2015 musings

And now, at 05:20 in the morning local time, some meditations for the new year. I am now a graduate student, studying pure mathematics, 8 months away from graduation. As anyone in a similar discipline will no doubt confirm, this is not merely a job but a way of life. It must be so — at least for most of us. I want to elaborate on what this way of life has given me, and what it has taken away from me. Really, I expect this post to be like a letter to (or perhaps an argument with) my former self — the hope of course being that from it, someone out there will manage to derive some meaningful insight. But first, let me reiterate how I got here — here as in right now, that is.

Long story short: childhood spent writing code -> descent into online gaming as a result of uninspiring course material -> poor marks interpreted by teachers as inability to keep up -> sudden realization on my part that this is happening -> last-minute frantic display of sentience -> aspirations of working on quantum computers in late high school -> somewhat bleak admission prospects to nanotechnology engineering program -> miraculous admission to aforementioned program -> ironic decision to enter dramatically less competitive physics program instead -> exposure to real math -> transfer to pmath/CS -> transfer to pmath/CO. That last arrow, or at least the change it brought about, is important. There are more links in this chain, but it is already long enough.

Minimalism adequately describes the approach I have taken towards many aspects of life: living arrangements, social behaviour, food, clothing, etc. When I moved into a new house (or rather, “mansion” as it came to be known; best house ever, by the way) just over a year ago, the contents of my room (besides essentials like clothing) consisted solely of a bunch of books, a mattress, and my laptop. It remained this way until a friend offered me a desk and bed frame. I accepted because neither effort nor payment was required on my part. I do not value material possessions, and lest I be labelled a reprehensible hypocrite as I sit here typing this post on my MacBook Pro, let me suffix that with “at least relative to many others in similar circumstances”. Fast Internet access is a game changer for me; it is probably the very last material possession I would give up (after all, it certainly subsumes physical books *HOISTS ENORMOUS RUSSIAN FLAG*, although I still prefer reading the latter to staring at a computer screen; call me old-fashioned).

To mention another example, I rarely wish people happy birthday, Christmas, Hanukkah, Ramadan, etc. nor am I offended in the slightest when my negligence to do so is reciprocated by others. There are a few reasons for this; in general these events bear little significance to me. Without even mentioning the arbitrariness of the units of measurement set forth by the Western calendar, many things people celebrate are specific to a certain religion, nation, culture, and so on. Although I do not denounce any of these provided they remain within reason (extremist sects that advise senseless mass murder and so on certainly fail this criterion), I do not particularly favour any of them either. I am Canadian because I was born here, not because I think Canada is the best country in the world. In fact, expressions of nationalism tend to irritate me, since I perceive them as egotistical. I speak English merely because of my initial conditions, not because I consider it better than other languages; conveniently, however, it seems to currently be the language of academia. However, I am not Christian; that is where the influence of initial conditions begins to wane. In fact, I am not religious at all, since no such belief system seems to me any more plausible than the others, and they tend to be pairwise incompatible. If I chose to be religious, why would I choose to be a Christian rather than, say, a Muslim or a Shintoist? Such questions seem to admit no satisfactory answer, so I rest my case.

In any case, I said I would talk about what math has given me, so let me do that now. My decision to study pure math was made with infinite confidence and zero doubt, and really, I have never once regretted it. This can be said about very few decisions I have made. The clarity with which it has made me able to reason and formulate thoughts is indispensable, and I can hardly understand how anyone (much less a scientist) gets away without it.

To my mild surprise, I recently noticed my developing ability to read and understand technical material at a faster pace, for longer periods of time. Teaching myself things seems to have become dramatically easier over the past few years; perhaps this evolved out of sheer necessity, considering my horrendous sleeping habits and often poor lecture attendance, even in graduate courses. As a result, whenever I consume any kind of media lately that is not a Springer GTM, I find myself floored by the comparatively low information density, as though someone suddenly decided to cut the frame rate of life in half.

Perhaps as another consequence, I have been developing interests in other areas, often choosing to spend time learning about more applied areas (statistics, computer science, engineering, physics, chemistry, even history) rather than bury myself in increasingly abstruse pure mathematics (cosheaves of Hilbert C*-modules, idempotent semisymmetric quasigroups, or what have you). This brings me back to my decision a year or two ago to drop my CS major. In itself it is fairly irrelevant, amounting only to the loss of some formal designation; what really is significant is that I actually stopped studying computer science (dropping a major and discarding an interest are two very different things). This was likely a mistake, which I justified by claiming things like “there are too many arbitrary details to memorize in anything other than pure math” and naively downplaying the importance of different kinds of knowledge. However, the Platonic realm was a kind of adrenaline, the likes of which I had never experienced, and in retrospect it simply “drowned out” everything else. Now I have sobered up, in a sense, and it seems that at the time I misinterpreted this as a genuine disinterest in other disciplines.

A part of me feels sad to have “wasted” these years, enrolling an unreasonable courseload every term (“Hey, look at all the cool courses offered next term! I will get killed if I enrol in all of these, but I’m going to do it anyway because I don’t want to miss out” -> essentially no free time all term, amidst constant onslaught of assignments etc.) pursuing very few interests apart from abstruse math, but another part of me says it was necessary to get to where I am now, and I should just begin this new phase with no regrets.

I do however have to admit that I consider myself a notoriously difficult person to entertain. Based on my observation, many people are content with lives that I would find insufferable: watching television, listening intently to the constant white noise of Hollywood and the lives of celebrities, social media, distracting themselves with chores, and so on. I thought that mathematical research might be my answer to the “big question”. So far, academia has not turned out to be the atmosphere I imagined (though I suppose this largely depends on location; if your friend circle, say, consists of a bunch of extremely competent mathematicians, and you all hang out together all the time and talk math, then yeah, of course you guys are going to end up doing great things — compare the similarly collaborative nature of many successful Silicon Valley startups). To be specific, it is a little dry, in the sense that it is too much sitting at your desk for hours on end, staring at some cryptic paper, and not enough learning from others. What might take me a whole afternoon to gleam from a paper can probably be very adequately explained in under an hour by a knowledgeable colleague. Perhaps this is just an artefact of my clumsiness at meeting people, but I have to say I sincerely doubt it. After thinking about prospects after graduation, I know for sure that I need to move to a big city, since that seems like my best shot at finding the massively collaborative intellectual environment I am after — precisely the “hacker culture” from which I may ironically have inadvertently ejected myself by giving up on programming a couple of years ago.

It is morning now, and I think that was essentially all I wanted to say anyway, although I could probably elaborate more on a few points.

Questions and comments welcome, and uh… ahem…

“Happy New Year”, and all that.

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About mlbaker

just another guy trying to make the diagrams commute.
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17 Responses to 2015 musings

  1. &c says:

    Grass is always greener on the other side.

  2. Sam says:

    Holidays like these exist for a reason, even if their locations in time might be arbitrary. Or maybe not, but at least they have some utility, regardless.

    The new year is a time where we can set aside some past mistakes and try to do things better (or simply differently) for the future’s sake. Sure, we can hypothetically do this anytime, but if our society is going to create an air of renewal for me to enjoy and use to better myself as well as provide a social aspect to this by nudging my friends to do it along with me, why in hell wouldn’t I take advantage of what’s being handed to me on a silver platter?

  3. “I am not religious at all, since no such belief system seems to me any more plausible than the others, and they tend to be pairwise incompatible” This made me laugh. It’s just a bit cliché : religion-explained-by-a-math-student ^_^ I’m a math student myself, so no offence, and I globally share your opinion, even if it’s mistaking oneself about what religion is.
    I’ve come here from your Youtube channel and your (assuming it’s you ^^) number theory video is awesome. Only one video though…so frustrating ^^ Did you plan to publish other videos ?

    • mlbaker says:

      Your first point is right on the nose, of course. I think I stopped making videos since I started giving actual talks, but yeah, I should do some more sometime.

  4. Mohamed El Alami says:

    It feels good to read these words and know that there are people who actually share similar thoughts with you. Beautiful.

  5. What is pmath/CO ?

    the hope of course being that from it, someone out there will manage to derive some meaningful insight.

    I think if I were writing this kind of thing I too woudl feel like it’s an “indulgence” … but no, reading it from the outside I think unadulterated honesty.

    (I found your videos on Youtube, was jealous of how far and fast you progressed as an undergrad in pure maths, so this totally satisfied my curiosity about “Who is this guy and how did he get to where he is?”. But seeing that it wasn’t easy for you is comforting and —- little details like that you were inspired by quantum computers in high school are actually super valuable. Understanding inspiration and hype are really useful for me — look at something like this:

    My undergraduates’ career plans are a peculiar mix of naked ambition and hair-shirt altruism. If they pursue investment banking, they do so not merely to make money. Rather, they wish to use their eventual wealth to distribute solar light bulbs to every resident of a developing nation. They’ll apply to the finest law schools in hopes of some day judging war criminals at The Hague. Countless want to code. They dream of engineering an app that will make tequila flow out of thin air into your outstretched shot glass. My students, I suspect, are receiving their professional advice from a council of emojis.

    Long story short, honest self-looks are useful guideposts for everyone else who’s not in your position. Thanks for doing it publicly.

  6. it is a little dry, in the sense that it is too much sitting at your desk for hours on end, staring at some cryptic paper, and not enough learning from others. What might take me a whole afternoon to gleam from a paper can probably be very adequately explained in under an hour by a knowledgeable colleague. Perhaps this is just an artefact of my clumsiness at meeting people, but I have to say I sincerely doubt it.

    What about MO / math.SE?

    • mlbaker says:

      They’re useful tools, but again, it’s not the same as having a good old-fashioned face-to-face conversation with someone about math — unfortunately a somewhat rare luxury these days, which isn’t exactly doing wonders for my motivation.

    • It’s interesting, I assumed this is what I am missing out on. (I’ve just done all my maths in the recent years by buying books and reading online.) Which sucks, for the reasons you’ve noted, but also because I like having normal friends and find [[the thing I really want to talk about but have no one to talk about it to]] coming out of my mouth when they really don’t care.

      I thought a graduate programme would be the place where you would get exactly this kind of interaction.

      Reminds me a bit of http://mathbabe.org/2014/03/20/optimizing-for-einstein-and-other-homo-erotic-theories/ (she describes a very solitary culture) versus — somewhere John Milnor said the exact opposite, that he had so much fun just shooting the breeze and playing relaxing games with people in the Princeton common room, and that’s where he learned cool stuff and got motivation on how to think, what’s interesting, etc. (I think that was instrumental in him getting a cool result as an undergrad.)

    • mlbaker says:

      Right, yeah. Most people are not mathematicians, and so trying to explain to them this awesome new thing you just learned will never fly, even if you go well out of your way to simplify it.

      I guess one issue is my research area: I don’t really know any other students working on (even vaguely) similar things, so that’s a bit unfortunate. More importantly, though, people usually seem too busy (with course work, projects, thesis, etc.) to just put things aside for a while and learn things out of interest.

      I guess the most collaboration I’ve had was doing assignments for formal courses. Seminars probably used to be a good place to give talks, but now almost everyone either zones out for the whole talk or just opens their laptop at the very beginning and ignores the speaker. That kind of kills the motivation for giving talks in the first place. I might as well just start speaking to my camera, like I so often did four years ago. If anything it provides an outlet, an opportunity to try to explain things in my own words, so the knowledge can be crystallized. On the other hand, the human interaction aspect is gone again.

    • Yeah. With normal people I feel like I can sort of say “I’m really happy about something right now” and just leave it to the emotional part.

      I’ve met a couple math grad students (now all graduated) on twitter, through blogging. A bit of conversation can flow there, and the math.SE chatroom seems OK (probably tea.mathoverflow if you’re more advanced). Still a bit stiff in my opinion (math.SE).

      I guess this is why Simons Foundation has grants for people to travel to conferences. The academic system promotes so much specialization that the 50 people in the world you can talk to about your area are not going to all be physically nearby.

  7. I have been developing interests in other areas, often choosing to spend time learning about more applied areas (statistics, computer science, engineering, physics, chemistry, even history)

    What history stuff?

  8. The clarity with which it has made me able to reason and formulate thoughts is indispensable, and I can hardly understand how anyone (much less a scientist) gets away without it.

    As you noted, though, it comes with an enormous cost. I think the onus is on mathematicians to make the stuff easier to digest. Sure, lots of people could benefit from it, but it’s unreasonable to ask everyone to give even more years of their life to a hated discipline than they already have.

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