Damnit the numbers don’t add up.
Here I sit and toil. The sun has long set, I look down at the scribbles in the open lab book which are illuminated by the green, white, yellow characters of my dark themed code editor.
I can see Dan now, he’s taken my notebook and is tsktsk-ing. You need to record everything, not just the numbers. What am I, a court stenographer or a physicist? Two out of five, Dan says.
Staring at the lab book I try to run through what I remember of the experiment. The hardware I inherited from a prior grad student. That suck up Didier. 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 get when you suck up to Professor Van.
Had I not understood the measurement pulses generated by Didier’s electronic stack? Well maybe I should go over for the tenth time the notes Didier left behind.
I spend 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 finds its way into 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 says.
Ok then what 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 seems that the probabilities don’t add up. Not in the metaphorical sense, no the literal sum of the probabilities was not one.
The dark night continues, it will be a humiliating group meeting tomorrow. 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 dream I’m on a yacht. No, that’s not correct, it’s not just a yacht, it’s a mega yacht. My lab book is open on a table and I’m scribbling in it, while the boat sales through a narrow fjord with spectacular snow to sea peaks. Why am I so obsessed with this lab book that I’m missing out on the scenery? It’s definitely me though, totally reasonable to have me fabulously wealthy and still piddling around in a lab book.
I wake up with a little spittle on the book where I have rested my head. What is wrong? What universe is this that makes even the most basic stuff fail: my probabilities don’t add up to one.
What will be even worse than Professor Van’s scowl will be that I will have to show my work in front of Gelfman.
There are two types of theoretical physicists. The first are those who can solve hard problems that others cannot solve. Just do the integral over the hyperbolic domain, they say, and it’s easy to see the poles are on the line x equals 2. These physicists are famous for argument by steam rolling your pathetic attempt at math.
Then there are the theorists who don’t solve problems but invent them. And among this set there is an even smaller set who don’t just invent problems to be solved, but create them so that they are born already solved. Gelfman was such a physicist. She’d been the one to notice that one could connect the Langlands classifications with an obscure approach to quantum gravity and when one did that renormalization was just, well, 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 is is now up, I make my way to the physics center. I’ve got a few more hours to debug, but my mind is 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. Slightly repulsive when you’re not one of those doing the scarfing.
This is a mix 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 hear. What? Yes, Gelfman has her hand politely raised. She’s even smiling (Prof Van is 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 use this experiment along side the real world, everyone else, who is assuming that probabilities do work, well their models will 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.