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Comment by photochemsyn | Hacker News Reader

The 1977 film Powers of Ten is short and simple but gives one a better feeling for what infinity represents (40 orders of magnitude isn't much in contrast to infinity, but is very large):

https://youtu.be/0fKBhvDjuy0

There's also an hour-long talk by Prof. Raymond Flood on Cantor's Infinities on YT that covers all the mathematical history.

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This is a somewhat glib but forty orders of magnitude, being a finite number, has no more to do with infinity that any other finite number. The nature of infinity is that you can’t get meaningfully closer to it.

> The car shot forward straight into the circle of light, and suddenly

> Arthur had a fairly clear idea of what infinity looked like.

> It wasn't infinity in fact. Infinity itself looks flat and uninteresting.

> Looking up into the night sky is looking into infinity - distance is

> incomprehensible and therefore meaningless. The chamber into

> which the aircar emerged was anything but infinite, it was just very

> very big, so that it gave the impression of infinity far better than

> infinity itself.

This is from one of the Hitchhiker's Guide to the Galaxy books. They're with Slartibartfast driving onto the factory floor for creating planets. Slartibartfast, as you recall, is a famous "world designer" who won an award for designing the Fjords of Norway.

Depends on how you measure, for example what about the stereographic projection of the plane into the sphere and then use the metric in R3? Distance from a point in the plane to infinity is then the distance from where it maps to in the sphere to the north pole.

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