Shufflebrain

In defining a subject, we draw a line around it and stake out not only what goes into the discourse but also what stays out. The rendering of an explicit definition implies that we already know the universe of our discourse--the coordinate system containing our subject. The moment we define our universe, we virtually guarantee in advance the presence or absence of certain features in our subject. Indeed, get good enough at the definitions business and you can prove or disprove just about anything you please. And definition can pluck so much off a subject that it's merely the skeletal remains of the original subject.

In ordinary mathematics, recall, we define relations between X and Y (or W and Z) within a prescribed coordinate system. Even when we are not conscious of it, we actually assume the nature of the coordinate system in advance. Our descriptions of X or Y, then, must always fit within boundaries imposed by our definitions. Should we want to transfer X and Y (or Z) to some other coordinate system, we must obey the rules we've imposed on ourselves. Thus, by definition, we can't begin on a Cartesian graph and make a transformation to any and all conceivable sorts of coordinates. But with tensors in a Riemannian kind of universe, we're able to make any transformations we please. How's come? The answer, remember, is that with tensors the coordinate system doesn't come in advance. Tensors reverse the conventional wisdom. With tensors the definition follows rather than leads the description. We must calculate the universe. It's not ours by divine revelation. To reach for the tensor is to imply an admission: we're too tiny to survey all that is and too dumb to know in advance where the edge of the world lies before our journey begins. We need a description of intelligence before we can even attempt a definition.

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There's more to intelligence than dimension. Yet if I correctly judge the reader's feelings by my own, there's just too much pi in the abstract sky for us to move directly from analytical hologramic theory to a description of intelligence that will ring true to our intuition. Thus instead of proceeding analytically, let's open with an imaginary experiment.

Let's reach into the technological future and invent a new kind of holography. Lets invent a hologram of a play, but a hologram whose reconstructed characters are life-sized, full-color, warm, moving and whose voices are in "holophonic" sound. Let's even give our characters bad breath and body odor. In short, let's invent the wherewithal for an imaginary experience far more eerie than my very real one with the dissected brain that wasn't there.

Now let's enter the theater while the play is in progress. Let's assume that out mission is to find out if the actors are at work or if they've taken the night off and are letting their holograms carry the show. What test can we use? We might try touching them. But wait! If we were at a séance, touching wouldn't be reliable, would it? If we pass a hand through a ghost, so what? Ghosts aren't supposed to be material, anyway. Just real. Thus for want of adequate controls, we'd better think up a more imaginative experimental test than touching. Suppose we sent a 515-pound alpha male gorilla up to the stage. What would live actors do? Although, their behavior would change, we could never specifically predict just how.

What about holographic images? We can accurately predict their responses with a single word: nothing! If the holographer stays on the job, the show will go on as though our gorilla isn't there at all. Indeed, as far as the holographic scene is concerned, the gorilla isn't there. He is of the present. They are of the past.

What's the theoretical difference between our live players and their holograms? Both depend on the same basic abstract principle--relative phase. And holography can be done with tensors. Yet the holographic players cannot let our gorilla into their universe. Our poor live actors wouldn't have had any choice.

The informational universe in our physical hologram is like a cake that has already been baked. If we want it continuously round (no cutting) instead of square, if we want the gorilla in the scene, we must make up our minds about that during construction--before the abstract dough congeals in the theoretical oven. The tensor calculations have already been made. The coordinate system has already been defined; it is what the philosopher would call, determinate. We cannot add the new dimensions of information our gorilla brings up on the stage.