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).

The origin of eukaryotes

John Maynard Smith

As I have said several times in this blog, the theory of evolution is now well established. However, it is far from explaining everything. Many mysteries still remain. I listed some of them in a previous post. A book by J. Maynard Smith and E. Szathmáry, The Major Transitions in Evolution (Oxford University Press, 1995), describes them in more detail.

One of these problems refers to the changes of level that have taken place in the history of life, which I made the central idea of ​​my book The Fifth Level of Evolution. As its title implies, during evolution, things have not happened in an orderly or stable manner. At various points, there were changes of state (similar to those in physics) where evolution passed a critical point that made it possible to reach higher levels and opened up huge new fields in the configuration space. These points are the following: