r0uv3n

Grad students do not solve problems such as the existence of non-sofic groups every day.

"Win32 is the only stable ABI on Linux" - https://blog.hiler.eu/win32-the-only-stable-abi/

This is not about preventing crawling entirely, it's about finding a way to prevent crawlers from repeatedly everything way too frequently just because crawling is just very cheap. Of course it will always be worth it to crawl the Linux Kernel mailing list, but maybe with a high enough cost per crawl the crawlers will learn to be fine with only crawling it once per hour for example

Eh, the social features of Komoot were never intrusive to me, and among social features of most apps they were some of the most well designed. Local community, very much focused on actually sharing tracks and trying out other people's routes (and maybe commenting with your experience afterwards).

There was a guy in his 60s regularly doing very nice circular hiking routes of 40 to 60 km in our nearby forests, and apart from that just being kind of awesome and impressive to see when you look at local routes, actually walking his routes was often a very nice experience with diverse landscapes often along nice small, less used paths. It was great seeing nice weather in the morning, and then oftentimes without any pre-planning just walk or bike to the forest and just start along one of this guy's routes within a few minutes, all in an incredibly hassle free manner and with a result which pretty much always beat out just following the official hiking trails shown on signs etc. I don't know if there's another app right now where you can so easily profit from the experience and knowledge of your local community.

Well, Komoot worked quite well for exactly that use case. I have also only very rarely found tools even in the desktop space that were quite as mature as Komoot for that use case.

Also the question remains, what do you navigate the planned routes / gpx traces? What happens if you notice you want to improvise and replan to hit some target on the way you saw in the distance while on the trail? This was (and currently still is) absolutely trivial and intuitive to do on Komoot. The best alternative I can think of is maybe brouter+ osmand, but that's really quite clunky in comparison with Komoot (similar to the experience you probably mean when talking about pulling your hair out)

That is about something entirely different. It more or less just says that energy might be lost if you have a flux towards infinity. It does not in any way claim e.g. that the divergence of the stress energy tensor is non-zero (which would be how I think most people would interpret energy/momentum conservation).

Eh, space inside or outside the horizon is only different in so far as to whether it can reach our timelike infinity. Locally you cannot even tell where any horizon might be (just look at a small patch of a Penrose diagram near a horizon), they are very much something related to global properties of the spacetime. In particular it's not problematic to talk about some extended volume in spacetime occupied by mass, as long as the divergence of the stress energy tensor is 0.

The point where our notions of geometry would break down would be near the singularity, not near the horizon, and we don't even know if a volume enclosed by a horizon (i.e. anything you might call a black hole) necessarily has a singularity inside, it's just that our simple mathematical models all assume one.

I think this is enough of a classic to be widely known even among younger people. I'm 23 (doing math msc) and I think all the CS people that I know would instantly recognize the 500 miles title.

Though I do somewhat envy the possibility of having read the article close to publication and feel in some sense part of the history when it crops up again like this.

2 for example is not in the sequence. Remember that you need the first differences to this sequence to obtain all natural numbers

Have you tried Plasma 6 yet? To me it feels way more modern than Gnome.

If you couple your system to a heat path that is at rest wrt a specific Lorentz frame, you of course lose Lorentz incariance. On the other hand the lagrangian of the standard model itself is to my knowledge fully Lorentz invariant.

Arguably Bayta is the lead in The Mule maybe? But of course the basic plot was very much influenced by Campbell still

AFAIU Firefox Sync is end to end encrypted, right? I interpreted the language here to mean that the data might be sent to Firefox outside of Firefox Sync. Have there been any changes to Firefox Sync that we know about?

This is a fantastic resource, and I used it heavily in 2018 before starting my BSc in Math while still in school to learn the stuff that interested me a bit in advance (and to some extent as a familiar reference for a few years afterwards).

I can only recommend this as a good starting point for anyone without the time for a full scale education, or in preparation for such, especially if you have some experience with math olympiads (as mentioned also in the introduction).

I only wished I had spent some more time with stuff like category theory before starting my studies, and had had the guts to take more advanced courses directly in my first semester.

With just a bit of prep from these notes I'm pretty convinced that it's possible to directly take e.g. Algebraic Topology, Differential Geometry, Category Theory, or Algebra during the first semester (don't know about number or measure theory, or anything requiring lots of functional analysis, have not engaged enough with those topics to know how good these notes would be as prep).

The dot product exists in any dimension

In some sense I think it does have quite a bit to do with (speculative) social science, especially once you see (spoilers) that there really is nothing supernatural going on at all.

It is specifically for websites offering help escaping domestic abuse or similar stuff:

> When to use this component > > Use the component on pages with sensitive information that could: > - put someone at risk of abuse or retaliation > - reveal someone’s plans to avoid or escape from harm > > For example, when a potential victim is using a service to help them leave a domestic abuser.

https://design-system.service.gov.uk/components/exit-this-pa...

IMO this seems quite well designed.

I do agree that the roundabout pictured in the article does not seem to include any considerations towards non car traffic, but at least in Germany the vast majority of roundabouts have seperate bicycle lanes and zebra crossings on all entrances, meaning foot and bicycle traffic has right of way. As a pedestrian I vastly prefer these to intersections in nearly every situation.

I guess you can just add some edges extra vertices and edges and give all the extra edges probability 1 of being deleted.

Love this idea for a wedding, a really unique effort that would seem like total magic to me when attending.

I also enjoyed the very clear explanations and seeing more or less the full process during the video.

Is the tooling for reverse engineering / patching Android apps similarly nice? Does someone know of good resources to learn to be able to do something similar for Android apps?

> ℤ ⊂ ℝ That is not at all obvious without some canonical isomorphism acting on ℤ, or at least is a behaviour strictly dependent on your particular set theoretic construction of the reals.

E.g. for the cauchy sequence construction of the reals, the image of the integer 1 under this canonical isomorphism would be the equivalence class of the sequence (1,0,0,0,...), but these are of course not the same object in a set theoretic sense.

What do you mean with reflection across the bottom/top of the curve?

With combination you presumably mean taking (polynomial+reflected polynomial)/2?

> physics has no formulation of spacetime in discrete terms

There are some attempts of working with discrete spacetime (e.g. causal set theory), but yeah, all our best descriptions so far very much assume smooth spacetime.

No, classical general relativity is entirely time symmetric: time symmetry means here that if you have a solution for the equations that describe nature, then you still have a solution after you make the coordinate transformation t -> -t. This follows directly from the fact that the Einstein field equations involve only tensors and are thus diffeomorphism invariant.

For the case of a black hole, the solution you get by reversing time describes a white hole., which is again an entirely valid solution to the Einstein field equations.

Note that the title of this post is just a personal opinion of Kerr. But he did show, as mentioned in the article, that the typical argument for the necessity of singularities within horizons (or more generally trapped surfaces) was faulty. Note that this is not about any Quantum Gravity stuff, these arguments concern what happens in pure general relativity.

Also, since this is not explained in the article (and mostly assumed as prerequisite knowledge in the paper by Kerr), some words on the difference between affine and geodesic length:

In general relativity, we consider so called geodesics: These are paths observers would take while moving only under the influence of the curvature of spacetime / under the influence of gravity, i.e. without any other forces acting on them.

There exist different kinds of geodesics depending on their speed: We distinguish between

- space-like geodesics (not relevant for this discussion),

- time-like geodesics (speed of geodesic is less than speed of light c), which are the paths all observers with mass will take and

- null geodesics (speed of geodesic = c), which are exactly the possible paths for light rays to take.

For all of these we can define the geodesic length. With the right sign conventions, this is equal to the length as measured in proper time, i.e. the amount of time that will pass for observers moving along the geodesic as they themselves will measure on clocks they bring with them. But importantly, for null geodesics this geodesic length is 0: For observers moving at the speed of light, no time passes! So in this sense, all light rays have the same length.

But there is a more general notion: Affine length. This affine length in general is not very well defined (it depends on an extra choice, the affine parametrization ([1]), that you have to make for each geodesic), but when considering a geodesic it is either finite for all of these parametrizations or infinite for all of them. Thus the concept of finite affine length makes sense to talk about, and this is defined for all three kinds of geodesics. Note also that a time-like geodesic has finite affine length if and only if it has finite geodesic length.

Now back to the question considered in the article: I'm pretty sure that if we knew that there existed time-like maximal geodesics (i.e. geodesics that you can't continue any further) with finite geodesic length, i.e. finite proper time passing along them, then they would necessarily end in some kind of singularity. So the question becomes: If you have a black hole (of which we can - from the outside - observe the existence of some kind of horizon boundary), then do there necessarily exist time-like geodesics of finite length inside it?

AFAIK we don't know the answer to this. But there is a slightly related result: We know that for any horizon boundary, there exist light rays of finite affine length (also denoted FALLs, which I think stands for finite affine length light rays) within it. This feels very similar to the result we wanted for time-like geodesics, but what Kerr's paper shows is that the intuitive belief that these FALLs must necessarily end in a singularity is wrong. There exist null geodesics inside one solution for the inside of a horizon boundary (the Kerr metric), that at both ends asymptotically approach a horizon boundary tangentially (never intersecting these horizon boundaries), but which have in total a finite affine length. In particular these geodesics don't intersect or end in singularities.

[1]: For time-like geodesics, we normally parametrize them by proper time, i.e. we distinguish the points along the path by the proper time that has passed since some starting time. We can describe the geodesics in this parametrization using the geodesic equation plus the additional condition that we normalize the four-velocity (you don't need to understand what this last condition means, just note that this is not necessarily a part of the geodesic equation). Affine parametrizations are a slight generalization of this, where we drop the condition on the four-velocity, i.e. we consider any solutions to the geodesic equation. We thus label the points on our curve by some more general number, called e.g. a, which does not necessarily have to be the same as the proper time, but which does increase as we move along the path.

For time-like observers, the geodesic equation ensures that this affine parameter a will just be some scaled and shifted version of the proper time, i.e. one can imagine going along the path with a clock that is going too fast or too slow (the constant shift doesn't really matter). As an equation we have

    a = lambda * tau + C, 

where tau is the proper time and lambda≠0 and C are some constants. In particular if we measure the length of the path with respect to the affine parameter `a`, we will just get `lambda` times the geodesic length of the path (the length as measured with respect to the proper time `tau`).

For null geodesics the proper time is not an affine parameter, but still any two affine parameters a and a' will be related by some scaling and constant shift, i.e.

    a = lambda * a + C. 

In particular if we consider the length of the path as measured with respect to an affine parameters (by just considering a at the endpoint minus a at the starting point of our geodesic), the lengths will either be finite for all affine parametrizations or infinite for all of them.

Also discussed two days ago here: https://news.ycombinator.com/item?id=38476206 (2 comments)

My bachelor's thesis was on the harmonic level set method of Stern and Co and had a lot of fun with it, so this was a great read. I'll have to look at the paper.

In general it still feels like there's a lot more to learn about this method (the article mentions the possibility of applications outside the asymptomatically flat case, for more see also section 9 of the survey article [1] of Bray and Co).

[1]: https://arxiv.org/abs/2102.11421