Infinities are an interesting case for rationality. On one side, they are totally made up: we do not have any example of an infinite quantity in our experience. On the other side, they seem to have a quality of coherence and persistence that is independent from our mind, in contrast with other kinds of fiction. They are complex and unintuitive, and it’s a problem that shines a light on the fact that even amongst the experts there are different degrees of expertise. A set theorist migh reply that due to the Transfinite Recursion Theorem, that summation really sums to omega, not any finite value, and that the only way to create a coherent infinite function is to specify a limit step: but someone who is not versed in mathematics will believe what a nice and lively professor seen on Youtube will say.
It is unfortunate that seen from ‘below’, all experts seem alike, and there are few ways to discern someone who is treading out of their area of expertise.
Infinities are an interesting case for rationality. On one side, they are totally made up: we do not have any example of an infinite quantity in our experience. On the other side, they seem to have a quality of coherence and persistence that is independent from our mind, in contrast with other kinds of fiction. They are complex and unintuitive, and it’s a problem that shines a light on the fact that even amongst the experts there are different degrees of expertise.
A set theorist migh reply that due to the Transfinite Recursion Theorem, that summation really sums to omega, not any finite value, and that the only way to create a coherent infinite function is to specify a limit step: but someone who is not versed in mathematics will believe what a nice and lively professor seen on Youtube will say. It is unfortunate that seen from ‘below’, all experts seem alike, and there are few ways to discern someone who is treading out of their area of expertise.