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Comment by epgui | Hacker News Reader

My argument is that the value of mathematics is not merely, or even principally, in whether it’s useful in everyday life (the first-order utility), but that it is in fact in how it helps you to think better (the higher-order utility).

The author, as decorated as he may be, seemingly fails to appreciate the latter: in his own words, he has a “very low opinion of this self-serving nonsense”. The exercise of fleshing out the argument against the higher-order value of mathematics, you will note, is left as an exercise to the reader.

This is by definition an anti-intellectualist position: defending such a position, which goes contrary to what should be the default position in general, should require a very high burden of proof, not an offhand dismissal.

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> The second argument is the one I always hear around the mathematics department: mathematics helps you to think clearly. I have a very low opinion of this self-serving nonsense. In sports there is the concept of the specificity of skills: if you want to improve your racquetball game, don’t practice squash! I believe the same holds true for intellectual skills. In any case, the case for transference of mathematical skills is unsettled.

Directly from the article.

So in other words, his case against the higher order of mathematics is:

- He doesn't have a high opinion of it

- He makes a vague allusion to some unspecified conflict of interest (?!)

- He argues that first-order skill development is most effective (which may be true, but misses the point).

- He says that higher order value of mathematics is "unsettled".

As he is defending a fundamentally anti-intellectual position, I'm going to need a little more than that.

You keep on assuming your conclusion and name calling and acting like you’ve made an argument.

I’m sure the author has a high opinion of mathematics as an intellectual pursuit. He is a Math professor. That’s separate from his argument, that it has very limited practical use, even to most engineers and others you would assume would be highly selected for finding it useful.

If Mathematics was enormously useful for teaching argument and precise thought in a reliable way Economics would have eaten all the other social sciences already. Economists know far more Math than the others. Math is uncommonly useful but if it was that good at teaching people how to think, if the transfer of learning argument was true, it would not need to be argued. It b would be bloody obvious.

Please point to me exactly where I did any name calling.

There's this thing called the burden of proof, in philosophy. When you take a difficult position, you must displace this burden. The author has not done so, and it is not my responsibility to show how he is wrong: he has not shown how he is correct.

> Please point to me exactly where I did any name calling.

Anti-intellectual. You keep on saying that the author is anti-intellectual for denigrating the practical value of Math.

Allow me to clarify: I do not mean to say that the author is an anti-intellectual person. I have read nothing else that he has written, and I do not know him.

What I am saying (or at least what I intend to say) is that he is defending an anti-intellectualist idea/position, which is just a fact by definition.

> What I am saying (or at least what I intend to say) is that he is defending an anti-intellectualist idea/position, which is just a fact by definition.

Saying something is of limited practical value is not an anti-intellectual position. I do not think most people get any practical value out of the chemistry or physics they learn in school.

> I do not think most people get any practical value out of the chemistry or physics they learn in school.

This is a good example of an anti-intellectual comment or attitude.

The transference of mathematical skill is only "unsettled" in the sense that it is unclear what would it would be transferred to. It is already an entire epistemological category. How much more transference is required?

“It is already an entire epistemological category.”

Very eloquent phrase, I’m going to steal this!

>that it is in fact in how it helps you to think better

And we do use that in everyday life. Learning higher maths doesn't help us solve problems we encounter all the time or everyday, at least not directly. But it helps us frame them and our thinking conceptually in a quantitative way, and maybe even sometimes in a qualitative one, which is incredibly helpful generally.

You’re just assuming your conclusion, that the thing you enjoy and value, intellectual stimulation, should be supported by default. Both of the people you’re dismissing are intellectuals. They’re just self aware enough that they don’t think their preferences should be enforced on others without a rash justification.

Lovers of physical exercise, the production of art or combat can sing the praises of their joys and the benefits according thereto. We don’t rearrange the world to force their interests on the world. If we’re going to do it for our interests we should have actual reasoning behind it, not hand waving.

I understand that the author is "an intellectual", but he is nonetheless defending a fundamentally anti-intellectualist idea.

This is not compatible with an inquisitive, academic or intellectual mindset, no matter that he is a professor or that he holds a PhD. He's free to advance arguments in support of this position, but he should be met with extreme skepticism, as he is defending a difficult position.

> This is not compatible with an inquisitive, academic or intellectual mindset

The world has millions of things to learn about. Why is Math specially subsidized? That’s good argument. That’s not anti-intellectual.

> He's free to advance arguments in support of this position, but he should be met with extreme skepticism, as he is defending a difficult position.

Again, you’re just assuming[edited] your conclusion. You and I and he are people who like ideas and arguing over ideas. He’s arguing that what he teaches isn’t that useful and asking why it gets so many resources. There’s nothing there about the beauty or joy of Math, which I presume he could wax rhapsodic about as a professor. You’re attacking a position that doesn’t appear in article. It’s about the practical value of advanced Math.

> Why is Math specially subsidized? That’s good argument.

First, that's a question, not an argument.

Second, math is special because it's an exact science, as opposed to a natural science. Encompassing the study of "logic", "information", "things that change", "symmetry", "equality" or equivalence... it applies to pretty much everything. In other words it's one of the skills that has the most potential to be widely applicable.

> Again, you’re just aiming your conclusion.

I'm not sure what you mean by "aiming", but I am referring to the burden of proof [1], which the author has not shifted one iota.

[1] https://en.wikipedia.org/wiki/Burden_of_proof_(philosophy)

The author addresses the claim about “thinking better” in TFA.

No, he really doesn't. His argument against the higher-order value of mathematics is focused on first-order matters, and a vague allusion to an unspecified conflict of interest (?!). This essentially amounts to no more than "brushing off the argument".

Caplan is fantastic at identifying mathurbation in academic navel gazing. His (and the cited author's) opinions are well informed, even if not universal. In economics the concept is called a separating equolibrium

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