When sorting eigenpairs of a dense matrix, usually tou end up with a Schur decomposition. The basic operation that you can do is swap two adjacent eigenvalues on the diagonal, so bubblesort is a natural candidate.
We are constantly losing technology as the treadmill of technological progress continues. Casette tapes, CRT displays, and perhaps photographic film are some examples. One can argue that there are "strictly better" technologies available now, but there are always niche cases where the new and obsolete technology are not quite fungible. What if for some reason a modern industry gets wiped out? Then we'd have to revisit the lost art.
As an immediate example, my wife's business needs p-channel small signal JFETs. These apparently are no longer fabricated, and with the way the semiconductor industry moves, they are likely never coming back in any appreciable quantity. So once the world's supply of obsoleted semiconductors dries up, the technology will basically be lost.
I don't understand why you believe Banach-Tarski to be obviously false. All that BT tells me is that matter is not modeled by a continuum since matter is composed of discrete atoms. This says nothing of the falsity of BT or the continuum.
All that BT tells me is that when I break up a set (sphere) into multiple sets with no defined measure (how the construction works) I shouldn't expect reassemlbing those sets should have the same original measure as the starting set.
> Everyone ... outside of China is forgetting and losing capabilities.
To me this is the fundamental problem with the notion of intellectual property and its protection: so much of it is trade secret and undocumented (let's be real, we disclose as little in patents as we can get away with). Companies come and go, and in the process, institutional knowledge of how to do things is lost because there is no incentive to make it public for others to replicate. This also means that once lost, it must be rediscovered later.
This is why open source software is stronger than ever despite its shortcomings and efforts of large orgs to kill it. Rather than bending backwards and treating it like property (as originally demanded by Bill Gates in his open letter decades ago, we did the right thing and treated it like knowledge (e.g. like mathematics).
Intellectual property was a horrible flawed idea that the world will continue to pay for dearly for decades after it is finally discarded.
For general polynomials, it matters a great deal in what basis it is represented. The typical monomial basis is usually not the best from a numerical standpoint. I am aware of some modern methods such as this: https://arxiv.org/pdf/1611.02435
For polynomials expressed in e.g. a Bernstein basis, there are often much faster and stable tailored methods working solving for the eigenvalues of a companion matrix of a different form.
That doesn't sound right, nearest-point queries for cubic Béziers take at least a quintic solver, and this library uses a subdivision-based algorithm with Bernstein polynomials that is seemingly designed to work with any degree [0]. (Or at least, it doesn't have any code that complains when the degree is too large.)
My apologies, it looks like it was switched over [0] to an external root-finder crate poly-cool [1] soon after I wrote my comment. (I should know better than to link to branches directly, but there weren't any useful tags on the repo, so I got lazy. For reference, I was trying to link to [2].)
Curiously, the poly-cool crate appears to use the monomial basis instead of the Bernstein basis that the old version was using.
Speak for yourself. Some of us see the difficulty in sustaining and maintaining this fragile technology stack and have decided to do something about it. I may not be able to do all those things but it is worth learning, since there really is no downside for someone who enjoys learning. I am tackling farming and cpu design at the moment and it is tremendously fun.
Good for you, I guess, but your hobbyist interest in farming is not an argument against using AI. The point of my comment is that the our technology stack is already large enough that adding one more layer is not going to make a difference.
I think that is only a partly correct way to think about it. I live up in the Sierra foothills in a very rural area, and based on what I see, I think the effects of wildfires are indeed negating climate policy. Allow me to explain.
For people who have never lived in an area that is both rural and wildfire prone, pile burning to eliminate yard waste is an activity that is entirely foreign. You see, out here, most people believe that the primary method of eliminating yard waste is by burning it in a pile. I happen to live in town where there is trash pickup service available, but I opt to simply take stuff to the dump myself. Most people don't want to pay or don't have such service available. Burning yard waste is almost always extremely polluting. One burn pile full of leaves and pine needles can often smoke out my entire town. Fortunately, pile burning is only allowed on certain days (when the weather is such that wildfire risk is reduced). That is not to say that pile burning is always so bad; it has to be done properly. If the pile is hot enough, there is little smoke. But most people do not burn them hot enough with enough long-burning materials (i.e. wood).
So why did I bring this up, since a wildfire is just this on a massive scale? Well, I do not personally believe that properly managed fuel management would result in as much smoke and particulate pollution, for two reasons. One, indigenous peoples here used to regularly set fire to the forest to manage the fuel load. This was done regularly enough that there simply wasn't as much material to burn, and done when weather was cooperative (e.g. before rains). A modern wildfire can burn with such ferocity that most trees end up burning, instead of just the undergrowth. This represents a much greater release of long-captured CO2. And second, there is now a culture of placing responsibility on individual residents to maintain "defensible space", asking them to perform pile burning regularly. As I mentioned above, this results in what feels like disproportionately dense particulate pollution, with annoying regularity throughout the cooler times of year.
As far as CO2 is concerned, wouldn’t burning “yard waste” be neutral year over year? If you’re only burning this year’s growth, you can’t release any more carbon than the plants took in to grow in the first place. The wildfires might not be neutral because our forests are overgrown, but if they happened more frequently and only burned a years worth of undergrowth, they would be
As far as CO2 alone is concerned, that is true. The issue is that if you burn a fire cleanly, you (ideally) produce only CO2. If you burn the fire poorly, you produce less CO2 per se, and a _lot_ more particulates, which is bad for air quality. On burn days, the sky is noticeably smoggier all throughout the mountains, and the sunsets are tinted red. I imagine this would have the effect of trapping in daytime heat similarly to how cloudy nights after sunny days are warmer. And since pile burning generally happens during the day, we get an amplified greenhouse effect up here.
Smoke particles reduce overall solar radiation absorbed by the earth-atmosphere at local and/or regional scales during individual fire events or burning seasons.
I don’t think this is true. I live in the middle of nowhere, but there are homes an hour out further in nowhereness with addresses that I cannot imagine could ever receive mail. Those people all have PO boxes in town.
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