Comments URL: https://news.ycombinator.com/item?id=48496156

Points: 34

# Comments: 94

Comments URL: https://news.ycombinator.com/item?id=48210535

Points: 1

# Comments: 0

Comments URL: https://news.ycombinator.com/item?id=48023047

Points: 1

# Comments: 0

hopefully you also enjoy the next one which imo makes a fun connection between the linear algebraic CRT and the fourier transform :)

I think that part should've been "vector subspaces" rather than vector spaces since that is how U and W are defined in the paragraph prior.

I'll add this as a note, thanks!

Thanks for reading though!

Comments URL: https://news.ycombinator.com/item?id=47975166

Points: 62

# Comments: 7

this preprint answers that in the affirmative

otoh, (x, y) -> 1/(x-y) does not answer this question at all. you can argue that the preprint does so "via the infinite series in an operation" (which I have no idea what that means; surely if exp(x) qualifies then so must 1/(x-y) if we pick a monomial basis?) but ¯\_(ツ)_/¯

now, do I think that this is groundbreaking magical research (as I'm currently seeing on twitter) no... But it's neat!

Comments URL: https://news.ycombinator.com/item?id=47443805

Points: 3

# Comments: 0

Comments URL: https://news.ycombinator.com/item?id=47128861

Points: 2

# Comments: 0

That's what I think people do with other numbers like "pi" at the end of the day, no? :)

> That is what I meant by "interesting", i.e. the necessity of using symbols of such numbers, obviously for use in symbolic computations, since in numeric computations you would never use the actual numbers, but only some approximations of them.

It's very much an encoding problem, I think. Though we probably, on aggregate, use "unnamed computable numbers" implicitly on the order of as much as we use "named computable numbers" the former just has way more of a "tail" of uses where the "encoding of the symbol" is, e.g., "here's the PDE you use to compute this number"!

(It gets a little weird since we're kind of not distinguishing between the approximation that can be used to construct said numbers to arbitrary precision vs the specific program instance that constructs one specific approximation, but the idea is mostly there.)

I don’t think this is true at all. For example: the solution to a generic PDE that has no closed form solution at some point of import is likely transcendental, not algebraic, but definitely computable. (Think, say, Navier-Stokes being used for weather predictions in some specific place.)

The points being made are fine, I think, but look, if it's faster for you to generate than it is for us to read, I think this qualifies as denial-of-service-lite.

Comments URL: https://news.ycombinator.com/item?id=46638813

Points: 2

# Comments: 0

Yes definitely a great extension would be to add a camera in the image plane (alternatively, defocusing the image slightly and using a photodiode would also be fun!)