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This is: Gravity Turn, published by alkjashon the LessWrong.
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[The first in a sequence of retrospective essays on my five years in math graduate school.]
My favorite analogy for graduate school is the gravity turn: the maneuver a rocket performs to get from the launch pad to orbit. I like to imagine a first-year graduate student as a Falcon X rocket, newly-constructed and tasked with delivering a six-ton payload into low Earth orbit.
Picture this: you begin graduate school, fresh as a rocket arriving at Cape Canaveral and bubbling with excitement for your maiden voyage. Your PhD adviser, on the other hand, is the Hubble Space Telescope. Let's call her Dr. Hubble (not to be confused with the astronomer of the same name). Dr. Hubble is ostensibly the ideal guide for your first orbit insertion. After all, she is famously good at staying in orbit - she’s been up there since 1990.
But problems quickly arise as you probe Dr. Hubble for advice on how to approach the launch. Namely:
She left Earth more than thirty years ago, and space technology has since been completely revolutionized.
She states all advice at an extremely high level with birds-eye-view detachment, observing, as she is, from a vantage point a thousand miles overhead.
Most fatally, the Hubble Space Telescope vessel does not include the lower-stage rockets that brought her into space. In fact, she doesn’t include large engines of any kind. Her thirty years of experience free-falling in orbit will do you very little good until you break out of the stratosphere.
The problem is even worse than this, however. It is not that Dr. Hubble, despite her best intentions, gives outdated advice. It is not even that Dr. Hubble cannot consciously articulate all the illegible skills she’s reflexively performing to stay in orbit. The problem is that even if you could perfectly imitate what Dr. Hubble is doing right now, you would likely still crash and burn.
What I didn’t understand going into graduate school is that academic mathematicians are often working in a state akin to the free-fall of orbit. The Hubble Space Telescope remains in orbit around Earth because it travels horizontally so quickly that, even as it’s continuously accelerating towards the Earth, it continually misses. The laws of physics have arranged it so that it is not possible - barring deliberate sabotage - for her to fall back into a sub-orbital trajectory.
Similarly, a successful research professor is embedded in an intricate system that, as surely as Newton’s laws, keeps her in a state of steadily producing new research. Many of her ground-breaking papers are not one-off productions - they produce sequels, variants, and interdisciplinary applications year after year. She has cultivated dozens of long-time collaborators of the highest level who freely share ideas and research directions, and has the reputation to find more at will. She attends conferences every other month that keep her updated on the leading edge of the field. Every year her research group grows, as if by clockwork, adding a couple graduate students and postdocs to whom she can delegate projects with only the gentlest supervision. As a result, the careers of many other people depend on Dr. Hubble to continue producing research at a steady rate. Every incentive is aligned for objects in motion to stay in motion, and it would take deliberate sabotage to bring Dr. Hubble out of her successful research trajectory.
This is not to say that academic researchers all start cruising in free-fall after they leave graduate school or make tenure. It is perfectly normal for a spaceship that reaches orbit to proceed onto its next adventure after some rest, continuing on to visit another planet or leave the solar system altogether. The best researchers I know are similarly courageous, ta...
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