Is space infinite?

Georg Cantor

According to Georg Cantor, one of the first to study the concept of infinity in depth, there is not just one concept of infinity, but three different ones. Let's see how he expresses it:

The actual infinite arises in three contexts: first when it is realized in the most complete form, in a fully independent other-worldly being, in Deo, where I call it the Absolute Infinite or simply Absolute; second when it occurs in the contingent, created world; third when the mind grasps it in abstracto as a mathematical magnitude, number, or order type. I wish to make a sharp contrast between the Absolute and what I call the Transfinite, that is, the actual infinities of the last two sorts, which are clearly limited, subject to further increase, and thus related to the finite. (Georg Cantor, Gesammelte Abhandlungen, Springer, 1980. Translation taken from Rudy Rucker, Infinity and the Mind, Princeton University Press, 2004).

George Ellis and the multiverse

George Ellis

George Ellis is a South African cosmologist who rose to fame almost half a century ago when he wrote a book together with Stephen Hawking (The Large Scale Structure of Space-Time, 1973), today considered a classic.

In an earlier post in this blog, published in November 2014, I mentioned that there are six independent theories about the multiverse, almost all of them incompatible with each other. In a recent article titled Theory Confirmation and Multiverses published in the book Why Trust a Theory?, edited by Radin Dardashti, Richard David and Karim Thébault (Cambridge University Press, 2019), George Ellis updates the different multiverse theories. He does not mention six, as I did five years ago, but nine, although he has left out one of the six I mentioned in my post (Smolin’s), perhaps because this theory has been abandoned in the meantime. The nine theories are: