Educating Carlton: Part 3

Dimensional perspective

There’s a lot to consider in physical dimensions. Let’s look, in turn at 1,2,3, and 4. Let’s do it as a being in each dimension.

So we’re a one dimensional being, we live on a line along with billions of other one dimensional beings. We know two of them. We’ll call them Left and Right. While we live on the line Left is always on one side of us and Right is on the other. That is the extent of our ability to measure our surroundings. We may be able to expand ourselves from one inch to one light year, but all we know of our surroundings is Left is on one side and Right is on the other. If the line curves in 2 dimensions Left is on one side and Right is on the other, our experience hasn’t changed at all. If the line coils in 3 dimensions Left is on one side and Right is on the other, our experience hasn’t changed at all. If the line hoop-di-doos, or whatever it does in 4 dimensions Left is on one side and Right is on the other, our experience hasn’t changed.

Now let’s be two dimensional and live in a plane. Now we have a much greater ability to measure the world around us. We can significantly change our experience by moving through our world, which we could not do in line. Ownership becomes relevant because we can own a large or small area of our plane. This is much like our experience on the surface or earth, or, perhaps more so, as a boat on the ocean where we’re limited to the surface. We can move around freely left, right, fore and back and can’t even imagine and up or down (unlike the boat on the ocean where down is a frightening thought). If our line had been like a piece of string that we could lie our straight or curved on our desktop, or wrap around our finger, then our plane is like a piece of cloth. If our plane lies flat then our experience is left, right, fore and back. If our plane hyperboles then our experience is still left, right, fore and back. If our plane is wrinkled our experience is still left, right, fore and back. We would be completely oblivious as we went on about our lives. But in our plane we can measure. So we take a line and we turn it back on itself, we put in a bunch of beings to take up a fixed area inside the bite, so now the line surrounds roughly a circle. We post a few beings where the line comes together to keep it pinched in, it looks kind of like the Mississippi near New Orleans. We can measure the amount of line around all these beings and mark the line off in feet. We start our measurement at 0 feet and go around the loop, where the line comes back to itself is 1000 feet and we have a fixed area inside of that 1000 feet perimeter. Now we pull the line. Something amazing happens. We still have the same, fixed area inside the loop but the marked off measurements are moving past our stationary observers where the line comes back to itself. Those inside the loop can measure out their area and it is the same. Those outside the loop can measure the area and it is the same. To those making measurements the line may have appeared to stretch, but only where it encloses this area not in the straight parts they’re pulling on. Perhaps the measurements at the observers are now 10 and 990, 0-10 is 10 feet and 990-1000 is ten feet, but 10-990 is a perimeter around an area that takes 1000 feet to encompass. As three dimensional observers we can see that the plane puckered. To do this experimentally at home take a plane (cloth) and run a line in a circle (weave a thread through in a circle) then pull the ends of the line (thread). This will approximate what happened in the two dimensional world. But generally the experience in the plane didn’t change, left, right, fore and back. There was an observed anomaly, which could be explained away as stretching, even though you and I know the line didn’t stretch, the world puckered.

Now let’s be a being in three dimensions. This one shouldn’t be too difficult to imagine, as we actually are beings in three dimensions. We have left, right, fore, back, up and down. We can measure, we get volume this time, or space. No matter what we do, our experience of left, right, fore, back, up and down are the same. Here’s where I need to interject. We’ve all seen the drawings of space being warped around a black hole. Looks like graph paper on LSD. But really, if we take a cube 10 light years on a side it contains a volume of 1000 cubic light years. If that cube is around “empty” space its volume is 1000 cubic light years. If that cube is around a star its volume is 1000 cubic light years. If that cube is around a black hole its volume is 1000 cubic light years. Those grid lines don’t mark off distance, they represent a gravity well. They deal with lines of trajectory of a particle (or photon) in free fall near an object with mass. Our measurements of space remain the same. These lines only describe what will happen to our travel through space. For all we know turning on the TV creates a field that warps our three dimensions, we just don’t see that warping because our left, right, fore, back, up and down are experienced the same way to us.

Now to instantaneous travel across warped dimensions.

If our one dimension warped around and touched itself we may be able to transfer to a new spot on the line. We’re going along like always, the line warps, we can’t tell, it warps more, we still can’t tell, it touches itself, nothing happens and we can’t tell, it wriggles, we can’t tell, then it touches itself again and suddenly we’re between Sam and Ted instead of Left and Right. Hello.!?

In our two dimensional world we could travel from point A to point B. We’d go by a route that had some distance and we’d travel at some speed which would mean it took an amount of time. If that world warped over and A touched B we could be at A one instant and then at B the next instant. Travel time of 0. The same amount of time it takes me to travel from here one instant to here the next instant. None. We would go point to point. No route. No speed. Technically not infinitely fast because, no route, no distance travelled. The distance between the points may be great, but still 0 meters travelled in 0 seconds. Some might want to say that is 0m/0s and it is division by 0 and therefore infinite speed, however my here to here in no time is the same and I am definitely not moving at infinite speed. This is also not travelling through a third dimension. We’re not being taken off the plane and placed back on it somewhere else. We never leave the plane, just go from one place on it to another, non-adjacent place. This will become important when we get to “Windows and wormholes” a little later. An important thing to remember is that, except for non-adjacent places touching each other making them the same place for an instant, the distance between those points is constant in the plane. They never get closer to one another except in a third, unknowable dimension.

Now we get to three dimensions again. There’s really not much to say now. You either get it or you don’t. Warping space could make two places closer in a fourth dimension, but not in these three. This may have application in wormhole technology. More on that in the next installment. Space warping back and touching itself may “open a window” between two points that we could step through. More on that in the next installment.