Leaving space

Suppose that we are in an infinite Euclidean space, and that a rocket accelerates in such a way that in the first 30 minutes its speed doubles, in the next 15 minutes it doubles again, in the next 7.5 minutes it doubles, and so on. Then in each of the first 30 minutes, and the next 15 minutes, and the next 7.5 minutes, and so on, it travels roughly the same distance, and over the next hour it will have traveled an infinite distance. So where will it be? (This is a less compelling version of a paradox Josh Rasmussen once sent me. But it’s this version that interests me in this post.)

The causal finitist solution is that the story is impossible, for the final state of the rocket depends on infinitely many accelerations, and nothing can causally depend on infinitely many things.

But there is another curious solution that I’ve never heard applied to questions like this: after an hour, the rocket will be nowhere. It will exist, but it won’t be spatially related to anything outside of itself.

Would there be a spatial relationship between the parts of the rocket? That depends on whether the internal relationships between the parts of the rocket are dependent on global space, or can be maintained in a kind of “internal space”. One possibility is that all of the rocket’s particles would lose their spatiality and exist aspatially. Another is that they would maintain spatial relationships with each other, without any spatial relationships to things outside of the rocket.

While I embrace the causal finitist solution, it seems to me that the aspatial solution is pretty good. A lot of people have the intuition that material objects cannot continue to exist without being in space. I don’t see why not. One might, of course, think that spatiality is definitive of materiality. But why couldn’t a material object then continue to exist after having lost its materiality?

Reality is strange

The doctrines of the Trinity, the Incarnation and transubstantiation initially seem contradictory. Elaborate theological/philosophical accounts of the doctrines are available (e.g., from St. Thomas Aquinas), and given these, there is no overt contradiction. But the doctrines still seem very strange and they feel like they border on contradiction, with the accounts that remove contradiction sometimes looking like they are ad hoc designed to remove the contradiction from the doctrine. This may seem like a good reason to reject the doctrines.

But to reject the doctrines for this reason alone would be mistaken. For similar points can be made about Relativity Theory and Quantum Mechanics. To say that simultaneity is relative or that a physical object has no position but rather a probability distribution over positions borders on contradiction, and the philosophical moves needed to defend these seem ad hoc designed to save the theories. If we’ve learned one thing from physics in the 20th century, it is that the true physics of the world is very strange indeed.

Nor are theology and science the only places where things are strange. Similar things can be said about the mathematics of infinity, or even just common sense claims such as that there is change (think of Zeno’s paradoxes) or that material objects persist over time (think of the Ship of Theseus and the paradoxes of material composition).

We can, thus, be very confident that created reality is very strange indeed. And hence, shouldn’t we expect similar strangeness—indeed, mystery—in the Creator and his relationship to us?

Materiality revisited

I’ve long been puzzled by materiality.

Here’s a thought: What if materiality isn’t characterized by anything deeply metaphysical, but by a physical quality? Perhaps to be material just is to have something like inertia, or mass, or energy?

(I think that to have zero of some quality like mass is still to have mass. A mass of x is a determinate of the determinable mass even if x = 0. Photons have mass, while numbers don’t.)

Can something material become immaterial?

Two angels are playing chess. They are immaterial, but have the causal powers of moving physical pieces on the board. Along comes a big snake and swallows the board. No worries: the angels keep on playing, but now the positions of the chess pieces are kept track of in their minds instead. So the king, say, was first a material object. But the king then became an object wholly constituted by the angels' thoughts, and hence immaterial. And it is the same king. While in chess you can get a new queen by promoting a pawn, you don't get a new king within a game.

(Of course, I suspect that the true ontology doesn't include artifacts like chess kings.)