# Tractability and Fidelity

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.