We're number one!

Just how is it that I manage to see that red Lamborghini Countach I'm planning to buy as soon as my luck turns? Pretty much everyone agrees that when I see it, I must have some sort of representation of it, but how does that work, exactly? I don't have an exact copy; the Countach is not a big car, but it's still too big to park under my skull. Nor is it a miniature. I'm quite sure there are absolutely no tires in there, however small. No, the representation has to be done in neurons, synapses, neurotransmitters, action potentials and such -- all very much unlike a red Lamborghini Countach -- but that's okay, because the symbols involved in a representation don't have to resemble the things they represent; they just have to play their part in the overall scheme.

There's still a problem, though. In general, any sort of representation can be fleshed out by showing how the various symbols in the representation refer to the things being represented. This "fleshing out" is called an interpretation, and it means pretty much what it seems to mean -- an assignment of meanings ("referents") to symbols: the name "George" refers to George, the word "snow" refers to snow, etc. Very simple stuff. Once a collection of symbols is given an interpretation, we can see whether sentences composed of those symbols are true in that interpretation. If "snow" refers to snow, and "white" refers to that very pale color, then the sentence "Snow is white" is true.

This works very nicely when we're dealing with nice public stuff like snow, because we have no trouble assigning referents to the words we use: Here's some snow. When I say "snow," I'm referring to stuff like that. But now we're asking a trickier question: "How is my internal representation of the external world to be interpreted?" The problem here is that I'm in no position to give an interpretation. All I've got is the representation. I don't have any access to the external world except by way of the representation. So any interpretation might be as good as any other! My "internal" Lamborghini Countach might refer to a really fantastic car, or it might refer to a pile of bat guano, and there's no way I can tell the difference!

Maybe it's not as bad as all that. Interpretations are not all created equal. Some -- maybe most -- just don't fit with the representations they interpret; they don't fit in the sense that the sentences we form just can't be true in those interpretations. For example, if "7" means the number of days in a week, "5" means the number of corners on the Pentagon, "12" means the number of months in a year, "=" means identity, and "+" means the subtraction operation, then the sentence "7 + 5 = 12" is false. Clearly, that interpretation isn't very useful or interesting. So let's agree to consider only those interpretations in which our beliefs -- i.e., sentences in our representations of the world -- are actually true. (These interpretations are called models of our beliefs about the world.) That should cut the problem down to a manageable size.

Well, no, not really. It's a consequence of the Löwenheim–Skolem theorem -- trust me -- that every theory (set of sentences) that has a model, has a model whose domain (the set of things to which symbols refer) is the set of natural numbers (0, 1, 2, 3, ...). So if our internal representation of the world has an interpretation that makes it true -- a model, it also has a model where the "world" consist of absolutely nothing whatever except for natural numbers!

"Big deal," I hear you cry, "who cares if such a model exists? That's not the interpretation I'm using, so it has nothing to do with my representation of the world." Oh yeah? How do you know? Everything you know about the world comes from your representation of it. You can't escape the representation to point out what your symbols mean. So, I'm afraid, you have no reason whatsoever to imagine that anything other than natural numbers exists!

This is ridiculous, of course, but it follows from the assumption that my "access" to the external world is by way of representation. I don't know about you, but I'm not prepared to believe with Pythagoras that "all is number," so I'm giving up the representation idea. The external world and I have a much more intimate relationship than that. When I figure out what it is, you'll be the first to know.

The Buddha was one hoopy frood

Gautama (The Buddha) spent his life trying to understand why there was so much suffering in the world, and his great realization was that the source of all suffering is desire. No desire, no suffering. So the whole point of the religion is to learn how to free oneself from desire, and thus attain eternal peace. Meditation is part of that -- a technique that you can learn, not so much to stop thought altogether, but to stop planning or preparing for things, because these only make sense in the context of desires. The ultimate goal ("Nirvana") of complete freedom from desire is damnably difficult to reach, though, because as soon as you realize how blissful that state would be, you desire it. Oops! Back to the beginning. When enlightenment does come, it sneaks up on you and takes you by surprise -- the Zen version hits you with a stick for good measure. You just have to be prepared for it.

Meanwhile, in physics, time is just a dimension, pretty much like the three dimensions of space, and nothing more. The three spatial dimensions have no natural direction; that is, there's nothing about left that makes it more "special" than right, and similarly for up and down, and backwards and forwards. What's especially important is that there doesn't seem to be anything about the basic laws of physics that has a preference for one temporal direction over the other, either. A movie played backwards is just as consistent with the laws of mechanics as the same movie played forwards.

Most physicists (not all) believe that spacetime is like a four-dimensional container of events, as opposed to a three-dimensional container of things that change over time, and doubt that there's any fundamental distinction between past and future, at least as far as laws of nature are concerned, even if the two really look different to people.

One of my favorite books (Time's Arrow & Archimedes' Point, by Huw Price) makes a really good (but rather complex) argument that time really and truly doesn't have a direction at all. Price doesn't say this explicitly, but this seems to be where he's going: The reason for the "uncertainty principle" of quantum mechanics, and for all of the associated fuzziness, is that the determinants of an event are not all in the event's past. Some are in the event's future, effectively backwards causation. (This is 100% consistent with all known physics, so it's not a new physical theory, just a new philosophical perspective.)

The problem for people is that they can't think this way. We're "agents," which means that we plan things, arrange things and do things, always with a view to the future. You can't make any sense whatever of a reversed life. What makes death more frightening than birth is that death puts a stop to our status as agents; that's it, you're not doing anything more, so stop planning.

So, to tie all this together before the reader's eyes glaze over, in the real world of physics, the freedom presumed by all our planning and preparation -- the "power" to do things -- is illusory; it's just a curious fact of human psychology that we can't help thinking we're free. From the four-dimensional perspective, with directionless time, you exist (in a tenseless sense of the word), with clear boundaries in spacetime, which define your entire life, and it doesn't really matter which way you look at it, east-to-west, death-to-birth, it's all the same. But this really hurts a person with desires. Desires make death look like a terrible ending when there are still things you want to do. To be at peace in the real universe, you have to come to grips with the fact that "agency" is nothing but an illusion; that is, you have to "overcome desire." A difficult trick, but at least the Buddhists have the right idea. (Prayer-wheels and incense don't help much, though.)