Ben Spitz (63/100 improv meals)

Sheaf herder. I believe in you 🔥

[Ben Spitz (63/100 improv meals) @DiracDeltaFunk]

I worked with UVA undergraduate Seth Bernstein on this fun project in homotopical combinatorics: https://t.co/YoChjFisuz

He'll be presenting a poster on it at the JMM this year! https://t.co/wUVxvBlL3K

[Ben Spitz (63/100 improv meals) @DiracDeltaFunk]

@NoahJSnyder Life moves fast

[Ben Spitz (63/100 improv meals) @DiracDeltaFunk]

@BigGuyHimself @tritlo @ShriramKMurthi Lol fair

[Ben Spitz (63/100 improv meals) @DiracDeltaFunk]

There's a classic (invalid) proof by induction that all horses are the same color: the inductive step P(n) ⇒ P(n+1) fails only at n=1.

Is there a fun non-theorem that would be true by a nice inductive argument, except that the inductive step fails only for n=7, or something?

[Ben Spitz (63/100 improv meals) @DiracDeltaFunk]

@mark_bikes This one has the problem that the base case is also wrong

[Ben Spitz (63/100 improv meals) @DiracDeltaFunk]

@tritlo @ShriramKMurthi Right but it's hard to write an faulty inductive step for this one.

[Ben Spitz (63/100 improv meals) @DiracDeltaFunk]

@Ryan_Triplett I would love to see a faulty proof by induction for the circle-region problem!

[Ben Spitz (63/100 improv meals) @DiracDeltaFunk]

@davidbessis Ok but that one's not fun :)

[Ben Spitz (63/100 improv meals) @DiracDeltaFunk]

E.g. some argument that implicitly assumes in the inductive step that every automorphism of S_n is inner? Would fail only at the P(6) ⇒ P(7) step

[Ben Spitz (63/100 improv meals) @DiracDeltaFunk]

@HunterEKozak @LinkofSunshine The choice here is between

guaranteed 0.1*X
vs.
1% chance of 10 billion dollars,

in a hypothetical world where your yearly income is 0.9*X, where X denotes your current yearly income.

It is *not* a choice between guaranteed 100 million vs. 1% chance of 10 billion.

[Ben Spitz (63/100 improv meals) @DiracDeltaFunk]

@anderssandberg The basic idea to use rings of integers of number fields is actually pretty obvious -- the problem is reminiscent of the classic "which quadratic rings of integers are euclidean domains?"

Disclaimer: I am not a number theorist

[Ben Spitz (63/100 improv meals) @DiracDeltaFunk]

@BibimbapNom @MTabarrok Because it's a logic puzzle, not a sphinx riddle

[Ben Spitz (63/100 improv meals) @DiracDeltaFunk]

@SpiritDirtbag @MTabarrok But there are not just 2 people on this island! If everyone already knows the information in the guru's announcement, being perfect logicians, couldn't they just run the inductive argument before the guru says anything? Would the outcome be exactly the same if there was no guru?

[Ben Spitz (63/100 improv meals) @DiracDeltaFunk]

@MTabarrok rot13:

Rirelbar xabjf gung gur theh frrf fbzrbar jvgu oyhr rlrf.

Naq, rirelbar xabjf gung rirelbar xabjf gung gur theh frrf fbzrbar jvgu oyhr rlrf.

Ohg, vg vf *abg* gehr gung rirelbar xabjf ... (99 gvzrf) ... gung rirelbar xabjf gung gur theh frrf fbzrbar jvgu oyhr rlrf!

[Ben Spitz (63/100 improv meals) @DiracDeltaFunk]

@chmonke My martingale gambling strategy is to just wander randomly around the casino floor

[Ben Spitz (63/100 improv meals) @DiracDeltaFunk]

@chmonke Think step-by-step, make no mistakes

[Ben Spitz (63/100 improv meals) @DiracDeltaFunk]

@gro_tsen I'm pretty sure he had early access to the result.

[Ben Spitz (63/100 improv meals) @DiracDeltaFunk]

@KnightShore Thanks, I should have been more specific -- I mean pure math

[Ben Spitz (63/100 improv meals) @DiracDeltaFunk]

The new arXiv policy is obviously v good for papers in math, where a paper has your name on it if and only if it is your work. The new policy enforces the very low bar that you read your own paper before you submit it!

Of course, this is not how authorship works in other fields.

[Ben Spitz (63/100 improv meals) @DiracDeltaFunk]

If you're going to have a culture where you get academia points for having your name on good papers you didn't contribute to, you need to also receive negative points when the papers are bad / have serious problems. Not reading your own paper is a serious problem.

[Ben Spitz (63/100 improv meals) @DiracDeltaFunk]

For comparison, imagine someone in your lab writes a paper which is completely fraudulent -- they just totally fabricated the data or whatever. All of the authors should suffer some consequence, even if they did not actually write the paper or contribute to it in any way!