Adrian Miranda

Low dimensional category theorist from Australia

[Adrian Miranda @AdrianTMiranda]

@TaliaRinger Same here! The thing I want to know is if there are people who have the opposite disposition (finding spheres intuitive and cubes counter-intuitive), and if so how do they think about them?

[Adrian Miranda @AdrianTMiranda]

@DmitryRybin1 Ramanujan did more than find spurious coincidences and mysterious formulas lol. Some of his work had an impact on the decades to come. The Ramanujan bot from 5 years ago, while clever, did not do that.

[Adrian Miranda @AdrianTMiranda]

@miniapeur https://t.co/mEHFvaZjOB

[Adrian Miranda @AdrianTMiranda]

@GaryMarcus I agree that generalisation of this kind of achievement to non-verifiable domains has not yet been demonstrated. Yet this kind of thing happening by now was almost unthinkable a year ago, including to you iirc.

I too get accused of moving goalposts when I'm just updating priors.

[Adrian Miranda @AdrianTMiranda]

@eshear The only approximation that is arbitrarily precise is the exact approximation! Maybe you mean interacting with a (computable?) function that takes as input an error threshold and outputs an approximation to within that threshold?

[Adrian Miranda @AdrianTMiranda]

@JDHamkins Good point! I wonder if there is an interesting (i.e. neither obviously true nor obviously false) version of Collatz for ordinals.

Incidentally, what is omega -1 in this natural ring of ordinals? Also, addition of ordinals is not commutative, right?

[Adrian Miranda @AdrianTMiranda]

@JDHamkins * 3*alpha +1, sorry!

[Adrian Miranda @AdrianTMiranda]

@JDHamkins Yes: If alpha = 2*beta for some ordinal beta, collatz( alpha ) = beta. Else collatz( alpha ) = 3*beta +1.

Then, refining what I said above, the collatz conjecture might say that all non-limit ordinals are eventually sent to the ordinal successor of a limit ordinal.

[Adrian Miranda @AdrianTMiranda]

@AcerFur Ah yes, elementary century old open problems.

[Adrian Miranda @AdrianTMiranda]

@ElliotGlazer CH doesn't have a TV in ZFC (assuming ZFC is consistent), but it does in stronger set theories which are able to settle it. Analogous statements hold for AC. We don't yet know if GC has a TV in PA. The parallel postulate has different TVs in different axiomatizations of geometry.

[Adrian Miranda @AdrianTMiranda]

@Noahpinion Progress has greatly exceeded most people's expectations, but I don't see the demand for professional mathematicians decreasing due to new tools. We will just spend our time doing different things, like how we calculate less by hand now vs 100 years ago.

[Adrian Miranda @AdrianTMiranda]

@scaling01 Shouldn't a bounded fit eg logistic be taken for average score?

[Adrian Miranda @AdrianTMiranda]

@ElliotGlazer I imagine it's not the 10^200 doing the heavy lifting here?

[Adrian Miranda @AdrianTMiranda]

Even a rationalist utilitarian who values themselves > others > 0 should take into account what other people would do.

eg you are playing your millionth round of scissors paper rock against someone who has played rock in all previous rounds.

Do you

1) play paper
2) randomise?

[Tim Urban @waitbutwhy]

Everyone in the world has to take a private vote by pressing a red or blue button. If more than 50% of people press the blue button, everyone survives. If less than 50% of people press the blue button, only people who pressed the red button survive. Which button would you press?

[Adrian Miranda @AdrianTMiranda]

@mangassmangass Tbc I was referring to the quoted tweet, not my own.

[Adrian Miranda @AdrianTMiranda]

Let x be proving this statement. Find y.

[Anthony Bonato @Anthony_Bonato]

∀x ∃y (x is a problem → y solves x)

[Adrian Miranda @AdrianTMiranda]

@CarinaLHong I get that this makes competition on this benchmark unfair, favouring richer corps. But since these are open problems, isn't there "no such thing as cheating" including by training on the test set? I.e. progress by any means is signal. Genuinely curious and happy to be corrected!

[Adrian Miranda @AdrianTMiranda]

@AcerFur https://t.co/vW7V7uaQH6

Sorry not sorry lol

[Adrian Miranda @AdrianTMiranda]

@scaling01 The person @hankgreen was interviewing was... literally a professional domain expert in computer security.