The quantum performance thing is real, but that the random circuit sampling problem they are tabling as the benchmark here is for a quantum circuit.
So really what is being claimed is that classical computers can't easily simulate quantum ones. But is that really surprising?
What would be surprising would be that kind of speedup vs classical on some kind of general optimization algorithm. I don't think that is what they are claiming though, even if it does kind of seem like it's being presented that way.
Three grams of explosives in each device used by a hostile military organization.
I don't think it could possibly be more targeted. Literally just devices issued by Hezbollah themselves to their own members.
Maybe it wasn't perfect. That seems to be the bar you are setting.
But much closer to perfect than I would have imagined possible. And closer to perfect than I think most people would have imagined. Maybe that is aggravating to people ideologically set against literally anything they might do.
But far superior, and less disruptive to innocent people to tactics used elsewere by Israel. Far far more more targeted and less disruptive to innocent people than the tactics used by Hezbollah themselves.
I think it would look something like that if you were looking directly east, since the distance and the perspective would bring it to the vanishing point in the center of the image.
So, from that POV, the rings would not be able to go past the center of the image.
This view would still be possible if this is a cropped down section of a larger image that was pointed slightly to the left I think.
> Then we will never be able to find the Nth beaver number for the corresponding N.
This is pretty clearly what people are asking about when asking if BB(6) is "uncomputable" then.
I understand (now) the point about the specific meaning of the term of art "uncomputable". If you want to speak precisely on the topic, it's not the right question to ask.
But it still seems like the question, "will we ever be able to find out the Nth beaver number", is the more interesting question.
So, we can define ZFC axioms that classify the beavers we can know together with the beavers we cannot know. So what? Then that is just skipping the interesting question. Maybe that just means for this specific problem that is not the best construction to decide to use to classify them?
I would be more interested in a classification that would assign one label to beavers we could possibly hope to calculate, and another for beavers where the calculation is impossible.
I was on this exact same journey, so our taste must be similar. Love his stuff.
Just in case our taste is VERY similar, I have really enjoyed every book I've read so far except the middle book in the Orthogonal series.
The first was great, third was back in form. I would recommend, if you are reading the second one, and start to wonder why you should press through, just skip to the third one.
I'm not really qualified to make any judgements about the overall quality of it, but it's moreso the tone of it that I am talking about. I wonder if he was going through something when he wrote that one or something.
Isn't saying BB(6) is computable the same as assuming that it is an integer?
I thought this was not necessarily true.
For example, one beaver might halt after some integer number of steps. This would be the potentially very large integer the author is referring to.
Another might go into an infinite loop, and clearly never halt.
My understanding of the where incomputability entered the discussion is the third possibility, that a beaver might have complex behavior that neither ever halts or ever loops.
The author touches on answering this, drawing the distinction that a specific answer might not be provable. But I'm not sure I understand.
How would the answer for a specific integer be computable if it's impossible to determine what the value for the function of is for that integer?
If you have some terminology you don't like, provide an alternative.
Main is fine.
But like what is the alternative to cargo cult provided here? It's a very concise representation of a pretty complex idea.
"You are valuing the ritual associated with an outcome instead of the outcome."
Is that my alternative?
Main is more concise than master. But how do I boil that down without saying "cargo cult"?