Exactly, the whole point is that she wasn’t a loser at all. It was about self-perception.

How could I forget about eigenvalues?

Abstract reasoning is the most “useful” intellectual ability you can have. However, the most important would be the normative insights we usually call “wisdom” (which isn’t taught but learned — for instance by reading literature and living life with curiosity). Critical thinking and other philosophy goes without saying.

You know people who use the unit circle on a regular basis? How about conic sections or the quadratic formula? These topics take months if not years to learn in school. We do so not because they’re useful in any practical sense for most people, but because they instill intuitions about how the world works.

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Most professions don’t require mathematics, and we’ve automated so much of it anyway.

Abstract versus applied math. It looks different. More like studying numberless patterns and proof methods.

Sure. And for the 90% of kids who correctly say they won’t use math, it doesn’t matter. We are doing math so they can learn to navigate formal systems of reasoning. We could honestly teach deductive logic instead, or set theory, or group theory, or finite field topology. It doesn’t have to be algebra or anything remotely practical.

Additionally, we don’t encourage kids to read books so they can become better at communicating. We push them to read so that they can have something worth communicating. You need words, concepts, and experiences, not just the ability to form empty sentences.

Yep. We don’t teach kids math so they can learn to do math. We do it so they can develop an intuition for abstract reasoning.

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I replied to the wrong person. Sorry

Math exists in the minds of humans, [not animals].

This is incorrect. Every animal we’ve ever researched, including insects like bees, can do arithmetic.

Anyway, not a single one of the examples you’ve given involves second-order reasoning. These are all prosaic interactions with the environment, which is how most animas (yes, including dumb humans) experience the world.

First-order reasoning: “What is moral?” Second-order reasoning: “Do moral beliefs constitute knowledge claims?”

First-order reasoning: “One plus one is two.” Second-order reasoning: “number theory is either inconsistent or incomplete.”

First-order reasoning: “What does this word mean?” Second-order reasoning: “How do words connect with their meanings?”

The examples I gave you are extreme, but to be fair so is your confusion.

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Elephants are wise in that they’re concerned with (some of) the things that matter most — social bonds and creature comforts. But, as far as we know, they can’t scrutinize these concerns in abstraction, or reflect on the nature of wisdom or the metanormative conditions of their own experience.

We can do that — due to some freak accident of evolution that probably has to do with the recursivity of language and the self-referential nature of subjective experience. And again, when I say “we,” I mean some humans sometimes. Many “wise” humans are just like the elephants.

I don’t want to conflate the pragmatic use of tools or manipulation of the environment with questions about the meaning of life. Even most humans can’t do the latter. We have a lot of depressing research showing that most people can barely engage in abstract reasoning at all, let alone effectively.

I think nearly every sentient creature can be depressed and understand how badly life is going. But that’s different.

The information that aliens created us for some particular purpose is empirically interesting but normatively insignificant.

It’s not that cats can’t ask questions. It’s that they can’t ask abstract questions. That’s quite different.

if you wake up in a compound, catered to your every need by weird alien captors, “why am I here?” is a pretty obvious question.