macrolocal

Russell's paradox was 1901. Likely afterwards.

Russell once remarked that all of mathematics would be trivial to a sufficiently intelligent being. It builds conceptual tools for limited minds, that lets them understand far beyond their natural reach.

In a world with ASI, having that capacity is vital.

Nb. This isn't about Lie theory.

Say what you will about Peter Thiel, he does have a sense of humor.

By analogy with stacks, my intuition is that Spec(N) still has a one-dimensional geometry, but with a (-1)-dimensional tier from quotienting out the prime points by a semiring action.

Yep, you need category theory to express something as trivial as the definition of a monad.

Upvoted. USAID has been misused plenty: political meddling in Bangladesh, Cuba's ZunZuneo op, boomerang aid in Haiti, Afghan contractor enrichment, etc. I could go on.

But understand: the soft power isn't going away, just the doctors, food shipments, and vaccines.

To be fair, if we're living in a simulation, Jesus does feel a bit like a Chekhov's gun.

Imagine chess played on a board with opposite sides identified, like in the video game Asteroids. Does white have a winning strategy?

In the right dynamical framework, I bet I'm a strange autoregressor.

Lieven Le Bruyn is just in the habit of cataloguing how algebraic geometry culture shows up in unexpected places, eg. http://www.neverendingbooks.org/what-about-simone-weil/ . Surprising to see on Hacker News.

FWIW, Achenbrenner discusses some of OpenAI's motivations here:

https://youtu.be/zdbVtZIn9IM?si=F7evv4xfSjsS-Gob

It looks like we've hit a reply depth limit, which is maybe for the best, because I don't think we're making any progress here.

> You did use tautologies...

You seem to think calling something a tautology is a way to dismiss it. Almost everything in mathematics is a tautology-- most of what I say is a tautology. Any rigorous argument is tautological; it's the aspiration of literally all formal reasoning.

> Lots of uninteresting and bad music is also entropic.

And here, you seem to think someone is claiming that entropy is equivalent to music quality, not just a useful correlate or eg. indicator of something that might be more likely to show up in good music than bad music. I don't know of anyone making that claim; all the examples I gave require mild correlation.

You said I was using tautologies as straw men, which is incoherent and suggests you’re not arguing in good faith.

Anyhow, of course entropy correlates to music quality; maximum entropy music is white noise! I’ve even had luck finding interesting jazz musicians from the distribution of key signatures they use—- anything more entropic than the Real Book is a great indicator. Similarly, network entropy makes it easier to identify musicians with a flexible arsenal of riffs. You could adapt it to chord progressions to find unusual reharmonizations in live jazz to study and practice. It could be a helpful regularizer for neural network music generation. Entropic methods are among the most powerful in statistics.

Tautologies don't make for good strawmen, and network entropy doesn't need to identify the quality level of music on its own to be useful.

Of course network entropy provides useful information—- just maybe not the particular kind of depth you seem to be looking for.

I’m also curious why you’re arguing with my tautologies!

Sorry for the cliché, but "the most exciting phrase to hear in science, the one that heralds the most discoveries, is not "Eureka!" (I found it!) but 'That's funny...'" --Asimov

My point is just that proving known facts can be useful and interesting.

As for the paper, network entropy and node heterogeneity seem to be perfectly sensible statistical concepts, and encode useful information. They also dovetail conveniently with powerful tools in machine learning. Criticizing this paper for lack of potential applications feels unreasonable.

You might be missing my point somewhat. :)

First, the methods of the paper don’t have to be a Mendelssohn replacement to be useful. Second, if you don’t like that potential application, consider all the other predictive models that could benefit from these features.

You might be missing the point somewhat. With these methods, you could eg. test the vast swaths of potentially overlooked composers to see if any of them merit closer listening.

A killer app for me would be proper Blender integration, say with VR viewports.

Also, error bars qua statistics can indicate problems with the underlying data and model, eg. if they're unrealistically narrow, symmetric etc.

Nb. Plato claims Solon found written records of 'Atlantis' on a visit to Egypt, around 600 BC. That seems consistent with the Santorini hypothesis and Egyptian historians.

FWIW, that one line is the parallel postulate.

This is a legit topos.

For most of this era, I find it helpful to think in terms of the Angevin empire, not England.

For automorphic forms, absolutely.

Right, that's 1823, about the time of Frederick William III. Beethoven might have dedicated a symphony to you.

All they need to do is slightly bias their recommendation engine, maybe in different ways for different users. Not too hard using Monolith.

> And if that happens, the audience moves on.

For what it's worth, this idea that propaganda is noticeable is itself propaganda.