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Comment by adastra22 | Hacker News Reader

No, I don’t care. Until there is a real, practical result, I don’t care. There are plenty of examples of math discovered in service of solving a problem. There is nothing that says math has to be purely abstract first.

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Dudeee how far up your hind do you need to be to nit even appreciate the groundwork being laid out?

Like imagine Einstein without access to geometry work. You had others point you to number theory. What about Boole's algebra.

There is a pretty big list of seemingly useless pure math things suddenly finding a very practical use. Sometimes quite a bit later too. And we have no way of knowing beforehand.

And it's fine to not want to do such work yourself. But to dismiss it is, well, not very thoughtful.

Imagine Newton without access to calculus. Poincaré and the three-body problem without topology. Gibbs and Heaviside without vector calculus. Or Fourier without, well, Fourier analysis.

The lack of mathematical tools posed no special challenge for any of them. They invented the math they needed to do their work.

You are presenting a false alternative history, where they would not be capable of making great insights without the math coming first. But the causality is often the other way around.

Because clearly we’d have invented GPS if we had asked ourselves “how do I create a global positioning system with centimeter accuracy”?

That is how we invented GPS...

And without relativity theory positioning error would be measured in kilometers.

I've always wondered - if special and general relativity weren't known, could the GPS engineers have just measured the error and empirically accounted for it? I don't know relativity or GPS or engineering well enough to answer.

It's possible, but it seems more likely that the first tests would have shown "weird timing errors we couldnt diagnose" and then the project never got a follow up.

For something so militarily useful? When the Soviet Union was still seen as a threat to the US? When it was already so expensive anyway? I guess it's possible, but it's hard to believe they'd just give up like that.

The problem with "it's hard to believe" is that this is an area where I'm not even sure how to effectively estimate the counterposition, I've seen things that I thought were interesting get cancelled or have no follow up all the time, and it makes sense, no idea if it will matter, or even work, and even if it does, how much will it cost to realise any value?

Who knows how often really impactful tech is gated behind some non-obvious thing which we never follow up on.

I mean Douglas Engelbart basically bet his entire career behind the Mother of All Demos[0], if it had flopped, modern computing as we know it would be fundamentally different, same with Hiroo Kinoshita and Extreme Ultraviolet Lithography[1][2], we just would have had Moore's law falling off a cliff.

-[0]: [The Mother of All Demos, presented by Douglas Engelbart (1968)](https://www.youtube.com/watch?v=yJDv-zdhzMY)

-[1]: https://spie.org/news/photonics-focus/mayjune-2023/developin...

-[2]: [The Closest Thing We Have to Alien Technology by Veritasium](https://www.youtube.com/watch?v=MiUHjLxm3V0)

Yeah, absolutely. You'd be surprised how much high-precision engineering absolutely relies on "this but you have to mill a tiny amount off the end because if you do the maths it comes out ever so slightly too big, and then adjust on test".

Yes, the clock slippage is a constant factor, entirely predictable. If made public it would probably have catalyzed the discovery of special relativity soon afterwards, but then people would’ve been super confused because its predictions still wouldn’t match the observations and indeed would widen the discrepancy rather than narrowing it!

A modern-time retrograde of Mercury.

Of course, the good-old-fashioned retrograde of Mercury would still be a real puzzler in that timeline, too.

Relativity is required to explain the time dilation, but it's not needed to notice that the GPS clocks run 40µs too fast. It wouldn't take too long for them to measure enough data to create an empirical skew-versus-altitude table, which should then be enough for them to correct the time skew, even without understanding what was going on.

I think this is a difficult counterfactual to assess, we didn’t develop clock accurate enough to notice the time dilation until 50 plus years after the theory of relativity was published.

Still, how long would it take someone to work it out empirically enough to have confidence that there wasn’t just some bug somewhere? Maybe they would mothball the GPS project for not working before figuring it out? It’s hard to know, 50 years in an alternate timeline allows for a lot of domino effect

> Still, how long would it take someone to work it out empirically enough to have confidence that there wasn’t just some bug somewhere?

They probably would just assume that it's a bug at first, since "our clock is slightly broken" is far more likely than "we've discovered some cool new physics". But I don't think that that would be an issue here, since even if they thought it was a bug, they'd still try to work around it.

> Maybe they would mothball the GPS project for not working before figuring it out?

I doubt it, since if you think about all the possible issues after sending a complex untested satellite to space, a 40μs clock discrepancy is fairly minor.

doesn't it use special relativity or some modern physics?

If only we could figure out how to get rid of the pesky ionosphere....

... at least in a way less intrusive than https://www.sciencedirect.com/science/article/pii/0021916964...

You can't imagine how that severely limits the potential size of the discovery space shackling it to present day problems?

I think the poster is distinguishing between currently practical and ever practical. Galactic algorithms can never be realized.

The constants can be made lower. If we didn't know about the galactic algorithm beforehand, we couldn't begin to do that.

And that's fine, caring about everything is exhausting, someone has to solve real world problem. But dismissing a result since it's not practical is not fine

Why not.

Not everyone needs to care about everything and there is reason to say that a result like this one from openai is quite sterile and possibly damaging to the socio-cultural dynamic of the field.

Ironic username as I doubt we'd get to the stars with your philosophy.

And I don't care about your opinion. Checkmate: two conflicting, essentially valueless, opinions.

How far are you willing to go? In your radical pragmatism, are you an intuitionist, or even a finitist? Oh wait, these are pure math topics that you do not care a about!

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