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Leo C. Stein

@duetosymmetry.com

837 Following4.4k Followers

Physics Prof @ U of MS. Sloan Fellow. Black holes, gravitational waves, general relativity & beyond. Formerly Caltech MIT Cornell. Need thin pizza + fruity coffee. He/him

🌐 https://duetosymmetry.com/
@duetosymmetry everywhere

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@duetosymmetry.comOct 10, 2026, 4:09 PM

No, because in Reissner-Nördstrom, we again have full spherical symmetry, but you can also "avoid" the singularity just like in Kerr

@jakemgrumbach.bsky.socialOct 9, 2026, 4:54 PMReposted by @duetosymmetry.com

New working paper: the Norwegian wealth tax was a huge success. The "exodus" of wealthy people never happened (less than 100 individuals left). Tax revenue increased by 71.5%. No changes in business activity or investment.

www.nber.org/papers/w35854

Taxing Entrepreneurial Wealth: Evidence from
Norway, 2021-2025
Marius A. K. Ring
WORKING PAPER 35854|
DOl 10.3386/w35854
ISSUE DATE October 2026
Whether imposing higher taxes on business owners adversely affects business activity by constraining investment and inducing capitalist flight is a central question in the ongoing debate on how to tax the ultra wealthy. To shed new light, I exploit a series of related Norwegian reforms during 2021-2024 that increased dividend tax rates, removed migration-related capital gains tax loopholes, and nearly doubled the effective marginal tax rate on business wealth. These reforms spurred international debate and, allegedly, an "exodus" of Norwegian billionaires (Financial Times,
2023). While I document clear effects on migration, these responses are concentrated among the top 0.1% of the wealth distribution and mostly confined to 2022 and 2023. My results indicate that at most 100 individuals left due to the reforms. I find no evidence of significant outmigration or reduced inflows of startup founders or inventors. I estimate that absent any outmigration, wealth tax revenues would have increased by 75% from 2021 to 2024. Reform-driven outmigration lowers the revenue gain to 71.5%. My findings further show that outmigrating owners' firms remain economically active and do not reduce investment. In a broader set of analyses, I examine whether business outcomes are affected, regardless of whether owners outmigrate, since firms may reduce investment both due to liquidity constraints or distortions to owners' savings decisions. I compare firms owned by Norwegian individuals subject to the wealth tax with firms owned by foreigners and other tax-exempt entities. By merging historical ownership data from Orbis with the Norwegian shareholder register, I perform these analyses on both Norwegian and foreign-domiciled firms.
Across settings, I find no evidence that Norwegian-owned firms pay out more dividends or invest less after the reforms,…
143
@duetosymmetry.comOct 10, 2026, 1:39 PM

Working examples!

@duetosymmetry.comOct 10, 2026, 1:57 AM

Drawing spacetime diagrams is second nature to me because I've been doing it for so long... I think reasoning from spacetime diagrams is attainable for anyone interested!

@duetosymmetry.comOct 10, 2026, 1:55 AM

Anyway... Back to the original story. I think it's important for people to grasp that they are always moving through spacetime, going forward in time. In much of the universe, that includes both "closer" and "farther" from some BH. Once you cross the EH, your future can't contain any "farther" dirs

@duetosymmetry.comOct 10, 2026, 1:52 AM

(this too of course is thought to be non-generic; there is probably a null singularity at the Cauchy horizon or earlier)

@duetosymmetry.comOct 10, 2026, 1:52 AM

The symmetry argument doesn't really help explain "why" there's a singularity, since in the maximal analytical extension of Kerr, you can avoid the singularity.

@duetosymmetry.comOct 10, 2026, 1:51 AM

If you allow yourself to go back in time, then you can get to literally anywhere in the causal diagram. Not sure what question this is actually answering... Back to the symmetry direction thing, that is too Schwarzschild-centric (ha!). A generic BH doesn't have symmetries, say one in a binary

@duetosymmetry.comOct 9, 2026, 5:47 PM

Difficult comparison when the process for humans to find the proof is to understand. But has anybody gained understanding by a giant repo full of claims that nobody has the time to read?

@mcnees.bsky.socialOct 8, 2026, 9:14 PMReposted by @duetosymmetry.com

Occasional PSA, 2026 edition: @duetosymmetry.com and I made a graph paper package for LaTeX.

Various styles (graph, quadrille, hex, iso, dot grid, etc) with pre-defined or custom colors. Print it or make templates for your tablet. 🧪

Github: github.com/mcnees/LaTeX...
CTAN: ctan.org/pkg/gridpapers

A light blue grid on a white background.
A red isometric grid on a pink background.
A brown grid with major and minor lines, on a pale yellow background.
A green hex grid on a light green background.
@duetosymmetry.comOct 8, 2026, 8:45 PM

Heart-ing not to say that I like your situation but rather to lend moral support

@duetosymmetry.comOct 8, 2026, 7:48 PM

I have to be cheeky and ask: Now show how to visually represent the AGM! (I spent about 10sec googling which led to me a wonderful visualization of the geometric mean, and the AM/GM inequality)

@duetosymmetry.comOct 8, 2026, 3:58 AM

TIL automated theorem prover = "we" "understand"

@duetosymmetry.comOct 8, 2026, 3:31 AM

Somebody with much better knowledge explained it here: arxiv.org/abs/2610.08144 . Sounds like my intuition (to distrust such machine-generated Lean proofs) was right!

@duetosymmetry.comOct 8, 2026, 12:17 AM

My cakes are not symplectic because they do NOT preserve my volume

@duetosymmetry.comOct 8, 2026, 12:12 AM

After I die I will continue to make cakes but only with spectral methods

@duetosymmetry.comOct 8, 2026, 12:11 AM

Easiest approach to getting the boundaries of your cake just right? Shoot it

@duetosymmetry.comOct 8, 2026, 12:10 AM

Call me a Monte Carlo sampler the way I bite into the cake at random

@marwellaspaceart.bsky.socialOct 7, 2026, 11:49 PMReposted by @duetosymmetry.com

😔

news.mit.edu/2026/margare...

@duetosymmetry.comOct 8, 2026, 12:05 AM

Richardson extrapolate to the limit of an infinite number of layers in my cake

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