My thesis (variations on a theme)
Jun. 24th, 2005 02:28 am![[personal profile]](https://www.dreamwidth.org/img/silk/identity/user.png){kind=small}
pyesetz(Forewarning: in this post I never actually say what my thesis *is*.)
A long time ago, when I was in grad school, one of my tasks was to find a thesis topic so I could write a dissertation. Topics must revolve around a kernel of a new idea, but the main requirement is that you have to be interested enough in your thesis to keep plugging away at it during the soul-withering anomie of the ABD period.
So I thought up a thesis and discussed it with some potential mentors. They told me that I should wrap up my idea in aluminum foil, store the foil in a paper bag stapled shut, seal the bag in a plastic sack tied in a knot, and place the sack in a commercial dumpster far from my usual haunts, in the middle of the night, making absolutely sure that I was unseen and thus no one could possibly connect me with this thesis. Okay, I exaggerate slightly, but I was told (in a quiet voice, so no one could overhear that we were even discussing such a thing) that people who worked on theses like mine either went crazy, or committed suicide, or ran away and tried to pretend that such thoughts had never crossed their minds—and only this last group went on to have successful academic careers.
Having no acceptable idea of my own, I was assigned a thesis topic that had government-grant money behind it. It was an easy life, but the assigned topic was barren and I didn't think I could ever make a dissertation out of it, so I bailed out with a Master's and left academia. Meanwhile, the foil-wrapped thesis just sat there, in a dumpster of the mind.
* * * * * * * * * *
In the 1960's, Frank Rosenblatt had staked his career on perceptrons, cybernetic models that he claimed could learn *anything*. In 1968 Marvin Minsky published a book of proofs showing that lots of things *couldn't* be learned by perceptrons, including the dinky little "XOR problem" that anyone could solve with just three transistors, but wired together in a way that perceptrons couldn't be wired. That book cast a pall over the entire field of cybernetics: "25 years with no useful results and Minsky says there never will be any". Research funds dried up. Rosenblatt committed suicide. Anyone still working in the area pretended to be doing something else, writing grant proposals for respectable things while secretly continuing to work on cybernetic algorithms. In 1986 David Rumelhart and James McClelland published a proof that a connectionist cybernetic model could learn the XOR problem. Rumelhart's paper oversimplified the difficulties and at that time I was cursing him as a poor scientist while trying to replicate his results, but in the end his proof really does (barely) work. After Rumelhart, researchers came out of the woodwork with results that they had been hiding in their desk drawers because no publisher would touch them. Today, connectionist methods are commonly used in video games to make the NPC's play better.
My thesis is also in a field that has a reputation for having never produced any useful results and it also has had some famous nay-sayers who claimed that there never would be any. But there's no way that I could ever pull a Rumelhart because (a) I don't have the math skills and (b) my thesis deals with a much messier part of the universe.
* * * * * * * * * *
The Four-color thesis was discovered in 1852. Various proofs were proposed over the years, but none of them really worked. Eventually a valid proof was published in 1976 by Appel and Haken, who solved the problem by chopping it up into 1,936 parts and writing a computer program to prove each one. Fellow mathematicians hated their proof because (a) it used a computer; (b) the 1000-page proof was too complex to verify by hand; and (c) it lacked "explanatory power": it proved the theorem to be true but didn't explan *why* it had to be true. Since then, other people have simplified the proof to only 633 parts, yet still the theorem is hated by some because it is irreducibly complicated and can't be covered in a 50-minute lecture. But some parts of the universe are just very complex and no "simple" theorem can explain those parts.
I don't know how many parts my thesis has; I don't think anyone knows yet. Perhaps someday 10,000 parts might be known. I might have to prove several hundred parts before people would become comfortable admitting that they're working on this problem.
* * * * * * * * * *
Fermat's last thesis was discovered in 1637. It has always been called "Fermat's Last Theorem", although for 357 years it was well-known as the theorem with the largest number of *incorrect* published proofs. So many had made laughingstocks of themselves trying to prove this thesis that it became the exemplar of the kind of problem you don't want anyone to know that you're working on—not if you're bucking for tenure, anyway.
Andrew Wiles worked on this theorem. For seven years. In his attic. He told no one. Perhaps he watched the episode of Star Trek: TNG in which Picard asserts that the problem would still be unsolved 200 years from now. Wiles said nothing, except to his wife. Now that Wiles is famous, she *claims* she was behind him all the way and never bitched at him to get out of the attic and spend more time with their children. Yeah, right.
* * * * * * * * * *
Still the foil-wrapped thesis sits in its dumpster. It does not fester; it will not explode. It just sits there, like a prophecy waiting to be realized, patiently waiting to see whether I will ever get around to it before my allotted time is up and I must shuffle off this mortal coil. Every so often I get a seemingly-bright idea about how to chop off a small part of the thesis so I can actually get some results with only a Herculean quantity of effort. For a while I follow the crystallized dream, but then the "easy answer" morphs into a sea of writhing bugs because my thesis is quintessentially uncompartmentalizable.
At one point I had written a program that just barely missed being deserving of the label "complete and utter failure", so I wrote up a paper about it. (If your program works, start a business; if it fails, write a paper!) I showed the paper to a co-worker of mine and asked him to review it. He trashed my paper. "Who is your target audience? You talk too much about practical stuff for an academic audience, but your results are too meager to interest any practical folks. And just delete all that pie-in-the-sky bullshit about what your thesis says about the universe—nobody in computing wants to read that." I never did publish that paper, but years later I wrote a paper about something else; my co-worker gave me many helpful comments on that one and it was eventually published and I still consider him a good friend.
* * * * * * * * * *
My father had a thesis. He took it with him to his grave. It had something to do with the frequency distribution of digits among large prime numbers, but he never told me the details. When he retired, he indicated some interest in having me help him with his thesis, but I didn't want to get too involved in *his* problem and just offered him programming advice. After his death I asked a mathematician friend of his to look around on Dad's desk and see if he had actually come up with anything. The friend said there were computer programs to generate primes and lots of printouts of primes with some of the numbers circled, but no notes on what Dad might have been looking for and no indication that he was anywhere near finding it.
Later I saw that somebody had published a paper on digit-frequencies in prime numbers. Did someone else prove Dad's thesis, whatever it was? I will never know.
Update: Made one attempt to publish this, which failed.
A long time ago, when I was in grad school, one of my tasks was to find a thesis topic so I could write a dissertation. Topics must revolve around a kernel of a new idea, but the main requirement is that you have to be interested enough in your thesis to keep plugging away at it during the soul-withering anomie of the ABD period.
So I thought up a thesis and discussed it with some potential mentors. They told me that I should wrap up my idea in aluminum foil, store the foil in a paper bag stapled shut, seal the bag in a plastic sack tied in a knot, and place the sack in a commercial dumpster far from my usual haunts, in the middle of the night, making absolutely sure that I was unseen and thus no one could possibly connect me with this thesis. Okay, I exaggerate slightly, but I was told (in a quiet voice, so no one could overhear that we were even discussing such a thing) that people who worked on theses like mine either went crazy, or committed suicide, or ran away and tried to pretend that such thoughts had never crossed their minds—and only this last group went on to have successful academic careers.
Having no acceptable idea of my own, I was assigned a thesis topic that had government-grant money behind it. It was an easy life, but the assigned topic was barren and I didn't think I could ever make a dissertation out of it, so I bailed out with a Master's and left academia. Meanwhile, the foil-wrapped thesis just sat there, in a dumpster of the mind.
* * * * * * * * * *
In the 1960's, Frank Rosenblatt had staked his career on perceptrons, cybernetic models that he claimed could learn *anything*. In 1968 Marvin Minsky published a book of proofs showing that lots of things *couldn't* be learned by perceptrons, including the dinky little "XOR problem" that anyone could solve with just three transistors, but wired together in a way that perceptrons couldn't be wired. That book cast a pall over the entire field of cybernetics: "25 years with no useful results and Minsky says there never will be any". Research funds dried up. Rosenblatt committed suicide. Anyone still working in the area pretended to be doing something else, writing grant proposals for respectable things while secretly continuing to work on cybernetic algorithms. In 1986 David Rumelhart and James McClelland published a proof that a connectionist cybernetic model could learn the XOR problem. Rumelhart's paper oversimplified the difficulties and at that time I was cursing him as a poor scientist while trying to replicate his results, but in the end his proof really does (barely) work. After Rumelhart, researchers came out of the woodwork with results that they had been hiding in their desk drawers because no publisher would touch them. Today, connectionist methods are commonly used in video games to make the NPC's play better.
My thesis is also in a field that has a reputation for having never produced any useful results and it also has had some famous nay-sayers who claimed that there never would be any. But there's no way that I could ever pull a Rumelhart because (a) I don't have the math skills and (b) my thesis deals with a much messier part of the universe.
* * * * * * * * * *
The Four-color thesis was discovered in 1852. Various proofs were proposed over the years, but none of them really worked. Eventually a valid proof was published in 1976 by Appel and Haken, who solved the problem by chopping it up into 1,936 parts and writing a computer program to prove each one. Fellow mathematicians hated their proof because (a) it used a computer; (b) the 1000-page proof was too complex to verify by hand; and (c) it lacked "explanatory power": it proved the theorem to be true but didn't explan *why* it had to be true. Since then, other people have simplified the proof to only 633 parts, yet still the theorem is hated by some because it is irreducibly complicated and can't be covered in a 50-minute lecture. But some parts of the universe are just very complex and no "simple" theorem can explain those parts.
I don't know how many parts my thesis has; I don't think anyone knows yet. Perhaps someday 10,000 parts might be known. I might have to prove several hundred parts before people would become comfortable admitting that they're working on this problem.
* * * * * * * * * *
Fermat's last thesis was discovered in 1637. It has always been called "Fermat's Last Theorem", although for 357 years it was well-known as the theorem with the largest number of *incorrect* published proofs. So many had made laughingstocks of themselves trying to prove this thesis that it became the exemplar of the kind of problem you don't want anyone to know that you're working on—not if you're bucking for tenure, anyway.
Andrew Wiles worked on this theorem. For seven years. In his attic. He told no one. Perhaps he watched the episode of Star Trek: TNG in which Picard asserts that the problem would still be unsolved 200 years from now. Wiles said nothing, except to his wife. Now that Wiles is famous, she *claims* she was behind him all the way and never bitched at him to get out of the attic and spend more time with their children. Yeah, right.
* * * * * * * * * *
Still the foil-wrapped thesis sits in its dumpster. It does not fester; it will not explode. It just sits there, like a prophecy waiting to be realized, patiently waiting to see whether I will ever get around to it before my allotted time is up and I must shuffle off this mortal coil. Every so often I get a seemingly-bright idea about how to chop off a small part of the thesis so I can actually get some results with only a Herculean quantity of effort. For a while I follow the crystallized dream, but then the "easy answer" morphs into a sea of writhing bugs because my thesis is quintessentially uncompartmentalizable.
At one point I had written a program that just barely missed being deserving of the label "complete and utter failure", so I wrote up a paper about it. (If your program works, start a business; if it fails, write a paper!) I showed the paper to a co-worker of mine and asked him to review it. He trashed my paper. "Who is your target audience? You talk too much about practical stuff for an academic audience, but your results are too meager to interest any practical folks. And just delete all that pie-in-the-sky bullshit about what your thesis says about the universe—nobody in computing wants to read that." I never did publish that paper, but years later I wrote a paper about something else; my co-worker gave me many helpful comments on that one and it was eventually published and I still consider him a good friend.
* * * * * * * * * *
My father had a thesis. He took it with him to his grave. It had something to do with the frequency distribution of digits among large prime numbers, but he never told me the details. When he retired, he indicated some interest in having me help him with his thesis, but I didn't want to get too involved in *his* problem and just offered him programming advice. After his death I asked a mathematician friend of his to look around on Dad's desk and see if he had actually come up with anything. The friend said there were computer programs to generate primes and lots of printouts of primes with some of the numbers circled, but no notes on what Dad might have been looking for and no indication that he was anywhere near finding it.
Later I saw that somebody had published a paper on digit-frequencies in prime numbers. Did someone else prove Dad's thesis, whatever it was? I will never know.
Update: Made one attempt to publish this, which failed.
