Anyone have the source for the three Waymo serious injuries or deaths? I feel like I would have heard about these on HN. Only thing I've heard of is one feline fatality and a school-aged pedestrian who was bumped, but appeared not to be injured.
Once the longer number starts repeating digits, then it's not n^2 anymore. Multiplies get replaced with lookups. And we're only counting the multiplies. That's all they counted in the article. Not the adds, not the shifts.
They don't count the additions or shifts because they're both linear time operations, and thus provably at least as fast as multiplication (both in an asymptotic and exact sense). In any case where multiplication is super-linear, this means that addition and shifting are are not the temporal bottleneck at any stage in the algorithm where you have a constant number of those operations surrounding at least one multiplicative recursive call (on numbers of similar magnitudes).
If additions were truly free, an even easier optimal algorithm would just be repeated addition involving zero multiplications.
The complexity of Karatsuba's algorithm, because it's a recursive one that gets "wider" at every level, is dominated by the width of that recursion. The top level always has a small number of operations, so we don't explicitly count them there, but the bottom has the truly huge number of operations that contribute to the algorithm's complexity, because each level of recursion dramatically increases the number of operations. Some number of those operations (most of them, in fact) will be single-digit additions.
Memoizing number-by-digit multiplication doesn't make multiplication O(1) because one must still do an N-digit addition (which is O(N)) for each digit.
The American average is actually ~$35,000 apparently. Though that comes from the wedding industry so they probably undercount small ceremonies and have some incentive to juice the numbers besides. I couldn't really find a good clean table that went back further than the 90s, but qualitatively it sounds like spending spiked in the 80s / early 90s and has mostly stayed with inflation since. Personally, even though I could comfortably afford it, the financial aspect of such an expensive affair would completely suck all the joy and life out of my wedding for me.
Decompiling binary blobs is a strong suit for LLM AI, right? Maybe progress on this will be faster than I expect? Does the FSF spend money on non-free AI services? That is, do they have ethical issues with that? Or do they only use AGPL licensed services (or similar)?
If you only care about the two surfaces matching each other, you don't even have to worry about your indicator. Just grind them against each other, or use some lapping compound to speed up the process. If you want to get the surfaces truly flat, then you use three surfaces that you successively grind against each other.
That's a fascinating link, and it sounds like what I'm talking about is what's called "engineer's blue" in the link.
But I think it would be vastly more difficult to grind two massive stone blocks against each other than to just ram one against the other. Not unless you stacked them, anyway, and if you stacked them I'm not sure if you could move the top one side to side in order to do the grinding. Maybe with some kind of grit, I don't know. Still seems harder.
Also, grinding methods end up removing more material (bad for teeth!), and I would expect more overall physical work to be done in order to remove that material (bad for massively heavy stone blocks).
As for making them flat, that seems unnecessary to me. But then, I'm not a pharaoh. (Even for a pharaoh, it seems like only the seems would need to be straight. Nobody could tell about the faces after assembly.)
Then again, after some quick researching, it seems like there's a good chance that the well-fitting blocks (which are not all of them) may have been cast out of a concrete-like slurry, not hewn.
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