Proof by Flatland

YOU WANT PROOF?

 

You want scientific proof? You can't think theologically, you'd rather do it mathematically? OK chum, you asked for it. You are, I'm sure, aware that it is mathematically possible (I've met people who call it simple, but that's their problem) to construct a geometry using four dimensions – or, for that matter, five, six or eleven dimensions. Somebody involved with String Theory has recently proved that eleven is the limit, so there are probably lots more. Unfortunately, as human beings live in only three (length, breadth, height, all at right angles to each other), we are incapable of actually visualising a fourth dimension, at right angles to all three. That's why we have all this difficulty with the Ascension; we have to say Jesus went up, while knowing that if he went anywhere, it was neither up, nor down, nor back, nor front, nor left nor right, but some otherwhere.

We can, however, approach the problem from another direction; by imagining for ourselves a world with only two dimensions; completely flat, whose inhabitants can look left or right, in front or behind, but who have no conception of up or down. The mathematician Edwin Abbott, a hundred years ago, called it Flatland.

Now, if one inhabitant of Flatland looks at another, what does he see? He sees, because he has no conception of height, a horizontal line, and only a line, as defined by Euclid, with length but no thickness. Presumably, there are subtleties about this line which enable him to distinguish between his friends, but they are all lines. To us, however, who see them from above or below, they may be circles, squares, triangles or complex incurved dodecagons.

We, in our turn, are invisible to Flatlanders unless some part of us actually intersects their space, in which case we are seen by them as – a line.

 

As we move in and out of their space, our line will appear and disappear. At any time, we could (should we so wish) see from above, or indeed touch, any of the complex workings of a Flatlander's interior; we can, if it tickles our fancy, breathe upon his very heart.

It follows that the poor Flatlander can perceive us, by means of his senses or his intellect, in three different ways. First, we can be all around him, but unseen and unfelt because we do not physically intersect the plane on which he lives. Secondly, we can be present in his world with him, and he can see us as a line, similar to himself and his friends, at the point where we intersect. Thirdly, we can be inside him, felt as a breath or a touch which comes, we say from above, he can only say from within.

Down the ages, the most mystifying of our Christian doctrines and Festivals has been the last of our year, that of the Trinity; yet it is, as we have just seen, the Trinity that is the most easily susceptible of mathematical demonstration. There is, of course, no such place as Flatland, a world of only two dimensions; but there is no grounds for supposing that the universe stops short at three dimensions, and a being who lives in four or more would appear to us pretty much in the way we would appear to a Flatlander; around, beside and within, Father, Son and Spirit.

The existence of another dimension, at right angles to all our own three, also answers such questions as, Where is Heaven, Daddy? or, Where is the soul? or, Where is God? or any spiritual question beginning with Where? which is all the more welcome since the existence of another dimension is scientifically demonstrable. Ask any quantum physicist, who will tell you strange tales of particles which move from A to B, millions of times their own length, in literally no time at all, because the Universe is so folded that from A to B via Dimension 4 is no distance at all.

Imagine the events of Spring taking place in Flatland; Good Friday, Easter Day, Emmaus, the lakeside breakfast, the Ascension, Pentecost; the actions of a three-dimensional being in a two-dimensional world, and no liberties taken with the laws of Physics. Then imagine them as the actions of a four-dimensional being in a three-dimensional world, and finally ask the crucial question, which is neither Where? nor How? but Why?

Why does God give us a demonstration of the fourth dimension? Is it a mere conjuring trick? Is he showing off, saying, I can do this but you can't? Or is he saying, I can do this, and so can you? Here is a demonstration that that which we call the Spirit, the Soul, the Life within us, is greater than our physical body, free of length and breadth and height and capable, once released from the physical, of infinitely more in an infinitely larger space.

O Death, where is thy sting? O grave, where is thy victory?

HGB