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'?
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'?
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?
'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.
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.
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:
That's not sexist though, it is just equivalent to noting she's a woman (like calling her "her" and "she") because we can reasonably offer the same criticism about a man. A man can have an extremely arrogant demeanour instead of the controlled gait and bearing proper to the stronger sex. And adjusting for language drift people do make that sort of complaint of men, I remember one criticism of Biden being that he walked in a frail way and fell over a lot - literally complaints about his gait and bearing giving a bad impression. Not a very strong criticism but he was male and it was made.
We might reasonably infer that she got called arrogant for doing something that wouldn't be considered arrogance in a man, the article has unhelpfully elided that detail (maybe the original author did as well). But we've also got to admit she might have actually been unusually arrogant, that does happen from time to time. If I were in charge of a military I'd be standing around even more arrogant than I already am.
pjc50 offered a good example of something that was actually gendered - women not being able to own property in their own right for whatever unfair reason. The quote isn't that sort of out-and-obvious sexism. Said quote could almost be modern political whinging.
PS I'll add in an acknowledgement that words did mean different things back then so possibly at the time the only reasonable reading was with an "[as with all women]" on the end, but the fact is that as written this quote is making specific accusations of arrogance and arbitraryness that are not contained to either gender and are bad in all leaders, female or otherwise. He didn't write "women are all arrogant" or "women are all arbitrary". If anything the thrust of the quote is most women weren't either of those things. It doesn't support the idea of double standards or ludicrous criticism that would never be made of a man.
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.
Arguing that a criticism focusing on her behaviour allegedly not being "proper to her sex" isn't gendered whilst handwaving away all the well established historical context about how women were treated to invent new context where she deserved everything she got is bold, I'll give you that...
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.
I don't think that's why it's called a "Privy Council". Just because the only meaning for privy that you know, today, is a toilet, does not mean that the word in another context means toilet, any more than the fact you know the verb "do" in English can be slang for sexual intercourse means that when Marlo says "Do it or don't" in The Wire he means for his soldiers to have sex. He's indicating that he doesn't care whether they murder Bubbles.
"Privy" more generally means private or personal, which explains its use for a group which advises specifically the monarch alone.
> According to the Oxford dictionary the definition of the word "privy" in Privy Council is an obsolete one meaning "Of or pertaining exclusively to a particular person or persons; one's own",[3] insofar as the council is personal to the sovereign.
> 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.
Analogies are like models, some are useful, but they're all wrong. Just because we can analogize between protein folding and narrative/storytelling doesn't mean that we can derive anything particularly useful about one from the other except maybe to give an intuition about complexity. The mechanisms and math behind protein folding and an analogy between that and storytelling doesn't necessarily give us any mechanism for or deep understanding into storytelling.
Yes — I get unreasonably upset when people nitpick holes in good analogies as if it is evidence of intellectual weaknrss, rather than working with and around them or suggesting overlapping analogies that address those limitations. And the hole in the analogy may even be the most valuable thing about it.
The fact of a hole in an analogy is not in itself information. Of course there's a hole.
The video is about congnition specifically, and not necessarily about communicating with analogies.
> I get unreasonably upset when people nitpick holes in good analogies…
What you’re describing is exactly why I strongly recommend avoiding analogy when communicating: Don’t tell me what a thing is like, tell me what the thing is. This forces really thinking about how to describe the thing precisely and succinctly. (Edit: The listener will make their own analogy.)
On the contrary, analogy is absolutely a foundational communication technique.
But you do have to choose an analogy that your listener does not need to consider first. They need to know the subject of the analogy without having to question your description of it.
> You would conclude that storytelling is higher structures of some base unit
I'd be very surprised to meet someone who learned that lesson by comparing protein folding (suggesting a high level of intelligence and probably education in order to understand) to storytelling, rather than having learned that stories are made up of parts in grade school or as a child just hearing, reading, thinking about, and making stories.
> Analogies are like models, some are useful, but they're all wrong.
Very much agree. Every abstraction loses something and so is wrong in some sense, but some shave off in clever places, and allow new shortcut paths of thought and insight, sometimes to an existing place... but sometimes to a new place that was previously unreachable, or not sufficiently reachable by the necessary type of attention/minds.
> The mechanisms and math behind protein folding and an analogy between that and storytelling doesn't necessarily give us any mechanism for or deep understanding into storytelling.
Respectfully, I actually disagree (as someone trained in biochemistry).
For one example:
proteins = 1D chemical structures, peptides popped onto end one-at-a-time, that in the right chemical environment, fold into a low-energy 3D state that transforms its environment through work
stories = 1D semantic structures, words popped onto end one-at-a-time, that in the right cultural/cognitive environment, fold into a low-energy HD mental model that transforms its environment through work
This has led me to render embeddings of sliding windows of narrative streams (to investigate shapes of broadcast stories), and look for analogs to "active sites" in the way that a story interacts with the cultural medium, measured through dimensional reduction of aggregate valence reactions amongst a viewing audience.
Obviously there's more to the metaphors I use than that, but that's the one I'm leaning on to inform my work with sensemaking and map-making from valence response data. Aggregating crowd-sourced valence reactions to linear narratives gains a lot of insight by reflecting it off how we process and think about linear peptides in protein folding.
I've been developing tools inspired by these metaphors, and my research and prototypes are directly informed by what knowledge of the biological domain inspires me to port into social domain. I'm lucky to have interactions with interested parties associated with federal government, practitioners of democratic reform, and academics investigating platonic space hypotheses. I'm definitely on the edge of an ecosystem, but anything I've done of value has been guided by the metaphors that direct my attention to potential applications and research. Someone could get to my conclusions another way, but the metaphors are my cheat codes to arrive there early :)
And it goes both ways along a good metaphor -- People who develop tools in the biological sciences have told me that my porting their methods into my own distant domain has inspired them to improve their tools to ask better questions of their own biological data. So it's very fruitful work that I wholly credit to travelling both ways across an insightful metaphor. https://i.imgur.com/AeYxx7p.png
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.
You've made me realize much of the value is in trying to port tools and methods from one domain into another. It's that when you realize the analogs across domains on either side of a good metaphor, you realize how investigations in one domain (perhaps with more obvious data to collect, or more obvious value in analysis) can be run in the other domain, and sometimes generate non-obvious value.
I expect because it's overly reductive to the point of falsehood. Two sufficiently complex systems will likely exhibit enough parallels to form a useful analogy, but that does nothing to reflect the ways the systems aren't alike.
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