If you measure the circumference and diameter of a pencil circle, the best you can hope for is a close approximation, because measurement is never perfectly accurate. And one must not mix up dreams with verifiable experience.
So does infinity exist? Well, it does in the mind, because there is a whole mathematics of it; but Georg Cantor who first explored the mathematics of infinity went mad, and I would have thought it was a risky business to cut oneself off from the possibility of verification in the natural world. And I cannot see that there are any infinities in the natural world; I may be wrong, but I cannot see them. Just as there are many risks in mountaineering that I was unwilling to take, although I might have got away with them; so I would have thought one risked disorientation if one got too involved in the imaginative world of infinities, and soon found one ceased to see things in proportion in the real world of flesh and blood and spirit.
If I am right that in any attitude of mind, there is an envelope of consciousness which disciplines all thought in that attitude of mind, then the largest envelope possible is the entire knowable world, stretching to the furthest galaxy of which we can have knowledge. In this frame of mind, one views the cosmos as a whole; and one can speculate innocently enough on what God’s purposes might be. But if you go beyond this, are you not bound to lose any envelope of consciousness that has any meaning? And I would have thought at the same time, you were in danger of losing track of the unspoken and unconscious assumptions on which your attitude of mind is based. Of course one can invent fantasy worlds, Lewis Carol did with Alice; but is not the danger that one makes words mean what one wants them to mean? Should we not submit to the constraints of the world we live in? This is the great virtue of War, that it winnows terribly reality from illusion. I am in favour of letting the imagination run riot occasionally, as my “Reconciliation with Science and War” and “Man’s Relationship with God” make abundantly plain; provided it submits to the constraints of the created world.
So can one verify that one is speaking to God, although He is spirit and invisible? Or does one risk here too getting lost in a world of imagination and make-belief? Yes of course one can, to one’s own satisfaction at least. All family affection and loyalty is in the world of the spirit, and is invisible. It may be manifested in visible acts; it may be proved by acts of heroism. But in itself affection is spirit, and invisible. In the same way one can confidently assert one knows God, even though agnostics and atheists would say one is deluding oneself. One consequence of my theory of consciousness is that religious experience is the same as any other sort of experience. So experience of God can bring verification, as the needle of a galvanometer in a laboratory, or trusting a companion on a climbing rope. It is all one world.