The Shortest Distance Between Two Points

"The only difference between Dali and a madman is that I am not mad." ~Salvador Dali

Before heading to the Dali Museum at the end of 2011 I wanted to be sure I remembered how to get there, so I checked out Google Maps for the correct exit to reach 398 5th Ave SE, Saint Petersburg, FL. The beltway around Tampa Bay is Highway 275. The exit you need goes onto Highway 175.

What intrigued me about this map, however, was that Highway 175 is but a few blocks long. Because of its brevity it seemed strange to call it a highway. At the time I almost wrote a blog entry about it titled, "The Shortest Highway In America." But then I considered some facts about the matter.

First, is it really the shortest highway in America? And second, how long is it, exactly?

If my math experience serves me well, this little road just happens to be the shortest distance between two points, or in math lingo, it is a line from point A to point B. But, according to math theory if you cut the line in half into two equidistant line segments, each one in itself would be composed of an infinite number of points because by definition if you keep cutting the segments into halves, you can keep cutting them into smaller and smaller sections forever because between any two points is an infinite number of points.

In short, I concluded that this small stretch of highway is the same length as Route 66, from Chicago to L.A.

It's easy, then to see why the Greeks had such a problem with the concept of infinity. It can turn common sense into nonsense, just like a lot of our government's laws and regulations today. How tall is a mountain of red tape? Don't ask, because you just don't want to go there.

In the meantime, I believe I'm reaching the end of my rope. I think I've made my point.

Infinity

"To infinity, and beyond!" ~Buzz Lightyear

Been thinking about infinity lately. It's easy to see why mathematicians have had such a troubling time with it. Take, for example, this common conundrum.

You have hotel with an infinite number of rooms. An infinite number of people show up one night because of your Vacancy sign. (Maybe it is Grandma's Marathon weekend.) So, you give them all of your infinite number of even numbered rooms, 2,4,6, ad infinitum. They check in all happy and your clerks are impressed because you still have an infinite number of vacancies, in case you get more business.

Well, obviously, infinity throws a wrinkle in things if you treat it like an absolute number.

Here's one I have toyed with lately. Between any two points there are an infinite number of points. If you have a line segment three inches long, and one that is six inches long, why can't you simply say 3 = 6 since both contain the same number of points?

For the Romans, infinity simply meant a very large number. Galileo later suggested that the infinite does not correspond to mathematical rules in the same way as a common integer. Correctamento, Galileo!

When I was young I used to toy with the idea of time being a "duration" like miles of road, and that between two points in time, let's say four o'clock and eight o'clock, there is an infinite amount of time just as in the number of points in a line segment. (I know that waiting can feel that way sometimes, especially when waiting to open Christmas presents or waiting for relief when going through some personal hell.)

And so... if there is an infinity between a few hours, what about a few minutes? Or between two moments? And how long is Now? Is it infinitely small or infinitely something else? Or is Now only an illusion that occurs between the infinite past and infinite future?

This leads naturally into questions about the nature of time itself. Why do some days go fast and others slow when they all have the same number of hours?

What about space? Is outer space infinite? Or does our universe have an "outer wall" or some kind of endpoint? What would the end of the universe look like? How would you know when you got there?

And then, what about inner space? Maybe this is what Blaise Pascal was talking about when he wrote, “There is a God shaped vacuum in the heart of every man which cannot be filled by any created thing, but only by God, the Creator, made known through Jesus”