Note that the word "coordinate" used here feels a bit disingenuous to me, because that's how one might refer to the nth property defining a mathematical object or another.

For example: The third coordinate of the rational number 1/2 is a bijection.

Coordinate here actually means: third property in the definition of a rational number in Lean. Here, this property is the statement that the denominator 2 is not zero. This is not so absurd, if we define a rational number as a tuple consisting of a natural number for the numerator (property 1) and an integer for the denominator (property 2), with the added restrictions that the denominator is not the integer zero (property 3), and that the numerator and denominator are in least terms (property 4).

But the part where the proof that the denominator is nonzero can be viewed as a bijective function, is to me indeed type-theoretic weirdness. If I'm not wrong, it's just the proof viewed as a zero-argument function. (proofs for theorems that begin with e.g. forall are functions that take arguments).

Lean defines a != b as a = b => False, so it seems that we have a function from proofs of a = b to proofs of False. I guess this being bijective means that there are no proofs of a = b, since there are no proofs of False, which is an equivalent way of looking at a != b.

Thanks, this is a very good analogy.

Do you have an academic source that describes this difference in pronunciation in native speakers in normal usage?

So why would 3D printer companies in China bother innovating rather than sit back and cash the government check?

Because there are over 200 competing 3d printing companies in China.

Because the owners want to get rich, not live as pensioners.

Why does anyone innovate? When I sell something I don't care if the dollars come from the end user or the subsidy, I just want more of them.

Because China is actually a capitalist free market economy not a communist one.

Chinese companies compete with eachother ferociously. And Chinese society itself is dog eat dog. Everyone wants to make money.

Well, save for the part where the government directs the parts of the economy they care about.

Maybe literature is just a terrible medium for culture except for the relatively brief period in human history when they were extraordinarily cheap to produce and disseminate compared to other cultural products.

Edit: but insofar as media criticism in education is bound to the book rather than the dominant forms of the day, I think children are being done a disservice.

It's still by far the best medium that requires you to be active and imaginative while packing the best information density and usability. Plus it works offline, without power, you can carry it around, &c.

Books forge you in a way short "content" we consume all day long today will never be able to, there are a few long form podcasts here and there that could be comparable but that's not the bulk of the media kids "consume"

It is still extraordinary cheap to produce and disseminate novels. If not more so, if you include ebooks or longform blogging.

I really need to caution against looking too deep into taking these generalized words literally and deriving some insight from them that does not have independent evidence for the insight. "great" literally means big and is related to "gross", "perfect" literally means "completed", "passion" literally means "suffering", but people who use such words these days don't even have such imagery in mind at the point that they utter these words in everyday use.

This is just a puff piece for an AI startup

You can radiate the excess energy away on the non-sun facing part on Earth almost just as well..., though corrosion is an issue.

"just as well"?

I man you totally can radiate excess heat energy on earth, but your comment implies that the parents idea of radiating off excess "energy", specifically HEAT energy in space is possible, which it isn't.

You can radiate excess energy for sure, but you'd first have to convert it away from heat energy into light or radio waves or similar.

I don't think we even have that tech at this point in time, and neither do we have any concepts how this could be done in theory.

>specifically HEAT energy in space is possible, which it isn't.

https://en.wikipedia.org/wiki/Black-body_radiation

I see, yes. I was thinking more along the lines of radiating heat energy at a scale that's useable for cooling, not at the more extreme levels of over 500°C/1k fahrenheit

That's technically correct I guess, at some temperature threshold it becomes possible to bleed some fractions of energy while the material is exceedingly hot.

Yeah, my comment was intended to be mildly sarcastic in that the proposed heat transmission mechanism already happens on Earth and is yet so dramatically insignificant at usual temperatures that we struggle all the time with managing heat transfer through other means.

Don't you still have close friends to lean on when the going gets tough, and your friends, you?

I'm pretty certain that children are quite perceptive, and will sense an unease that something is not quite right at home. It would be a service to them to put something concrete to that unease.