This being the case, it is evident to me that we worms mean something quite different when we say we talked to a fellow worm than what you humans would mean. I thought I should clear up that point. Now to return to my conversation with Klaus.
“Suppose there exist solid intelligent creatures like us, who live on other worlds Out There—”
“In other worlds, you mean,” Klaus said.
“No, that’s just the point. I’ve been thinking: what is there to prevent the existence of solid intelligent creatures like us, living on the outer surface of a world, rather than in it.”
“Let me consider the immediate implications,” Klaus said. “These hypothetical intelligent creatures living on their world would, I presume have direct experiential contact with the surface of that world, and so would be able to establish fixed coordinates and thus know the shape of their world.”
“Let’s just say, for argument’s sake, it’s spherical,” I said.
“The actual shape is unimportant. What is important on this hypothetical world of yours is that its shape, whatever it is, can be known, and therefore all directional and topological facts about that world can also be known.”
“That seems to follow,” I said. “And I postulate a further condition…”
“My dear fellow,” Klaus said, “don’t bother to go on. I must tell you that further speculation along this line is fruitless, since it piles fanciful hypothesis upon even more fanciful hypothesis. Aren’t you aware that the organum of worm science and mathematics, of which I think I may claim some slight knowledge, has never been able to establish the absolute existence of a surface to our own world? That’s why we refer to it as the veritable surface.”
“That doesn’t mean a surface couldn’t exist somewhere else,” I told him.
“Of course not. Anything is possible, including the existence somewhere of worms who live by consuming their own tails. Possible, but so improbable as to be beneath consideration. If we are to have a reasonable discussion, even on a hypothetical point, it must be based upon the laws of nature as we know them, not as we would like to imagine them.”
“I think you’re taking much too high and holy a tone,” I told him. “Why, dammit, worm, we always assume that our world has a surface, even though we don’t know where it is, except at the moment of breakthrough/cancellation when it doesn’t do us much good.”
“The transformation which takes place at the veritable surface, which we refer to as breakthrough/cancellation, or B, is most decidedly not proof of the existence of an actual surface to our world. We do assume in our everyday life that our world has a surface. It’s a necessary psychological construct (though an artificial one, I must insist) for setting direction of wormhole. But philosophers don’t believe in the existence of a veritable surface anymore.”
“That’s news to me,” I said. “What do they believe, then?”
“The current trend is to consider that our world has a pseudo-surface, sometimes called an imaginary surface. It is a useful concept, because mathematically the pseudo-surface has to exist, whether a veritable surface exists or not. So it’s useful for certain mathematical functions.”
“I don’t see the difference between your pseudo-surface and your veritable surface,” I said. “Aren’t you just calling the same thing by a classier name?”
“Not at all. The term pseudo-surface is used to express indeterminacy.”
“The hell you say,” I said.
“You see, dear boy, surface is pseudo-surface, or P/S, and is indeterminate because you cannot investigate it experimentally, since investigation involves cancellation of the investigator when the undetectable pseudo-surface is broken through. If you see what I mean.”
There was quite a lot of pomposity to Klaus’s vibrations when he communicated that. He calls himself a Transcendental Pragmatist. I think he’s just clever at twisting concepts. Sometimes I think that when Klaus pontificates on one of his subjects of knowledge, there is literally nothing there to understand. It’s just a lot of old wormhole, to use a term of ours for something that has form but no substance.
Still, Klaus is a recognized philosophical thinker, and if he couldn’t at least take my proposition as a postulate from which to extrapolate—well, I probably wouldn’t do any better with anyone else, except the people who will believe anything, whom I’m not interested in reaching.
“You’re just being obstinate because you don’t want to consider my conception,” I told him. “Surface is a necessary conception. For Godworm’s sake, worm, we spend our lives digging wormholes and you’re trying to tell me they’re imaginary!”
“Have you ever seen the surface of a wormhole?” Klaus vibrated coolly.
“Well, not from the outside, of course not. It’s impossible for a worm to encounter wormhole without cancellation. Everybody knows that! But a worm damned well knows that he’s laying down wormhole, and the wormhole he lays down has surface.”
“That, of course, is the common-sense ‘worm’s in his wormhole; all’s well with the world’ view,” Klaus went on in his infuriating manner. “We can assume what we please, but as long as the evidence is circumstantial rather than experiential, the thing in question cannot be ascertained with certainty. I will admit that some circumstantial evidence is very strong—as the philosopher said when he came up with a bump against the crystalline face that his theory said didn’t even exist.”
I gave him a very short burst of appreciation-vibration: it was an old joke and I had heard it many times before.
Klaus went on, “Let’s leave absolute truth to itself for a moment and postulate that the indeterminate pseudo-surface exists somewhere as a veritable surface. You want me to imagine that there are objects of known dimensions in the Universe? Very well, that’s not too difficult. But you also want me to imagine solid, three dimensional creatures like us living on this surface.”
“That’s the construct.”
“Well,” Klaus said mildly (but with ill-concealed ironic vibrational overtones), “they would have to be very strange creatures indeed, then. Your creatures living on the surface would be in the position of worms exposed to wormhole breakthrough, not just for an instant, which is long enough to cancel any of us, but continually!”
“Why don’t we just invent a special law that says he can do just that?” I suggested.
“To what purpose?” Klaus asked. “Conjecture can be entertaining as well as instructive, but why should we create a baseless fantasy that goes against all our experience of how the world really works? This surface creature that you want to hypothesize, my dear boy, could only exist in accord with laws that (since no necessity exists to even consider them) can only be considered capricious, frivolous, and unlikely in the extreme to actually exist anywhere or anywhen.”
I vibrated a shrug. “Okay, Klaus, forget it.”
He vibrated donnish self-approval. “My boy, a solid creature living on the surface of a spherical world of known dimensions would be a very strange creature indeed, as would be his world and the laws that govern it!”