Try an experiment with me. On a warm, cloudless day, about sunset, find a nice large open space with grass and lie down on your back. Imagine I am a questioner lying next to you. Close your eyes.
We are going to talk about the dimensions of our universe and our existence.
“How many dimensions do we live in?” I ask.
“Three spatial dimensions and one time dimension. Albert Einstein said so,” you say.
“And what about the other dimensions? Are there any non-spatial dimensions?”
“I am not sure I know what you mean.”
“Ok. Let’s step back a bit. What is a dimension?”
“Well, time is a dimension. It is like a line made up of moments, going in a direction, toward the future. Space has three line-like elements, length, breadth and height, made up of inches and feet or meters and millimeters. They go off in three directions, ninety degrees from each other.”
“And time is ninety degrees from each of the other three?”
“Well,” you laugh, “not exactly, no.”
“So time is not really a spatial dimension?”
“No, but it can be treated like one, as Einstein said. You need four coordinates to locate a point. Without a time coordinate, the point could be anywhere in the history of the universe.”
“So it is a matter of locating points. I think this use of ‘locate’ already assumes space and time as a background. But points have no dimension, no degrees of freedom. The only way to use time and space coordinates to locate a point precisely is by using very small units of measure and calculating to many, many decimal places, an infinite number, in fact. That assumes space and time are continuous. If they are granular, then you only need enough decimal places to get down to the minimum unit, or quanta, of each. They would still be very, very small.”
“Well, yes, but what we actually do is estimate roughly to find objects that are larger than points.”
“Objects? How did those get in the picture? I thought our universe was only made up of points in three spatial and one time dimension.”
“Well, objects are sets of points that have four dimensional locations.”
“I now want to show you that objects have more coordinates than just those four. Open your eyes now and tell me about the first object you see.”
“A bird just flew across my field of vision.”
“A bird? How do you know it was not an airplane?”
“It was closer, smaller and flew differently than it would have had it been an airplane.”
“It is interesting that you did not mention the sky, made up of points in three spatial dimensions and one time dimension, colored a certain blue that falls somewhere within the additional three or four dimensional framework of color.
“But I want to suggest now that you are in fact referring to other dimensions anyway. You could not say much about that first object you saw if all you knew was its location in three spatial dimensions and one time dimension. I think you avoided saying that the bird was a different color than an airplane because you did not want me to jump on the three or four dimensions of color, as we know them. That is fine. I will work with what you gave me.
“It was closer than a plane. This is the dimension of range. It was smaller than a plane. This is the dimension of scale. It flew differently than a plane. This is about the dimensions of motion in space and time.”
“But those are just possible variables,” you say.
“Yes,” I say, “but that is what a dimension is, a possible variable, a degree of freedom, a coordinate on some imaginary line. And that is all your ‘space’ and ‘time’ are, variables on some imaginary lines.”
“But range, scale and motion are not the same as spatial dimensions.”
“But they deal with objects in space and time. What is so special about space anyway? Dimensions are dimensions. Sound is not color and texture is not sweetness. So what? The fact of the matter is that we live in a universe of many dimensions, many that we can see and hear and feel and smell and imagine. They can all be mapped onto imaginary lines and have given points of location on those lines. These are the everyday, common knowledge dimensions that I am talking about here. I am not going into what we might call hyperspace, the additional, compacted dimensions physicists talk about in String Theory. ”
“But they are not ninety degrees from each other,” you say, “and, unlike points, they are not made up of identical, interchangeable units.”
“You said that time is not ninety degrees from length, breadth and height too. You said that it is a matter of the number of coordinates needed to locate a point. You admitted that you do not really deal in points but in objects much larger than points. Objects are not identical or interchangeable, generally speaking. And what is sacred about ninety degrees? You lose that as soon as you go into spherical and hyperbolic space, non-Euclidian geometry. Are you saying that those are not really space either?”
“My brain is getting tired. Do you mind if I take a nap now?” You close your eyes again.
“No,” I say, “not at all, but I will still be here, in all our dimensions, when you wake up.”
You are cordially invited to visit
Vesper’s Cave, The Repository of The Mazen Saga.
http://www.mindspring.com/~vesper
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