Infinity and LaPlace’s Demon (a Wacky Wednesday Post)

Well, it’s Wednesday again, so I divert from my travel stories posts and speak to another wacky topic. Today it’s back to math and science. Yeah, I know, I can feel your eyes rolling now!

When I was in high school, I was introduced to a paradox that bothered me for many years. Most paradoxes are easily resolved as being an impossible situation to begin with. But this one seemed quite logical, and I could not resolve it with logical thinking. Yet I knew practically it was an impossibility.

The paradox goes like this:

A turtle and a hare begin a 10 mile race. The hare runs at a constant 10 miles per hour whereas the turtle runs at only 1 mile per hour (yeah this is a fast turtle). The hare gives the turtle a 15 minute head start. Who wins the race?

Well, simple math would correctly answer the question. Of course, the hare would quickly overcome the 15 minute lead he gave the turtle. After all, after 15 minutes the turtle only moves 1/4 mile, leaving another 9 3/4 mile to travel when the hare starts his ten mile run. The hare finished that ten mile stretch in an hour at a speed of 10 mph. But in that hour the turtle only travels another one mile. Thus, math tells us the turtle only travels 1.25 miles of the ten mile race when the hare crosses the line. Despite giving the turtle a sizeable lead, the hare still wins.

This math is unquestionable. It's an easy proof that the hare will win. Most grade school kids can do the math. Without doing the math, you would know it intuitively. So then, what's the paradox?

The paradox is introduced when looking at the problem a different way. Applying logic only without math. Let's look at the problem differently. If the turtle gets a head start, how can the hare ever catch him? By the time the hare travels the 1/4 mile he gave the turtle for a head start, the turtle will have advanced further in that time span. By the time the hare travels that extra increment, the turtle advances another incremental distance. Now, if the turtle never stops advancing, this cyclical logic continues in continuum, therefore, by this logic, the hare can never catch the turtle.

But we know he does catch him and passes him! How do we overcome the logic of the non-mathematical argument?

Well the logic would be valid if space were divisible an infinite number of times. In other words, if there was no such thing as a smallest length of space. The logic falls apart when there is a finite length. And there is a finite length called the planck length which is 1.6x10-35 meters. Never mind the number, it's incredibly small but it is finite!

I actually learned of the Planck length in high school yet never correctly applied it to the logic of the argument of this paradox. As is often the case, I might have all the information necessary to solve a problem, but I don't correctly apply it.

Infinity does not exist in the real world. Things may be so incredibly large or small it may seem like there is no end. It might seem like there are an infinite number of atoms in the universe, but that would be an error. If we had the capability we could count every one of them and know that only a certain number exists.

Some believe if we knew the location, speed, and all the information every atom contained in the universe, we could correctly predict the future of all things through science alone. There is a name for this theory and it's called LaPlace's Demon.

If that Demon had all the information of every small particle that makes up the universe, he could correctly predict everything that would happen in the future.

The logic behind LaPlace's Demon is that we are nothing more than the aggregate of all these subatomic particles. If we had all the information of every subatomic particle, we can know the future with perfect knowledge of the present.

Of course, if you adhere to that theory, that takes away free will. That says everyone's future is already predetermined based on the unstoppable unfolding of events that take place at the subatomic level.

Although I don't believe in infinity, it's difficult for me to give in to this Demon and believe I don't really have the free will I think I have. But then, what do I know? The one thing I'm sure of, is the more I learn, the more I know of my ignorance.