Spheres Part 4
Original: Spheres Part 4 on Saturday Morning Breakfast Cereal
Transcript
Header: PART 4 OF 5! PRESS FORWARD TO CONTINUE! >>
Panel 1 (narration box): For instance, in 2022 Maryna Viazovska was awarded the Fields Medal (one of the highest honors in mathematics) in part for her solution of the sphere packing problem in 8 and 24 dimensions.
[Image caption: (E8 diagram by JLrobo, found on Wikipedia. CC BY-SA 3.0, which means this comic is also CC BY-SA 3.0.)]
Panel 2 (narration, man gesturing toward a cluster of icons labeled ROBOTICS, MACHINE LEARNING, ENCRYPTION): These turn out to be very special, with unexpected connections to many other areas of mathematics.
Panel 3 (narration box): Another question mathematicians asked was: what if we study packing problems, but in a space that is discrete instead of continuous?
Left character: The universe is CHUNKY!
Right character: The universe is SMOOTH!
(The left figure wears a shirt reading "Computer Scientist"; the right figure wears a shirt reading "Physicist.")
Panel 4 (narration box): One type of discrete space that computer scientists are particularly interested in is the "Hamming cube," which is a cube whose vertices represent strings of bits.
Man (holding up fingers, a 0 and a 1): ...(0s and 1s) of a given length.
Panel 5 (narration box): Strings of two bits form a two-dimensional square; strings of three bits form a three-dimensional cube; and so forth.
[Diagram: a labeled cube with binary vertex labels 000, 001, 010, 011, 100, 101, 110, 111.]
Panel 6 (narration box): There is a discrete analogue of a sphere on the Hamming cube, coming from bit errors in digital transmission.
[Diagram: a dashed red circle around a cube with binary labels and a tree of 000 / 100, 010, 001.]
Panel 7 (narration box): Suppose you want to send a message to someone.
Green blackboard text: To Jenkins: Algebraists RULE, geometers use mental models of a 3D universe which for many purposes are an inadequate TOOL.
(A small figure wearing an "A" shirt points at the blackboard.)
Panel 8 (man at a telegraph key, speech bubble): You can't just send letters down a wire. But, you can do something like Morse code.
[Morse code dots and dashes shown above the telegraph.]
Panel 9 (narration box): You might be tempted to do the obvious thing and just assign the 26 letters to binary combinations. Let's say you have 9 bits to work with. You could do something like this:
A 0: 000 000 000
B 1: 000 000 001
C 2: 000 000 010
D 3: 000 000 011
E 4: 000 000 100
F 5: 000 000 101
G 6: 000 000 110
Panel 10 (narration box): If signal transmission is perfect-no interference from electromagnetic radiation, cosmic rays, vengeful geometers messing with the wire-then this is fine.
Bottom narration: The shortest distance between two points has been BISECTED!
[Image: a figure wearing a "G" shirt sits atop a telegraph pole holding scissors, having cut the wire.]
Panel 11 (man shrugging, speech bubble): But perfection is rare in real life. And, for instance, 000 000 101 (F) looks a lot like 000 000 111 (H), which might be dicey if you're sending a message to your friend Huck.
Votey: (none)
Panel 1 (narration box): For instance, in 2022 Maryna Viazovska was awarded the Fields Medal (one of the highest honors in mathematics) in part for her solution of the sphere packing problem in 8 and 24 dimensions.
[Image caption: (E8 diagram by JLrobo, found on Wikipedia. CC BY-SA 3.0, which means this comic is also CC BY-SA 3.0.)]
Panel 2 (narration, man gesturing toward a cluster of icons labeled ROBOTICS, MACHINE LEARNING, ENCRYPTION): These turn out to be very special, with unexpected connections to many other areas of mathematics.
Panel 3 (narration box): Another question mathematicians asked was: what if we study packing problems, but in a space that is discrete instead of continuous?
Left character: The universe is CHUNKY!
Right character: The universe is SMOOTH!
(The left figure wears a shirt reading "Computer Scientist"; the right figure wears a shirt reading "Physicist.")
Panel 4 (narration box): One type of discrete space that computer scientists are particularly interested in is the "Hamming cube," which is a cube whose vertices represent strings of bits.
Man (holding up fingers, a 0 and a 1): ...(0s and 1s) of a given length.
Panel 5 (narration box): Strings of two bits form a two-dimensional square; strings of three bits form a three-dimensional cube; and so forth.
[Diagram: a labeled cube with binary vertex labels 000, 001, 010, 011, 100, 101, 110, 111.]
Panel 6 (narration box): There is a discrete analogue of a sphere on the Hamming cube, coming from bit errors in digital transmission.
[Diagram: a dashed red circle around a cube with binary labels and a tree of 000 / 100, 010, 001.]
Panel 7 (narration box): Suppose you want to send a message to someone.
Green blackboard text: To Jenkins: Algebraists RULE, geometers use mental models of a 3D universe which for many purposes are an inadequate TOOL.
(A small figure wearing an "A" shirt points at the blackboard.)
Panel 8 (man at a telegraph key, speech bubble): You can't just send letters down a wire. But, you can do something like Morse code.
[Morse code dots and dashes shown above the telegraph.]
Panel 9 (narration box): You might be tempted to do the obvious thing and just assign the 26 letters to binary combinations. Let's say you have 9 bits to work with. You could do something like this:
A 0: 000 000 000
B 1: 000 000 001
C 2: 000 000 010
D 3: 000 000 011
E 4: 000 000 100
F 5: 000 000 101
G 6: 000 000 110
Panel 10 (narration box): If signal transmission is perfect-no interference from electromagnetic radiation, cosmic rays, vengeful geometers messing with the wire-then this is fine.
Bottom narration: The shortest distance between two points has been BISECTED!
[Image: a figure wearing a "G" shirt sits atop a telegraph pole holding scissors, having cut the wire.]
Panel 11 (man shrugging, speech bubble): But perfection is rare in real life. And, for instance, 000 000 101 (F) looks a lot like 000 000 111 (H), which might be dicey if you're sending a message to your friend Huck.
Votey: (none)
Alt text
A tall vertical SMBC comic titled "PART 4 OF 5! PRESS FORWARD TO CONTINUE!" explaining sphere packing and coding theory. Narration notes that Maryna Viazovska won the 2022 Fields Medal for solving the sphere packing problem in 8 and 24 dimensions, shown beside a colorful circular E8 lattice diagram (credited to JLrobo, CC BY-SA 3.0, making the comic also CC BY-SA 3.0). A man gestures toward icons for robotics, machine learning, and encryption, saying these packings have unexpected connections to many areas of math. Mathematicians ask what happens with discrete instead of continuous space: a "Computer Scientist" figure shouts "The universe is CHUNKY!" while a "Physicist" figure shouts "The universe is SMOOTH!" The comic introduces the "Hamming cube," a cube whose vertices are bit-strings, illustrated with cubes labeled in binary (000, 001, ... 111) and a discrete-sphere diagram with a dashed red circle and a tree of bit values. To explain sending messages, a blackboard reads a sarcastic note "To Jenkins: Algebraists RULE, geometers use mental models of a 3D universe which for many purposes are an inadequate TOOL," with a small figure in an "A" shirt pointing at it. A man at a telegraph key explains you can't send letters down a wire but can use Morse code (dots and dashes shown). A table assigns letters A-G to nine-bit binary codes (A 0: 000 000 000 through G 6: 000 000 110). The narration says perfect transmission would make this fine -- "no interference from electromagnetic radiation, cosmic rays, vengeful geometers messing with the wire" -- shown by a figure in a "G" shirt perched on a telegraph pole with scissors having cut the wire, captioned "The shortest distance between two points has been BISECTED!" Finally a shrugging man notes that perfection is rare, and that 000 000 101 (F) looks a lot like 000 000 111 (H), which could be dicey when sending a message to your friend Huck. There is no votey.
Transcribed by Claude Opus 4.8.