G2 shall be my favorite group! Well, for now. For a while. Or maybe for longer. It's the smallest of the exceptional Lie groups. Found 1893 by Élie Cartan. It was he who suggested to think about it in terms of rolling balls.

Picture two spheres, one three times larger than the other. Imagine them rolling on another without slipping nor twisting. Rolling surfaces have their own branch of mathematics: contact geometry!


Goodbye , it has been a fun weekend! Oh, and I love your opulent centraal station building, a sweet distraction while waiting for about an hour for our train.

HaloSim is specialized raytracer (for windows) which can generate ice halos. It can even show halos as they might appear in the atmosphere of Saturn!

> Halos from octahedral ammonia crystals as might exist in the cold high level clouds of Jupiter and Saturn. The 42° circular halo has four associated sundogs. The inner halos are produced by rays reflected within the crystal.


I got here from watching sixtysymbols' latest, on ice halos:


Boole didn't use bit vectors, because vectors weren't officially invented yet! Instead, he used multi-variable polynomials. He also used F₂ writing multiplication as 'and', and calling addition 'or', while curiously disallowing 1+1. Picking neither disjunction nor xor, he left this fight to his successors.

wp> The house at 5 Grenville Place in Cork, in which [George] Boole lived between 1849 and 1855, and where he wrote "The Laws of Thought"

See here for a newer image:

→ dynamical billiards (in a spheroid)
→ hamiltonians
→ symplectic geometry
→ differential forms
→ exterior algebra
→ weyl algebra
→ ...?


The seahorse's tail, ubiquitous in its home valley, well deserves the highlight and its own five minutes of fame. What is value, after all?

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Here’s another one with City Hall near the red UFO un the center, which is a reflection from the interior.

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As part of this year’s christmas market in Bonn there’s this tower/ufo attraction, like a carousel, but for old people, which slowly lifts you 100m in the air. From up there you have a terrific view. Here’s an snapshot my wife took just this evening. It’ll be here until christmas eve, so you have about a week left.

You can see the “Bonner Münster” on the left, and at the bottom right there is a Ferris wheel and a tiny bit of illuminated christmas market.

Sometimes there's a dominant structure turning out too strong. Try burying it in a noise colored Flokati. Nevermind that the wool will find its way all over the place.

Pure as knitted by my old friend .

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I wanted stripes, but it's difficult to obtain a striped palette by pressing "p" in XaoS. So I went for binary decomposition. Fading from black&white via gray to white&black is what this picture aims to show off. It yields a kind of 3d look.

made wielding

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This one is about as big as it can get. If you try and pull apart empty space further than that, the microcosm inside will quickly snap back to mu set shape, after which the gap closes quickly with a hiss and emitting lo-fi phonons. They aren't stable, and this one will persist for roughly five years, and collapse on... Friday, April 7th... around 21:43 UTC... and nine seconds.

Repost, forgot the image, sorry.

> In fact, Gaudi designed a church in Barcelona using a web of strings and weights to find correct shapes for the arches -- of course, the actual building would have a shape like the reflection in a horizontal mirror above the strings

Also from ch1 of that mechanics textbook:

Woot Gaudi!


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> Let's define an ideal arch as one that doesn't have a tendency to fall apart sideways, outward or inward. This means no shear (sideways) stress between blocks, and that means the pressure force between blocks in contact is a normal force -- it acts along the line of the arch. That should sound familiar! For a hanging string, obviously the tension acts along the line of the string.

> […] the ideal arch shape is a catenary.

Source, ch 1 from a textbook on mechanics:


Minimal surfaces minimal style, made from paper strips.

+Alison Grace Martin has left a trail of these, mostly triaxially woven, topological (or rather conformal) exercises here on g+:


Joel David Hamkins is a well known research-level logician, and he usually posts about models of set theory, programs that only halt after a multiply infinite amount of time, and about infinite chess.

But this post is different, and very practical. Given a greeky straightedge and compass construction, like for example the one for finding the midpoint of a line segment, how much do errors grow while propagating. And what will their final shape look like?


The earlier Lagrangian mechanics involved an extra parameter for the time t, and it always uses the derivative of the first kind of coordinates as the second kind of coordinates.


The extra parameter t amounts to another coordinate dimension, making the resulting spaces odd-dimensional. This is called contact geometry and it is closely related to symplectic geometry.



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