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A Blog of Geek Eccentricities
As we will see, the time travel paradox—the possibility of changing our past—seems intractable only because it conflicts with our notion of ourselves as beings with free will. Consistent stories are possible, even in space-times with closed timelike curves.
To illustrate this point, imagine that you stumble upon a time machine in the form of a gate. When you pass through it in one direction, it takes you exactly one day into the past; if you pass through in the other direction, it takes you exactly one day into the future. You walk up to the gate, where you see an older version of yourself waiting for you. The two of you exchange pleasantries. Then you leave your other self behind as you walk through the gate into yesterday. But instead of obstinately wandering off, you wait around a day to meet up with the younger version of yourself (you have now aged into the older version you saw the day before) with whom you exchange pleasantries before going on your way. Everyone’s version of every event would be completely consistent.
We can have much more dramatic stories that are nevertheless consistent. Imagine that we have been appointed Guardian of the Gate, and our job is to keep vigilant watch over who passes through. One day, as we are standing off to the side, we see a person walk out of the rear side of the gate, emerging from one day in the future. That’s no surprise; it just means that you will see that person enter the front side of the gate tomorrow. But as you keep watch, you notice that he simply loiters around for one day, and when precisely 24 hours have passed, the traveler walks calmly through the front of the gate. Nobody ever approached from elsewhere. That 24-hour period constitutes the entire life span of this time traveler. He experiences the same thing over and over again, although he doesn’t realize it himself, since he does not accumulate new memories along the way. Every trip through the gate is precisely the same to him. That may strike you as weird or unlikely, but there is nothing paradoxical or logically inconsistent about it.
We know what the answer is: That cannot happen. If you met up with an older version of yourself, we know with absolute certainty that once you age into that older self, you will be there to meet your younger self. That is because, from your personal point of view, that meet-up happened, and there is no way to make it un-happen, any more than we can change the past without any time travel complications. There may be more than one consistent set of things that could happen at the various events in space-time, but one and only one set of things actually does occur. Consistent stories happen; inconsistent ones do not. The vexing part is understanding what forces us to play along.
Our concept of free will is intimately related to the idea that the past may be set in stone, but the future is up for grabs. Even if we believe that the laws of physics in principle determine the evolution of some particular state of the universe with perfect fidelity, we don’t know what that state is, and in the real world the increase of entropy is consistent with any number of possible futures. A closed timelike curve seems to imply predestination: We know what is going to happen to us in the future because we witnessed it in our past.
Closed timelike curves, in other words, make the future resemble the past. It is set in stone, not up for grabs at all. The reason we think the past is fixed once and for all is that there is a boundary condition at the beginning of time. The entropy of the universe started very small (at the time of the Big Bang) and has been growing ever since. Ordinarily we do not imagine that there is any analogous boundary condition in the future—entropy continues to grow, but we cannot use that information to draw any conclusions. If we use a closed timelike curve to observe something about our future actions, those actions become predestined. That’s extra information about the history of the universe, over and above what we normally glean from the laws of physics, and it makes us uncomfortable.
The first is a word that represents the bird in the English language. But not if you don't speak English. If you don't speak English, it's just a bunch of angular black markings. The second is not a chicken either. It's a picture of a chicken. Both are drawings that represent my mental concept of a chicken (but not necessarily yours), but neither is an actual chicken, or else you would be able to eat it.
Nor are they equivalent. The expression does not equal the concept. The first does not even look like a chicken, and the second is not even a picture of a chicken. It's a drawing representing a chicken, but not a picture of an actual chicken. We look at the drawing and guess that it stands for a chicken, but if it were a substantially more abstract drawing, we wouldn't even know that. It is only because it approximates a two-dimensional expression of a chicken that we share in common that we are able to communicate the concept of 'chicken' through it. As an objective reality, neither is an actual chicken.
The only way that a language could be objective is if all of its components are operating from an agreed-upon code. If, let us say, the authors of the Constitution had a fixed dictionary in the words had only one meaning and only certain constructions thereof had discrete functions, then one might say that it would be possible to objectively know the meaning of their text.
But language very rarely operates this way. Only constructed languages could even attempt it. Natural languages -- those that spontaneously form and change over time as they are used by a population -- can be roughly understood by philologists, but their meanings cannot be contained because users use words based upon what they think that they mean, not what official dictionaries and grammars say that they mean.
It's possible to gain a sense of what the authors of the Constitution thought that words and phrases meant by reading documents of the era to see how words were used in relation to each other. But this data set is vastly incomplete because it does not even come close to encompassing every use of the words and phrases that they used. Our data set consists entirely of a comparative handful of surviving written communications, and none of the oral communications whatsoever.
We may, however, make good guesses about what the authors of the Constitution meant by a written expression by analyzing how these words and phrases were used in the context of their writings. But we cannot know with objective certainty in the same way that we can know that 2+2 will always equal four.
Even though this is an educated guess, it is a superior way of knowing than asserting that units of a language can have objective meanings. Remember that these units of language are communications -- imperfect attempts to express inner thought to an outer world. If you're not attempting to discern what the speaker or writer is trying to communicate, then you're rejecting communication conceptually. And if you're rejecting communication, then uses of language might as well be random.
But for a moment, assume that language meaning can be objectively knowable. How would you test the hypothesis "Communication X represents concept Y"? If X and Y are not placed in reflection of other uses of X and Y, and there is no codebook in which to look up X and Y, how can their meaning be known?
This problem does not go away, as Kevin suggests, because a unit of language is a law. Laws remain attempts to communicate concepts. If you're rejecting original intent, you're deciding not to try to discern the communications of the authors of the law, and are left without any guide as to what the words and phrases in a given law mean.
"What it says is" simply isn't knowable. What the writers were trying to say is, at least, researchable.