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Some Mathematicians Don't Believe in Infinity
- jjgreen 1y agoWittgenstein in a lecture once asked his audience to imagine coming across a man who is saying “...5, 1, 4, 1, 3 — finished!”, and, when asked what he has been doing, replies that he has just finished reciting the complete decimal expansion of π backwards. A. W. Moore The Infinite, Routledge, 1990
- tocs3 1y agoI don't get it.
- jjgreen 1y agoWhen you recite the figures of pi, 3, 1, 4, 2, ... it goes on for ever, and no-one seems to object to the "..."; Wittgenstein turns it around, by reversing the sequence he places the infinity in the present, a potential infinity becomes an actual infinity and most people find that disturbing. But infinity has nothing to do with time, it is outside it, so our discomfort being time-direction dependent illustrates that we should have been disturbed by the "...", in the first case -- this is Wittgenstein's brilliance.
- tocs3 1y agoAh, I read the π as n.
- nyc111 1y agoMathematician Norman Wildberger has been criticizing the embrace of infinitiy by modern mathematicians for decades: https://www.youtube.com/@njwildberger/search?query=infinity https://www.youtube.com/@njwildberger/search?query=infinity
- taylodl 1y agoCurrent evidence points to the universe being infinite, therefore infinity exists in reality and isn't just a mathematical abstraction.
- sohkamyung 1y agoThe observable universe is finite, though [ https://en.wikipedia.org/wiki/Cosmological_horizon https://en.wikipedia.org/wiki/Cosmological_horizon ]. "A cosmological horizon is a measure of the distance from which one could possibly retrieve information. This observable constraint is due to various properties of general relativity, the expanding universe, and the physics of Big Bang cosmology. Cosmological horizons set the size and scale of the observable universe."