On Uncertainty, Bayes’ Theorem, and Love
The math was manageable if I squinted my eyes hard enough, but the big picture had yet to coalesce. I was out of chia pudding, and the last of my coffee was gone. I was stumped.
Then the unexpected happened.
I was at a coffee shop working on everything but my obligated research projects, like good graduate students do. My latest distraction was neuroscientist Karl Friston’s Free Energy Principle. It’s a bold attempt at a unified theory of the brain involving lots of heady math like information theory, dynamical systems, computational neuroscience, and others. At its heart though is Bayesian statistics, a school of statistical thought that had recently captured my attention.
She was sitting two seats to my right reading a red paperback. Stray threads of black fell across her dark eyes, and a slim mask covered her face. Feathered earrings were hiding behind her long black hair. Her blue summer dress was dotted with pink flamingos.
She asked if it was fine to sit nearby, and I said yes. I threw myself back into my textbook shortly after, but couldn’t help and be reminded of my hopelessly romantic fantasy of dating someone I had met in a bookstore or coffee shop. It was a silly thought, and I retreated to the certainty of my Bayesian equations.
But what if?
Bayesian statistics is built atop of Bayes’ Theorem, a simple mathematical framework for quantifying how one should update their beliefs in light of new data or information. It’s a powerful tool in the research setting, but some people also use it as a heuristic for thinking and decision making in their personal life. This seems like a stretch to me, but uncertainty makes us do crazy things. Like statistics. Or falling in love.
She asked for a pen to borrow, and I lent her my spare. I continued to work for the next hour or so, but it wasn’t long before I felt completely out of brain juice.
I’m prepared to leave when she asks me about what I was working on. I mentioned something about math, statistics, uncertainty, and the brain, and she shared her thoughts on the red paperback in her hands. Time stuttered in its steps as stories were exchanged. By the end she was in possession of mine, and I a phone number.
It’s usually intractable to compute the posterior distribution – the Bayesian object that quantifies the uncertainty surrounding our updated beliefs – because most of the problems we care about are complex and involve too many variables to account for. What’s often done instead is that the posterior is approximated. We construct an estimated picture using samples drawn by a computer. With more guesses and draws, the picture gets better and better until it’s close to the solution we’re looking for. But it’s no guarantee that the solution is right.
- Walking Home
- What if the sun wanted to sleep in?
- What if the seat next to me was taken?
- What if I understood myself and Bayesian statistics?
- What if her friends had stuck with their plans?
- What if she didn’t like coffee?
- What if everything that made sense didn’t make sense?
- What if magic was in the eyes of the beholder?
- Would the world still be as beautiful?
Friston thinks the brain works like this. He claims it’s akin to a Bayesian inference machine, something that is constantly processing information from our senses and internal states in order to create accurate mental models of the world so that we can operate in it with some degree of certainty. The world is uncertain, and it’s the brain’s job to reduce it to something more manageable. But what do we lose in the process?
I liked her. I liked her a lot. She was smart, funny, and a good conversationalist. I felt comfortable and wholly myself in her presence. But I was still holding onto someone from the past.
It had been awhile since I last saw her. We were good to and with each other, but she was dealing with her own struggles. A new adventure in Washington DC was also on the horizon. I wanted her to grow and be happy, but a part of me was still hanging onto the hope that things would somehow work out. I knew they wouldn’t, but I hadn’t cut my heartstrings yet.
It was only after I met the girl in the coffee shop that I realized I was ready to let go of hope and embrace the uncertainty.
“All models are wrong, but some are useful” – it’s a phrase that’s preached to all up-and-coming researchers and scientists. The idea is that models are simple caricatures, small worlds used to describe the larger, messy whole of reality.
We need them, but they’re silhouettes, shadows, not the real thing. They help us become less wrong, but never truly right. No matter how good our models are, there’s always a degree of uncertainty involved. So what’s left when our models fail?
Feathered earrings. A blue summer dress dotted with pink flamingos. Stray threads of black strutting across dark eyes.
Possibility exists in the dance between ease and tension, between knowing and uncertainty.
We’re on a walk, the sun is beaming, and I want to pay close attention, note every detail, savor the moment.