they can teach. Writing, especially writing well outside the "house style", is also hard.

So fine, present your mathematics work in a way that allows a layman to grasp it. But is it too much to ask for a mathematician who wants to do that to do the work and craft necessary to pull it off the humor and flourish?
posted by deanc at 7:11 PM on December 9, 2015


Polymodus, I don't have any real quarrel with your last paragraph, though I think what you've said there is very different from calling the thesis a triumph of "style over substance." I think your analysis also doesn't take into account that there are different degrees of "permitted," and so it disqualifies works that are, for example, uneasily or uncomfortably accepted as opposed to wholeheartedly accepted, or accepted by some but viewed suspiciously or rejected by others. I think you're also sort of moving the goalposts when you note that there are indeed hardline traditionalists who have been made uncomfortable by this thesis, but then say that these traditionalists are likely to have been unmoved (this also seems kind of tautological, since hardline traditionalists by definition are unlikely to be receptive to new ways of doing things).

Also, as far as Princeton is already a comparatively comfortably liberal intellectual environment goes, I'm not sure I understand what things you're comparing and what you are basing that comparison on.
posted by en forme de poire at 7:20 PM on December 9, 2015


Nice try, but I never called it as such. What I did say was, again, "Where does the author explain how this thing (systemic oppression) arises?" Frankly, it's the thing I want to know about, since it's one of the burning questions for every critical theorist and/or Marxist.

Meanwhile, a few people thought my original question was purely rhetorical or insinuative of an attitude that I would in no way stand for. Whatever, I don't expect everyone to follow my personal context, right?

And instead, the author provided no such answer. Which is fine! Instead, Dr. Harron sidestepped it and took a totally constructive approach - she turned speech into a progressive action (i.e. summarized in the one paragraph of mine that you had no quarrel with). But if this was revolutionary, how is it revolutionary? If it was critique, how is it a critique? Certainly not in the classical, rationalist, or modernist sense where STEM dissertations explicitly write out what they mean. She could have done the ambitious thing like the UBC architecture paper. Or the one where an author goes so far as to argue the mathematical formulas themselves are misogynist, and so on; it's possible (probable, sadly) the snippet of that paper I saw was just a joke, but therein lies the idea. So, with this background in mind, these are fair questions to ask in order to clarify and explicate the text. What's "revolutionary" or "brutally honest" is a subjective judgment - let me make super clear, my original worry upthread was This isn't brutal/radical/transgressive enough! -, whereas looking at how the text works allows me to reconstruct an argument and find meaning and significance.

(Consider also deanc's comment "The style grates on me because it is so familiar to me among some people I knew as an undergraduate who were obviously intelligent but had an inner need to constantly turn every interaction into showing how creative and clever they were." -- the converse of which, do you want the privileged people i.e. "happy scientists" to mistake Harron's work as merely an extended XKCD joke? I think that would be missing the point.)

(The stuff about what's permitted and prohibited - that's a whole subarea of thinking for social theorists and the like. Suffice to say my point about rites is relevant as a first-order sketch of the issue. If you want to refine the issues, go ahead.)

(...traditionalists who have been made uncomfortable by this thesis, but then say that these traditionalists are likely to have been unmoved No, the former was about certain views in this thread. The latter is about people affiliated with the author's institution plus the broader academic network. I could care less about the peanut gallery here, if you get what I mean. What matters is who the paper would influence - is it the people in privileged positions? Or the marginalized intellectuals? I.e., the audience(s). And again, I'm really warming up to the author's method; the personal impact is that it's like a breath of fresh air.)

So, I don't think my process is really moving goalposts. More like, I slept over it, and read over more sections of the pdf (I was actually quite moved by certain parts in it), and thought about it more. If you'll allow that, I'll allow the mefites who like to naysay my comments.

Also, as far as Princeton is already a comparatively comfortably liberal intellectual environment goes, I'm not sure I understand what things you're comparing and what you are basing that comparison on.

It's simply my opinion, because I was there a long time, etc. It does things to you.
posted by polymodus at 10:52 PM on December 9, 2015


but then say that these traditionalists are likely to have been unmoved

To put it concisely, my problem was this: falling on deaf ears.
posted by polymodus at 11:09 PM on December 9, 2015


Polymodus, I really don't think she was trying to start a revolution, or get any big institutional or cultural changes made. I think she was just trying to write something that isn't the kind of highly affected voice she hated reading.

It's okay if she doesn't smash the system with this. It's okay if she just captures the results of her years of work in a way that doesn't make her feel like a hypocrite for perpetrating the same kind of writing she's complained about. I think that's really the whole agenda here. It's not political.

It's just about wanting to be represent herself and her work honestly, without being forced into an uncomfortable pose. And maybe as a bonus her mom or her husband or her kids, some day, will be able to get a better sense of what she does. And maybe she can hand this on to the newer grad students and be helpful to them, without feeling like she's being dishonest about how hard all of this was. And if other people are inspired to be more honest about what it took to get their results, so much the better. But really, writing your thesis is a once in a lifetime opportunity to do a big hard thing exactly the way you think it should be done, and it's hard to generalize her choices here to other situations, where there are more constraints (and to people who aren't such good writers.)

It's not about speaking truth to power. It's just about speaking truth, period.
posted by OnceUponATime at 10:51 AM on December 10, 2015 [3 favorites]


I liked the beginning of section 1.4:
What I wanted for this section was to explain why mathematicians might find this interesting. Am I not a mathematician? Could I not simply tell you why I find it interesting? Well... people tell me I'm weird, and I believe them because I put a comic strip in my math thesis. For me to find something interesting, I have to have prior knowledge of it or something related. I just don't have the necessary experience with math, outside of this thesis, to find abstract research-level math "interesting."
I think this is a pretty common reaction to writing a math Ph.D. thesis, actually: you might well need more time, context, and experience to see why your result should matter to anyone else than the process of writing your dissertation provides. I want to say it gets better-- and if one goes on doing math research, it does-- but the academic job market isn't exactly friendly to researchers who need more time to make connections.
posted by yarntheory at 12:58 PM on December 13, 2015 [2 favorites]




I am always on the defense re: arguments about "accessible" academic writing (sometimes a valid critique, sometimes naive hand-wringing for people who don't know what they're talking about, IMO), but I thought this was rather nice. It's totally un-prescriptivist (she's resisting doing the thing that she hates, resisting the voice that made her feel unwelcomed, without telling everyone else to do it the same way, just taking the piss a bit) and it feels like a good balance of interesting and "woke," to use today's parlance. I don't know. As a woman in STEM, all this stuff is true. She dealt with it her way, and it is cool, feels punk.

Her story is really interesting, too-- someone who left grad school and had kids, which is supposed to be when the fulfilled modern woman/person realizes that grad school is bloodless and meaningless and a waste of time compared to family and children. Instead, she realized she still didn't feel good about leaving it hanging, and she finished it. I feel like there is a lot of banging on about women having it all these days that doesn't really get into why we would want to... ? Or which doesn't encourage this kind of messiness? It brings compelling narrative into a world that resists it (and needs it) and it just feels genuine and good.

I mean, confronting academia with the reality that there are people who are very serious about their field and who have families and children and all possible gradations and combinations of the above is a good thing, right now. Academia wants to pretend that the vacuum of academic research-- the impersonal marionette or Research Voice or Scientist who makes order from chaos-- is a real condition of life and a possible reality of the workplace, which is ridiculous and oppressive and most unfair to women. I like to see acknowledgement of the fulfillment of academic work with a challenge to the idea that we actually are the dry, laser-focused, utterly bloodless narrators of our work.
posted by easter queen at 3:04 PM on December 26, 2015 [3 favorites]


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