People in general are pretty good at understanding 1 to 1 matching for finite sets, and have to readjust their intuition for infinite sets. Thus first thing to help them break their intuition is going through the logic of https://en.wikipedia.org/wiki/Hilbert%27s_paradox_of_the_Grand_Hotel After someone realizes the universe is not what they expected it to be, you help them build a better intuition. If you are lucky, you get to the Cantor’s diagonalization argument. Mind you, the argument requires a certain level of intelligence, it is just completely beyond some people.
Yep, absolutely! It was actually through explaining Hilbert’s Hotel that Bruce helped me come up with the Bruce Framework.
I do think it is odd though that the mathematical notion of cardinality doesn’t solve the Thanos Problem, and I’m worried that AI systems that understand math practically well but not theoretically well will consider the loss of half an infinite set to be no loss at all, similar to how if you understand Hilbert’s you’ll believe that adding twice the number of hotels is never an issue.
People in general are pretty good at understanding 1 to 1 matching for finite sets, and have to readjust their intuition for infinite sets. Thus first thing to help them break their intuition is going through the logic of https://en.wikipedia.org/wiki/Hilbert%27s_paradox_of_the_Grand_Hotel After someone realizes the universe is not what they expected it to be, you help them build a better intuition. If you are lucky, you get to the Cantor’s diagonalization argument. Mind you, the argument requires a certain level of intelligence, it is just completely beyond some people.
Yep, absolutely! It was actually through explaining Hilbert’s Hotel that Bruce helped me come up with the Bruce Framework.
I do think it is odd though that the mathematical notion of cardinality doesn’t solve the Thanos Problem, and I’m worried that AI systems that understand math practically well but not theoretically well will consider the loss of half an infinite set to be no loss at all, similar to how if you understand Hilbert’s you’ll believe that adding twice the number of hotels is never an issue.