hah the model should get extra credit for discovering this!
> Now I understand the situation perfectly! The issue described in the problem statement is a real bug that was already identified and fixed in later versions of pytest. Since we're working with pytest 5.2.4, we need to apply the same fix.
> The Gemini embedding model, gemini-embedding-001, is trained using the Matryoshka Representation Learning (MRL) technique which teaches a model to learn high-dimensional embeddings that have initial segments (or prefixes) which are also useful, simpler versions of the same data. Use the output_dimensionality parameter to control the size of the output embedding vector. Selecting a smaller output dimensionality can save storage space and increase computational efficiency for downstream applications, while sacrificing little in terms of quality. By default, it outputs a 3072-dimensional embedding, but you can truncate it to a smaller size without losing quality to save storage space. We recommend using 768, 1536, or 3072 output dimensions. [0]
looks like even the 256-dim embeddings perform really well.
> Both of our new embedding models were trained with a technique that allows developers to trade-off performance and cost of using embeddings. Specifically, developers can shorten embeddings (i.e. remove some numbers from the end of the sequence) without the embedding losing its concept-representing properties by passing in the dimensions API parameter. For example, on the MTEB benchmark, a text-embedding-3-large embedding can be shortened to a size of 256 while still outperforming an unshortened text-embedding-ada-002 embedding with a size of 1536.
It's a practical feature. Scaling is irrelevant in this context because it scales to the length of the embedding, although in batches of k-length embeddings.
One of the extremely stupid reasons kagi needs to develop a browser is because ios safari prevents setting kagi as the default search engine, so they have to do some terrible hacks to get it to kind of work.
I really hate that you can't set the default search engine easily like in other browsers, or that you can at least easily submit your company to be included in the defaults.
But with the Kagi extension all my searches are always redirected to Kagi on both Safari on iOS and Safari on macOS so I don't really see this as a real blocker as a user.
I understand that this is an onboarding problem, but for a technical user that's really not something preventing me from using Kagi (Like the other comment mentions).
That and Apple anti-competitively preventing non-Safari browsers from using Safari extensions, despite all iOS browsers being essentially Safari under the hood.
I don't remember the last time I used Safari on iOS, but once I started using Kagi, I was naturally drawn to Orion and that's been the best browser experienced I ever had on mobile.
The included ad-blocker being a big factor in the great UX.
That seems wild to me, but admittedly I don't search from the address bar at all. Is setting your preferred search engine as your homepage and opening a new tab to search really such a huge burden?
Yes. I do not tend to launch new tabs. I almost always use a single tab for browsing. Only when I need to keep something around then I launch a new tab to preserve the old one.
That means the address bar is my main interaction with the browser.
I think today's answer is actually incorrect. Or at least the reference animation has a hitch where it shows all red for frames 12 and 13. if it shows 2 purples for frame 13 then the animation is smoother and actually the math is much simpler.
Not a physicist, but the more accurate “intuitive” explanation I read is that an accelerating observer sees thermal radiation in a vacuum. This is called the Unruh effect [0]. And since a black hole requires an accelerated observer to not be pulled in you will always have thermal radiation coming from the black hole UNLESS you are free falling into it. Physicists please correct me where I’m wrong!
Note that this is proper acceleration which is measurable locally with e.g. a weighted spring, contact with a piezoelectric scale, or any other sort of accelerometer apparatus.
> a black hole reuires an accelerated observer to not be pulled in
There are an infinite number of free-fall trajectories outside a black hole, most of which never go near the black hole in the first place. There are also infinite numbers of hyperbolic orbits which "graze" a black hole and an infinity of various elliptical and (quasi-)circular orbits.
An accelerometer on one of these trajectories will report zero proper acceleration. Yet none of these trajectories cross the horizon from the outside.
There are additionally free-fall trajectories which cross the black hole horizon from the outside. Who knows what happens not long after that: flat-space physics like the Standard Model of Particle Physics curved spacetime physics like General Relativity give conflicting answers.
Finally there are also an infinity of trajectories which are somewhere properly accelerated. Most of these won't cross the horizon, but some can: one can turn on one's rocket engines and carefully steer a course that crosses the horizon.
(There are multiple types of horizon; the interesting one is the apparent horizon which can be measured locally with various types of apparatus. An event horizon -- if there is one -- can only be determined with reference to the entire global spacetime and all its contents from infinite past to infinite future. There's a variety of other horizons too. Visser catalogued some of them in <https://journals.aps.org/prd/abstract/10.1103/PhysRevD.90.12...>).
Note that trajectories in my paragraphs above correspond to everywhere non-spacelike curves of all sorts. Free-falling trajectories are geodesics (timelike or lightlike) and one can grind out the geodesic equation for the central mass in a Schwarzschild spacetime, for example.
Finally, proper acceleration is difficult to maintain for long, let along perpetually. (Although one can stand on the surface of a rocky planet and with an accelerometer measure over a very very very long term practically constant acceleration, and might for practical reasons want to assign that approximately constant acceleration to e.g. little "g"). So most curves where there is some proper acceleration also have some free-falling segments eventually.
One consequence is that a traveller who undergoes different accelerations (including none -- free-fall) along its path through spacetime will count different numbers of particles at different points along the traveller's sometimes-geodesic/sometimes-accelerated timelike curve.
A black hole doesn't really change this other than that the formation of some types of horizon induces an acceleration between freely-falling observers before the horizon forms and observers after. The later freely-falling observers see more particles than the earlier ones, and they bunch up not very far (but not preciesly on) the appropriate horizon.
The Unruh effect introduces an Unruh horizon attached to an observer undergoing proper acceleration. That observer sees more particles when it is accelerating than when it is/was freely-falling.
Some of the radiation is massless or has so little mass that it flies out to infinity. Around some types of horizon near a central mass, we'd call that Hawking radiation (as opposed to e.g. Unruh radiation, or radiation associated with e.g. a cosmic horizon in an expanding universe). And as Baez notes, over lonnnnnnnnnng times one would want to take into consideration how the central mass evolves as these particles fly away. Over much shorter durations (fuel is limited!) one would want to take into consideration how Unruh radiation and proper acceleration co-evolve.
The idea in the paper (which Baez dismantles in the linked blog entry at the top) is that no type of horizon is necessary for an apparently particle-free vacuum to look like a particle-rich patch of spacetime. That's a pretty wild claim. Why don't electrons evaporate on their own, in that case?
> I think another good historical analogy is the invention of writing. In Phaedrus[0] Plato argued that it may make people dumber.
No, he doesn't. Plato quotes Socrates quoting a mythical Egyptian king talking with the god that had supposedly created writing and wanted to gift it to the Egyptians. The entire conversation is much more nuanced. For one, writing had existed for three millennia by the point this dialogue was written, and alphabetic Greek writing had existed for several centuries.
Plato does make the point that access to text is not enough to acquire knowledge and it can foster a sense of false understanding in people who conflate knowing about something with knowing something, which I think is quite relevant when you see people claiming than can learn things from asking LLMs about it.
I remember that episode being excellent! Scientists could tell that Venus’s crust was somehow reforming because of the crater pattern but the didn’t know whether it was gradual change or something catastrophic, and the thickness of the crust would point to one way or the other but they didn’t have that data.
> The paper used modeling to determine that its crust is about 25 miles (40 kilometers) thick on average and at most 40 miles (65 kilometers) thick.
> KrebsOnSecurity reviewed the Google Ad Transparency links for nearly 500 different websites tied to this network of ghostwriting, logo, app and web development businesses. Those website names were then fed into spyfu.com, a competitive intelligence company that tracks the reach and performance of advertising keywords. Spyfu estimates that between April 2023 and April 2025, those websites spent more than $10 million on Google ads.
The Apple watch Workout app has a heart zone view while you're working out, but I don't think it has a workaround summary of how much time you spent in each zone.
The app is not just getting heart rate measurements from workouts but in general. But as mentioned the interesting thing is that it's doing a sum per day, week, month, last 7 days and last 30 days
> Now I understand the situation perfectly! The issue described in the problem statement is a real bug that was already identified and fixed in later versions of pytest. Since we're working with pytest 5.2.4, we need to apply the same fix.
https://gist.github.com/jacobkahn/bd77c69d34040a9e9b10d56baa...