Higher Multipoles of the Cow | Hacker News Reader

Higher Multipoles of the Cow

arxiv.org

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.

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.

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.

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.

for 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...

Hence for all practical purposes, zero-dimensional cows are spherical.

This deserves a simulator

and 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_(relativi...

Ah yes, indeed, the well-known point-cow approximation!

The point-cow is simply the zero-dimensional generalization of the spherical cow.

Perhaps this approach should be known as "The Method of MOOments"?

Near miss of nominative determinism; the authors name (Lehmann) is almost the same as the Finnish word for cow (Lehmän)

Submission 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)

That's dedication.

My physics teacher takes the spherical roast beef as an example for heat convection.

We should get more of these here. My Arxiv queue is all inference stuff, this is fun!

I suggest reading the proceedings of SIGBOVIK: 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.

Also "A Probabilistic Challenge-Response Algorithm for Repairing All Roads in Lebanon Via Papal Visits"

The usage of the word hexapentacontadictapole is very good

The Acknowledgements section, at the end of the paper, is very entertaining (as is the rest of the paper)

Berkeley has been on the frontier of cow detection and tracking for decades.

https://www.youtube.com/watch?v=10JSPdTDFsI

Hmmm… Today is Sep 1st, not Apr 1st. That cow is a bit out of season :)

> Submitted on 1 Apr 2025 (v1), last revised 1 Apr 2026 (this version, v2)

This is some bull

But has anyone ever analyzed the aerodynamics of a cow? Yet another point where SCA breaks down.

There was a rather well-known French study.

[0] Python, Monty (1975), Monty Python and the Holy Grail

What udder nonsense.

Seems legitimate to me. Did you find any technical error?

Perhaps the conclusions simply weren't mooving.

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'.

Anna Cramling, women’s international chess master, should review this paper, having popularized the Cow Opening.

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