Juan David Campolargo

Calculus: Reaching the Unreachable

Calculus is about an idea called limits. This idea is a mental model to understand that which we can never approach. A limit is like an unreachable goal. You can closer and closer to it, but you can never get all the way there. 

This idea made me reflect on a bigger paradox of life because, in many areas, we see this phenomenon occur. Yet we have trouble making sense of it.

I’ll give you a few examples:

For instance, happiness. We have a sequence of emotions such as:

This sequence gets closer and closer to happiness

The limit of this sequence is happiness. None of the values is equal to happiness, but they get closer and closer to happiness.

If you find this hard to grasp, this will help: how do we know there are infinite different happiness emotions? It’s not like we’ve counted them all and got to happiness. 

We know they are infinite because for any happiness emotion there’s another happiness emotion that’s even larger than that (almost happy, almost almost happy, almost almost almost happy....) There's always another one and another one. [1]

The same applies to wealth, satisfaction, and truth, and the rest of the examples above. 

That’s where calculus comes in and gives you a hand to help you reach the unreachable. 




[1] Inspired by Khan Academy’s explanation of limits. If you want to teach yourself calculus (like I did), Khan Academy is the way to go. 

I got stuck during a calculus test, and of course, I wrote an essay to get unstuck. Look at the original draft.

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Tags: mathematicsphilosophy