> On the second day, there are two gaps: “between nothing and zero” and “between zero and nothing”. Two numbers spawn in those two gaps. Call them –1 and 1.
Got lost here. I think I'm officially too dumb for math.
I think it's just we don't have a way to say/write these numbers. So you make up a way to write them (-1 and 1) and continue.
The numbers don't matter and you could replace -1 and 1 with anything. It's just easier to begin your new fake number at - 1 and 1. Because position does matter.
It’s a terrible explanation. A surreal number is defined as a pair of sets of surreal numbers (where you fiddle around the recursion in that definition by defining them in waves, so strictly speaking you’re defining “the surreal numbers born at time T” for each individual T given access to the surreal numbers born at all earlier times, and then you “take the union across all times”). Zero is a surreal number but the LLM is using the word “zero” to mean “the set containing just the surreal number 0”; “nothing” here is the LLM’s obtuse word for the empty set. Wikipedia may actually be easier to follow.
Someone please vibe code a proof that ZFC is inconsistent.
> On the second day, there are two gaps: “between nothing and zero” and “between zero and nothing”. Two numbers spawn in those two gaps. Call them –1 and 1.
Got lost here. I think I'm officially too dumb for math.
I think it's just we don't have a way to say/write these numbers. So you make up a way to write them (-1 and 1) and continue.
The numbers don't matter and you could replace -1 and 1 with anything. It's just easier to begin your new fake number at - 1 and 1. Because position does matter.
It’s a terrible explanation. A surreal number is defined as a pair of sets of surreal numbers (where you fiddle around the recursion in that definition by defining them in waves, so strictly speaking you’re defining “the surreal numbers born at time T” for each individual T given access to the surreal numbers born at all earlier times, and then you “take the union across all times”). Zero is a surreal number but the LLM is using the word “zero” to mean “the set containing just the surreal number 0”; “nothing” here is the LLM’s obtuse word for the empty set. Wikipedia may actually be easier to follow.
I feel the same way. Want to become a dumb and dumber duo? I believe you could be my friend.
Pitch: a mini-series where a Dumb and Dumber duo get access to unlimited tokens via a roommates's account (who is an intern at a frontier lab).
In each episode they make a major science-fiction style breakthrough and grapple with the consequences without revealing themselves.
“Guy amuses himself in token burn rpg while simultaneously demotivating anyone who would have found value in this process.”