@RefurioAnachro

Not arguing, just surprised - why would a mathematician follow a psychedelic musician?

At 19 pages and 68 references, I've finally reached a point with this book review that I can draw breath.

sunclipse.org/wp-content/downl

#quantum #physics

@ejk Stokes' Theorem: \( \int_{\partial M} \omega = \int_M \mathrm{d}\omega \)

James Grime is back! Last week, he was seen posting a video about chess. It was about how to avoid repetition during a game:

singingbanana – The Infinite Game of Chess (with Outray Chess)
youtube.com/watch?v=ZwJlOJuhbO

An today came a nice feature explaining why the popular ELO scoring system is the way it is:

The Elo Rating System for Chess and Beyond
youtube.com/watch?v=AsYfbmp0To

Burkhard Polster has news about constant width shapes!

Mathologer – New Reuleaux Triangle Magic
youtube.com/watch?v=-eQaF6OmWK

Some of the more complex arrangements made me think about pumps and motors.

@ejk I go for Shannon's entropy: \(H = - \sum_i P_i \log P_i\)

What's your favorite equation?
Mine is Euler's identity:
\(e^{i\pi}+1=0\)

Four of Conway's five $1000-prize problems (oeis.org/A248380/a248380.pdf) remain unsolved:

*The dead fly problem on spacing of point sets that touch all large convex sets, en.wikipedia.org/wiki/Danzer_s

*Existence of a 99-vertex graph with each edge in a unique triangle and each non-edge the diagonal of a unique quadrilateral, en.wikipedia.org/wiki/Conway%2

*The thrackle conjecture, on graphs drawn so all edges cross once, en.wikipedia.org/wiki/Thrackle

*Who wins Sylver coinage after move 16? en.wikipedia.org/wiki/Sylver_c

Just yesterday I watched Scott Aaronson chat about quantum computing, philosophy, ai, and stuff that interests him, on video. It's a 5 part series published this january, some 20m, some 5m, starting here:

youtube.com/watch?v=BvVciA5iXH

Now I wonder, is he about to publish a book, or are these interviews related?

@enkiv2

H.S.M. Coxeter's "Introduction to Geometry" is most delightful! Most of it's yummy chapters contend with a single page. They're all carefully written, and decorated with citation, references, and footnotes! At first it's all in plane sight, later it gets hyperbolic...

Erm. Excuse my strange thought of geometry. Apparently, I confused left and right.

@tomharris @enkiv2

Three-regular, each 5-bit label appears exactly once, each vertex is the sum (xor) of its neighbors.

I wrote some simple code to find the size (how deep to zoom) of n-fold embedded #Julia sets in the quadratic #Mandelbrot set.

Input:
r_o, the size of the outer island;
r_i, the size of the inner island;
m, for n =2^m-fold symmetry.

Output:
r_J, the size of the embedded Julia set.

Code:
```
r_J = r_o;
for (int k = 0; k < m; ++k)
r_J = sqrt(r_J, r_i);
```

Untested closed form solution:
```
r_J = pow(r_o * pow(r_i , (1 << m) - 1), 1.0 / (1 << m));
```
It may work out slower, as `sqrt()` is usually faster than `pow()`. Not likely to be a bottleneck in any code I can think of though.

Haven't worked out yet how to generalize it to higher power sets, maybe I'll play around with it later.

Conjecture that it will work reasonably well also for Burning Ship etc.

Who even needs the binomial theorem?
(20+25)²=2025
(30+25)²=3025
(68320+14336)²=6832014336
(60494+17284)²=6049417284
and so on.

The shape of the combined horizon of merging black holes can look quite strange. Here's a baby horizon:

youtube.com/watch?v=p4MTsCDtHM

And here's a 'toroidal' one with a hole in it!:

youtube.com/watch?v=CeNP5NyW0z

,

Here you can see, briefly at the end, that the overall spin magnitude went down a little:

youtube.com/watch?v=tY3xCamzMZ

Which makes sense as gravitational waves can carry angular momentum.

Someone told me that, if the spin of the original black holes were close enough to the theoretical maximum, the two black holes would bounce off of each other. I'd love to see that animated, but haven't found any examples.

as ,

When was the last time you looked at Wikipedia's article about black holes? I think, for me, that's about two years ago. And boy has it changed!

en.wikipedia.org/wiki/Black_ho

To save bandwith I have shortened the animation, and also to emphasize the ringing of space at the end. It's from the "Simulating eXtreme Spacetimes (SXS) Project".

Try their youtube channel for more animations:

youtube.com/user/SXSCollaborat

or their website:

black-holes.org

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