Damn it, the numbers didn’t add up.
I sat toiling. The sun had long set, I looked down at the scribbles in the open lab book which were illuminated by the green, white, yellow characters of my dark-themed code editor.
I could see Dan now; he had taken my notebook and was tsktsk-ing. “You need to record everything, not just the numbers.” What was I, a court stenographer or a physicist? “Two out of five”, Dan would say.
Staring at the lab book I tried to run through what I remember of the experiment. The hardware I inherited from a prior grad student. Didier the suck-up. He’d gotten, not just a named postdoc appointment, but also a plum faculty position guaranteed after his postdoc completed. Lord, the way he’d always taken credit for what we’d done in the lab. I guess that’s what you got when you suck up to Professor Van.
Had I not understood the measurement pulses generated by Didier’s electronic stack? Well maybe I could review the notes Didier left behind for the hundredth time.
I spent the next hour reading unintelligible techno jargon. I used to think that science papers were hard to read because I was dumb. Then I realized they were hard to read because half the field had barely functioning language skills.
It didn’t seem to be my understanding of the measurement device that was the problem.
“Make it simple.” Dan’s ghost echoed in my head. “What are you actually trying to do here? You’ve meandered off into focusing on the details, take a step back and find the easiest place where your results are obviously inconsistent.”
“Three out of five”, Dan would say.
What, then, was the crux of my problem? What was the simplest way I could explain what was wrong? Well at the end of the day it just seemed that the probabilities didn’t add up. Not in the metaphorical sense. No the literal sum of the probabilities was not one.
The dark night continued. Tomorrow’s group meeting would be humiliating. I could already picture Professor Van’s scowl. “Your probabilities don’t even add up to one.”
Maybe a little cat nap to see if my subconscious can help.
I dreamed I was on a yacht. No, that was not correct, it was not just a yacht, it was a mega yacht. My lab book was open on a table and I was scribbling into it, while the boat sailed through a narrow fjord with spectacular snow to sea peaks. Why was I so obsessed with this lab book that I was missing the scenery? It was definitely me though, totally reasonable to have me fabulously wealthy, and still piddling around in a lab book.
I woke up with a little spittle on the book where I have rested my head. What was wrong? What kind of universe was this where even the most basic calculations fail: my probabilities did not add up to one.
What would be even worse than Professor Van’s scowl would be that I would have to show my work in front of Gelfman.
The world had created two types of theoretical physicist. The first were those who could solve hard problems that others could not solve. “Just do the integral over the hyperbolic domain”, this type would say, and “it is easy to see the poles are on the line x equals 2.” These physicists were famous for argument by steam rolling your pathetic attempt at math.
Then there were the theorists who don’t solve problems but invent them. And among this set there was an even smaller set who don’t just invent problems to be solved, but created them so that they are born already solved. Gelfman was such a physicist. She had been the one to notice the connection between the Langlands classifications and an obscure approach to quantum gravity; renormalization, then, was just obvious.
Gelfman was a visitor of Professor Van, or at least that was what she had been for twenty years. She was allowed to wander intellectually where she liked, but the one condition Van had given her was that she had to attend the group meeting.
Mostly she’d just sit quietly. She didn’t ever appear to be listening, nor did she appear to actually be thinking about something else. But every few months, in the middle of the presentation at the meeting, we’d hear a polite “excuse me” and look back to see Gelfman with her hand raised.
What followed was always profound and sometimes transformative. It was always “have you considered that what you are saying implies X” where X was something not at all obviously connected to what the speaker was speaking about. One time a result about codes somehow was related to how angles obeyed some modified laws and this “obviously” led to quantum gravity.
What would Gelfman say when my probabilities didn’t even add up to one. Definitely no “excuse me” was in my destiny.
The sun was now up, I made my way to the physics center. I still had a few more hours to debug, but my mind was jelly. So I grab a coffee and a seat with a view up towards the mountains. Maybe this weekend I’ll take a hike, contemplate whether this grad school thing is right for me.
Everyone shuffles in for the group meeting. There is food, but I can’t eat, and for the first time I notice the speed and efficiency with which the grad students devour the food. It was more than slightly repulsive, when you’re not one of those doing the scarfing.
This is a mixed-media talk, I start with a few slides, go to the chalkboard to do derivations, and then return to slides for the data analysis.
The moment of truth. “But these probabilities, well, they don’t add up to one.”
“Excuse me,” I heard. What? Yes, Gelfman had her hand politely raised. She was even smiling (Prof Van was all scowl of course).
“Have you considered that maybe the probabilities don’t add up to one and that you should start a hedge fund?”
“I’m sorry, what?”
“Well maybe your experiment has shown that the world does not have to always follow the axioms of probability. So you’ve shown how to get the physical word into a state where this manifests itself experimentally”
“If you used this experiment along side the real world, everyone else, who was assuming that probabilities did work, their models would be broken.”
The mega yacht, I will say, is quite nice. But yes, I do find myself still working through experiments in my lab book. Like all good things, the arbitrage only lasted until word spread. And now I get to lead a world class set of scientists in the new field of experimental probability. We’re confused, but well fed, and it’s a wonderful life.