Someone call @keithw. He put a tremendous amount of brainpower into getting the Unicode side of this puzzle "right" (or, as "right" as it is possible to be) when he wrote mosh. I'm sure he and Hashimoto could have a grand old (but zero-width non-joining) conversation!
If the analogy to warped spacetime was exact, then there would be a “scale factor” for every point depending on the local transit speed. Then it would be possible to do as this page does and for the answer not to depend on starting point.
However in the real city the transit speed at any point is not isotropic, the space is 3-D, and some paths are forbidden (getting on-off the train between stops).
Does it still go rancid if it’s kept at boiling temperatures? I’m guessing that if it’s too hot for microbes, then you only have to deal with oxidation at the surface, which can maybe be fixed with periodic skimming. Maybe?
iirc I kept it hot (scalding) but not boiling. I was worried it would boil dry overnight and burn/ruin the pot, but maybe I just need to keep the liquid topped up enough so that doesn't happen. I'll try this next time, thanks!
You don't have to keep the soup perpetually simmering in modern times. You let the pot cool to room temp after eating, then throw in the fridge. Next day, bring to boil before dinner with enough time for the new ingredients to cook. This also makes sense for a home setup, unlike a restaurant where the replacement dynamics are very different.
Assuming you are only doing this for one meal a day, and not eating it for all your meals.
AIUI, there is a technical criterion for an ambient EM field to imbue circuits within it with broken time-reversal symmetry.
One example of a system that meets the criterion is a ferromagnet. Another is this altermagnet.
One example of a system that doesn’t meet the criterion is a diamagnet. Another is the anti-ferromagnet.
Roughly speaking, some systems are microscopically “asymmetric enough” to be useful in a certain way, and others are “too symmetrical.”
Ferromagnets have a downside that altermagnets avoid: their microscopic fields don’t average out to zero over macroscopic distances.
I think, but honestly don’t really understand, that the goal is to cause the material to treat currents of spin-up and spin-down charge carriers (think electrons or holes) dissimilarly. Constructing materials that distinguish between charge carriers of differing spin is a step towards spintronics. Again, I don’t know why that’s important, but it is what it is.
To add a bit more to this, it's really a new class of magnetism. Traditionally we might think of ordered magnetic materials as being one of two: ferromagnets, which is what you think of when you think of magnets, and antiferromagnets. Antiferromagnets locally order their magnetic moments antiparallel so any which way you measure it, you measure no magnetization.
The application is this: We would like to use ferromagnets and spin currents to make spin-electronic devices ("spintronic") where only the spin information is transferred without any large electrical currents. The goal of this is to save energy from Joule heating as spin can flow with significantly lower energy dissipation.
Ferromagnets run into a lot of problems: they have a stray field, so patterned elements will interact and interfere with each other that sets a limit on how dense each nanostructure can be. Antiferromagnets have a big problem: they are extraordinarily difficult to measure and that is a challenge to overcome.
So the benefit that altermagnetic materials presents is a clear union that tries to overcome the problems of both while retaining the strengths of both.
The exact definition of the ordering of an altermagnet is a bit subtle and it mostly comes from an understanding of how the electronic band structure is different as compared with normal antiferromagnets.
Renegadry aside, for those who are more interested in the Information Theory perspective on this:
Kolmogorov complexity is a good teaching tool, but hardly used in engineering practice because it contains serious foot-guns.
One example of defining K complexity(S, M) is the length of the shortest initial tape contents P for a given abstract machine M such that, when M is started on this tape, the machine halts with final tape contents P+S. Obviously, one must be very careful to define things like “initial state”, “input”, “halt”, and “length”, since not all universal machines look like Turing machines at first glance, and the alphabet size must either be consistent for all strings or else appear as an explicit log factor.
Mike’s intuitive understanding was incorrect in two subtle ways:
1. Without specifying the abstract machine M, the K complexity of a string S is not meaningful. For instance, given any S, one may define an abstract machine with a single instruction that prints S, plus other instructions to make M Turing complete. That is, for any string S, there is an M_S such that complexity(S, M_S) = 1 bit. Alternatively, it would be possible to define an abstract machine M_FS that supports filesystem operations. Then the complexity using Patrick’s solution could be made well-defined by measuring the length of the concatenation of the decompressor P with a string describing the initial filesystem state.
2. Even without adversarial examples, and with a particular M specified, uniform random strings’ K complexity is only _tightly concentrated around_ the strings’ length plus a machine-dependent constant. As Patrick points out, for any given string length, some individual string exemplars may have much smaller K complexity; for instance, due to repetition.
I love the drama of how the abstract is written, but TBH I don't think this is a surprise. I believe it's well-known among color theorists that large perceptual distances are inconsistent with sums of small differences. So maybe the most generous thing to say here is, good on them for bringing awareness of this subtlety to a broader audience.
Not only that, it is also well known that the smallest perceptible color difference (ΔE=1) is not actually consistent, even in the "perceptually uniform" color spaces.
So ΔE is actually 1 in some parts of the space, but up to 4 in others. However, that is "good enough" for the purpose for which these color spaces were created: quality standards for color ("can I buy more of the same color and it will look the same?"). If your measured and computed ΔE is below one, the difference will not be perceptible by most humans regardless.
And last I checked, new and improved "perceptually uniform" color spaces are proposed every couple of years.
I don’t see how the author’s arguments about impossibility results pertaining to “distributed sub-symbolic architectures” apply any more strongly to LLMs or DNNs than they do to human brains. Human programmers aren’t magically capable of solving the halting problem either, but we muddle through somehow.
Yea. Most of what we do isn't that rigorous and it's fine. When we do need rigor, we use external tools, like classical computer programs or writing math down on paper. LLMs can use external tools too. We're also hopeless at explainability - people usually have no idea why they make most of the decisions they do. If we have to, we try to rationalize but it's not really correct because it doesn't reproduce all the intuition that went into it. Yet somehow we can still write software!
https://arxiv.org/abs/2405.02389