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Comment by vincent-toups | Hacker News Reader

My view is that everyone should study calculus more or less for the same reason we almost all study Shakespeare or The Bill of Rights or whatever. Its an enormous human accomplishment whose cultural impact virtually cannot be overstated and a basic understanding of these sorts of things is the birthright of every human being alive.

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Sure, but calculus is even less tangible than Shakespeare and the Bill of Rights. Good luck getting the folks who don’t care or struggled through algebra to stay engaged.

Scratching my head...that just isn't true. For example go throw a rock into the sky and watch its path. Calculus. Very tangible.

I'm curious how you envision a calculus class that would make the topic more tangible. I think we can agree that typical calculus classes are more abstract (for lack of a better term) than typical english, history, or science classes.

Physics and calculus should be taught as a single class, it's a mistake when they are separated.

I'm a physicist and it happens to be the case for me that I didn't really _get_ math until I understood I could do physics with it. So you'd think I'd agree.

But after I was sensitized to it by physics, I've come to see pure mathematics as just as interesting and worthy of being taught standalone. In fact, one does mathematics an enormous disservice by suggesting that its tightly coupled with physics. Roger Penrose himself points this out in The Road to Reality: mathematics is actually substantially larger than that part of it which we require for physics. That fact alone is fascinating.

The pitch I'd give for pure mathematics is that its really the study of precisely what we all do on a daily basis when we "reason" about things. Our daily experience suggests reasoning is useful and in many ways concrete, but a detailed study of the process almost immediately produces challenges and paradoxes and great landscapes of mystery.

I agree that mathematics is much bigger than applied mathematics. However, for precisely this reason, pure mathematics, like philosophy, isn't for everyone.

The main argument for teaching it this way is a pedagogical one. If it took physics to prompt the geniuses of the day to discover calculus, then following in their footsteps is probably the easiest way for us to get there as well.

I think philosophy is much more for everyone than physics or mathematics. I can't conceive of a model of the human condition which I would want to adhere to that said philosophy wasn't for everyone.

We _all_ think about value and about the relationship between what we think and what happens in the world and these are the fundamental elements of philosophy. If people feel that philosophy isn't for them, its a failure of the teachers rather than the people.

Its my opinion, anyway, that children don't always know or appreciate what they ought to learn and that adults do them a disservice when they fail to teach them that which is not immediately interesting just because they don't want to learn it.

Some amount of practical philosophy or received wisdom is necessary for everyone, just like some amount of mathematical awareness. The formal study of philosophy as a discipline, like that of pure mathematics, is not for everyone. For most people it would be deeply unpleasant for almost no benefit.

I'm not 100% sure if I agree with this or not, but a related idea is that physics shouldn't be taught without the necessary math as a pre- or co-requisite. I'm thinking particularly of non-calc-based mechanics classes, which I loathe.

Another definition of tangible is "clear and definite; real". In that sense, abstract mathematical concepts are certainly less tangible than those other two examples.

Throwing a rock into the sky isn't "doing calculus", in the same way that the first caveman to throw a rock didn't "discover calculus".

> Its an enormous human accomplishment whose cultural impact virtually cannot be overstated

That's just your opinion. I think Shakespeare is trash. I don't think most people can even comprehend the Bill of Rights.

We should replace Shakespeare with Super Mario. Outside of socialite circles, literally no one cares about Shakespeare. How many kids you see walking around in Shakespeare T-shirts or reading Shakespeare on the school bus? Those kids are into Super Mario, and so are many adults. Super Mario is the embodiment of art, international relations, technology and engineering of the sum-total of humanity at the time. Shakespeare is just some words.

I'm rolling my eyes so hard they could fall out of my head. You can only form an opinion about Shakespeare (or Mario (though the kids are into Fortnight these days, they tell me)) if you are exposed to them. Both things have enormous cultural importance and are part of the human experience and all people deserve to be able to engage critically in culture.

Shakespeare very well could be trash. The Bill of Rights is by and large a shockingly hypocritical document. But both are part of our history, along with a lot of other stuff about which we could say all sorts of things visa vi what ought to be in a curriculum. But my point is that humans deserve to know their history and their culture and that takes resources and time and energy which are, in the final analysis, justified by the inherent dignity and rights of people.

> But both are part of our history

Shakespeare is not part of my history, I'm not English, nor am I anglo-american. Shakespeare was never important, only popular, but that's easily confused in the US. Just one of the first generations of celebrity-worship culture.

> humans deserve to know their history and their culture

People get culture from family and society, not from government run schools.

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