Spheres Part 3
Original: Spheres Part 3 on Saturday Morning Breakfast Cereal
Transcript
Top banner: PART 3 OF 5! PRESS FORWARD TO CONTINUE!
Panel 1: Supermarkets often use this packing to stack oranges and other round fruits in their bigger section.
Caption: Customers will appreciate the connection, maximum efficiency orange-packing!
Panel 2: Higher computer that has the density of this packing was about 74%. That is, about 74% of the available space was occupied by the spheres, and the remaining 26% by the empty space between them.
Label pointing at a sphere: There is probably not a better way.
Panel 3: He conjectured that this was the maximum possible density. There was no other way to pack spheres that could achieve a density of greater than 74%. (Accompanied by a pie chart diagram of a packed sphere arrangement.)
Panel 4: This "Kepler conjecture" attracted the attention of many brilliant mathematicians for centuries.
Names beneath portraits of mathematicians: Gauss / Thue / Toth / Rogers
Panel 5: It then only solved in 1998 after countless works culminating in a 300-page paper by Thomas Hales and Samuel Ferguson. (Was) also needed extensive computer calculations to complete the proof.
Speech: We used proof. We have proven the maximum number of theorems into the proof.
Reply: Yep!
Panel 6: This by itself didn't revolutionize the way cannonballs or oranges were stacked.
Speech: Wow, is the proved maximum-efficiency orange-packing?
Reply: Kepler-approved.
Panel 7: But once mathematicians study one question, they are inspired to explore other related questions. That often becomes the motivation of the original problem.
Caption: The Kepler conjecture is about packing spheres in three dimensions. Mathematicians asked: what happens instead in two dimensions? Four? A million?
Panel 8: This is exactly a problem. If you need to answer the mathematical object.
Speech (figures labeled A, G, C around a table with a wavy ribbon): Fingers getting tired from all those symbols, Thompson?
Labels: A / Natural Log / C / Grumble
Panel 9: But not if you want to do your math.
Speech (figure 1): Hahaha! Wheres your precious 'visual intuition' now, Jenkins?? Hahaha!
Speech (figure 2): But higher-dimensional spheres aren't just useless for making decimeters cry... (trailing off)
Votey: (none)
Panel 1: Supermarkets often use this packing to stack oranges and other round fruits in their bigger section.
Caption: Customers will appreciate the connection, maximum efficiency orange-packing!
Panel 2: Higher computer that has the density of this packing was about 74%. That is, about 74% of the available space was occupied by the spheres, and the remaining 26% by the empty space between them.
Label pointing at a sphere: There is probably not a better way.
Panel 3: He conjectured that this was the maximum possible density. There was no other way to pack spheres that could achieve a density of greater than 74%. (Accompanied by a pie chart diagram of a packed sphere arrangement.)
Panel 4: This "Kepler conjecture" attracted the attention of many brilliant mathematicians for centuries.
Names beneath portraits of mathematicians: Gauss / Thue / Toth / Rogers
Panel 5: It then only solved in 1998 after countless works culminating in a 300-page paper by Thomas Hales and Samuel Ferguson. (Was) also needed extensive computer calculations to complete the proof.
Speech: We used proof. We have proven the maximum number of theorems into the proof.
Reply: Yep!
Panel 6: This by itself didn't revolutionize the way cannonballs or oranges were stacked.
Speech: Wow, is the proved maximum-efficiency orange-packing?
Reply: Kepler-approved.
Panel 7: But once mathematicians study one question, they are inspired to explore other related questions. That often becomes the motivation of the original problem.
Caption: The Kepler conjecture is about packing spheres in three dimensions. Mathematicians asked: what happens instead in two dimensions? Four? A million?
Panel 8: This is exactly a problem. If you need to answer the mathematical object.
Speech (figures labeled A, G, C around a table with a wavy ribbon): Fingers getting tired from all those symbols, Thompson?
Labels: A / Natural Log / C / Grumble
Panel 9: But not if you want to do your math.
Speech (figure 1): Hahaha! Wheres your precious 'visual intuition' now, Jenkins?? Hahaha!
Speech (figure 2): But higher-dimensional spheres aren't just useless for making decimeters cry... (trailing off)
Votey: (none)
Alt text
A tall full-color SMBC comic with a top banner reading "PART 3 OF 5! PRESS FORWARD TO CONTINUE!" The strip explains the Kepler conjecture about sphere packing. Early panels show stacked oranges and a diagram of spheres filling space, noting that the densest packing fills about 74% of space, leaving 26% empty, and that Kepler conjectured this was the maximum possible density. A panel labeled with portraits of mathematicians (Gauss, Thue, Toth, Rogers) notes the conjecture drew attention for centuries. Later panels describe its 1998 proof by Thomas Hales and Samuel Ferguson, a 300-page paper relying on heavy computer calculation, with a wry exchange about "proving the maximum number of theorems" and an orange-packing being "Kepler-approved." The closing panels show mathematicians at a table covered in symbols and a wavy ribbon, with figures labeled A, G, and C, joking about generalizing sphere-packing to two, four, or a million dimensions, and one mathematician mocking another's reliance on 'visual intuition' since higher-dimensional spheres can't be pictured. There is no votey.
Transcribed by Claude Opus 4.8.