So a tesseract is a term for a specific geometric shape that exists in 4 dimensions. Specifically it refers to a 4-d version of a cube, in the same way you could say that a cube is a 3-d version of a square. It is a shape with eight corners and and all right-angles.

You may have seen a tesseract represented as two cubes, one inside the other, with their corners connected (example: …wikimedia.org/…/Schlegel_wireframe_8-cell.png). This is best understood as a drawing of a tesseract. Just as you can draw representations of 3-dimensional shapes onto a 2-dimensional piece of paper, you can also draw representations of 4-dimensional shapes onto a 3-dimensional space. The “cube within a cube” representation is kind of like drawing a cube as a square within a square, with the corners connected (left image here: www.math.brown.edu/tbanchof/…/image01.jpg). It is a perspective drawing of the cube in wire-frame, viewed end-on. The outer square is the near face of the cube and the inner square is the far face of the cube, smaller because it is farther away. The other four faces are depicted as the four trapezoids formed between the inner and outer squares; these actually represent square faces but they are distorted into trapezoids by the perspective.

So the cube-within-a-cube drawing of the tesseract is just the next-dimensional version of this. It is a tesseract viewed end-on, with the outer cube being the near cell (in 4-d geometry, the 3-d shapes that make the outer surface of a 4-d shape are called “cells” - kind of like how the 3-d shapes that make the outer surface of a 3-d shape are called faces; a cube is made of six square-shaped faces, while a tesseract is made of eight cube-shaped cells), while the inner cube is the far cell, smaller because it is farther away (in the extra, 4th dimension), while the other six cells are the six “3d trapezoid” (a “frustum” is the technical term for this shape) spaces formed between the two cubes; these actually represent cube-shaped faces but they are distorted into frustums by the perspective.

4-d is hard to visualize. We live in a world of 3 spatial dimensions so visualizing that comes naturally to us, but we have to strain to understand higher dimensions beause our visual system can’t help us in the same way. Analogy to 3-d is one way, in particular looking at how we represent 3-d objects using a 2-d image (a common thing for us to do), and trying to do similar things to represent 4-d objects using a 3-d “image”.

The trunk fell off

I came out to my D&D group and it went really well! Everyone was super supportive. I thought they would be but it’s still a huge relief!

I hate those. Even worse are error messages that are clear, descriptive, and wrong (“incorrect username and/or password” when actually the server or your internet is down)

“Mom… dad… I’m a closet”

Rook thinks he’s so clever until he gets clobbered by that bishop

Humanity had a good run. Until the evolution of rocketspiders.

All gifts are accepted by Aranaktu

To my undestanding chess is based on the Arabic game Shatranj, based on the Indian game Chaturanga, and in both the piece next to the king in both games is the “general” or “minister” which moves one space diagonally.

www.chessvariants.com/historic.dir/shatranj.html

www.chessvariants.com/…/chaturanga.html

If you think about it, and I suggest you don’t, this is a Markov model for all people regardless