LolWolf

It's so wild to have a whole paper about this... that's also LLM written.

What are we even doing here?

what were your favorite projects?

The whole thing is unbelievable slop ! I think the whole article is llm-generated unfortunately (just reading the first paragraph I got an immediate smell).

ha, thank you! it's very fun to write these

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

yes, definitely some of it is (purposefully) fast and loose, though (ideally!) mostly unambiguous with reasonable assumptions

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!

Fair on all accounts! Surely, this could be made way more lively if I were in front of a blackboard waving my hands and drawing images, but alas, the medium is what it is :)

Thanks for reading though!

well, the statement is: is there a single operation, built from elementary operations, such that all _other_ elementary operations have finite representations.

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!

I think the point is that it is _finite_. if you allow infinite expressions then the basic monomial basis or quotients thereof are “even simpler”

I don't think this can do any of the "standard" constants or what we generally consider to be closed-form expressions, though ! (E.g., no e, pi, exp, log, etc.)

yeah it’s slop; multiple sites also confirm this, seems like they are using clawdbot or whatever

> True, but with such numbers you will normally not do anything else except computing an approximate value of them.

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.)

> few of the computable numbers that are not algebraic are interesting, the main exceptions being the numbers that are algebraic expressions containing "2*Pi" and/or "ln 2".

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.)

I don't want to put OP on blast here, but this is unfortunately just complete slop writing.

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.

Sweet thanks!

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!)

it is thoroughly _fine_ advice stated in a shitty way that misses the entire point of this cheap demo

ah very cool, I see!

good luck! are you posting updates anywhere?

sure ! I’ll give it a try a little later once I’m at a computer !

(you can too, if you’d like, the CAD files are all online as .step files :)

Ooh, great question. Usually fractions (~1/20th?) of a turn for alignment, it’s hard to go below that since the mounts are so small and the springs don’t have the tension to keep it super stable. (This is plenty for such a “coarse” set up like a Michaelson but might not be up to par for more delicate ones. This can be improved very easily but it was enough for this experiment!) If you want to observe something on the outputs, you have to do something like exhale on one of the arms or put a soldering iron near one of them—merely touching one of the screws gives you indiscernible output, even if the mirrors are aligned.

Very interesting re: JWT, I will definitely take a peek, thanks !

I think getting an electron source and creating a robust-ish adjustable set up is v doable, but is definitely more of a Real Project(TM) than this silly little interferometer :)

I think that’s very much right :)

I see, what’s the min step size you’re going for?

i’d probably just get it milled only if you had the CNC handy, the complexity isn’t enough to justify 3d printing it in metal (probably a decent bit more expensive too!)

but at “get it done in JLCCNC” prices I think a thorlabs mount is probably in your future :)

it’s an interferometer with like 5cm arms made for 3 bucks, it’s not made to be anything other than a basic demonstration !

ah I see!

Yes this is very cool (hope you make it open source :) but have you taken a peek at the openflexure project? They make a fully motorized 3-axis microscope that is 3d printed and relatively inexpensive (parts+motors+electronics - PLA net out to USD 250?)

it’s very cool! maybe you can also take some ideas from there :)

https://openflexure.org/

yes ! but it also assumes you have: a good optical breadboard + bench + dampeners, a beautiful set of lenses, all sorts of nice lasers and kinematic mounts and linear stages etc etc

so yes, we _also_ (back in my phd lab) built equipment in that sense, but there was a pretty good foundation of Fairly Fancy stuff already sitting around !

thank you!

and ha, that one requires a little more fancy equipment :)

oops! ran out of netlify credits. should be good now !

yeah, even breathing nearby this thing (or putting a soldering iron near the paths) will show a visible change!

yeah I cheated a little bit, but

> Ok, time to confess: I did cheat a little in calling it the “cheapest” Michelson interferometer, since technically even this beam splitter is like 16 USD, but it is very possible to use a microscope slide instead at the cost of some contrast, which will net out to < 20 cents, even at pretty expensive per-unit prices.

:)

Yes! Michelson interferometers are an amazing first lab experiment since it teaches you the basics of a bunch more techniques which are handy in more advanced experiments, while still having a satisfying outcome when done correctly (which is not as finicky as other experiments with less fun outcomes).