Stokes' theorem. Almost the same thing as the high school one. It generalizes the fundamental theorem of calculus to arbitrary smooth manifolds. In the case that M is the interval [a, x] and ω is the differential 1-form f(t)dt on M, one has dω = f'(t)dt and ∂M is the oriented tuple {+x, -a}. Integrating f(t)dt over a finite set of oriented points is the same as evaluating at each point and summing, with negatively-oriented points getting a negative sign. Then Stokes' theorem as written says that f(x) - f(a) = integral from a to x of f'(t) dt.

We aren't trying to establish that neurons are conscious. The thought experiment presupposes that there is a consciousness, something capable of understanding, in the room. But there is no understanding because of the circumstances of the room. This demonstrates that the appearance of understanding cannot confirm the presence of understanding. The thought experiment can't be formulated without a prior concept of what it means for a human consciousness to understand something, so I'm not sure it makes sense to say a human mind "is a Chinese room." Anyway, the fact that a human mind can understand anything is established by completely different lines of thought.

This fails to engage with the thought experiment. The question isn't if "the room is fluent in Chinese." It is whether the machine learning model is actually comparable to the person in the room, executing program instructions to turn input into output without ever understanding anything about the input or output.

O notation has a precise definition. A function f : N -> R+ is said to be O(g(x)) (for some g : N -> R) if there exists a constant c so that f(n) <= cg(n) for all sufficiently large n. If f is bounded, then f is O(1).

It depends on your velocity

I'm not suggesting that. It just looks like he did in fact choose to have that hair color.

It looks dyed

That's not necessarily wrong, but not the big explaining factor here I think. The technological challenges behind aligning ML models with factual reality aren't solved, so it's not an engineering decision. It's more that AI is remarkably easy to market as being more capable than it is

The benefits don't halve. It's the difference between noticing stroboscopic effects and not noticing them. Between not being able to comfortably track fast moving objects and being able to. 1000Hz is a point at which several limitations of LCD technology become invisible.

It's extremely easy to tell the difference. I can't tell you what's wrong with their experiment as I don't know exactly what they did, but they clearly fucked it. If you're looking at a static image, you can't differentiate 240Hz from 30Hz. You need a test that actually demonstrates the difference.

Mesa is usually pretty quick to update, it's just that stable distros won't update mesa all that quickly. I assume most of them have some way to install a newer mesa from a community repo or something.

I once had the flu so badly I couldn't get out of bed or yell for help. My parents put on "Flushed Away" (movie about some fuckin rats) on dvd and it looped at least 4 times before anyone came back to turn it off. One of my core traumas