Stained Glass

Modern mathematics tends to obliterate history: each new school rewrites the foundations of its subject in its own language, which makes for fine logic but poor pedagogy.

(Source: youtube.com)

The rainbow color map confuses viewers through its lack of perceptual ordering, obscures data through its uncontrolled luminance variation, and actively misleads interpretation through the introduction of non-data-dependent gradients.


Listen to an encoding of someone’s brainwaves whilst sleeping. The frequency was ×70. You can hear that the brainwaves were different during REM sleep 2:30–4:20.
by Anastas Stoyanovsky

sphere tangle

Limit set of Maskit’s version of the 11/120 double cusp group. (The colored circle chain reveals the fraction 11/120.)
by David J. Wright
(Source: klein.math.okstate.edu)
hi-res

Cézanne was always looking for the most convincing and honest method of recording his sensation of nature, but ultimately felt himself a failure.
In his later career, he preferred watercolor as a medium for still lives such as this one. He altered both the way we look at the world and the way we record it.
→ Read more about the beauty and complexity of Cézanne’s watercolors on the Getty Iris here.


- Minkowski sum of two shapes
- direct product of two shapes
- two complementary planes in 4-D will only intersect at the origin
(polytopes are higher-dimensional polygons … not necessarily regular and they can even go backwards into themselves. Basically a filled-in shape cut out by straight or flat lines/planes/hyperplanes.. So think for example most of the boundary conditions in optimisation. (I usually see something like: a convex function, restricted to a filled-in irregular convex polytope, eg ◣ ⏢ or ◺ ▲ ▶ ◆ , ▷ or ⬠ ⬟ ⌂ 🏠 or a ☖ ☗ ⛊ ⏢ ⬡
(non-polytopes in the Unicode sets where I was searching for those include ◫, ◙, ◶, ▤, ▣, ◐, ◠, ⍟, ⌫, ⌻, ⌘, ⌧, ⌰, ⌑, ⍉, ⍋, ⍾, ⎎, ⎍, ⎌, ⏪, ⏚
You can make a convex polytope from ∩ of half-spaces, or from a convex-hull of vertices.


