## Thursday, July 28, 2016

### Of balloons and transubstantiation

Our three-dimensional space is curved, say, like the surface of a balloon--except that the surface of a balloon is two-dimensional while space is three-dimensional.

Now imagine you have an inflated balloon. Draw two circles, an inch in diameter, on opposite sides, one red and one blue. Put your left thumb in the middle of the red circle and your right thumb in the middle of the blue circle. Press the thumbs towards each other, until they meet, with two layers of rubber between them. The balloon now looks kind of like a donut, but with no hole all the way through. Imagine now that you press so hard that the two layers of rubber between your thumbs coalesce into a single layer of rubber.

Now the single layer of rubber between your thumbs is at the center of the red circle and at the center of the blue circle. We can think of each circle as defining a place, and the coalesced rubber inside it is found in both of these places.

Replace the red circle with a drawing of a church and the blue circle with a drawing of heaven. The same coalesced layer of rubber is both inside (a drawing of) a church and inside (a drawing of) heaven. Suppose now that the rubber is infinitely thin, and that there is a space that coincides with this rubber, and little two-dimensional people, animals, plants and other objects inhabiting this space, much as in Abbott’s novel Flatland . Suppose that the pictures of the church and heaven are replaced with two-dimensional realities. Then the space of the church and the space of heaven literally overlap, so that there is a place that is located in both. An object found in that place will be literally and physically located both in the church and in heaven. In one sense, that object is physically located in two places at once. In another sense, it is located in a single place, but that single place is simultaneously located both in heaven and in the church.

There is no serious additional conceptual difficulty in three-dimensional space curving in on itself similarly.

(This is largely taken from a forthcoming piece by Beckwith and Pruss.)

SMatthewStolte said...

According to this model, someone could arrive in heaven by means of a very fast vehicle. If the balloon is big enough, we might suppose that this means of getting to heaven would pose all sorts of engineering problems. It might even be unfeasible given the shortness of life and the limitations of relativity.

But that doesn’t seem to match up with the way we should think of heaven. Church isn’t a workaround to otherwise insoluble engineering problems.

Alexander R Pruss said...

But the area which is in both heaven and earth coincides with the Eucharistic host. So only if your vehicle managed to be in the same place as the host could it go to heaven.

SMatthewStolte said...

I am assuming that ‘earth’ is just a synonym for ‘universe’ in this context.
I am also assuming that the red and blue circles are both bigger than my thumbs, so there is some place in the church which is not the host and there is also some place in heaven which is not the host.

Part of my problem is that it seems like you need our universe to be the entire surface of the balloon, and you also need it not to be the entire surface of the balloon. You need it to be the entire surface, because there is a path from every point on the balloon to every other point, and there would be even if I didn’t bring my thumbs together/there were no consecration of the host. But you need it not to be the entire surface, because you first need a distinction between heaven and earth in order to make the fact that the two places which the host occupies theologically interesting (rather than merely interesting for the physicist).

Perhaps the red and blue circles should not represent one church and heaven but rather two distinct churches. And heaven should be represented by the surface of my thumbs.

Alexander R Pruss said...

I misunderstood your worry. You're rather worried about the implication that heaven is spatially connected to us. I do doubt that it is spatially connected to us, but it might be - I think the view that it's connected was the predominant view among Christians until recently. Even the name "heaven" suggests that.

If it's not connected to us, then we can just imagine the surfaces of two balloons merging in one place.

SMatthewStolte said...

Okay, I’m happier now.