Do we Need Math? Imagine our Life Without It
By: Andrew Zhuravchak
Tags: Technology, Mathematics, Tech, Learning, Science

Do you remember your math classes in school? I definitely do, and on my mind was always:

“Why do I need this formula? Where will I use that theorem?”

You heard or even asked the same questions. After that, the teacher used to explain that we can use integral to find the area and derivative to get the acceleration from speed.

“And what?” — the question always appeared but was newer asked. Most people will never be trying to find a minimum/maximum of the function in daily life.

However, all of us need math, and it’s essential in your career, decision making and any field of life.

The reason is abstractions

Do you remember that day when the teacher started writing letters instead of numbers? Was this easy for you?

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I was always pretty good at math, but it took me a lot of effort to stop fearing letters in formulas.

Why do I write fancy letters in formulas instead of numbers?

A familiar feeling? But the idea is that everything in math is an abstraction.

You understand what is apple, but what is the number? Right, it’s the abstraction to help us to count apples. The same with any other idea in math, either it’s multiplication or Newton–Raphson root-finding algorithm

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Math is abstract because numbers are not real entities. They are purely imaginary concepts. We cannot experience numbers. We can make up stories about them, such as “1+1=2”. But, we can never experience such operation since there is no such thing as ONE of anything in our experience. If there is no such thing as ONE of anything in our experience, there can be no such thing as TWO of anything in our experience, etc. When we do math, we are playing a game in a world of imagination. Like fairy tales, numbers are the characters in that imaginary world, while the operations are the activities that those fairy tale characters perform. And just like fairy tales, math can be beneficial, even though neither numbers nor fairy tale characters really exist. Berj Manoushagian, Philosopher.

Why are abstractions crucial?

Because it’s an amazingly powerful tool. Even more powerful than mathematics itself.

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Let me back up a little bit. Forget mathematics. When was the last time you made pasta? You know how to make pasta, right? Boil water, add pasta, wait a little bit, then take out the pasta. If you’re feeling fancy, add some other stuff.

Already, you’re taking advantage of abstractions. How do you know how long to boil that pasta? Isn’t it conceivable that one noodle of pasta differs in some way from another noodle of pasta, even in the same box? But you avoid those questions by abstraction. You don’t worry about the specific noodles of pasta you have, but you treat it like this abstract collection of stuff that you only need to boil for, say, 10 minutes.

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As you go forward with your pasta making, you learn that there are yet other shapes. Maybe you boil those shapes differently, but you realise that they’re pretty interchangeable from a culinary point of view. In other words, if you have a recipe for bucatini all’amatriciana, and you have all the ingredients for the dish except you have spaghetti instead of bucatini, by the power of abstraction you can still make an excellent dish: spaghetti all’amatriciana.

It goes on: what if your all’amatriciana recipe calls for guanciale and you have none? You know that pancetta is pretty close, while tofu is not close at all. And on, and on. When you study cooking, you don’t even understand a recipe in terms of ingredients, you understand it in terms of roles. You identify the balance of sweet, salty, acid, fat, spiciness, umami, or other flavour categories. In other words, you understand a recipe abstractly. The abstract approach lets you identify solutions quickly.