> In other words, after arranging the five black pieces, it must be impossible to place the white king anywhere without it being in checkmate.

These two sentences mean very different things in the normal rules of chess. And if you replace the word “checkmate” with the word “check” in the second sentence it still doesn’t mean the same thing as the first sentence.

The first sentence implies that all the pieces must be defended.

Edit: Eh, I guess it depends on how you view the word “attack” since all the pieces are the same colour.

At some point someone will realise that backpropagation and adjoint solves are the same thing.

Additionally, some songs even change keys, which makes “per-song” not enough of a constraint.

GEMMs are dense O(N^3) work operations that have roughly the same access pattern and data reuse properties across all matrices. Of course, I’m simplifying things a lot here; tall-skinny and short-fat patterns are much harder to get performance out of but the spirit of the approach is the same as big square matrices.

Sparse LU solves have a different character. There is nowhere near O(N^3) work. You typically expect something closer to O(N^2) but getting performance out of these operations is notoriously difficult because it depends a lot on the sparsity pattern of the linear system. Making matters worse is that you may commonly have a sparse A that factorises to dense L and/or U matrices.

Woah, that is extremely cool. Very nice work, sir.

That seems to track. The vast majority of requests won’t go half way around the Earth, so maybe halving that time at 0.06 seems like a reasonable target.

You could compute in the reverse direction, starting from 1/n instead of starting from 1, this would produce a stable floating point sum but this method is slow.

Edit: Of course, for very large n, 1/n becomes unrepresentable in floating point.

Thank you.

What if that person has also lived in Texas for 30 years? And what if they had a family member that died during that power grid failure in 2021? I personally would find it quite difficult to communicate to them the nuance of a local problem and a state-wide problem when the end result is the same: no power.

In the future, you might consider approaching an interaction online with more balanced judgement.

Edit: Actually, looking back at the original comment, it's not even clear they're talking about the Texas power outage in 2021. All they said was "Hope they have ample backup power." Seems like a reasonable thing to hope for what might be critical infrastructure.

Texas had the most number of power outages between 2019 and 2023 [1].

It wasn't one time. And it's not a joke. Infrastructure weatherization is a very real overlooked (and expensive) investment that still has not taken place.

[1]: https://www.congress.gov/118/meeting/house/116952/documents/...

I have no expertise in this field.

Is it actually even more aligned? Or is it simply aligned with the elements of Japanese culture and/or media that are exported to the West?

Can you elaborate?