Most technically minded people will probably take me to task over what I am going to say in this article. That is OK, though. I’m used to it. Not only are my writings quirky—I am quirky. Hey! This is QuirkyScience. I want to talk about points and lines in the real world—in other words, discrete mathematics.
What is Reality, What Fantasy?
To a mathematician, the point may be a dimensionless object in 3D space, a mathematical object with an x, y, z coordinate in Euclidean space. A line would be a collection of such dimensionless points lined up all in a row. But that is in the world of the mathematician. In the real world, there can be no such thing.
Rather, in the real world, a discrete point, in size, would have to be represented by the smallest subatomic particle that exists and nothing smaller. It has to have real dimensions. Yet, it must be considered to have, at least in some sense, no dimensions at all.
Discrete Mathematics, Discrete Time?
A logical question arising from this discussion is: would it be possible to invent a mathematical system based on the assumptions delineated within this article? Would there be a form of mathematics that would enable calculations, and all the other actions one needs to be accomplished in such a discrete system? Indeed, does any of this discussion make sense?
Some will say, No! It makes no sense. But wait a minute. If it does make sense and if it is true, then the time it takes to travel at the speed of light across the diameter of a point is the minimum unit of time, as well. This would mean both distance and time are (for all practical purposes) quantized, would it not?
Of course, we are speaking discretely.
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I don’t have enough maths to say one way or the other but I do know I spent inordinate amounts of time in class trying to visualise a dimensionless point
I don’t think there are can be a physical straight line between two points, since space is curved and that point must remain absolutely still and occupy the tiniest fraction of space. The universe is constantly expanding and nothing stands still. And I guess a point must have some kind of physical dimensions, but still generalized or at best approximate dimensions.