https://arxiv.org/abs/2405.02389

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).

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.

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.

The author puts a lot of breathless energy into airing grievances and lodging accusations. I find I don't much care: I want to know whether they have identified an experimental, quantitative, or pedagogical problem to be solved. The crypto-gnosticism of allegedly-suppressed history has everything to do with a perception of injustice and nothing to do with physics.

Another red flag is the parenthetical structure of the diatribe. Rather than picking one point at a time and making it well, the author runs into the metaphorical theory-space blasting wildly in all directions. What does thermodynamics have to do with any of this? It seems to be mentioned at the beginning and the end mostly to imply that Clausius and Helmholtz have been involved in some kind of conspiracy to suppress history: an argument which this margin is, apparently, too small to contain.

A third red flag is the absence of quantitative, minimal test cases: worked-out homework problems with testable predictions. Einstein's gedanken-experiments have become an irreplaceable part of the pedagogy of special relativity precisely because they are such an effective tool in focusing the learner's attention on one mystery at a time. A teacher who tells you "this is simple, really, anyone can understand it!" may be overly enthusiastic or even wrong. But a teacher who tells you "this is complicated, nobody can understand it! See, here's a Gordian knot of inseparable ideas! Don't let anyone tell you they can understand this!" bears the burden of proof that the indicated concepts cannot be developed individually.

If we set aside the emotional power of an appeal to our sense of injustice, the remaining content of this piece doesn't stand on its own. Yeah, sure, lots of things happened in the 19th century that I don't know about. Lots of wrongs have never been righted. Other than a half-hearted implication that gravity and electromagnetism can be unified (remarkably without any mention of Kaluza or Klein), or that something is rotten in the state of thermodynamics, this piece adds nothing substantial to my understanding of the universe.

The entire world production of neodymium was on the order of 80k ton/yr the last I checked (though that was quite a few years ago).