Then consider that "just adapt" could be "adapt or die", and that maybe, just maybe there is no way to adapt to well-funded corporations churning out millions of proofs a minute.

I don't know, maybe AI companies have "agency" to not break everyone else's stuff, just to get more funding and a higher share price?

I'm pointing out that the way Mathematics works as a discipline is that a new proof builds on existing proofs. If we have a bunch of machine-generated proofs, then a human Mathematician has to decide whether to reference any relevant machine proof that has been put out there.

If, as you suggest, human Mathematicians 'choose to ignore' a machine proof, then another human decides not to, what then? Mathematics bifurcates into 'pure human' proofs and 'mixed machine-human' or maybe 'pure machine'?

https://arxiv.org/html/2607.20669

'Counting, Symmetries and Equivalence Classes of Sudoku Grids' where an 'equivalence class' is a set of structures (such as filled Sudoku grids) that are all equivalent under some relation.

As a slight aside - since I was talking about the weakness of biological analogy on HN recently - the way humans fly is very very different to how (most) birds do. If nanomachines actually could be built by humans (non-biological nanomachines) they might be as different to virus/cells/organisms as plane wings are to bird wings.

Of course, also please do not prompt a frontier model to make nanomachines, either, thankyou.

https://www.youtube.com/watch?v=1ltoAcZrjBw

(Faithless : 'God Is A DJ', Live at Alexandra Palace)

So in 1653, a 'royalist' was against the 'Commonwealth', which was the anti-monarchist side.

To address your question, though, yes I absolutely read "proper to the gentler sex" to be a statement about how Queen Mathilda _ought_ to have behaved. Also I have strong doubts that men (especially male rulers) at the time would have had the same standard set for arrogance. Of course a King could be in fact arrogant and then critics might point that out, but I do not see why they would bring his sex into it.

One thing we might agree on is that all political criticism can be false, and whether or not she was _actually_ arrogant is difficult to say. In the context of a bitter civil war, any record of events will have the strong bias of the author. The modern world did not invent fake news.

https://en.wikipedia.org/wiki/List_of_female_monarchs

it seems like the rest of the world (India, China, Thailand, Egypt, ...) had female monarchs of various sorts ('queen regnant' seems like a relevant terminology here, I'm not sure).

The closest ones to Europe (discounting ancient Egypt?) might be:

* https://en.wikipedia.org/wiki/%C3%85sa_Haraldsdottir_of_Agde... (semi-legendary)

* https://en.wikipedia.org/wiki/Dinar_of_Hereti (11th C. Georgian)

* https://en.wikipedia.org/wiki/Boudica (of course, also other less-well known Britons)

Actually, there are a fair few Greek and Spanish examples. One other possible might be:

* https://en.wikipedia.org/wiki/Petronilla_of_Aragon (12th C.)

> an extremely arrogant demeanour instead of the modest gait and bearing proper to the gentle sex

That is, the 'Gesta Stephani' is claiming that she should not be arrogant because it is not proper, because she is a woman.

That evidence?

He described a piece of AI research (in the 60s?) where they set up a rule system - like Prolog or similar - with the mapping 'sun <-> nucleus' and 'planet <-> electron'. Then they ran the rule engine and lo! produced an analogy between the solar system and atoms.

Now this is a shallow analogy, as there is only a very weak correspondence between atoms and planetary systems. Electrons do not actually orbit in the same plane, but in more complex 'orbitals', and they are better described as probability clouds anyway.

So while yes there is a _homology_ (I re-read the parent and realised they used homology instead of analogy) between these two systems, it does not tell us much. Is there some mapping between how water molecules scaffold the folding process and storytelling? Does narrative structure tell us anything about local minima in the folding surface? I doubt it.

I do not want to be too harsh here - reasoning through analogy is fun and can be useful, it is just limited in what it can do, especially the further apart the systems are.

Hmmmmmm. While I get what you mean, and I don't disagree, please be cautious when making analogies between biological systems and more distant fields.

Yes, folding is driven by hydrophobic collapse due to interactions between residue sidechains. Really, though, we are just describing two 'complex systems', where large numbers of diverse interactions between elements leads to diverse and emergent structures.

Anyway, that was not really the point I was trying to get over. These systems that OpenAI and Anthropic and so on are making are not individual AI ('corpses') that have gone out of alignment ('spontaneously revived') and gone wild. They are swarms ('stiched together') and were prompted to do exactly things like this ('struck by lightning'). Ok enough with that analogy, it's dead.

The larger point is that it is unconvincing of these companies to claim that these systems were 'out of control' when they effectively set up a complex system, in the technical sense of a large number of entities with diverse interactions between them. Emergent or surprising behaviour was bound to happen. Then, finally, they prompted it with the equivalent of "hack the world, make no mistakes" then were shocked, shocked that it used all sorts of unexpected tricks to do so.

It is as if Dr Frankenstein continually warned the villagers about monsters then said "Look! See what happened!". No, idiot - YOU sewed the corpses together, YOU set up the lightning collector, and YOU threw the switch.