4th Dimension Explanation

Welcome to a short introduction of the "fourth dimension".

     You may be asking yourself how it is possible to visualize a "four dimensional" object given the fact that all of our human experiences are in three dimensions? Henry More, in the sixteenth century considered spirits to be "four-dimensional." H.G Wells suggested that the fourth dimension was time in "The Time Machine". C. S. Lewis alludes to it in "Out of the silent planet" and Madeleine L’Engles’ book "A wrinkle in time" is about dimensional travel.

     The New Testament Book of Ephesians 3:17-18 says "that Christ may dwell in your hearts through faith; that you, being rooted and grounded in love, may be able to comprehend with all the saints what is width and length and depth and height". Paul could only explain this analogy using three dimensional words, requiring the duplication of two but stressing all four by the placement of the "and' between each one.

     In the ground breaking PBS series "Cosmos" the late Dr. Carl Sagen took us on a magical journey into space and time. In discussing the large-scale structure of the Cosmos, astronomers are fond of saying that space is curved, or that there is no center to the Cosmos, or that the universe is finite but unbounded. What ever are they talking about? Let us imagine we inhabit a strange country where everyone is perfectly flat. Following Edwin Abbott, a Shakespearian scholar who lived in Victorian England, we call it Flatland. Some of us are squares, some are triangles some have more complex shapes. We scurry about, in and out of our flat buildings occupied with our businesses and dalliances. Everyone in Flatland has width and length but no height whatever. We know about left-right forward-back, but have no hint, not a trace of comprehension, about up-down except for flat mathematicians. They say " Listen, it's really very easy. Imagine left-right. Imagine forward-back. Okay so far? Now imagine another dimension at right angles to the other two." And we say "What are you talking about? 'At right angles to the other two'! There are only two dimensions. Point to a third dimension. Where is it??" So the mathematicians disheartened amble off. Nobody listens to mathematicians. 

Every square creature in Flatland sees another square as merely a short line segment, the side of the square nearest to him. We can see the other side of the square only by taking a short walk. But the inside of a square is forever mysterious, unless some terrible accident or autopsy breaches the sides and exposes the interior parts.

One day a three- dimensional creature shaped like a apple, say, comes to Flatland, hovering above it. Observing a particularly attractive and congenial-looking square entering its flat house, the apple decides, in a gesture of interdimensional amity, to say hello. "How are you?" asks the visitor from the third dimension. " I am a visitor from the third dimension." The wretched square looks about his closed house and sees no one. What is worse, to him it appears that the greeting, entering from above is emanating from his own flat body, a voice from within. A little insanity, he perhaps reminds himself, runs in the family.

Exasperated at being judged a psychological aberration, the apple descends into Flatland. Now a three dimensional creature can exist, in Flatland, only partially; only a cross section can be seen, only the points of contact with the plane surface of Flatland. An apple  slithering through Flatland would appear first as a point and then as progressively larger, roughly circular slices. The  square sees a point appearing in a closed room in his two-dimensional and slowly growing into a near circle. A creature of strange and changing shape has appeared from nowhere.

Rebuffed, unhappy at the obtuseness of the very flat, the apple bumps the square and sends him aloft, fluttering and spinning in to the mysterious third dimension. At first the square can make so sense of what is happening; it is utterly outside his experience. But eventually he realizes that he is viewing Flatland from a particular vantage point: "above". He can see into closed rooms. He can see into his flat fellows. He is viewing his universe from a unique and devastating perspective. Traveling through another dimension provides, as a incidental benefit, a kind of X-ray vision. Eventually, like a falling leaf, our square slowly descends to the surface. From the point of view of his fellow Flatlanders, he has unaccountably disappeared from a closed room and then distressingly materialized from nowhere. "For heaven's sake," they say, "what's happened to you?" "I think," he finds himself replying, "I was up". They pat him on his sides and comfort him. Delusions always ran in his family

In such interdimensional contemplations, we need not be restricted to two dimensions. we can, following, Abbott, imagine a world of one dimension, where everyone is a line segment, or even the magical world of zero-dimensional beasts, the points.

I want to make this easy to see and understand so let’s use a "Geometrical Hypercube" to visually guide us as our example: First we must define a dimension as being a direction, so let’s create those directions now.

First we begin with a point, in the world of dimensions a point, although it exists, does not occupy any space.

Next we take a second point, and place it 2" inches from the first point. So far so good. (But remember a point does not occupy any space.) Then we draw a line and connect them together. What we have done is create a one-dimensional line segment. Let’s say, for practical purposes, our line segment has created depth.

Now we have to move our 2" line segment at right angles to itself. In doing so we create a two-dimensional plane 2" inches by 2" inches square and in the process we have added width. Now if our plane is perfectly square, as it should be, our corners will all be 90 degrees’.

We now move our two dimensional plane at right angles to itself. That creates a three dimensional cube 2" inches in depth, 2" inches in width, and now we have added 2" inches in height. Once again if our cube is perfectly square all the corners will be 90 degrees.

All in all this is pretty easy so far wouldn’t you agree? DEPTH, WIDTH, HEIGHT, one, two, three dimensions.

But now comes the interesting part.

Remember how we defined a dimension as being a direction? Well now we are about to enter into the realm of the fourth dimension.

Next we move our three-dimensional cube at right angles, right angles un to itself. When we do that we create a four-dimensional Tesseract (or Hypercube). Now the hard part is I can’t show you a Tesseract or a Hypercube because the only place they exist is in the fourth dimension. You see in the fourth dimension every corner of every cube of the Tesseract or Hypercube would have to be at a 90-degree angle to every other corner. 

I can however show you the most unique shadow our three dimensional world has ever seen of the this four dimensional object.

When you hold a three-dimensional object over a flat surface of a table you can see the two-dimensional shadow of that object on the table. Since the table is flat you only see the depth and the width of the object on the table, and it’s shadow has no height. The same is true when you take a photograph of a tree; the photo has width and height but no depth.

When you hold the "Geometrical Hypercube" or look at it you are seeing the world’s most unique three-dimensional shadow (just like the shadow on the table) of that four-dimensional object that has ever been seen before. Nothing has ever existed like this unique geometrical art piece before. This is the world’s most unique sculpture.

There are lots of theories as to where and what the fourth dimension might be. Some people call it "Heaven". Some call it in/out or to/from. Where ever it is or what ever it is there is no doubt that it DOES exist mathematically. Simply gaze into the "Geometrical Hypercube" and let your imagination awaken. Let this unique geometrical sculpture carry you to new places and dimensions you have yet to visit.