3 ms·
Higher Multipoles of the Cow
- Bowes-Lyon 2mo agoHmmm… Today is Sep 1st, not Apr 1st. That cow is a bit out of season :)
- jitl 2mo ago> Submitted on 1 Apr 2025 (v1), last revised 1 Apr 2026 (this version, v2)
- turbostar 2mo agoAnna Cramling, women’s international chess master, should review this paper, having popularized the Cow Opening.
- lhd1 2mo agoOne of the cool facts about gravity is that the gravitational field of a body 'feels' spherical at a distance, even if those bodies are not spherical themselves. There are higher multipoles but they are increasingly suppressed the further you are from the body. So at least for gravity the spherical approximation turns out to be good and justified.
- DroneBetter 2mo agofor simulating gravity in particular you can do one better, since a sphere is in turn gravitationally indistinguishable from a point mass due to the https://en.wikipedia.org/wiki/Shell_theorem#Force_on_a_point_outside_a_hollow_sphere https://en.wikipedia.org/wiki/Shell_theorem#Force_on_a_point...
- lhd1 2mo agoand you can do one better than that - Birkhoff's theorem, the relativistic analogue of the shell theorem. https://en.wikipedia.org/wiki/Birkhoff%27s_theorem_(relativity) https://en.wikipedia.org/wiki/Birkhoff%27s_theorem_(relativi...
- naklitechie 2mo agoThis deserves a simulator
- setopt 2mo agoAh yes, indeed, the well-known point-cow approximation!
- Sharlin 2mo agoThe point-cow is simply the zero-dimensional generalization of the spherical cow.
- classified 2mo agoHence for all practical purposes, zero-dimensional cows are spherical.
- dguest 2mo agoBeyond a "cool fact", this is the only reason that physics works, where I'm defining physics as the human study of physical laws, not the laws themselves. If we couldn't neglect higher moments systems from planetary motion to the large scale structure of the universe would be computationally intractable. And it's not just gravity, it's also electromagnetism: charge arrangements (i.e. ions) look like point charges at a distance, meaning you can neglect the electron orbital structure. Light sources act like point sources at a distance too. A lot of the equations you learn in introductory physics rely on the higher moments vanishing. - The planetary motion equations (Kepler's laws) assume gravity as a point source (the three body problem can be approximated by replacing two of the bodies with 1) - E = mgh -> assumes a homogeneous gravitational field, which is a special case of gravitational monopole near an equipotential surfaced. And of course parabolic motion and pendula only work because this holds.
- sandworm101 2mo agoAnd if they were intractable, motions would be so irregular that pheneomena such as billion-year stable orbits would not be possible... leading to a lack of evolution and life generally. So it is a very good and necessary thing that cows remain mathematically spherical.
- lhd1 2mo agoThis point of view is essentially codified in effective field theory, which tells us why so much of classical physics (EM, fluids, gravity) can be seen as low order approximations of some more complete theory that we found later on. One of the great insights from 20th century physics imo.
- colechristensen 2mo agoSubmission history From: Benjamin Lehmann [view email] [v1] Tue, 1 Apr 2025 07:55:39 UTC (2,401 KB) [v2] Wed, 1 Apr 2026 12:28:24 UTC (3,845 KB)
- account42 2mo agoThat's dedication.
- analog31 2mo agoWhat udder nonsense.
- setopt 2mo agoSeems legitimate to me. Did you find any technical error?
- addag 2mo agoMy physics teacher takes the spherical roast beef as an example for heat convection.
- mohamedkoubaa 2mo agoThis is some bull
- DonHopkins 2mo agoBerkeley has been on the frontier of cow detection and tracking for decades. https://www.youtube.com/watch?v=10JSPdTDFsI https://www.youtube.com/watch?v=10JSPdTDFsI
- rcarmo 2mo agoWe should get more of these here. My Arxiv queue is all inference stuff, this is fun!
- philipwhiuk 2mo agoI suggest reading the proceedings of SIGBOVIK: https://sigbovik.org/ https://sigbovik.org/ Sample papers: * The Ballmer Peak: An Empirical Search * Selected investigations into egg logic * Are Centaurs Actually Half Human and Half Horse? * Unconventional Commits: An Exploration Beyond the Mundane * Use-After-Freemoji: How Custom Emoji Replacement Retroactively Corrupts User Intent I assume this paper will be submitted for a conference - if not it should have been.
- 220hertz 2mo agoAlso "A Probabilistic Challenge-Response Algorithm for Repairing All Roads in Lebanon Via Papal Visits"
- fghorow 2mo agoPerhaps this approach should be known as "The Method of MOOments"?
- MrOrelliOReilly 2mo ago[dead]
- lorenzohess 2mo agoBut has anyone ever analyzed the aerodynamics of a cow? Yet another point where SCA breaks down.
- quercusa 2mo agoThere was a rather well-known French study. [0] Python, Monty (1975), Monty Python and the Holy Grail
- ninju 2mo agoThe Acknowledgements section, at the end of the paper, is very entertaining (as is the rest of the paper)
- ninju 2mo agoThe usage of the word hexapentacontadictapole is very good
- lawlorino 2mo agoNear miss of nominative determinism; the authors name (Lehmann) is almost the same as the Finnish word for cow (Lehmän)