Purity and learning


When I was little, I loved learning almost everything. I didn’t need material I was learning to be useful in order to enjoy the information or the process of acquiring it. For many years, I prized knowledge on its lack of utility: information I couldn’t use was worthwhile, and information that I could use was tainted in proportion to its likelihood of being helpful to me at some point in the future.

I think I’ve always loved mathematics as much for its purity as for its intrinsic beauty and the satisfaction of knowing some of the very few things that are undeniably true. Until I got to graduate school, mathematics was completely useless to me, so I had no reason to avoid spending hour upon hour reading mathematics, for example in the Pendola lounge (prior to my partially self-imposed exile), an environment I found most conducive to learning, much of the time.

At that point in time, mathematics was a pre-career for me. It would eventually become a career, and then I would get paid to think about useless (and thus prized) information, and I would pass on information that is only slightly more useful (and thus very slightly less prized). What a wonderful life that must be!

The reality, however, is a bit different. When I started graduate school, and thus getting paid to do mathematics, it stopped being useless. Sure, to the well-being of the world, it is useless. But to my lifestyle, it is of the utmost use, for if I do not think about mathematics, I will ultimately get kicked out of graduate school and left with nothing to do.

With my last vestige of useless learning suddenly becoming highly useful for my life, I’m left with little recourse to useless knowledge. If I could find something else that holds even ten percent of the appeal of mathematics and is similarly useless, my life would surely be immeasurably improved. (Feel free to consider that an invitation for recommendations, by the way!) However, I don’t know of any such thing.

Worse still, perhaps, is that I try to learn many things nowadays as a form of competition. Reading philosophical essays on food and religion doesn’t give me new information; I’ve already seen it all, and I get no further insight from reading such essays. However, I still do read them, and I do so because I want other people to have more trouble defending themselves when talking to me about these issues. And since it takes me about 40 minutes each way to walk between my home and my office, I have 80 minutes each day to think about whatever I want that isn’t math, and not feel guilty about it. Much of that time is devoted to recalling essays I have read recently, going through sample conversations I could see myself having with other people, and refining my responses.

I certainly believe that being able to talk confidently and competently about one’s beliefs is an important skill for a person to have, but surely learning should be motivated primarily by something more than competition. So, how should I motivate myself to learn interesting things? And which interesting things should I encourage myself to learn?

Perhaps learning things that are expressly useless is an inherently childish thing to do. If that’s the case, however, I don’t want to give up on my childhood just yet. Or ever.

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About Simon

Hi. I'm Simon Rubinstein-Salzedo. I'm a mathematics postdoc at Dartmouth College. I'm also a musician; I play piano and cello, and I also sometimes compose music and study musicology. I also like to play chess and write calligraphy. This blog is a catalogue of some of my thoughts. I write them down so that I understand them better. But sometimes other people find them interesting as well, so I happily share them with my small corner of the world.
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6 Responses to Purity and learning

  1. zebrallama says:

    I assume music is good because you count it as useful.
    How about Go?

  2. zebrallama says:

    For a moment there I forgot that you like chess! So how about spending more time on that?

  3. openidless says:

    Hardy was described as a “very pure” mathematician. I wish I could comment on the situation better, but I enjoy seeing math applied in AI, science, etc. too much to subscribe to the purist aesthetic. In the words of Terence Tao, “I just like mathematics because it is fun.” Sounds like I should relish my days as an undergraduate! I have a hint of what you’re experiencing, going from high school math contests to full time university studying; perhaps you should try studying one area of math only on your free time and let it be disconnected from work. I can’t think exactly what this might be, but I strongly suggest any of E. Dijkstra’s work. It is remarkable.
    On the subject of your philosophical essay reading, maybe you would try something new to think about. “Escape From Leviathan” is a philosophical book I have heard good things about. I wouldn’t want to focus exclusively in one area too long, we humans are too susceptible to deeply-held beliefs that cloud our thinking on issues we are passionate about. Once you have been wrong in the past, you will never think you’re right again so easily.

  4. teratoma says:

    why not study some theoretical physics?

  5. mariabrenna says:

    well, i would suggest going about usual business and if you happen to find something interesting and fun learn about it. I don’t think I have any suggestion to do otherwise.

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