Ask HN: Apart from programming, how have you used algebra in the real world? | Hacker News Reader

Ask HN: Apart from programming, how have you used algebra in the real world?

5 pointstagawa11 comments

My son's struggling a bit with algebra and asked the age-old question - "when will I use this?" He wasn't being sulky, just genuinely confused.

My instinct was to say programming but after that I was stuck. When he was learning percentages I used shopping offers and discounts as a concrete example of that being useful. What's a similar example for algebra?

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That's a difficult question to answer, like the question, "when will I use the ability to understand big words, read sophisticated prose, or follow complex logical arguments?" The answer depends on what kind of life you lead--a challenging one or a simple one.

I think ivan_ah has it right. You can't seriously work with numbers--any numbers--without algebra. Arithmetic isn't enough. One needs to know how to rearrange equations in order to validate or explore, e.g., a simple statistical claim that a politician or marketer makes. Or to repurpose an equation for another task. Any professional in any field should find themselves doing that on a regular basis, otherwise they're just echoing whatever they're told and not adding much value.

OTOH, you can get really far in this world by just echoing and passing on whatever you're told. So algebra isn't needed any more than taking an interest in social studies is needed to be able to vote or even become President. While algebra and social studies are prerequisites for being a good citizen, being a good citizen isn't a prerequisite for much of anything, though I'd like to think it still makes success in life more likely.

Very good point. That sounds similar to when I try to explain why it's good to try to exceed expectations. It's hard to give a convincing reason because the benefit is often indirect or intangible.

I'll look out for statistics on TV and see if I can incorporate the algebra-as-a-foundation concept.

I think of algebra as a meta-math skill since it allows you to manipulate, simplify, or otherwise make use of structure in mathematical expressions.

The most important rule is the "do the same operation on both sides of the equation"-rule, but there are plenty of other "math verbs" that are useful: expand, factor, simplify, collect, etc. Interestingly, any expression in the computer algebra system SymPy has these methods:

http://live.sympy.org/?evaluate=(x%2By)**2%0A%23--%0A((x%2By...).expand()%0A%23--%0A

Math verbs - that sounds like something that I could go through and clarify with him. Thanks.

If he's around 8-9-10 years old don't lie to him or make up phony reasons. He'll see right through it and lose all respect for you. Like the generations raised in the era of "everyone gets a sports trophy" BS. Now we have multiple generations of low self-esteem, bitter cynics.

Tell him the truth, you use it as a programmer but you don't know what he'll want to be when he grows up so he may never use it. Tell him the truth, that algebra is the base[1] of more advanced math like geometry or calculus and used by engineers and scientist and maybe someday he'll want to be an engineer or scientist. Tell him the truth that as hard as it seems now, if he needs it later (but doesn't know it) to become what he wants to be it will cripple his chances and limit his choices. Tell him the truth, you are the dad and in your judgment he should know algebra even if he doesn't use it because it is difficult but will make him a better thinker which has value in ANY endeavor he may choose.

[1] As an ex-teacher, it has been my experience that when students struggle in math at level Y they didn't really learn level X, the preceding level, in the previous semester or year. (Alternatively, they are just dumb). At a certain age kids learn that they can just fake it and learn the mechanics of mathematical manipulation of the symbols with virtually no understanding of the underlying concepts or relationships. This is the end of their mathematical training. After that it is training parrots or monkeys. So my advice is to check and review his earlier work. He might have faked understanding it or just plain forgotten it.

He's a bit older than that but your comment about the honesty still applies.

And interesting that you bring up the previous level of study. We made him do a lot of Khan Academy when he was a bit younger and he seemed to make good progress, but maybe he just got used to the format and worked out how he was expected to respond. I don't want to pressure him beyond his limits but that sounds like something we can look into. Thank you for the insights.

I am the main developer of the MathPiper computer algebra system. When students ask "when will I use algebra?" it is a symptom of a deeper problem, which is what they are being taught is not algebra. Almost no math teachers know how the "game" of algebra actually works, and therefore they are incapable of teaching others how to play it. What are they teaching that is being called algebra? That's a good question. What would the game be called that operated exactly like chess, except the rules for how the pieces are moved were never written down and never taught explicitly? Lets call it c_es_. One critical ability that is needed to be good at c_es_ that is not needed to be good at chess is figuring out how the pieces are moved by only observing how other people move them.

Most people don't like playing games they can't win because they have not been taught how to play. Most people would not like playing c_es_ for this reason, so they would only play it if they were forced to. They would also start asking questions like "why am I being forced to play this illogical game?". The way to help your son is not by providing him with reasons for why he is being forced to play a game he has not been properly taught how to play. The way to help him is to simply teach him how algebra actually works. I can show you how to do this (my contact information is in my profile).

Yes. I've used it in graphic design when calculating ratios especially. I've used it when converting time tables for payroll at a previous job. I've used it in carpentry. That gets into geometry, but it's still algebra.

I have difficulties to separate algebra from the rest of the math -- it is just one important data representation and a toolbox, when you work some math you refer to this toolbox repeatedly and almost involuntarily.

you mean active use or passive use? passively you use it every second of your life of course.

actively you use it when navigating with a map&compass (yes, i am that old)

Ah, of course - scales on maps! Thank you.

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