It's the blessing and the course of a polynomial inverse: the inverse is the same degree as the polynomial, so its largest coeffecient is large and blows up.
Knuth-Eve and Pan use the root of a degree d polynomial, which is slightly less big, but still inpractical.
Technology depends on a lot of people cooperating around the globe. Disrupt a few critical chains (power generation, fertilizers, computers), add a bit of good old war and you'll soon be in the era before Haber process and a lot of people die. And then the remaining people will have trouble keeping that level of technology with how sudden the change would be.
Well yes that's what I said, it could destroy civilisations and their technology.
It seems much harder to kill every isolated tribe in the whole world, and every survivors of the destroyed civilisations.
I like the concept of separation logic as much as the next guy, but I don't think this is it. Just look at the examples, with loop invariants alone being longer than the whole example. It's not only a problem with ergonomics, but it leaves a lot of space for specification bugs.
And I suspect that cross section of people writing C code you want to verify with formal verification folks is not particularly big.
> And I suspect that cross section of people writing C code you want to verify with formal verification folks is not particularly big.
Perhaps not, but C is still used in a lot of critical systems. Things like this for proving properties of some core of your program can be very helpful.
> Rather, the remedy for Plaintiffs’ injuries lies in pursuing tort
claims, electing representatives who will better manage the public-water
system, and petitioning their representatives for other remedies.
which is easier said than done.
From outside of US this seems extremely ass backwards.
its hard to me to tell what this means formally(as I said I am not expert).
There is no "interpret" operator in zfc.
I believe what it says if you add some robinson axioms + some logical rules on top of zfc, you can carry your results.
It's the same way you don't need to have GCD in stdlib to say that you can compute GCD in C++. You can make your own using parts given.
You don't need to add any axioms, you just build some sets to represent numbers and make operations that act the same way as arithmetic, define some equality relations. Then you derive rules of arithmetic for your handcrafted arithmetic using ZF axioms and you're good. You get axioms of arithmetic derived from your regular axioms without adding them as new axioms to your theory.
You make relations and functions out of sets and prove theorems about them, reducing definition of things in terms of belonging to a set. This isn't particularly complicated.
No, once you start formalize this, it becomes complicated. There is a reason why looks like there is no "peano can be derived from zfc" theorem which would close dispute, and my opponents need to throw links on bro math from stackexchange in this discussion.
If this anything like CERN detectors, they get amounts of data so vast that they have to discard almost all of it to be even able to record it. Depending on heurestics you use to discard data you might be discarding what you are looking for and after adjustment will get some new interesting events, but still actually processing the candidates might take a long time.
This raises what is (I think) an interesting question. CERN is a collider, so they are _trying_ to produce lots of stuff, and they do (lots and lots of stuff). They can't write it all to disk, and most of it isn't interesting enough to try.
The work being done here falls into the category of "low background physics" --- they aren't trying to produce anything, and actually put quite a bit of effort into doing the opposite, by removing all sources of particles (e.g. sourcing materials free of radioactive contaminants, physically cleaning all surfaces and purifying all fluids involved, etc).
So the detector, if built properly, is fairly quiet, and you try to write as much data to disk as you can (e.g., if something even fairly-potentially interesting happens, you save it). Then when you analyze the data like this, you ignore the majority of what you've got --- only a teeny fraction makes it into an analysis of this caliber.
I still remember getting support mail every time Apple released an OS update. For a week or two there'd be reports of things crashing randomly with stacktraces that didn't seem to make much sense.
One of reasons why I stopped trying to make mac/ios apps.
If 30-40k timelines are right that's way before agriculture and any kind of "economy". It's firmly hunter-gatherers and there's not much of that to do when it's after sunset.
"Economy" by merits of its definition is an applicable term for hunter-gathering societies. And is used widely in this quality, in fact.
Nobody says they couldn't find a time to do carving (existence of the artifact shows they could). The issue in question is comparative value of the time spent on it. Hunting, gathering and concomitant works were certainly both physically and mentally very demanding activities, and their way of life required thoughtful spending of energy. Consequently, whatever irregular pastime they had should have to be extremely valuable. It makes 'toy theory' somewhat unconvincing.
Pastimes are in fact incredibly valuable. And it's possible the motivations that led to the creation of this artifact wasn't just all about the end product.
It could have been a member of the tribe that was disabled and had nothing but time. There's evidence to suggest that individuals like that weren't simply discarded.
There are a number of plausible explanations including just someone DID have the time and wasn't all that busy. That's even more likely but I wanted to call out the perspective that it might not have been the most typical situation that led to this.
I don't think so. I know, somebody recently re-popularized Sahlins theory claiming that HG essentially spent most of their lives happily dancing and singing around fires, but the popularity, I believe, is due to tapping into the lost paradise trope, not because it's well-established.
For instance, I heard Reich said in a podcast that genes linked to obesity, and diabetes, which in our times are, of course, seen as detrimental, were norm among Eurasian WHG population. And this suggests they weren't detrimental to them. Now, what would make quick fat in-body production beneficial? I guess, when your calories intake is uncertain and irregular. There are other researches on the same Kalahari Bushmen, Sahlins used to made the theory of HG affluence, which e.g. emphasize how food scarcity affects customs of food sharing. Similar observations made about "uncontacted" Amazonian tribes, where food theoretically is abundant, but the amount of time, and effort one needs to extract them with pre-metal era tools is still too high to go to rest without at least a slight feeling of hunger.
Reality is that Sahlins probably made observations in an unusually good year, and then romanticized them too much. And that's the only data point on which the theory rests to the best of my knowledge, with many points contradicting it.
One may argue that hunting with its short feedback loop, and camaraderie of a tight group relying on each other's help are healthier psychologically compared to office politics and closing boring tasks, or even farming work - not without merit. But uncertainty of survival, calorie deficit, and amount of both mental, and physical effort HG-ing required is definitely underappreciated among followers of "Original affluent society" theory. HG didn't have easy lifestyle with long creative rests. It's just something we'd love to believe, because of how cool it sounds.
reply