Before the question
More than I put in
Eureka! The estimate gives one million, three hundred eighty-eight thousand, eight hundred sixty-four — that is far more than I put in!
Rosencrantz · experimentalist
An argument in many dimensions
How many arrows can stand nearly sideways?
AsideRosencrantz and Guildenstern explore a peculiar thing that happens when we think far beyond three dimensions — one of the very keys that let Large Language models be, well, large.
Two different ideas
A perfect right angle
Two lines. They have met and immediately agreed to face elsewhere.
Rosencrantz · experimentalist
They meet at exactly 90°. Neither points even slightly along the other.
Guildenstern · theorist
Surely one more
The finger that will not fit
Your thumb and finger make two directions. There is plainly room between them.
Rosencrantz · experimentalist
Room for a finger, perhaps. Not for a third direction nearly 90° from both.
Guildenstern · theorist
A result without a theory
Guildenstern makes it sensible
The estimate gives 1,388,864 directions in 12,288 dimensions. The box was quite definite.
Rosencrantz · experimentalist
No, no, no — you cannot get there from here! A result arriving before its explanation is merely an ambush.
Guildenstern · theorist
The numbers change character
Multiplying room
One hundred dimensions. The box says 113.
Rosencrantz · experimentalist
A small excess. Possibly clerical.
Guildenstern · theorist
The Shared Board
What are they for?
But why hoard so many dimensions — whatever will you do with them all?
Guildenstern · theorist
Store things in them. Here — watch.
Rosencrantz · experimentalist