Dimensions:
A Perspective of Dimensions written by Daniel B. Murphy
Copyright © 2004 Daniel B. Murphy
All Rights Reserved

Some people know of the three undefined terms of geometry: point, line, and plane. They should be considered rather as concepts.

The concept of a point could be explained as an exact position. A point is not a tangible thing. I could describe it as the place where two perfectly shaped marbles (spheres) meet. There's nothing in between them, just the marble on the left, and the marble on the right, and the point (consisting of no space) in the middle that marks the position of where they meet.

Zeroeth Dimension

A Point

Since a point has no size, it is in no dimension. In the 3D world, we like to think of things as having a length, a width, and a height. Since a point has none of these, It, in itself, can exist in the zeroeth (0th) dimension. And a point is the only thing that can fit in the zeroeth dimension (unless there are negative dimensions, which I am not ready to contemplate yet, or at least to discuss).

First Dimension

Picture the point moving in one direction, point by point, position by position, sweeping out the shape of a line. The line has no height or width, but it does have a length. So now we have the first dimension. The line, and all of its points are the only things that can fit in the first dimension. So this point we were discussing earlier is also a member of the 1st dimension club too because it fits, so to speak.

Whichever direction it goes, as long as it remains straight, it is in the first dimension.

Second Dimension

Picture the line moving in one direction, perpendicular to the direction the point was moving. The shape it sweeps out is a plane (see image below):

If you paid attention in math class, you'll remember that an area can be measured length times width.

So now that we have length and width, therefore we've reached the second dimension. It's flat to us. And, obviously, a line can fit in there, because a plane could be described as a bunch of lines woven into a flat area (of course infinitely many lines). And a point can fit in there because a point can fit on a line and a line can fit in the plane.

Third Dimension

So those are descriptions of what points, lines, and planes are, however I've discovered that our geometry lessons have been incomplete. Another undefined term of geometry would be volume. Volume brings us to the third dimension by adding height (a.k.a. depth). Seeing how a point exists in zero lateral directions, a line exists in one lateral direction, and a plane exists in two lateral directions, volume would exist in a third lateral direction. Imagine a plane being the ace of spades. Now imagine several planes side by side, giving you a deck of cards. That deck of cards has the length and width of one plane, and the height (or depth) of 51 or so other cards. This is volume. points, lines, and planes can fit in this volume. Even other (obviously smaller volumes) can fit within this volume.

Fourth Dimension

A cube is a volume because it consists of length, width, and height. Those are the 3 dimensions of measurement, therefore we have reached the third dimension. The third dimension is the world we know, but what happens when you sweep a volume, point by point, position by position, in any given direction? I think the fourth dimension, which is what I'm trying to visualize, gives us the ability to move, and therefore the ability to have been in one place at one time, and at a different place in another time.

By sweeping a volume in any given direction, you're giving a point the ability to be in any position of the volume at any given time, but just as the volume sweeps point by point, so can a point only move one point (or position) at a time. Which leads us to our fifth undefined term of geometry, time. Perhaps a better term to use is timeline because then it's easier to refer to with diagrams. By the visualization that I have just described, time is very geometric, consisting of points, lines, planes, and volumes.

Lines are channels through which to travel from one point to another :: planes are channels through which to transverse from one line to another :: volumes are channels through which to move from one plane to another :: Time is a channel through which to move from one volume to the other (or from one volume with everything in it exactly where it is into another volume with all the same things in it as the first volume, some of which things are in different positions now)...And now the fifth dimension!

Fifth Dimension

The book, A Wrinkle in Time addressed the fifth dimension as being called the teseract. Others call it a "worm hole." so keep in mind that (Worm hole = teseract). I want to call it teseract because it's a cooler word. In this case, teseract would be the sixth undefined term in geometry.

The teseract is a channel through which to go from one time to another.

With a teseract, you could move without the necessity of time. Movement is otherwise dependent on time. Moving from one side of a room to the other requires time unless you zap there through a worm hole. Try to let that sink in...Try to understand that movement requires time and therefore movement is a product of time, not a product of depth. In this sense, i honestly think we move because we do have a sense of the 4th dimension. We do have clocks to measure time...just as we measure lengths, widths, and heights, we also measure time. But how is the teseract measured? What is a product of the teseract? One possibility is that the teseract is able to move or bend a timeline, so in essence, a different type of movement is a product of the teseract. And the measurement of the teseract is the measurement of just how much time it is able to move. So it is my theory that in order for time travel to occur, we must travel through a teseract, and on a similar note, we can travel any distance without the passage of time.

On the notion that the teseract bends a timeline, if at one time you are at point A, and at another time you are at point B, then through the teseract, you could move from point A to point B in no time.