07/18/2024
A very common student question: Why should I learn math?
It's been answered a hundred times before. For whatever reason, some of my students will only listen if I'm the one saying it:
We have a model of the world. You do your homework, and your parents reward you. You make a joke in class, your classmates are likely to laugh and, resultantly, people will be friendlier to you. You study for the SAT, which likely nets you a high score, which then translates to admission to a better college and higher overall academic achievement, and this, in turn, leads to higher earnings over the course of your lifetime, which means more prestige, comfort, and (maybe) happiness. A brief back-of-the-napkin calculation leads to a revelation: studying *now* is probably the highest-paying "job" you'll ever have in your entire life.
In following this train of thought, you've implicitly made many unconscious calculations: the likelihood that studying improves your score in a significant way; the likelihood that you won't burn out in a school that will ultimately be "harder" than one you would've otherwise ended up at; the likelihood that, after all that hard work, you won't wish you "took it easier when you were young".
You are doing complex calculations about your future. It may be that such calculations affect your decisions and your life.
Now, we didn't use any quadratics here (which I'm still pressed to provide a use-case for), but we did implicitly discuss exponents, ordinary differential equations, calculus, and probability.
When we imagine the future, we are acting like predicting machines. When we study history, we seek to predict the future trajectory of society. We study neuroscience so we can prevent dementia. We study linear algebra and computers so we can make even more general prediction machines.
At the root of all prediction is math. The measure of what "is" and what "will be". If you want to make a better prediction - and thereby ensure a better outcome - you should learn to represent your world-model mathematically. Once you've done this, you can use tools (which have been passed down across millennia) to project and predict the future. Finally, you simply have to make the right decisions and follow the model.
Unfortunately, the last step is sometimes the hardest of all!
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