narain

gregeganSF, 8 days ago (edited 8 days ago) to random

Are you OK, Science magazine?

“The therapy, an injectable monoclonal antibody callnative to antimalarials used in areas where malaria is endemic; those drugs have to be taed L9LS, offers a possible alterken for several days each month to be protective.”

https://www.science.org/content/article/news-glance-infrared-telescope-debuts-gm-rice-stumbles-maternal-mortality-drops

Edited to add:

This should almost certainly be:

“The therapy, an injectable monoclonal antibody called L9LS, offers a possible alternative to antimalarials used in areas where malaria is endemic; those drugs have to be taken for several days each month to be protective.”

@narain diagnosed inadvertent drag & drop.

narain, 13 days ago to random

I spent a couple hours today working out a Newton method for finding the closest rotation to a given matrix A, i.e. min ‖R − A‖² over R ∈ SO(3). Then I found out that Kugelstadt et al. already figured it out: https://animation.rwth-aachen.de/publication/0561/

Oh well. Glad to verify that I got the same result, but I like my derivation better; it's much shorter :)

narain, 15 days ago to random

Hey @lisyarus, I was going through your blog and saw that in your 2D soft-body physics engine post (https://lisyarus.github.io/blog/posts/soft-body-physics.html) you wrote about a technique you derived:

"I don't know a well-established name for this, and a quick google search failed to reveal anything of releavance, so I will call this method /shape matching/. If you know some resources on this, I would love to know them, since I had to derive all the equations myself :)"

Good news: it's literally called shape matching! https://matthias-research.github.io/pages/publications/MeshlessDeformations_SIG05.pdf

(P.S. I know your post is almost a year old, so I'm sorry if someone else has already told you this)

christianp, 18 days ago to firefox

Here's a #firefox question:
I have two virtual desktops on Ubuntu. On desktop 1, I have a firefox window with my email and calendar and mastodon tabs. On desktop 2, I have a firefox window with whatever I'm working on.
When I open a GitHub issue from an email, I'd like that tab to be in the window on desktop 2.
At the moment, the only way I know to do it is to drag the tab out of the window, then press ctrl+alt+shift+right to move it to desktop 2, then resize it and drag it onto the existing window there.

On the right-click menu on tabs, there's a "Move tab" submenu, but it doesn't offer the other window as an option, just "new window".
Is this something an extension could help me do?

demofox, 19 days ago to random

TIL if you do a comb filter (flange kinda) on a video, and invert phase, it amplifies motion. Neat!
https://youtu.be/JSm7Tp8iv3o?si=OcoTiR8ejk33R8p0

gregeganSF, 1 month ago (edited 1 month ago) to random

In differential geometry, if you have coordinates u and v on a surface, and someone talks about “the u-curves”, would you take this to mean:

(A) the various curves of constant u, and varying v
(B) the various curves of constant v, and varying u?

christianp, 1 month ago to random

who knew that if you multiply a small number by a big number you get a number big enough to worry about?

shaking here

narain, 2 months ago to random

An interesting counterargument to the recent popularizations of geometric algebra as the ideal language for doing geometry in physics, computer graphics, and so on.

I haven't actually worked with GA enough to have an opinion either way, but their basic argument seems compelling:

"1. The wedge product and the rest of Exterior Algebra is 100% amazing, S-tier stuff, definitely something everybody who uses mathematics should know about [...]
2. The geometric product, though, is kinda weird and bad.
3. A lot of other parts of GA are working around the fact that the geometric product is weird and bad.
4. The “better” version of Geometric Algebra [...] which we are... slowly unearthing... will be mostly the same as GA but it will discard the geometric product as a basic operation, to everyone’s benefit. [...]"

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

j_bertolotti, 2 months ago to physics

#PhysicsFactlet
The Lorenz system is a common example of chaotic dynamics and of a strange attractor.
Points with very similar initial conditions initially evolve very similarly to each other, until their trajectories diverge from each other, and start moving on a "butterfly"-shaped fractal.
#Physics #Chaos

Trajectories of a number of points following the Lorenz system equations, rendered as yellow tubes.

christianp, 3 months ago to random

They all laughed when I wrote code to simulate long division by hand!

Well, today I had a serious reason to use it.

Who's laughing now?!

(not me, I'm crying about the edge cases)

diffgeom, 3 months ago to mathematics

Three-sheet Monty, branched over the origin: The complex cubing map (top to bottom) and multi-valued cube root (bottom to top) branched along the negative real axis.

Complex analysis books generally describe the Riemann surface of the cube root as something like "three copies of the slit complex plane, with the lower edge of each cut joined cyclically to the upper edge of the next cut." This description is correct, but (for me, at least) hides the simple global picture: The Riemann surface of the multi-valued cube root function is itself a complex plane.

The discontinuity of the principal cube root across the branch cut is depicted geometrically in the top plane by the jump in position of the larger dot. The continuity of the multi-valued function is similarly depicted as a rotating equilateral triangle of cube roots.

Comparable pictures hold for square roots, fourth roots, etc.

#mathematics #MathArt

An animation loop depicting the complex cubing function and cube root multi-function against a black background. The plane at bottom is a gold rectangle with a blue Cartesian grid. The plane at top is a curvilinear dodecagon, the image of the Cartesian grid under the cube root. The principal cube root has the colors of the bottom, blue on gold. The other two branches, multiplied by non-trivial cube roots of unity, are gold on blue.

christianp, 3 months ago to random

arg, I'm in the office today and I've left my TODO file on my home PC without any way of accessing it remotely

christianp, 4 months ago to random

Inspired by @slowe sharing a chart showing a permutation, I nerdsniped myself into looking at how the curves between points are drawn, looking to make it easier to trace individual curves.
I've set up a @glitchdotcom experiment comparing curves with randomised control points against curves with fixed control points:
https://randomised-permutation-chart-curves.glitch.me/

I think the randomised one looks better more often than not, but it occasionally produces worse results.
If I was really getting stuck into this, I'd look into trying to make all the intersections happen as close to right-angles as possible.

ColinTheMathmo, 4 months ago to random

Live as if you were to die tomorrow. Learn as if you were to live forever. -- Mahatma Gandhi

gregeganSF, 4 months ago to random

TIL that “spinor” is pronounced “spin”+“or”, which makes perfect sense ... but either none of my physics lecturers used the word, or I forgot how they said it. When reading it in text for the last 4 decades, I’ve been mentally pronouncing it “spine”+“or”.

https://www.bbc.co.uk/programmes/m000fw0p

narain, 4 months ago to random

A few months ago I came across a paper about how rational numbers can be represented as LEFT-infinite digit sequences without a decimal point.

For example, in base ten,
−1 = ...9999
because adding 1 to it gives ...0000. Similarly,
1/3 = ...6667
because multiplying it by 3 gives ...0001. It's a fun exercise to verify that 1/3 − 1 = −2/3 indeed holds in this system.

I can't find this paper any more. Does anyone know what it might be?

christianp, 4 months ago to random

Thought I'd have a look at @mscroggs's advent calendar (https://www.mscroggs.co.uk/)

narain, 4 months ago to random

What is the area of a 3D polygon p₁p₂...pₙp₁? If the polygon is non-planar, this is not well-defined: if you split up the polygon into triangles pᵢpⱼpₖ and add up their areas ½‖(pⱼ−pᵢ)×(pₖ×pᵢ)‖, the result depends on the choice of triangulation. However, if you forget to take norms and just add up the vectors ½(pⱼ−pᵢ)×(pₖ×pᵢ) instead, you always get the same result: the "vector area" of the polygon! So if you're dealing with non-planar polygons, or non-planar curves in general, it makes sense to think of area as a vector rather than a scalar.

Further reading: https://en.wikipedia.org/wiki/Vector_area

narain, 5 months ago to random

(axiom|Advent|Alexandria)
(of|Ocasio)
(Code|choice|Cortez)

johncarlosbaez, 7 months ago (edited 7 months ago) to random

If you draw all roots of all polynomials whose coefficients are ±1, you get an amazing picture that raises lots of challenging puzzles!

I really hope someone reads our short article:

https://www.ams.org/journals/notices/202309/rnoti-p1495.pdf

and solves the main puzzle: why do the fractal regions of this set look so much like "dragon sets"? We have a good heuristic explanation, but no proof yet.

People sometimes get excited about math when they learn about fractals, and then disappointed when they discover rather few professional mathematicians prove theorems about fractals. If you ever wanted to prove a cool theorem about fractals, this could be your chance!

If you read part 2, I'll show you what I'm talking about.

(1/2)