The title is more aimed at being clickbait than attempting to be informative.
The only thing in the underlying article is that specific neural networks are good and efficient at producing approximate solutions to large sparse systems of linear equations. Nothing else.

Such big systems of equations result when you try to solve partial differential equations on a finite-element mesh by substituting a lot of base functions.

There are broadly 2 ways of solving such systems: direct (e.g. using the sweep method) or iteratieve. The neural networks are just a way of implementing the iterative method. The only thing interesting is that the specific neural networks proposed to do this can be calculated efficiently (also energy-efficiently) on specific hardware optimised specifically for that flacour of neural network.

The OP post tries to link 'math' and 'AI' here because, well, partial diffferential equations count as 'math', and neural networks are a form of 'AI', right? And that's how the OP 'justifies' its title.

Sorry folks, but his is a highly technical development which in no way merits the hoo-hah the OP throws at it.

Personally I find this explanation (the first link of the OP) quite clear and accessible (non-technical): https://www.sciencealert.com/f...
In summary: you can sustain denser plasma's if you can precisely control the way your plasma is started. That's useful because it helps your reactor reach a break-even point between energy cost (to make, maintain, and contain the plasma) and the amount of energy the plasma emits during its existence.

No they aren't. By your logic, any resistors in an electronic circuit would also be a 'bad idea' (which they aren't).
Tariffs add costs to imports. That cost increase is merely an instrument which can be used stupidly, indiscriminately, and inappropriately (like the Trump tariffs) or appropriately. As with any cost-structure adjustment, for it to have any impact at all, there must be positive effects for some and negative effects for others. Depending on your objectives the benefit can absolutely outweigh the cost.
Take the EU Carbon Border Adjustment Mechanism for example: it penalises any (steel) imports with excessive carbon emissions (e.g. from older coal-based production plants) compared to steel produced through more modern and less polluting processes.
What that does is to internalise external costs in order to clean up certain production processes.
Now why would that be a bad idea? (oh, and don't bother to reply if you only argument is that 'da gubbamint' shouldn't intervene in markets at all or if you feel that CO2-footprint reduction is either unnecessary or should only be done at zero marginal cost.)

I just hope that Mr. Trump and his advisors realise that this enactment of the Monroe doctrine implies that
(a) Asia is now China's backyard and Europe is Russia's (A deal is a deal, right?)
(b) national sovereignty has now become a lot more conditional (by common agreement).

By consequence, anyone who wants an uninterrupted supply of chips from TSMC had better be prepared to be extremely polite to China within a few years.

Apparently Europe is working to correct its mistakes and take back control of its strategic production lines. Just like the US.
Problem is: Europe's got a lot of ground to cover, they don't have a single government, and they're less prone to use import tariffs as a blunt instrument in every trade dispute.
Perhaps because they have more to lose and can inflict less pain on their trade partners than the US can.

Agreed. And well done to the EU for enforcing their own privacy laws.

I think this also proves that the comments one sometimes hears in US media (and certain political circles) to the effect that the EU is supposedly going after US companies, are nonsense.

Well, there are a number historical reasons for why Europe relied on the US for its defence and why the US was totally OK with that.

(1) Europe doesn't exist as a nation: it's like the US (states) without a federal government. That means it doesn't have an integrated defense industry or an army, which in turn means it doesn't have the economies of scale that enable the US to be a superpower. For a very long time this was considered to be in the US interest. US leadership was unquestioned, which had its use. Take e.g. the industrial side of the F16 and F35 fighter planes: those benefited (and continue to benefit) quite a lot from European clientele. The same holds for other types of weaponry. We're talking about 80 bln. in arms sales in 2023 and about 97 bln in 2024 to US allies (see e.g. here: https://www.state.gov/fiscal-y... and here https://www.defense.gov/News/N... ). Arms sales don't exist in a vacuum: it also represents a buy-in in the US as a partner.

(2) For the entire period from 1945 to the dissolution of the USSR in 1991, the US and Europe had this bargain: the US provides the military-industrial muscle and the nuclear umbrella, Europe provides the battlefield, about half the manpower, a robust first line of defense plus 100% of civillian casualties in anything but an intercontinental nuclear war. The US had a very clear interest in this tate of affairs, like e.g. keeping the USSR bottled up in a land-locked environment without practical (non-blockable) ice-free ports en a big counterweight to USSR expansion.

(3) For that reason the US had (for that period) been very much against Europe getting anything like a European army or an integrated arms industry. All that changed only when it realised that China had become an economic and military rival. With the Warsaw pact disbanded and Russia no longer a threat, US interests in Europe became more diluted and its commitments there more of a burden.

(4) Europe is indeed ramping up its spending, but there is of course a lead time (of 5-10 years or so) before it can get its 'own' military up to scratch. Withdrawing support before that time means risking Russian expansion once again. That could be an issue if Russia e.g. regains the industrial muscle and mineral resources of the Ukraina.

(5) Currently the situation is that the US has put Europe on notice to get a move on with financing its own defense needs and those of teh Ukraine. And this is having an effect already. Just for the record, US aid to the Ukraine is about 183 bln. by the end of 2024 ehile the EU has contributed slightly more than 50% of all military aid to the Ukraine to date (see e.g. here: https://www.bbc.com/news/artic... ). There is more to be done, but the figures mentioned by pres. Trump are outright misleading (as usual).

(6) It goes without saying that this development will (over the next 10 years or so) lessen US influence in that part of the world. With that withdrawal of influence there may also be a shrinkage of available military bases, and with it the ability to 'project power' abroad. That in its turn will further contribute to lessening US influence in the world. Whether or not this is desirable is another question, but I think it should be factored into any strategic decision makeing (which in my opionion currently is not the case).

Agreed, to a certain extent.

As I see it, the reason for going to school and acquiring skills such as how to do mathematics and/or how to write clearly and coherently is training the LLM that resides inside our skull. I think that the process of learning something makes you better at learning in general, which then applies to other things as well.

The question is: is it beneficial to learn how to use your brains? That would depend on who or what you want to be. Some people can be very successful being e.g. an Instagram celebrity or an 'Influencer', where being able to spell or do maths just isn't relevant.

On the other hand, I think that people with academic qualifications like being able to spell, write, and do maths can make better use of an LLM than most others who are deficient in that respect.

Of course that's a testable hypothesis. I curious as to how that turns out.

True, but that provides exactly zero reason, and even less justification, to build 'm into algorithmic black boxes an turn 'em loose on the public.

Yes. And? Red-lining people for loans on basis of their zip code reflects objective reality too. And it's illegal now. For excellent reasons.

Whee ... that's one big (and fallacious (and uninformed)) ball of confusion you're serving up here.

Let's see if I can disentangle that a little for you.

First of all, you seem to go off on a rant about while (and sometimes Asian) males supposedly being "blamed". We could have lots of fun with that alone (like where else you hear that kind of stuff) but let's leave that for the moment and instead look a bit further than the Engadget website and at some sites which have some sober reporting about what this newly minted New York position is and isn't about. This site: https://www.smartcitiesdive.co... is informative and also links to a source document (the NYC press release) here: https://www1.nyc.gov/office-of...

What New York city has done is to create a position with te following job description:

The officer will serve as a central resource to help city agencies with policies and best practices related to their use of algorithms. Another duty will be to provide resources for the public to learn more about the government's use of algorithms for decision making and service delivery. Equity, fairness and accountability will be at the forefront of the oversight and guidance.

The reason it did that is this:

The position was created following a review of recommendations in the recently released Automated Decision Systems Task Force Report. The task force spent 18 months holding meetings, public forums and gathering information for the report. The document examines how services and resources are provided to New Yorkers through the use of data, algorithms and machine learning or other artificial intelligence (AI). The report highlighted concerns with equity and implicit or explicit bias with data, algorithms and greater AI use. Bias is among the key concerns with new data-driven technologies. A report released by New York University's AI Now Institute went so far as to say the artificial intelligence industry has a "diversity crisis" across gender and race that creates bias and could influence how AI systems are designed and implemented. A Georgia Tech study earlier this year suggests that bias during the development of certain technologies used in autonomous vehicles may have made them perform poorly when detecting people who have darker skin. AI bias also has been found to affect low-income citizens.

So ... rather than 'blaming white males' it's about making sure that AI and machine learning that is actually deployed in real-life situations aren't the product of any old nitwit who managed to throw some data through a bunch of algorithms and thereby 'trained' them.

When you do that sort of thing the algorithms will (if the training suceeds) pick up correlations in the data. A few examples of what happens if you do that and you're really stupid is nicely described in this article: https://www.nytimes.com/2019/1... A fun quote is this:

Another notion of bias, one that is highly relevant to my work, are cases in which an algorithm is latching onto something that is meaningless and could potentially give you very poor results. For example, imagine that youâ(TM)re trying to predict fractures from X-ray images in data from multiple hospitals. If youâ(TM)re not careful, the algorithm will learn to recognize which hospital generated the image. Some X-ray machines have different characteristics in the image they produce than other machines, and some hospitals have a much larger percentage of fractures than others. And so, you could actually learn to predict fractures pretty well on the data set that you were given simply by recognizing which hospital did the scan, without actually ever looking at the bone. The algorithm is doing something that appears to be good but is actually doing it for the wrong reasons. The causes are the same in the sense that these are all about how the algorithm latches onto things that it shouldnâ(TM)t latch onto in making its prediction.

See what I mean? You really, really need someone who is a bit educated about statistics, machine learning, and AI to keep all kinds of 'practical minded' bozos from putting all kinds of garbage machine learning algorithms into production. When your statistics professor told you to be careful not to mistake correlation for causation, this is (part of) what he meant.

That's why this position is needed.

Oh, and read before you rant, Ok?

Unfortunately this post contains some major errors which I can't resist correcting.

(1) Norway does pay the EU. See here: https://fullfact.org/europe/no...

(2) The EU would be more than happy to give the UK a Norway option (see e.g. this slide: https://ec.europa.eu/commissio... ) The Norway option is shown as the second step from the left, just past full EU membership.

It's the UK that doesn't want this Norway option because it (a) absolutely refuses to accept any further free movement of people between the EU and the UK, (b) absolutely refuses to continue to make major financial contributions to the EU, (c) is adamant that it wants regulatory autonomy (i.e. no more EU regulations, especially since as a non-EU member it will have no more say in what those regulations entail, and (d) is adamant that it wants to pursue an independent trade policy (i.e. zero tariffs with e.g. Africa and China in order to obtain cheaper imports (the UK sports a really big trade deficit where goods are concerned).

Those conditions are known as the UK's "red lines", through which it has basically painted itself into a corner (i.e. leaving the EU without any deal in place).

Starting at midnight of the day the UK leaves the EU without a deal, its trade footing with the EU will basically be the same as that of Mongolia and Zimbabwe. That's the problem. Can you imagine the consequences if e.g. Mexico or Canada would, from one day to the next, be in a situation where they have absolutely no trade deal with the US? That's what the UK is facing with respect to the EU.

Excellent point. Code remains something that is handcrafted rather than machined. Besides which, as far as I understand, race conditions are difficult to find and easy to overlook in any event.

In fact, it illustrates the point that code correctness is one of nature's 'hard' problems. As in, the _only_ way to achieve correctness is to give a mathematical correctness proof for a piece of code. And anyone who's ever tried that knows how hard that is for any piece of non-trivial code (e.g. the textbook examples that information science students see the technique demonstrated on).

For those who don't know what I'm talking about, see e.g. here for a basic introduction: https://www.cs.cornell.edu/cou....

I like the understated way in which the lecture introduces the subject:

Today's dominant practice in the software industry (and when writing up assignments) is to prove program correctness empirically. The simplest form of this technique consists of feeding various inputs to the tested program and verifying the correctness of the output. In some cases exhaustive testing is possible, but often it is not. More sophisticated versions of this technique try to choose the inputs so that all, or at least the majority of the possible execution paths are examined. Independent of their degree of sophistication, these empirical methods do not actually that the respective program is correct. The only thing we can actually prove with the empirical approach is that the program is not correct - for this purpose, a single example of incorrect behavior suffices. Absent an observation of incorrect behavior, however, we can not know - in general - whether the program is correct, or whether we have just not tested it with an input that would trigger an error.

There are real-world examples where formal verification was used see e.g. https://cacm.acm.org/magazines... ts.data61.csiro.au/publications/csiro_full_text//Klein_AKMHF_18.pdf https://pdfs.semanticscholar.o... and https://www.schneier.com/blog/...

As usual, Wikipedia has some useful material o nteh subject too: https://en.wikipedia.org/wiki/... .

The drawback of this approach is that it tales lots of time, actual computer scientists (as opposed to coders or even software engineers), and hard work. In practice there is no budget for that. As far as I know, proving correctness of a few thousand lines of code is feasible, given a few manyears. Proving correctness of the 20 million or so (I have no idea how big the scheduling part of the kernel is) of lines in the Linux Kernel is currently out of reach.

What we all know happens in practice is that some functionality is designed, implemented, and tested. If software faults happen infrequently enough for the software to actually do some useful work, then it's released (and tested further in production). At least the company can start billing customers for the product to fund further development and bug-hunting.

Hmm.

You realise that "importing cheap labour" would not be profitable if employers paid decent minimum wages and "illegals" would never get work unless employers are happy to employ someone who can't show an ID?

And that the plain fact is that it's a lot easier to squeeze a superior work/wage ratio from people who are illegal (and thus truly desperate for their job) than from an average US-born Joe? And that illegals usually are the hardiest and most motivated segment of the population? What's not to like for an employer?

Razzing on "illegals" and "foreigners" is popular, but probably not the root cause of US wage problems.

In addition, just compare the number of jobs replaced by automation (30% of the workforce) with the number of "illegals" and "imported cheap labour" (get your estimates from reputable republican wall builders). You'll realise that imported labour can account for no more than about 5% of jobs.

Most of what Dirty Donald does is completely appalling. People write about that, it fills the Internet, so Google reflects it, as per the page-rank algorithm.

Nothing fishy or "biased" about that.It would be biased if those stories did *not* appear in the search engine.

Besides which, Dirty Donald has a long history of lashing out with accusations and conspiracy theories whenever he's pushed into a corner. As happened last week for example,

How? Well, the logical conclusion of Mr. Cohen's testimony seemed to be that Dirty Donald had personally ordered Mr. Cohen to commit a federal crime.

Combined with the conviction of Mr. Manafort olus the news that Mr. Allen Weisselberg (Dirty Donald's longtime financial man) was about to testify against him. Ouch.

That's the kind of stuff that could even get a sitting president in deep trouble. My guess is that it made Dirty Donald nervous. Very nervous.

And what does Dirty Donald do when people make him nervous? Well, he tries to divert attention from his predicament by changing the subject and he lashes out against people with all kinds of accusations. We saw him do both.

As to trying to change the subject, he suddenly started talking about a preliminary draft agreement with Mexico and desperately tried to pass of what he had achieved (a few minor adjustments to the existing NAFTA treaty) as a major win.Plus he was quite desperate to call it something other than "NAFTA-plus-a-few-minor-adjustments".Considering his base, he may well get away with that.

As to lashing out, he always picks whoever he thinks he can sufficiently muddy the water against. The media. Search engines. Institutions. Mrs. Clinton. Illegal immigrants. The Government. Anything really. As long as it resonates sufficiently with his base to provide a target for a good smear campaign. In this case that would be Google.

As regards explanations for his coverage this explanation looks much simpler than any conspiracy theory about who met whom how often three to four years ago. It's all based on known facts about Dirty Donald's behaviour. As reported in the media.

Small wonder he hates the media that consistently put his grotesque and puerile antics on display.

Does he really have any credibility left? Apart from his diehard fan-base that is?

In play? You mean the trade war against China that Dirty Donald has just kicked off?

You mean the trade war that had already begun with steel tariffs?

No, I mean the trade conflict that Dirty Donald has grown into a trade war by promising tariffs on 200 bln. worth of trade.

Business was (and is) strongly in favour of it.

"Business" is always in favor of making money, no matter the cost to somebody else or the longterm future of the nation.

You mean mainstream business ethics that has for the past century or so consistently made our firms No.1 in the world and is the cork upon which our collective prosperity floats?

You can either put in place conditions that take care of the needs of business (such as the rule of law, free trade, and fair shot at getting a level playing field), or you can sacrifice all that for a short-term BS publicity stunt trade war, and end up with a big recession in a world where the rule of law is absent and success is determined by whoever has the best collusion between state and business.

Take your pick. Oh wait ... you already have. Silly of me.

Surely you understand trade issue with China is still in play? No, you do not, because you are in Denial Land.

In play? You mean the trade war against China that Dirty Donald has just kicked off? Which is probably going to cost a few thousand soy-bean farmers their farms? After a humiliating display of inane backslapping, rudderless posturing in return for "concessions" that will benefit Japan, South Korea, and Germany more than the US? You call that a success? Who's in denial here?

The devil is in the details. Signing a bad deal to try and get a better deal with China doesn't make sense.

TTP wasn't "bad" in any sense of the word. Business was (and is) strongly in favour of it. That means there's money in in. If you're afraid that US workers aren't going to benefit from that, that's a totally different problem.

Plus it was still not quite settled when Dirty Donald withdrew. It would have ensured that US norms and values governed trade in the Pacific, if not world-wide. Not Chinese ones. And with one populist stroke of the pen Dirty Donald threw all that away. Wow, what a huuuge success, right?

And now he's (a) alienated and atagonised US allies in the Pacific by showing them that there is little advantage for them in dealing with a fickle US instead of with consistent Chinese (b) proven to them that the US is stupid enough to abandon long-term objectives in favour of chasing a limited, short-term objective, (c) driven home the fact that they had better be very polite to Chine and make sure their own long-term strategy is aligned with China's.

That's what doesn't make sense.

In the mean time Dirty Donald has adroitly manouvered the US to the sidelines so that developments in the Pacific will more or less run their course without the US being in the lead. Well, hoo-rah! Let's sell that to the fan-base, shall we?