Is history repeating itself?

Alexander Vilenkin

The idea that history repeats itself is a commonplace notion, often expressed through sayings such as man is the only animal that trips twice over the same stone. However, that is not what we are addressing here, as such repetitions are always partial—events never recur in exactly the same way. Here, we will discuss whether it is possible for history to repeat itself in such way that events unfold exactly as they did before.

In principle, there are two ways history could repeat itself:

·         In time: According to theories of cyclical time—accepted by various civilizations—time repeats itself. Greek astronomers like Hipparchus and Ptolemy calculated that the cycle of the precession of the equinoxes (the wobble of the Earth's axis) lasted about 36,000 years (one degree every 100 years). Believing that the position of the stars determined human destiny, some concluded that every 36,000 years—when the stars returned to the same positions—history would repeat itself exactly, and the same people would be born again. Although Saint Augustine rejected this theory in The City of God, some Scholastics revived it, and the Church was forced to condemn their ideas as heretical. I discussed cyclical time in two previous blog posts: Cyclic Time and Linear Time and Is Time Infinite?

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: