gilleain

Consider that 'calculator' used to be a title for a role a human used to do. That went away, which is probably fine as there were other jobs and likely it was tedious.

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?

No, obviously not ...

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'?

The Math community can "not use" a proof? How would that work? It's a little like coloured functions (async etc) - you have 'human proved' vs 'machine proved'?

Sadly my group theory knowledge is rudimentary, and rusty. Probably you could? No idea.

There is a way of understanding all this through group theory. eg:

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.

Interesting. I can replay or simulate other people's voices (real people, obv) and can 'hear' music I know by replaying it in my mind. Of course, not perfectly if I forget the words, it might fill in with some tum-te-tum, or only recall a fragment, but it's usually playing as at source. Makes earworms very annoying, of course.

Yes, but also viruses do not actually have goals as such - maybe 'replicate' could be their only goal. So a virus _could_ come up with a mutation that kills all its hosts, it just dies out as well in the process. Not very reassuring for the host!

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.

Going to church, you say? :D

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

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

The first English civil war started in 1642, Charles I was beheaded in 1649 and his son Charles II would not be king in England before 1660 at the restoration.

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

Ok, I suppose I understand but I really do not agree. Modern criticism of the US president is so far removed from medieval criticism of a female monarch as to be nearly irrelevant.

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.

No idea, but from this handy page:

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.)

Evidence such as this quote?

> 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?

Further, there were specific reasons why Elizabeth I was treated differently to her father. For example, Henry VIII used to meet with counsellors when he woke up in the morning, still in bed. For obvious reasons, this was not done when his daughter reigned.

It's a fair question - my concern is 'shallow' analogies. I can best describe this with an anecdote paraphrased from memory from one of Hofstadter's books.

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.

> Protein folding and narrative/storytelling have strange homology

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.

Not sure what you mean by "an artistically symmetrical piece observes no mathematical symmetry" - as in, the underlying structure has a (set of) symmetries but the 'decoration' on top is asymmetric?

About a minute and a half.

Thankyou for the correction, and for continuing the analogy. Unfortunately when the peasants get their pitchforks and torches, they may not distinguish the Dr Waldmans from the Dr Frankenteins either. Hopefully they will.

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.

But it is the very people who warned us about rogue AIs going out of control that set up a system that enabled and failed to conrol it.

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.

Syndicate!! Actually, this one feels especially appropriate to use an LLM for.

>>> len("[(x%3<1)'Fizz'+(x%5<1)'Buzz'or x for x in range(1,101)]")

57

This can be great - Tom from the Yogscast has run a few of these, and they can get pretty wild. It's a simple premise but works well.

A vanadium one, which (as mentioned in the piece) is symmetric.

The 'Just Have a Think' channel did a video on the Swiss battery here - https://www.youtube.com/watch?v=CPAFeTvjVzY

There is the saying "the empty vessel makes the loudest noise". This was part of the reason I eventually left Reddit, as I was getting sucked in to the habit of making empty meme-like responses to posts.

Some of the worst places for comments I've seen are on youtube - just the lowest effort ("who is listening to this in 2026?!") or the most obnoxious, or just misunderstood. Partly this is because of voting systems combined with large numbers of people. Partly because of bots I suppose.

Yes, dimethyl mercury is terrifying stuff - it killed Karen Wetterhahn from a few drops that went _through_ the gloves she had on:

> The case proved that the standard precautions at the time, all of which Wetterhahn had carefully followed, were inadequate for "super-toxic" chemicals like dimethylmercury

(from the Wikipedia page [3])

Both are fine, but I also prefer 'furnish', as in put in the main parts of your CV. In a way, 'burnish' is more like 'polish', suggesting an extra layer on top, rather than the fundamental parts.

> Your comment has three hands

Also sometimes known as 'The Gripping Hand'

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

Huh:

https://en.wikipedia.org/wiki/Helter_skelter_(ride)

First known appearance on Blackpool Pleasure Beach in 1906.

Great soundtrack. My favourite scene that uses music in the film is when 'Search and Destroy' plays when shooting pirates:

https://www.youtube.com/watch?v=XQbhuxiyv5c

Great article actually. Mirrors the mournful tone of the film.

"Blá nótt yfir himininn ..."

Some of the confusion here is from our history. This is my (likely confused) understanding:

James VI/I (https://en.wikipedia.org/wiki/James_VI_and_I) was king of _both_ England and Scotland and only later did the Union https://en.wikipedia.org/wiki/Treaty_of_Union combine the two. You might notice I've neglected Wales which was (considered?) part of England.

In any case, England is a country, yes. Also the UK is a country.