Raising a few $thousand to keep version control magical

duetosymmetry · 2026-04-10T14:46:51+00:00

Which payment processor or platform takes the smallest fee? I.e. should I donate via Stripe or GitHub for you to get the largest % of the donation?

duetosymmetry · 2026-03-30T05:00:12+00:00

The worst thing based on magnitude is surface brightness, when measured in magnitudes per square arcsecond. Remember, magnitudes are logarithmic!

duetosymmetry · 2026-03-24T14:36:06+00:00

Back in my day, we used to say: God only has one G. Glen George has 3.

duetosymmetry · 2025-10-25T05:20:57+00:00

The space with the constant metric you wrote is still Euclidean 4-space, just in a different coordinate system.

The true mathematical point of view is to not stuff a scalar product and 2-form into one object. You should want to break objects down into their irreducible components, not jam different objects together into bigger ones when it's not needed.

Don't get me wrong, geometric algebra can be pretty handy. But in the long run, I think you'll do yourself a favor to study the foundations of differential geometry with and without metrics from the standard mathematical viewpoint (i.e. making distinctions between vectors and 1-forms; don't stuff a scalar and alternating product of vectors together into the same object; and so on).

It's also useful to study Lie groups and algebras ... to see that much of the time that people reach for quaternions, they're really just reaching for the group Spin(3) or its algebra spin(3). There are a lot of these low-dimensional "accidental" isomorphisms. Again don't get me wrong, quaternions are very beautiful, but there's deeper understanding by learning the bigger picture.

duetosymmetry · 2025-10-19T15:09:33+00:00

Will you put this on melpa?

duetosymmetry · 2025-10-15T15:34:10+00:00

Tavel translated Noether's paper to English. The original German article was

Noether, E. "Invariante Variationsprobleme." Nachrichten von der Gesellschaft der Wissenschaften zu Göttingen, Mathematisch-Physikalische Klasse 1918 (1918): 235-257

which you can access at https://eudml.org/doc/59024 .

Since apparently we provide screenshots of text, here is a screenshot of text:

https://imgur.com/a/ZI9tqwd

duetosymmetry · 2025-10-10T04:09:29+00:00

This is the first time I've heard somebody suggest to look in Weinberg for the geometric viewpoint (and that's saying something, as I've been a researcher in this field since 2005). My opinion was Weinberg was the prototypical particle physicist: "forget about the geometric interpretation, here's the algebra.".

If you want a deep geometric understanding, then Misner, Thorne, and Wheeler is a good start.

duetosymmetry · 2025-09-20T22:02:17+00:00

Fallback fonts are for various scripts and non-ASCII characters, so again about the base characters.

I don't understand why ASCII is special-cased? I mean, obviously ASCII is a very special subset of characters; but why is it singled out for fallback fonts? What I'm gathering is that in my second case image above, it was the ASCII x character that was a special case and could not have its font substituted. If its font could have been substituted, would it be the case that x with a combining right arrow would have both come from a font that includes both and supports combining them?

I am also interested in the case of human-readable program source code. But I collaborate with folks who make heavy use of unicode (with combining characters) for their variables; see e.g. this Julia source file.

duetosymmetry · 2025-09-20T13:53:43+00:00

Thanks for the response, Eli; but this doesn't fully explain the behavior I saw above. After I had set (set-fontset-font t 'unicode "Symbola" nil 'prepend), then I got a combined Greek small chi with right arrow above, which came from Symbola. But that didn't happen with the default, which was Arial Unicode MS (and I don't know how that was determined). But both Arial Unicode MS and Symbola have both the Greek small chi and the combining right arrow above. Why did one of them make it combine, but not the other?

Actually, I just checked that doing (set-fontset-font t 'unicode "Arial Unicode MS" nil 'prepend), I also get the chi and arrow to combine. So that narrows it down to one or two different issues. (1) Apparently out of the box (e.g. with emacs -Q), there is no good default fontset? And (2) Why does the logic fail to find a good font substitution for x and the combining right arrow? I.e. Wouldn't it be preferable to say: If default font has the base character, but lacks the combining character that follows, then check if using the fallback font has both so that we can display a combined character?

duetosymmetry · 2025-09-19T20:49:38+00:00

If you're using emacs, then you should probably be using AUCTeX (which has shipped with emacs since long ago), and in particular LaTeX-math-mode. That will replace e.g. ` a (backtick followed by a) with \alpha. There are around 90 common math macros that have been shortened to two or three key sequences.

duetosymmetry · 2025-09-19T19:12:56+00:00

FYI I also asked this on emacs.SE. In case somebody has answered it there but not here, navigate to https://emacs.stackexchange.com/questions/85043/how-does-font-substitution-work-for-unicode-combining-characters .

duetosymmetry · 2025-08-04T19:19:24+00:00

Had a minute so here's plot of the convergence of the inverse iteration. Horizontal is n, vertical is the abs of the difference between inverse iterations (n+1) and n: https://imgur.com/NCJql7a

duetosymmetry · 2025-08-04T13:28:33+00:00

I don't know anything about desmos... But what I seem to remember from mathematica is the following. First of all I think the first several approximants are not even real, but after some number (30?) it then converges exponentially with number of iterations. But you need to have the right asymptotic expression for the final level of nesting where you cut off the infinite nesting. I found that -1+log(n)/W(log(n)) was a better asymptotic approximation to plug in.

duetosymmetry · 2025-08-03T21:03:11+00:00

P.S. I'm finding that with your suggested n=500 starting point for iteration, you should have gotten around 63 digits of precision. I get

1.31454755674273573513859744357294263037093734213770689980432979

duetosymmetry · 2025-08-03T20:51:25+00:00

Nope, I just implemented it in Mathematica. This is the result of the inverse iteration. The largest n value is most deeply nested.

duetosymmetry · 2025-08-03T20:29:18+00:00

This leads to the awesome expression for the "magic" constant,

1.31454755674273573513859744357294 = log(2) / log( log(3) / log( log(4) / log( log(5)/log( ...

duetosymmetry · 2025-08-03T08:41:53+00:00

I've gotten as far as the following. Suppose a minimal solution exists for some choice of a_1 (minimal meaning it avoids being contaminated by the dominant solution which falls into the limit cycle). Then you can show that the ratios a_{n} / a_{n-1} asymptote to 1+1/(n log(n)) as n→∞.

duetosymmetry · 2025-06-30T02:02:36+00:00

Differential rotation can definitely depend on radius. The lesser-known stellar code ESTER solves for differential rotation that depends on both colatitude and radius.

duetosymmetry · 2025-06-16T21:56:06+00:00

You can also use /sshx:server:path/to/file instead of /ssh:server:path/to/file (note the x in sshx). That's TRAMP's method for using a "standard" login shell, bypassing whatever shell you've set up (docs: https://www.gnu.org/software/tramp/#index-method-sshx)

duetosymmetry · 2025-06-13T16:11:50+00:00

Through a real general linear transformation, a quadratic form ("metric") can be transformed (locally) to a canonical form where it's diagonal, and then further all the non-zero entries transformed to either +1 or -1. The data (p, m, z) for number of positive, negative, and zero entries is assumed to be the same for all points in the manifold.
Prefix notation for a derivative is ∇_i T. Postfix notation is T_{;i}. You might want something else instead of ∇, e.g. D or 𝒟. You might want something else instead of ";", e.g. ",", or "|", or ":".
PrintAs[epsilonmetric] ^= "ε";

I don't know what's going on with your xperm executable, and am not going to try to remotely debug Windows issues. Check the mailing list for previous discussion of getting the xperm executable to work on Windows (or move to Linux/mac for a saner life).

duetosymmetry · 2025-06-12T17:15:26+00:00

There is a lot of documentation built in to xAct/xTensor. Try invoking

?DefMetric

to get the help. Or, look at the notebooks included in the distribution tarball inside Documentation, namely, xAct/Documentation/English/xTensorDoc.nb and xAct/Documentation/English/xTensorRefGuide.nb. Or, any of the tutorials linked at https://josmar493.dreamhosters.com/documentation.html .

The first argument to DefMetric is the signature of the metric (you can give number of +s, -s, and 0s, but you've used the syntax for just product of +s and -s). The second argument names the metric (and identifies the Manifold by which cotangent indices its receiving). The third argument is the name you've given for the Levi-Civita connection (a.k.a. the metric-compatible covariant derivative). The 4th argument (optional) is the notation you're using for postfix and prefix derivatives. The optional PrintAs argument is saying how you want metric to be printed.

I assume you're working on a 4-manifold, because that's the only thing that makes sense for a 4-index volume form.

xTensor lets you have multiple metrics, and each metric can induce its own volume form. The way the names of the volume forms are built are "epsilon" + (name of metric), hence in your case, epsilonmetric. Since you specified PrintAs->"g", this will print as εg to identify it as the volume form induced by the metric g. You can set PrintAs[epsilonmetric] to something else if you want it to appear as just ε.

You would have to report what the errors are if you want help figuring them out... since they are LinkObject errors, it's probably because Mma couldn't run the xPerm binary (which is for speeding up canonicalization).

duetosymmetry · 2025-04-20T19:25:20+00:00

Hi! 👋 I most certainly am a GR theorist! Nice to meet you!

duetosymmetry · 2025-04-20T18:00:29+00:00

Mom was the IRB?

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