Wait. What if by stirring I shook the glass and at the end set it back down a foot away from its initial location. Is this author claiming that Brouwer’s theorem guarantees a particle floating somewhere where the glass used to be? Unchanged?
I can imagine an unlimited number of scenarios where I can guarantee the water particles are displaced.
This seems like a bad application of the theorem, right?
As others have said, it's meant for mappings of the space to itself. So stirring the water, but not moving the glass.
But anyway, the theorem works only for continiuous mappings. The moment they started mentioning "water particles", instead of some hypothetical fluid that is a continuous block, the theorem no longer applied. You could break it by mirroring the position of every particle. There's still a fixed point (the line of mirroring), but there's no obligation that there's a particle on that line.
It's worth mentioning that there are higher level abstractions that are far more accessible than SAT. If I were teaching a course on this, I would start with either Answer Set Programming (ASP) or Satisfiability Modulo Theories (SMT). The most widely used solvers for those are clingo [0] and Z3 [1]:
With ASP, you write in a much clearer Prolog-like syntax that does not require nearly as much encoding effort as your typical SAT problem. Z3 is similar -- you can code up problems in a simple Python API, or write them in the smtlib language.
Both of these make it easy to add various types of optimization, constraints, etc. to your problem, and they're much better as modeling languages than straight SAT. Underneath, they have solvers that leverage all the modern CDCL tricks.
We wrote up a paper [2] on how to formulate a modern dependency solver in ASP; it's helped tremendously for adding new types of features like options, variants, and complex compiler/arch dependencies to Spack [3]. You could not get good solutions to some of these problems without a capable and expressive solver.
[0] https://github.com/potassco/clingo
[1] https://github.com/Z3Prover/z3
[2] https://arxiv.org/abs/2210.08404, https://dl.acm.org/doi/abs/10.5555/3571885.3571931
This is part of why I’m not worried about the current crop of generative AI. I am however both curious and concerned about what the tsunami of talent and $$$ chasing the current trend will achieve.
If this n^(4/3) alt transformer compute scaling is real (and there’s been many a pretender, so it’s too early to tell), then that could fundamentally change the overall AI scaling law, substantially lowering the brick wall.
And that could be a game changer.
If it's useless, it can hardly replace jobs, can it?
As I understand it, it's ok to reference a Pantone Color by name without a license (nominative fair use), but that gives you no idea how to use or display it. So photoshop files could store both the pantone color name (for printing and profressional color matching purposes) and a substitute color for display on screen when unlicensed.
The UI would either prompt users for the substitute color, or automatically fill it if they did have a license at the time they selected the color. That way files wouldn't break quite so horribly when licenses expire.
Can someone explain to me how, whenever wind energy is mentioned, any sort of of scepticism, and I don't mean "snarky internet contrarian" scepticism, I mean "human being who has lived on Earth" scepticism, ceases to exist?
Is there actually a large population out there who has never experienced outside weather conditions in which there was no wind?
Or do you... think that bad things will not happen to you if you just believe in transparent bullshit hard enough? Because I'm sorry, but they will.
How. Does this Shit. Get Written?
The best, most reliable sources of wind, FYI, are known by anyone in industry to be very far away from most built structures, and high.
The fact a few people might misinterpret it is a marketing bonus, but surely negligable, because no one could believe that.
Many of the points seem to be hallucinated. Either the author has a poor memory and an active imagination or there has been some poor-quality LLM input.
Examples
> There are apparently no sociopaths – Culture has to recruit an outsider when they need one
Banks describes several ways how such individuals are managed - such as offering full immersion level VR to satisfy extreme megalomania.
> We also see that there are a number of Eccentrics, Minds that don’t fully share the values of Culture. They’re not that rare, about 1% of the population.
I don't believe that 1% figure is mentioned anywhere. I'd be surprised if it was. Eccentrics seem to be much rarer than that.
> We even see GSV Absconding with Style stockpile resources without general knowledge of the other Minds.
This name is made up, and not by Banks. A Google search for "absconding with style" has only a few hits - mainly this article.
I could go on...
Some of these were my own supposition - 1% felt about right for how casually they are mentioned in story.
> Banks describes several ways how such individuals are managed - such as offering full immersion level VR to satisfy extreme megalomania.
I don't remember that at all, perhaps you could tell me which book to look at.