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gutenberg_org, 9 months ago to music

"L'art est le plus beau des mensonges."
Monsieur Croche et autres écrits (1901-1914)

Claude Debussy was born #OTD in 1862.

Debussy's Prélude à l'Après-midi d'un faune, written in 1894, was the first milestone of modern music, and immediately placed his work under the seal of the musical avant-garde. He was briefly a Wagnerian in 1889, then a non-conformist for the rest of his life, rejecting all aesthetic academicism. via @wikipedia

#music

dpiponi, 9 months ago to random

Oh cool! If I walk 20,000 steps a day I reduce my probability of an early death by (15*(20-4))%

ColinTheMathmo, 10 months ago (edited 10 months ago) to random

Just a quick question for the people here on Mathstodon.xyz ... where are you based?

If you're not in any of these, please let me know in the comments!

Please, if you're not on mathstodon don't reply here, but I'd love to hear from you another time.

georgemsavva, 10 months ago to art

Black and white or colour? A work in progress made with R and the magick package. Composite images in the thread.. #rtistry #abstract #art #mathart

Code: https://gist.github.com/georgemsavva/4e89a4b777570967dd85fb9a5de58c7d

An image made from points and lines like a piece of string art. Formed of overlaid grids of individual floral designs. A single light green design in the background, four blue designs in the next later nine purple designs in the next layer and 16 red designs in the top layer.

georgemsavva, 10 months ago to random

Which image is more interesting? The first one is the same as the second one but at a jaunty anglea and slightly cropped.

A mathematical image made of nine blue shapes arranged in a square. Each shape is a floral image made of lines like string art, with an empty area in the centre.

danderson, 10 months ago to random

I still have no idea what happened, but my guess is that it doesn't actually work right during initial library ingest, because of some kind of contention between batch work and interactive requests. So until all the indexing and metadata collecting and whatever is done, it's basically unusable... But once that's done, it becomes super snappy and nice? Maybe?

I/O and CPU were both well below redline, so this has to be some internal contention somewhere...

robpike, 10 months ago to random

As Yogi Berra said, you can observe a lot just by watching.

I learned yesterday, a talk by William McDonald from Leiden Observatory, that dark matter and visible matter can have markedly different shapes in some galaxy clusters. In the most striking, the dark matter has a large quadrupole moment while the "normal" matter settles to the center.

ColinTheMathmo, 11 months ago to random

Searches on both Google and DDG have failed to help ... recent emails I've received from a specific (corporate) person have started to include strange strings:

+2D3eCg-

+AD4APg-

Can anyone suggest what might be happening?

As always, thanks for any advice and/or assistance.

ColinTheMathmo, 1 year ago to science

An interesting and original (I think) puzzle from Micky Bullock.

"Last week Negligent Neil calculated length AC. He had forgotten to switch his calculator from radians to degrees but, fortunately, he still got the answer right.

"An inky splodge has now obscured the angle at A. Negligent Neil has forgotten what his answer was for length AC, but he insists it was between 40 cm and 50 cm.

"Find length AC to 3 significant figures."

#MathPuzzle #MathsPuzzle #Trigonometry #Puzzle #Math #Maths

johncarlosbaez, 1 year ago to random

String diagrams are really intuitive once you get the hang of them, but perhaps scary at first. I hope this helps the computer scientists out there:

• Robin Piedeleu and Fabio Zanasi, An introduction to string diagrams for computer scientists, https://arxiv.org/abs/2305.08768.

We've already seen some nice introductions for people interested in quantum physics - even whole books. But string diagrams are so universal that there should be many introductions from many viewpoints!

If you leave a comment saying "aren't these just flow charts?" I will know you didn't read this whole post. Flow charts are indeed an example of string diagrams. But string diagrams can do much more! For example, even electrical circuit diagams are examples of string diagrams. The end of Piedeleu and Zanasi's paper lists a bunch of other applications of string diagrams.

johncarlosbaez, 1 year ago (edited 1 year ago) to random

In the Clifford algebra Cliffₙ we start with the real numbers and then throw in n anticommuting square roots of -1. For example:

Cliff₀ = ℝ, Cliff₁ = ℂ, Cliff₂ = ℍ (the quaternions), etc.

With the quaternions, once you throw in i and j with i² = j² = -1 and make them anticommute (ij = -ji) you get k = ij for free.

Each Clifford algebra has 'representations': roughly, real vector spaces where elements of the Clifford algebra act as linear operators. The most famous representations of Cliffₙ are the 'pinor' representations, which describe spin-1/2 particles in n-dimensional space along with how reflections act on these particles. You get all the other representations by taking direct sums of pinor representations.

For example, in 2d space Cliff₂ = ℍ has a representation on itself, and this is the only pinor representation in 2d space. All other representations of Cliff₂ are direct sums of this one - so its category of representations is the category of quaternionic vector spaces!

This chart shows the categories of representations of the Clifford algebras up to dimension 7. After that they repeat.

The symbol ≃ means that two algebras have equivalent categories of representations. For example, Cliff₆ is the category of 8×8 real matrices! So it's not isomorphic to ℝ, but you can show they have equivalent categories of representations.

One last thing: Cliff₃ is isomorphic to ℍ⊕ℍ, meaning an element is a pair of quaternions. So a representation is a pair of quaternionic vector spaces - or equivalently, a quaternionic vector space that's been 'split' as the direct sum of two pieces. That's what I mean by 'split' here.

Do you see the surprising pattern in this chart? Very visible.