Mysterious Words

Bob and Elaine are scientists who live in a two-dimensional world called Finlandia. The people of Finlandia have a culture much like our own, including elaborately developed physics and mathematics. All of their physics and mathematics are in two dimensions. Everything they experience is in two dimensions.

One day, Bob has a vision of a three-dimensional sphere. He tries to explain his revelation to Elaine.

Bob: “I saw something grand and marvelous! Something unlike anything I’ve ever seen before!”
Elaine: “What was it?”
Bob: “Uh… It was this amazing thing! The most profound revelation I’ve ever had!”
Elaine: “Cool, but what was it?”
Bob: “It’s hard to explain. I think it might have been like the thing discussed in that old sacred text, ‘The Revelations of Thoth.’ I’m thinking of the passage that goes, ‘…and it shall be a form beyond form, a substance beyond substance, outside the world, without the limits of corporeal existence, and all men shall wonder at it.'”
Elaine: “But modern science has thoroughly falsified the Revelations of Thoth. Only the uneducated and superstitious believe in that any more. Are you slipping out of common sense, Bob?”
Bob: “Look, I know it doesn’t fit with science, but I saw it! It was right there in front of my eyes!”
Elaine: “Well, I’d like to see it for myself. Do you know how I can do that?”
Bob: “No, I have no idea. The vision just came to me.”
Elaine: “That’s no good. Well if I can’t see it for myself, can you at least explain clearly what you saw?”
Bob: “Yeah, the Revelations of Thoth explains it perfectly clearly.”
Elaine: “Hmm, well I don’t really understand it. I’m not sure that what Thoth is saying even makes logical sense. Can you try to explain it more clearly?”
Bob: “Sure, let me give it a try.”
[thinks for a few moments]
Bob: “I guess I saw outside space. I transcended space.”
Elaine: “What would that mean?”
Bob: “Uhh, there was this thing. It was like a circle, but it wasn’t anything like an ordinary circle. It was a super-circle.”
Elaine: “What is a super-circle? I mean, I know what a circle is, but what was ‘super’ about this circle?”
Bob: “It was outside space.”
Elaine: “That sounds like nonsense.”
Bob: “I’m telling you, it was outside space!”
Elaine: “What would that even mean?”
Bob: “Hmm, this isn’t working. I need to think more, and then I’ll get back to you.”
[the next day]
Bob: “OK, maybe now I can explain. So we have a circle, of radius r. Except that the circle is also every size smaller than r, and it repeats itself infinitely in super-space, without ever becoming more than one thing.”
Elaine: “Well that’s starting to look more like an explanation. But it’s full of contradictions and undefined terms. How could a circle be more than one size? How could something be repeated infinitely while only being one thing? And what the heck is super-space? You’re not even using your terms consistently. Before you said that thing was outside space; now you say that it’s in super-space. Which is it? And what would either of those even mean?”
Bob: “Well they really mean the same thing, you see. But you have a good point. I’m really bothered by my inability to explain this thing clearly. Let me try again and get back to you.”
[the next day]
Bob: “OK, I’ve got it now. Imagine a point, which expands to become a circle, and then shrinks back down to a point. Except this process is timeless. It is in every state at once, in an eternal state of superposition.”
Elaine: “Hmm… Here’s the thing, Bob. Your explanations sound sensible and scientific on the surface, but if you look more closely, they don’t really make sense. Like, what you said has a formal, mathematical flavor to it, but it can’t actually correspond to a coherent idea. What would it mean for a process to be timeless? How could a circle be more than one radius at once? And what do you mean by ‘superposition?’ I mean, I know what that word normally means in the context of physics, but you’ve appropriated it in a way that doesn’t make sense. I’m starting to lose faith in you, Bob. I think you’re just spouting pseudoscientific nonsense.”
Bob: “Huh! [storms off angrily]”
[a few days later]
Bob: “Elaine, I think I figured out why I can’t explain the super-circle to you. It’s beyond math, beyond physics, beyond language, even beyond thought. We can’t understand it with the intellect. It breaks logic. That’s why it can’t be explained in language. The only way to understand it is through direct experience. Anybody who hasn’t had a vision of a super-circle can’t make sense of discourse about it.”
Elaine: “…I don’t know what to say to that. I think you’ve lost it.”

Bob was not the first person to have a vision of a sphere. The person who wrote the Revelations of Thoth had also had such a vision; as had many Finlandian mystics. Even some Finlandian mathematicians had had visions of three-dimensional objects, but they generally kept the visions to themselves, for fear of being thought insane. So occasionally conversations like the one between Bob and Elaine would happen; but the concept of three-dimensional objects never gained wide acceptance in the scientific community.

This was true until several hundred years after Bob lived, when a mathematician laid down the theoretical framework which could generalize to arbitrary numbers of dimensions. This was harder for Finlandians to think of than it was for us, because they only had two data points from which to notice the pattern of N dimensions, whereas we had three.

Initially there was a great deal of controversy about the theory of higher dimensions. But it eventually became accepted, because it helped to resolve some obscure problems in physics and higher mathematics.

A lot of people regarded the theory of higher dimensions as nothing more than a meaningless formal device. Of course, the mathematician who formulated the theory was working from his direct experience of higher dimensions; and other mathematicians had such experiences, or intuited the possibility of such experiences. So there was an ongoing debate between the higher-dimensional formalists, and the higher-dimensional realists.

Why was Bob unable to speak clearly about spheres? I think the basic reason was that they were outside of “consensus reality.” Since there was no analogy to spheres in ordinary Finlandian experience, there was not even adequate language to talk about them.

At first Bob simply spoke in vast, empty superlatives: “super,” “transcendent,” etc. When pushed to make his ideas more logically precise, he ended up with things that half made sense, but were full of undefined terms and logical contradictions. It is understandable that he finally concluded that spheres were indescribable and ineffable, beyond the limits of thought.

Bob and Elaine’s dialogue is intended as an allegory about mysticism. Bob’s discourse is very similar to mystical discourse about God, the Tao, Brahman, etc.

“Tao” is a word much like “super-circle.” We know that we mean something by it, but we don’t know exactly what. “Tao” is a placeholder for “this mysterious thing that we have some vague ideas about but don’t understand well enough to talk about clearly.”

The further analogy between the Tao and the super-circle is that both of them refer to things which only some people experience. Somebody sees a sphere and then goes around talking about it, making no sense to the people who haven’t seen a sphere. That is also how it is for the Tao.

The person who has experienced the Tao thinks, rightly, that they will not make sense to anybody who has not experienced the Tao. But there is an additional level on which they don’t make sense even to themselves.

Nobody has a firm grasp on the Tao, in the way that we have a firm grasp on, say, trigonometry. The Tao is something that is mysterious unto us. So when we talk about the Tao, we are talking about something of which we have a very shaky understanding.

Philosophy is full of mysterious words like this. “Mind,” “consciousness,” “qualia,” “idea,” “existence,” “a priori,” “truth,” “probability,” “property,” “should,” etc. We know that we mean something by these words; but we don’t know exactly what.

Philosophy is almost exclusively a discipline of thinking about things that are mysterious unto us. This can account for many facts about philosophy. It can account for its lack of rigor, relative to math and science; for the lack of consensus among philosophers; for the way that problems go unsolved for thousands of years. These are all things that we would expect to see in a discipline of thinking about mysterious questions.

I do not think that an idea’s being mysterious, vague, or speculative is reason to refrain from talking about it. Surely there is use in talking about consciousness, thoughts, ethics — and yes, the Tao — even though we don’t really know what any of these things are.

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