“The direction of causation is also the direction of explanation” (Tim Maudlin)

zoloti vorota

This morning I read an interview with Tim Maudlin, a professor of the philosophy of physics at New York University, in which he talks about time. What interested me is how he sort of builds his ideas on topology, an area of mathematics I know so little about but find fascinating, in part because of my son Brendan. Topology comes from the yoking of two Greek words, the first, τόπος, meaning location, and the second, λόγος, meaning study. In mathematics, topology is concerned with geometric objects and how they are preserved under continuous deformation. Think of a Mobius strip or even a square, which can be stretched and pulled into a circle without breaking it. Topology is important in string theory and also in considerations of time-space.

For time to pass means for events to be linearly ordered, by earlier and later. The causal structure of the world depends on its temporal structure. The present state of the universe produces the successive states. To understand the later states, you look at the earlier states and not the other way around. Of course, the later states can give you all kinds of information about the earlier states, and, from the later states and the laws of physics, you can infer the earlier states. But you normally wouldn’t say that the later states explain the earlier states. The direction of causation is also the direction of explanation.

This morning I am also paying obsessive attention to the situation in Ukraine and although a country is not a geometry, it is a kind of topology. Over time, a country might be pulled one way or another, it might be temporally or spatially altered due to human interference or what used to called acts of God. But is there a moment when it is complete, the iconic version of itself, through time and in time? I’m thinking of a video I saw earlier today of Ukrainians singing their national anthem in the subway as Russian missiles struck Kyiv. I remember the subways of Kyiv, the long descent as though to the underworld, but sometimes the most beautiful mosaics (Zoloti Vorota, for example), and I could imagine, this morning, listening,  how the walls would hold the sound, shape it.

I’ve never been able to quite understand what the emergence of time, in its deeper sense, is supposed to be. The laws are usually differential equations in time. They talk about how things evolve. So if there’s no time, then things can’t evolve. How do we understand — and is the emergence a temporal emergence? It’s like, in a certain phase of the universe, there was no time; and then in other phases, there is time, where it seems as though time emerges temporally out of non-time, which then seems incoherent.

In time, in time. I am waiting for time to catch up to itself, like a Mobius strip. I am listening to the anthem in the underground of Kyiv, the glory of Ukraine echoing in time, each voice in time.

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