I recall a passage from a book on the philosophy of religion that set up a Gedankenexperiment about infinity: imagine an infinitely long bookshelf upon which sit black books and red books, alternating black, red, black, red ad infinitum. Now imagine that you remove all the red books such that only black books remain on the shelf. You've just subtracted an infinity of red books from a infinity of both red and black books. So could it be said that infinity minus infinity equals infinity?
The concept of infinity isn't the same as the concepts of existence and nothingness, granted, but it's a limit concept all the same, and it may share the same paradoxical traits as other limit concepts. Things get strange out on the edge.
I think in terms of smaller and larger infinities. Your comment, by the way, reminds me of Hilbert's Infinite Hotel. And there's probably a room with an infinitely large library of books. Indeed, in every room, such a library! Which leads to Borges's Library of Babel. Oh, this is endless!
I recall a passage from a book on the philosophy of religion that set up a Gedankenexperiment about infinity: imagine an infinitely long bookshelf upon which sit black books and red books, alternating black, red, black, red ad infinitum. Now imagine that you remove all the red books such that only black books remain on the shelf. You've just subtracted an infinity of red books from a infinity of both red and black books. So could it be said that infinity minus infinity equals infinity?
ReplyDeleteThe concept of infinity isn't the same as the concepts of existence and nothingness, granted, but it's a limit concept all the same, and it may share the same paradoxical traits as other limit concepts. Things get strange out on the edge.
I think in terms of smaller and larger infinities. Your comment, by the way, reminds me of Hilbert's Infinite Hotel. And there's probably a room with an infinitely large library of books. Indeed, in every room, such a library! Which leads to Borges's Library of Babel. Oh, this is endless!
ReplyDeleteJeffery Hodges
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