The video titled "Up and Atom" by Jade explores a thought experiment involving an infinite number of balls and a vase. The process begins with the addition of balls one to ten and the removal of ball ten. This pattern continues, with ten balls added and one ball removed at each time division until noon. The question posed is how many balls are in the vase at noon.
Jade initially suggests that for every ten balls added, one ball is removed, leading to an infinite number of balls in the vase at noon. However, she later realizes that if the balls are removed one by one, starting from ball one at the first time step, ball two at the second time step, and so on, all the balls will be removed, leaving the vase empty at noon.
This scenario is referred to as the Ross-Littlewood paradox, where two valid arguments lead to different conclusions. The video further explores the concept of one-to-one correspondence, a method of counting without explicitly counting. It demonstrates how this concept can be applied to infinite sets of numbers, and how it can help solve the paradox.
The video concludes by stating that both Jade and Blade were correct in their reasoning, but for different scenarios. The video also touches on the philosophical question of whether math is invented or discovered, and mentions a documentary by Hannah Fry on this topic. The video was made possible by CuriosityStream, a streaming service that offers award-winning documentaries.
1. The episode is titled "Up and Atom" and was produced by CuriosityStream. [Source: Document 1]
2. The host of the episode is Jade, who presents a thought experiment involving an infinitely large vase and an infinite number of balls. [Source: Document 1]
3. The experiment involves adding balls one to ten at one minute before noon, then adding balls 11 to 20 and removing ball 20 half a minute until noon. [Source: Document 1]
4. The process continues with adding balls 21 to 30 and removing both 30, one quarter of a minute until noon. [Source: Document 1]
5. The question posed is how many balls are in the vase at noon. [Source: Document 1]
6. The host attempts to solve the question by adding nine balls at each step and removing one ball, suggesting that at noon, there should be an infinite number of balls left in the vase. [Source: Document 1]
7. However, the host's friend Blade points out that if they remove balls one, two, three, and so on, in a one-to-one correspondence, all balls would be taken out and the vase would be empty at noon. [Source: Document 1]
8. The host admits that they failed to create a one-to-one correspondence, leaving an infinite number of balls in the vase at noon. [Source: Document 1]
9. The episode concludes with a discussion on the concept of infinity and its implications in our understanding of the world. [Source: Document 1]
10. The host mentions a feature video about the question of whether math is invented or discovered, created on a streaming platform called Nebula, which is supported by CuriosityStream. [Source: Document 1]