Paradoxes

On the heels of the previous post on time travel, I wanted to make a quick post talking paradoxes since time travel always comes with paradoxes.

What do we make of time travel paradoxes? Like the one where you go into the past and murder your grandfather. (Why so gruesome? You’d get the same effect if you married your grandmother before your parents were conceived, and the weirdness would be ever some much greater. Then you could be your father’s father and your own grandfather which is much odder than a being a cold blooded murder and more likely to keep you out of prison.)

I suspect paradoxes exist solely because the theories that suggest them are flawed. It could also be that some paradoxes are part of the lack of completeness (like we saw in the posting on atheism) but I suspect most are the result of wrong assumptions and wrong theories.

Let's look at one of the more famous paradoxes - Zeno’s paradox. Zeno made the analysis that if you shoot an arrow towards a target then before it can hit the target it first needs to go half way to the target. The after it goes halfway, it needs to go half of the remainder, etc. Then you need to go another halfway and on and on so the arrow would never reach the target because it needs to go through an infinite number of halves. There are a couple things about this that need to be addressed:

1. Of course, the arrow hits the target. So obviously there is something wrong with the logic. Too many times we think logic should drive reality. In this case, the reality trumps the logic.

2. One of the failures in the logic is that the sequence of distances can be written as ½ + ¼ + 1/8 + …. That’s because first the arrow goes through ½ the distance to the target (the first ½), then it goes through the second half (1/2 of ½ is ¼). It can be shown that the sequence adds up to one, so although it is an odd way to write 1, it is identical. (Similarly, .9999999… is another way to write 1. There was a lot of theoretical work required to handle infinities before this argument could be finalized.

3. Of course, the biggest issue in the paradox is how does the arrow get half way to the target? Why is it so special that the arrow first get halfway and then half of that, etc. We now have the paradox of how does the arrow get from where it is shot to the halfway spot. Zeno’s paradox is really about how does an arrow start moving. The answer is that the bow interacts with the archer and string to send the arrow towards the target. No paradox required!

Similarly, in the time travel paradoxes, I suggest that there are only pardoxes becuase there is no time travel so if you start your questions with, assume time travel is possible, then you can set up all sorts of non-sensical conclusions, some of whic hwill be paradoxical.