The determinant trick I'm referring to is used in prop 2.4 (in the Version I found via Google).
They use the determinant of the adjugate matrix if I remember correctly... But they just hit the reader with this without any motivation or even naming it.
> then that's a problem with the original question - not the solution itself
I think there's a good counterexample to this:
Atiyah/MacDonald proove the Nullstellensatz ultimately by using some trick involving determinants.
They give a very nice theoretical treatment of the content and context of the theorem. But the proof at one crucial point uses techniques that live conceptually outside of this context: While its possible to see that the argument is sound, it does not give a good explanation of _why_ it's true within the context of the theorem.
(You could of course argue that they did not give enough context
... but that's exactly my point: the trick makes the proof work but hides the explanation)
I think trying to iterate on a "spectral decomposition of your intent" - slowly working on increasinly refined breakdowns of what are the different aspects of your project are - both on the domain- and also the technical level; aka requirements and architecture. And then don't directly iterate on the code but rather regenerate/update the codebase based on the new intent and the old codebase... And a decomposition of the whole thing in terms of optics (open lenses, etc) where the decomposition respects the "spectral decomposition".
> A ProseMirror 2.0 with an incompatible interface would amount to the same but make it ambiguous what people mean when referring to ProseMirror. Trying to graft stuff on in a backwards-compatible way as an 1.x version would produce a compromised win32-style mess.
> If you look longer term, a society that does this will end up a lot poorer than one that doesn't.
Got data to back that up?
(On the serious level, I'm really curious; But on the polemic level I'll call BS - I highly doubt there ever was such a period in any capitalist country ever)
But I think there's a middle ground: You can definitely use GenAI to bring yourself to the page.
But that requires effort that goes beyond "draw me a pelican riding a bicycle".
I've used to create abstract art/(or "images that look like abstract art" if you prefer - let's not get distracted by this branch of the discourse) using midjourney: getting the AI to output something worthwhile would usually take me hours of iterating over a prompt - entering a feedback loop until two things happen: first, congruence between your intent and the output (both change during iteration! ); second, the output stabilizes with growing prompt length. and so generating the output turns from a slot-machine into something deliberate and personal
(lots of caveats of course but i think it's a worthwhile perspective)
PS -- What I forgot to mention: Its usually a hard fight to get out of the slop zone; The midjourney models have very boring default aesthetics and styles of composition (insultingly boring!)
isn't this exactly what a certain kind of real world dev would do?