One of my favourite parts about mathematics is its definitive nature. Once you’ve proved a result, it’s true for all of time. We can be confident that the chain of reasoning will hold, even without inspecting every part. This feature of mathematics has let us build incredible structures, and as a bonus, tools to help us reason.
At least in my mind, this definitive nature lends a certain gravitas to mathematics. I didn’t go into mathematics myself, but my field of theoretical physics is so adjacent that many within it are also mathematicians. This has biased me towards mathematics. In general, I would trust a mathematical result more than I would a claim based on an anecdote. The former uses reproducible and logical standards of reasoning, which I’ve culturally absorbed as more trustworthy and stronger than other ways of reasoning. Because of this, if I see someone using mathematics in their work, I’m more likely to see it as authoritative. I prefer seeing a mathematical model of a situation than “just” some anecdotal data.
More than ever, people use mathematics to investigate questions about society, from what we should do about the climate to possible financial downturns. The stakes are higher than when a few theorists work on physics models: The models we create will influence society. As a result, we want to tread carefully, ensuring that out models help us improve society for everyone.
But there’s a tension: Mathematics shines when a scenario has clear definitions, which is not the case for a lot of the questions we want to answer about our world. Faced with the messiness of our world, we need to simplify until we can handle the mathematical analysis. In other words, we have a tension between mathematical tractability and fidelity to our world.
In Escape from Model Land, Erica Thompson brings the reader on a journey whose main purpose is to highlight this tension, forcing the reader to pause and ponder how we use mathematical representations–mathematical models–to understand our world. Thompson acknowledges that mathematical models are an enormously powerful tool for investigating the world, but that we can often fool ourselves into complacency, swapping the model in for the complicated reality of life.
When I was completing my master’s degree, I was excited to be working on new research. While some students in my cohort worked on understanding the literature, my supervisor gave me a novel project we thought we could eventually publish it. The concept was simple and straightforward, motivating me to build the experiments, collect the data, and write up a paper.
But then I began hitting obstacles. The project involved machine learning, and I found myself navigating a lot of uncertainty as to how to interpret my initial underwhelming results. There were many knobs I could tweak and no clear instruction manual on how to choose the settings for the knobs. Couple this to results which weren’t competitive with the literature and long training times for the models, and it’s not surprising that I got stuck.
I completed my master’s project with these underwhelming results, thinking that I would be able to work through the issues by the end of the summer and then publish. I was totally wrong.
How much do you read in a day? How much do you remember?
As a scientist, one of my main jobs is reading papers. This is to learn about new work in my field, understanding the methods of others, and getting ideas for my own work. I also love reading fiction, which I do every day.
However, not all reading is equal.
A useful way I’ve found to think about reading is as a spectrum between consuming and absorbing.