At This Point In Time

According to this article, there's no such thing as a moment or instant (or whatever you want to call it) of time. There is also no such thing as the absolute position of an object when it is in motion. Zeno's Paradox arises from our misconception of time as a sequence of moments, and is resolved by the realization that time can be measured only in intervals, not as a sequence of discrete frozen states. Wow!

Some quotes:

"There's no such thing as an instant in time or present moment in nature. It's something entirely subjective that we project onto the world around us. That is, it's the outcome of brain function and consciousness."

Lynds' solution to all of the paradoxes lay in the realisation of the absence of an instant in time underlying a body's motion and that its position was constantly changing over time and never determined. He comments, "With some thought it should become clear that no matter how small the time interval, or how slowly an object moves during that interval, it is still in motion and its position is constantly changing, so it can't have a determined relative position at any time, whether during a interval, however small, or at an instant. Indeed, if it did, it couldn't be in motion."

The implications of this are, no doubt, very deep. If there's no such thing as determined position, then it seems to me that the most fundamental concepts of math and geometry -- the point and even the set -- are not a starting point for understanding, but a result. Everything we ever learned is backwards! A first derivative is therefore real, but a function itself is undefinable except as the integral of the derivative. Infinite series are the basis for calculus... and all mathematics... and using infinite series to solve Zeno's Paradox is a paradox of it's own -- because Zeno's Paradox isn't a paradox in the first place!

Just thinking about thinking about it makes my brain hurt. So, I say: Let's have some fun with it!

The next time someone says "Wait a moment" to you, tell them "Sorry. I can't. There's no such thing as a moment!"

The next time someone calls you up on your cell phone while you're driving and says "Where are you?", answer with "I can't say," or "Nowhere in particular..."

And when the day comes that your son or daughter brings home a math problem that involves plotting location against time, say "Tell your teacher that it can't be done. There's no such thing as location and there are no points in time." I kind of wish I had had that excuse during math and physics classes years ago!