@peter This is a word I know. See also "the plural of anecdote is not data":
https://quoteinvestigator.com/2017/12/27/plural/

@doop Well, Lengyel is definitely a "pixels on the screen" guy (see his Slug font renderer) and in general it seems that people like him who are associated with gamedev don't get sucked into maths they don't need. But this is also a kind of extreme conservatism which GA may never overcome.

@doop More recently Charlie Gunn and Eric Lengyel have produced teaching material. I'm not in the target audience, evidently, because it doesn't seem to rub off on me, or maybe it just never occurs to me to do computations it would help with.

More to the point is the kind of precision that let Cartan or Noether say to Einstein "hey, you're mixing vectors and bivectors and antisymmetric tensors" (or something like that). Obviously that awareness is important and very valuable.

@doop Well, having encountered the cultish presentation of it, I'm sympathetic to mathematicians who say "yes, all this machinery exists, we call it Clifford algebra when we use it" and less interested in the guys who said 25 years ago that "It is going to be the way computer science deals with geometrical issues." (https://staff.fnwi.uva.nl/l.dorst/clifford/index.html#:~:text=It%20is%20going%20to%20be%20the%20way%20computer%20science%20deals%20with%20geometrical%20issues.)

I attended the relevant Siggraph course in 2001, taught by (among others) that first year physics supervisor's wife (obviously!) https://history.siggraph.org/learning/geometric-algebra-by-naeve-rockwood-doran-lasenby-dorst-et-al/

@doop I do think it makes sense to introduce cross product and determinant together.

I arrived at Cambridge to find that my physics supervisor was a geometric algebra nut. So I'm definitely not pushing that stuff for pedagogy as it absolutely distracted him from teaching us the basics. I assume you have a bit of experience with / awareness of GA?

Ultimately, as this guy says: "What you probably want is just the concepts of multivectors and the wedge [exterior] product!

https://alexkritchevsky.com/2024/02/28/geometric-algebra.html

@doop I'm really not suggesting a digression. Given my own fairly disastrous learning experience with this stuff, I would prioritise demystifying it by just gesturing toward why it works.

@doop The way I see it, it would be good to have a resource called "you could have invented the cross product" which draws on the CG idea of rotating a 2D vector by 90 degrees by swapping components and negating one. That concept is very close to your matrix.

@doop this all works because the cross product, like the dot product, is distributive. And the exterior product has a similarly calculated magnitude, but works in other dimensions too.

@doop the cross product makes sense as taking a dot product after rotating one of the vectors through 90°. I don't know if you were taught the component formula for the cross product in school – I certainly wasn't. We were just told it involved the sine of the angle between vectors times the magnitudes. But it's related to the determinant: specifically it can be expressed as a formal determinant involving the unit vectors, each coefficient of which is a determinant of a 2x2 matrix.

@doop Reminds me of this
https://math.stackexchange.com/a/2365503/124777 but also...

@peter As a Dubliner, I'd say the Northern "now" is like "nye". That would make the IPA notation /naɪ/

https://youtu.be/sE21yRBpP_4

@doop I'm a long way from this stuff but could you get the Makefile to take care of this? A phony target that runs "touch"?

.PHONY: ready
ready:
touch configure

Rust doesn't help you when you do things unsafely:

"thread fl2_worker_thread panicked: called Result::unwrap() on an Err value"

https://blog.cloudflare.com/18-november-2025-outage/

Cottonwoods in the Rio Grande bosque near the Albuquerque Rio Grande Nature Center.

#FootpathFriday #hiking #NewMexico #FallColors

@akkana Reading the alt text, I noticed you refer to the International Date Line, but I recall that it's not a line of longitude – it has some squiggles. Clearly, the feature you're talking about is loading of tiles past 180° W, or something like that. If you were rendering the final image pixel-by-pixel I would think that some modulo arithmetic would sort this out. But with tiles maybe it is more complicated to avoid duplication etc.

@c_reider Well, there's also this: "These lines [...] consist of a number of short lines at various levels joined together perpendicularly. It seems that each of these short lines represents a note of music, and that the irregularity of their arrangement indicates the succession of these notes; so that each of these crooked lines signifies the movement of one of the parts of the melody, the four moving approximately together denoting the treble, alto, tenor and bass respectively"

@doop Time for nasty solvents!