One 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.
dguest 22 hours ago [-]
Beyond 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.
lhd1 21 hours ago [-]
This 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.
sandworm101 21 hours ago [-]
And 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.
Seems legitimate to me. Did you find any technical error?
rhet0rica 21 hours ago [-]
Perhaps the conclusions simply weren't mooving.
JadeNB 15 hours ago [-]
In case you missed the intentional misspelling, rather than are just going along with the joke: the word used was 'udder' (a cow's teats) rather than 'utter'.
MrOrelliOReilly 19 hours ago [-]
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turbostar 1 days ago [-]
Anna Cramling, women’s international chess master, should review this paper, having popularized the Cow Opening.
Rendered at 05:30:57 GMT+0000 (Coordinated Universal Time) with Vercel.
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.
https://en.wikipedia.org/wiki/Birkhoff%27s_theorem_(relativi...
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.
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)
[0] Python, Monty (1975), Monty Python and the Holy Grail
https://www.youtube.com/watch?v=10JSPdTDFsI