But, this is a contradiction. For, if space is infinite, then it must possess an infinite number of lines perpendicular and not parallel to one another.

Is infinity, then, a foolishness and does space necessarily have a limit? If it does have a limit, in what space does our space exist? But, if space does possess an infinite number of lines perpendicular to one another, then we must ask why we can only perceive three. If we exist in a condition of mind that perceives only three dimensions, this must mean that the properties of space are created -- or differentiated – by certain attributes within us. For some reason or another, the Whole is inaccessible to us.

Ouspensky wrote in an essay in 1908, entitled "The Fourth Dimension";

We may have very good reason for saying that we are ourselves beings of four dimensions and we are turned towards the third dimension with only one of our sides, i.e., with only a small part of our being. Only this part of us lives in three dimensions, and we are conscious only of this part as our body. The greater part of our being lives in the fourth dimension, but we are unconscious of this greater part of ourxelves. Or it would be still more true to say that we live in a foure-dimensional world, but are conscious of ourselves only in a three dimensional world. The fact is, Ouspensky was greatly influenced in his thinking by Charles Howard Hinton, an English mathematician. But, long before Hinton had a clue about the ideas of the "fourth dimension," there was Riemann. Michio Kaku tells the story in his book Hyperspace: A Scientific Odyssey Through Parallel Universes, Time Warps, and the 10th Dimension and I have pretty much followed his outline, though reducing the length and complexity of the story.

On June 10, 1854, at the University of Göttingen, Germany, Georg Bernhard Riemann gave a lecture entitled On the Hypotheses Which Lie at the Foundation of Geometry, sounding the death knell of the classical, linear view of the universe and introduced the theory of higher dimensions. As I noted in Noah, the prevailing view of physics eventually filters down to affect all our cultural and social interactions, and it was only 30 or so years after Riemann's talk that the "mysterious fourth dimension" would begin to profoundly affect art, philosophy and literature.

Sixty years after, Einstein used four-dimensional Riemannian geometry to explain the creation of the Universe and its evolution, and 130 years later, physicists would use ten-dimensional geometry to attempt to unite all the laws of the physical universe.

Euclidean geometry holds that space is three dimensional and "flat." In flat space, angles in a triangle always add to 180 degrees which omits the possibility that space can be curved, as on a sphere. For two thousand years, Euclid was "king" and all of Christendom marveled at his insights. Cathedrals were built and civilizations were born according to the principles of Euclid. Euclid and the Church - strange, but devoted bedfellows.

Most people can remember struggling with the theorems of Euclid: that the circumference of a circle is pi times the diameter, and that parallel lines never intersect. It was always pretty standard stuff except for one little problem that most people aren't aware of: try as they would for centuries, the greatest mathematicians simply could not PROVE these deceptively simple propositions. As long as you stay in "flatland," you were safe with Euclid. The instant you wandered into curved space, Euclid was your nemesis.

Riemann rebelled against the so-called "mathematical precison" of Euclid, because it was apparent to him that the natural world is NOT made up of Euclid's flat, idealized, geometric figures. It was clear that the REAL world was made up of curves that bend and twist in infinite variety.

Euclid said "it is obvious" that a point has no dimension at all. A line has one dimension: length. A plane has two dimensions: length and breadth. A solid has three dimensions: length, breadth, and height. And that's it! There is no more! Nothing has four dimensions, according to Euclid.

Another Greek who has dominated our culture for a very long time, Aristotle, stated categorically that the fourth spatial dimension was impossible. Ptolemy, the Egyptianized Greek went even further and constructed a "proof" that the fourth dimension was impossible. If you draw three mutually perpendicular lines, and then try to draw a fourth line that is perpendicular to the other three lines, you will discover that it is impossible. More than three mutually perpendicular lines are not only impossible to draw, they are impossible to comprehend.

But, what Ptolemy REALLY did was to demonstrate that it is impossible to visualize the fourth dimension with our three-dimensional brains! Today, mathematicians and physicists KNOW that there are many objects that can be shown to exist mathematically, which cannot be visualized.

As Michio Kaku writes: "Ptolemy may go down in history as the man who opposed two great ideas in science: the sun-centered solar system and the fourth dimension."

It is a curious thing that many mathematicians, obviously deeply influenced by Christianity, and their faith in the Bible as the "True and only word of God," regularly denounced the idea of the fourth dimension calling it a "monster in nature." And so, Euclid and the Church dominated our minds, brainwashing humanity into thinking that things cannot exist that we cannot picture in our minds. It was, oddly enough when you consider the purported "spiritual goals" of religion, a curious descent into gross materialism.

As mentioned, the story of Riemann and how and why he prepared his famous lecture is nicely told in Michio Kaku's Hyperspace, well worth reading. But, what concerns us here is that Riemann developed the idea of the metric tensor and also was one of the first to discuss multiply connected spaces, or wormholes. To visualize this, take two sheets of paper and place one on top of the other. Make a little cut on each with knife or scissors, and glue the sheets together along the two cuts only. If a bug lives on the top sheet, he may one day accidentally walk into the cut and find himself on the bottom sheet. He will be puzzled because everything is in the wrong place. After much experimentation, the bug may discover that he can re-emerge into his original world by passing again through the cut. As long as he walks around the cut, everything is fine and looks normal, but when he tries to take the "short-cut" he has a problem.

"Riemann's cuts" were used with great effect by Lewis Carroll in his book Through the Looking-Glass. Riemann's cut is the looking glass.

Soon after Riemann, researchers all over Europe began to popularize the idea of the fourth dimension for the layperson. As it happened, Riemann's advanced mathematics was so far in advance of the thinking of the day that there was no physical principle to guide further research. It was only after another hundred years had passed that physicists even caught up with him! But, one thing that DID happen was the realization that a being from the fourth dimension would have what would seem to us, God-like powers. Kaku writes:

Imagine being able to walk through walls.

You wouldn't have to bother with opening doors; you could pass right through them. You wouldn't have to go around buildings; you could enter them through their walls and pillars and out through the back wall. You wouldn't have to detour around mountains; you could step right into them. When hungry, you could simply reach through the refrigerator door without opening it. You could nver be accidentally locked outside your car; you could simply step through the car door.

Imagine being able to disappear or reappear at will.

Instead of driving to school or work, you would just vanish and rematerialize in your classroom or office. You wouldn't need an airplane to visit far-away places, you could just vanish and rematerialize where you wanted. You would never be stuck in city traffic during rush hours; you and your car would simply disappear and rematerialize at your destination.

Imagine having x-ray eyes.

You would be able to see accidents happening from a distance. After vanishing and rematierializing at the site of any accident, you could see exactly where the victims were, even if they were buried under debris.

Imagine being able to reach into an object without opening it.

You could extract the sections from an orange without peeling or cutting it. You would be hailed as a master surgeon, with the ability to repair the internal organs of patients without ever cutting the skin, thereby greatly reducing pain and the risk of infection. You would simply reach into the person's body, passing directly through the skin, and perform the delicate operation.

Imagine what a criminal could do with these powers. He could enter the most heavily guarded bank. He could see through the massive doors of the vault for the valuables and case and reach inside and pull them out. He could then stroll outside as the bullets from the guards passed right through him.

With these powers, no prison could hold a criminal. No secrets could be kept from us. No treasures could be hidden from us. No obstructions could stop us. We would truly be miracle workers, performing feats beyond the comprehension of mortals. We would also be omnipotent.

What being could possess such God-like power? The answer: a being from a higher-dimensional world. [Kaku, 1994]

In 1877, a scandal in London brought the idea of the 4th dimension to public awareness in a big way. A psychic named Henry Slade was holding seances in the homes of prominent people, and was arrested for fraud "using subtle crafts and devices, by palmistry and otherwise." [Kaku, 1994]

Slade was convicted of fraud by the court, but he insisted that he could prove his innocence by duplicating his feats before a scientific commission and Johann Zollner, professor of physics and astronomy at the University of Leipzig, gathered together a group of scientists who were willing to take a scientific look. Their reason for doing so was made public and consisted in declaring that the feats Slade claimed to be doing were, indeed, possible by manipulating objects in the 4th dimension! In so doing, the media coverage gave the public a real idea of just exactly what was possible in this strange world of ours.

Among Slade's defenders were William Crookes, inventor of the cathode ray tube; Wilhelm Weber, Gauss's collaborator and the mentor of Riemann; J.J. Thompson, who won the Nobel Prize in 1906 for the discovery of the electron; Lord Rayleigh, one of the greatest classical physicists of the late ninteenth century and winner of the Nobel Prize in 1904.

First, Slade was given two separate, unbroken wooden rings. Could he push one wooden ring past th other, so that they were intertwined without breaking it? If Slade succeeded, Zollner wrote, it would "represent a miracle, that is, a phenomenon which our coneceptions heretofore of physical and organic processes would be absolutely incompetent to explain."

Second, he was given the shell of a sea snail, which twisted either to the right or to the left. Could Slade transform a right-handed shell into a left-handed shell and vice versa?

Third, he was given a closed loop of rope made of dried animal gut. Could he make a knot in the circular rope without cutting it?

Slade was also given variations of these tests. For example, a rope was tied into a right-handed knot and its ends were sealed with wax and impressed with Zollner's personal seal. Slade was asked to untie the knot, without breaking the wax seal, and retie the rope in a left-handed knot. Since knots can always be untied in the fourth dimension, this feat should be easy for a fourth-dimensional person. Slade was also asked to remove the contents of a sealed bottle without breaking the bottle.

Could Slade demonstrate this astounding ability?

Today we realize that the manipulation of higher-dimensional space, as claimed by Slade, would require a technology far in advance of anything possible on this planet for the conceivable future. However, what is interesting about this notorious case is that Zollner correctly concluded that Slade's feats of wizardry could be explained if one could somehow move objects through the fourth dimension.

For example, in three dimensions, separate rings cannot be pushed through each other until they intertwine without breaking them. Similarly, closed, circular pieces of rope cannot be twisted into knots without cutting them. However, in higher dimensions, knots are easily unraveled and rings can be intertwined. This is because there is "more room" in which to move ropes past each other and rings into each other. If the fourth dimension existed, ropes and rings could be lifted off our universe, intertwined, and then returned to our world. In fact, in the fourth dimensions, knots can never remain tied. They can always be unravelled without cutting the rope. This feat is impossible in three dimensions, but trivial in the fourth. The third dimension, as it turns out, is the ONLY dimensions in which knots stay knotted!

Similarly, in three dimensions it is impossible to convert a rigid left-handed object into a right-handed one. Humans are born with hearts on their left side, and no surgeon, no matter how skilled, can reverse human internal organs. This is possible (as fist pointed out by mathematician August Mobius in 1827) only if we lift the body out of our universe, rotate it in the fourth dimension, and then reinsert it back into our universe.

Zollner sparked a storm of controversy when, publishing in both the Quarterly Journal of Science and Transcendental Physics, he claimed that Slade amazed his audiences with these "miraculous" feats during seances in the presence of distinguished scientists.

Zollner's spirited defense of Slade's feats was sensationalized throughout London society. Supporting Zollner's claims was his circle of reputable scientists, including Weber and Crookes. These were not average scientists, but masters of the art of science and seasoned observers of experiment. They had spent a lifetime working with natural phenomena, and now before their eyes, Slade was performing feats that were possible only if spirits lived in the fourth dimension. [Kaku, 1994; emphases, mine]

There were, of course, savage critics and detractors, but in my opinion, none of their arguments hold water. In fact, such evidence has been demonstrated time and again over the centuries, far into the distant past, and there have always been the detractors and "savages" criticizing on behalf of their materialist masters or gods.

The interesting thing about Kaku's descriptions of the abilities of a "4th dimensional being" is that they happen to be precisely the type of things that characterize the "Alien Phenomenon" that interacts with our reality to a greater and greater extent with each passing year. What's more, there is a great body of evidence that beings with such powers have interacted with humanity for a very long time, though in ages past they were called fairies, demons, vampires, and so forth. Further, these abilities that are being described as "4th dimensional," are exactly what the Cassiopaeans term "4th density," rather than dimension.

In 1884, after a decade of controversy, Edwin Abbot, headmaster of the City of London School, wrote the novel Flatland: A Romance of Many Dimensions by a Square. Abbot was a clergyman, which wasn't too surprising because they now had a "place" to put heaven and hell and angels and demons - in the fourth dimension (which probably wasn't too far off in terms of accuracy!) The unique thing about Flatland was that is was also a biting satire of social criticism. Abbot poked fun at the pious people who denied the possibility of the 4th dimension. It is a book well worth reading for the many examples it makes of bigotry and narrow mindedness that prevail, even today, in scientific and religious communities.

-- SAR01 (rauch01@yahoo.com), April 20, 2001