In which I am locked in a room and asked to spin straw into gold

Then my dissertation advisor locked me in a classroom. He was not happy. The proof was suppose to be simple, it was just a jump from one dimension to two. We needed it for an obvious, intuitive claim I was making. In mathy circles, however, obvious and intuitive doesn’t count for squat so we needed the proof. And it should have been easy.

A few weeks before, my advisor told me to make sure all my ducks were crossed and all our ‘i’s lined up by proving a simple thing that both of us agreed should be easy enough because, well, it was just an extension of a well known result, so I skipped home singing with the telephone line blue birds, paired and swaying, while a happyfaced sun bobbed along with me humming among fluffypuffy clouds in a unicorn-magic blue sky. But the proof would not come. I tried for a week. I worked on little else, twisting my brain this way and that, trying to lug veiled knowledge from the Platonic world of forms. It defeated me.

Broken and humble, I walked into my adviser’s office, eyes cast down, mumbling that I could not seem pull it together. He scowled and told me to keep trying, reminding me of his great confidence, and patting me on the back heartily and with ‘chin up ol’ boy’ expressions of encouragement, sent me back down the hall to my grad student cubicle (crucible?). I redoubled my efforts, filled my mind with positive energies, sang songs of courage and determination, worked late into the night filling up pages and pages of equations, took cloudy walks on the green-way trying to see if I could bend my mind in new ways. I reexamined the proofs used in the one-dimensional case, and tried to articulate where I was going astray. It was to no avail. I was a failure.

The next week, I returned to my adviser’s office shamefaced and embarrassed. This was a character flaw. A failure of personhood. He listened to me try to explain my shipwreck. He looked disappointed, which turned to impatience, which turned to frustration, which was expressed in a cold, “This is NOT a hard problem!” Whereupon, he took me by the arm and marched me, like an miscreant child to an empty classroom and threw me in and said, “Don’t come out until you’ve finished the proof.” My first thought was, “What if I have to go to the bathroom?” then I sighed and sat down at one of the enrowwed desks. Forsaken of hope. I said an empty faithless prayer and turned to the task. But my mind was locked into modes I had tried over and over the last two weeks. I kept hoping that some Rumpelstiltskinish figure would poof into the room to spin my straw scribblings into some hard math currency. The little mythical creature did not appear.

And so I sat for three hours (with one secret, and dangerous, guilt-ridden, trip to the bathroom) but the last hour was really spent picturing what my wife would say when I didn’t come home that night. Finally, my advisor peeked in. He was genuinely surprised. And vexed. But, like a kindly father figure disappointed in his errant child, he sat down and said, “Let’s see what you are doing.” I showed him my approaches, and he nodded genially, “Yes, very promising.” Then he said, “Look all you have to do is . . .” He tried something, “um . . . let’s see, if we just . . .um . . .” Then he was off to the races. I watched him go through the same motions I’d been trying. And ending up in the same places I did. “Um . . . I’m sure if we just . .” more writing. Pages of equations were now falling on the floor, expressions of frustration, “ . . . um . . . this is harder than I thought . . .” The minute hand crawled past the place marking an hour we’d sat together.

Self-satisfaction now is running through me like a narcotic as I watch him try to come at it from the bottom. Like I had. It doesn’t work, it always brakes down right there, right when you try to bring it together from the forward or backward direction. However, my advisor is no slouch and he once studied under a great Princeton biomathematician and is of similar genius. Suddenly he rockets into the starry realms of math that I had only dim hints existed. He abandons the entire the framework in which I am seeped (like someone raised in the ‘angle ABC’ methods of Euclidean geometry, suddenly watching someone switch to algebra to solve a problem). It was stunning. I watch breathlessly as he pulls off some wondrous, cleaver, brilliant moves; his hands are flying, his mechanical pencil dancing esoteric alchemy across the page, his eyes glazed like a zen mystic staring simultaneously at both the page and an ethereal world where truths are manifest only to the initiated; he is improvising like a Jazz musician. Yes, only the mixed metaphor of dance, zen masterizing, and Jazz can capture what he did. Banach spaces are pressed and twisted and wrung out in way that can only be called occult. He commands the Gods of Lebesgue integration to perform deeds that would have made a Riemann integral blush. Topological battles are fought on turf that can only be described as manifesting the quality Unteraliceimwunderlandheit–a place of such strangeness that Alice’s Wonderland would seem a tame and provincial country. Then like some kind of cosmological surgeon he stitches it all together. The proof is done.

He finishes with a satisfied harrumph. He looks over at me, his arms folded and says, “That was harder than I thought.” We both stared at what he had done. “I not only would not have thought of that, I could not have thought of that. Not in ten years.” I said in awe. He chuckled. “Oh, I think in three or four years you could have pulled it off.” He patted me on the back and walked out smiling. I had had enough stochastic process theory to follow, mostly, what he’d done, but it was a creative act I could never have duplicated.

Easy? He could not, as it were, write with my mechanical pencil until he had set down and wrestled with the problem himself. From the position of his office, this was something so easy that any graduate student should have been able to do it. I believed I could do it. Until I tried. But it was a non-trivial problem. Only, in the experience of his trying to do what he asked me to do, did the difficulty of the proof appear. A proof I could have never done. Not in a million years.

Comments

  1. Kevin Barney says:

    There are times when I wish I had done mathematics. But most of the time I’m properly sane. Loved the story!

  2. SteveP, too, has looked on Beauty bare.

  3. We can never judge rightly until we’ve written the proof in another’s graphite.

  4. I know this isn’t an academic blog, but this might be the best description I’ve every read for both the frustration and wonder of the later half of the PhD process.

  5. Can we see a type and shadow of the atonement in this experience?

    The Professor doing for you what you could not do for yourself. The awful arithmatic of the atonement – Elder Maxwell comes to mind.

    Just some random thoughts provoced by this post.

  6. Margaret Young says:

    Beautiful, SteveP.
    Oh empathy–the key to forgiveness and spiritual progress, I think. It is so easy to approach someone else’s problem (even a problem we ourselves have presented to them, or created for them) and insist that they find the “correct” solution without considering what their foundation actually is, or how hard the problem might be FOR THEM. I am far more likely to listen to a woman who has, for example, had a daughter with an eating disorder than I am to listen to someone tell me about how love and prayer will solve our problems and quoting me something inspiring from the _Ensign_, implying, “This is NOT a hard problem! Correct placement of a really good cliche will take care of it!” When we insist on viewing another’s challenge according to our own imagination of what it is; when we isolate them in their chamber of shame (or so it will feel to them) by easy, dismissive answers, we damage or sever our relationship, and turn down our invitation service. This is perhaps most relevant in marriage, during those times when we KNOW how our spouse ought to act, and emotionally banish them when they fail–never considering how many other things might be impacting their behavior, or how we ourselves might have created a problem far bigger than we had realized.

  7. Skull sweat. Nothing like it to find your limitations.

  8. At first I wa wondering why I kept reading and how this connected to church but I really like where it took me. Sometimes I think math is the language of God kind of thing, everything can be explained and made with math. :) I really liked the that you left it open for the reader to take from it what they would.
    I was leaning toward an atonement analogy, God sending his son so he would be able to understand how hard life is for us and show the way we can get through it even if we can only mimic without fully comprehending all that’s been done.
    However I also like the more earthly explanations people have offered about how we treat others. I think I often think like the professor that the problem is easy, why don’t you just deal with it? Even with my own trials I think this is simple, you’re just being too lazy to deal with it properly (probably there’s a lot of truth to that). I don’t know that there’s any easy way to change your thinking unless we go get our hands dirty with whatever the person is trying to overcome.

  9. Margaret, I think that is right, when we look at others, it’s easy to see how they ought to behave and fix their not hard problems, not recognizing the complexity of their lives or how we world really do it, and especially in close relationships like marriage.

    Mike @5 and Rebeckila@8, I had not seen the atonement analogy, but it works. I like the image of getting your hands dirty to experience directly what others are feeling. I think, that is what my professor realized.

  10. The allegory of the grad student.

  11. Wow, this was an amazing post. I loved the metaphor of the Jazz musician. Thank you for putting this out there — it’s something that is familiar to all, whether mathematicians or not.

  12. Excellent story. Does your professor have time to help my kid with his algebra?

    In the 80s/early 90s, we were expanding missionary work in Alabama to focus on African-Americans. Many were eager and excited to join the Church, but due to their culture and upbringing did not understand leadership, or Mormonism. I heard members in many wards (especially my own) that bristled, asking why these folk could not pull themselves up from their own bootstraps (literally asked of me). We sometimes have to do for others what they are incapable of doing for themselves.
    As your professor noted you could figure it out in a few years, such a solution would not have helped you in finalizing your thesis. You needed his full expertise to resolve the problem, even though you may eventually gain such mathematical experience to recreate such by yourself.
    While Christ’s atonement gives us that which we cannot do for ourselves, the difference is with hard work and time, you COULD learn the same mathematical theories he used. We can never satisfy the requirements of salvation without the atonement.
    What we can do, is provide for the spiritual and temporal needy, who cannot do for themselves at this time.

  13. Cool post! I really liked it. I also note the few spelling errors (I think anyway) that make the post even more interesting (note “brake” instead of “break” and “cleaver” instead of “clever”).

    I am currently walking in these shoes right now. Things seem obvious to my advisor and after beating my head against the wall for months I still don’t quite see it. When I meet with her she seems to solve problems in 30 minutes that take me hours and hours to solve. Of course maybe I’m just slow!

  14. Great story!! It is hard to see how someone struggles with something you yourself feel shouldn’t be an issue. And it is a humbling act to put yourself at their level and come to grips with how difficult a situation could be.

    Great post!

  15. I imagine the relationship between God and man to be like that of teacher and student. Where both can see the answer, they get the same answer. But the teacher can see further where the student cannot, yet is unable to get the student to see along, like telling a blind person what colors are.

    One example that continues to impress me is the analytic continuation of the power series y(x) = 1 + x + x^2 + x^3 + …. The beginning student would take a lifetime to add this up (and then only approximate the answer), the way we might understand moral issues. Some imponderable thoughts (like the value of y(2)) even seem impossible to us, and then the teacher (like God) comes along with greater understanding and a simpler way of seeing things with the equivalent but more widely valid formula y(x) = 1/(1 – x). It is (to me) very unobvious that such an infinite thing could be made finite and “improved” in such a simple manner. Nor is it easily demonstrated that the two are equal, or why they should be so. Those unwilling or unable to prove that something is true must content themselves with faith.

    I wonder what other deep mysteries of the universe are actually quite simple when seen from God’s perspective.

Follow

Get every new post delivered to your Inbox.

Join 9,474 other followers