Null in His Lonely World
(Note: Original Story of fmjr)
Null is a zero-dimensional creature who lives in a zero-dimensional world. In Null’s world, he has a very limited freedom of movement. He cannot go beyond the place where he is standing but he is free to turn-around and yet Null never realize that he is doing such thing because he has no sense of direction. Beside that, Null cannot also sense the differences in shapes, distances nor time because those things never existed in his zero-dimensional world. Sad to say, Null lives a boring life and that makes him very lonely.
Null did not notice that days were passing by until one day a “miracle” happened. Suddenly, he can able to move forward and backward and that makes him very excited. But he also noticed that every time he turns to his left or to his right, he senses nothing and so he avoided turning on either sides for fear that he might be brought back to his old world.
The next day, Null was practicing his backward motion when he suddenly bumped on to “something”. He heard a voice who cried, ‘Ouch! ...watch out where you’re going’ Wondering, Null asked, ‘Who is it? Where are you?’. The mysterious voice replied, ‘I am Mull, I’m behind you!’. Null asked, ‘Behind? Where is it?’. Mull noticed that Null is a new guy, so he instructed him, ‘Just turn to your left or to your right, twice!’. But Null replied, ‘I’m afraid. I don’t want to go back to my old world …it’s lonely out there. ‘Trust me’, said Mull. Although afraid, Null did what Mull instructed and he was surprised to sense a shape in front of him (a dot). Mull welcomed him and they talked all day. Null learned many things about his new world and since then, he never felt lonely.
Jack in A Flat Land
(Note: fmjr's original story)
Jack is a two-dimensional prince who lives in a two-dimensional world. In Jack’s world, he is free to move as much as he wanted. He can move vertically (up and down), horizontally (back and forth) or diagonally (in an angle). He can even do a 360 degree turn and that makes him very happy.
Unknown to Jack, he perceive only two kinds of geometrical figures, limited to points and vertical lines w/ different lengths. Jack doesn’t know the difference between his right side and his left side. He doesn’t even know how to move sideways because in his two-dimensional world, such things never existed.But Jack has his own ways of sensing things 1) He knows it well that if he moves backward from a dot in front of him, it will surely disappear. 2) If he moves forward and it remains a dot, surely, it’s a dot. 3) If he moves forward and that dot turned out to be a vertical line, he can assure himself that what he taught to be a dot is really a vertical line that is far from him. 4) If Jack stays in his place and senses a dot forming into a vertical line that keeps on extending, he knows it then, that “something” is moving, towards him. 5) If he senses a vertical line diminishing into a dot and disappears, he knows it too that something is moving, away from him.
One day, Jack accidentally jumped out from his world and was brought into a three-dimensional world. Unknown to him, he happened to be in front of his old world. What he senses to be “something” moving towards and away from him is actually a square that is repeatedly moving from left to right, then right to left. But Jack perceives it differently. He was puzzled to sense a vertical line that suddenly changing into two separate dots and instantly re-appear as a vertical line. In his mind, such event is impossible because it doesn’t agree with the natural laws known to him. If Jack only knew that he is in another dimension, he might accept that reality that sometimes, such things are possible in another world.
Tom In A Strange World
( Note: Original Story of fmjr)
Tom is a small boy who lives on a two-dimensional world. In Tom’s world, he is free to move as much as he wanted. He can walk, run, jump or sit like any other normal kids. But Tom is a very sad boy. All day, he always looks down just to view his world beneath him. He knows well what a circle or a square looks like but he had no idea at all what a sphere or a cube really is.
One day, Tom’s fairy godmother came and gave him the gift to perceive things in a three-dimensional world. Now, he can see things around him and that makes him very happy. Suddenly, a cube, appear in front of him. At first, he thought it was a square but as he moved in a different angle, the square changed into three different quadrilaterals that are connected to each other. In his old world, it is very unusual to see such thing. Tom cannot figure out what he saw but at the end, he simply told himself, indeed, it’s very strange to be in another world.
Views in Different Dimensions
The stories above are simple descriptions of how one can project himself into another dimension and experience them personally. These stories are important tools in able to visualize, the possible existence of a fifth dimension.
In the first story, Null, being a zero-dimensional creature is actually a geometrical figure known as a “point’. There is this common misconception that a point is one-dimensional, that is wrong. A point does not have a length, width or height therefore it is, zero-dimensional. The only one-dimensional geometrical figure is a “straight line”, (one may argue that a ray is also, one-dimensional, that is true but it is only a subset of a straight line). Null, living in a zero-dimensional world only represent an expression of living in a very limited space where he is imprisoned by his own existence, without the freedom to move from one place to another. The straight line in that story not only represents a geometrical figure, it also represents an additional dimension, the dimension of “time”. In his old world, he cannot sense direction or differences in shapes or distances because one can only determine the passing of time if he senses changes in his surrounding. Another thing, motion is a property of time and vice versa. Without continues motion, there is no passing of “time”. Jack, being two-dimensional (a card of Jack of Heart), can never live in a dimension of time represented by a straight line. He needs at least a flat surface, to exist. But if Jack is also confined in a very limited surface just exactly equal to his size, he would then be on the same situation as to Null in his old world. So, he needs a very wide surface to freely move.
Three-Dimensional Space Plus One Temporal Dimension of Time
There is a debate between four-dimensional space-time as either spatial or temporal, that is, space and time are interconnected as represented by a tesseract (as a best example), or time is a part of space but as a separate dimension. Time is a “property of continues motion” and the fact that one can only appreciate the beauty of a tesseract is by spinning it, that is, in a constant spinning motion. Therefore, time is temporal and the passing of time is due to the continuing expansion of the Universe. Null could continue to explore his new world if and only if his one-dimensional world is infinite, represented by an “infinite straight line”. The same thing as to Jack, if his flat world is constantly expanding as represented by, the continues widening of a two-dimensional surface. Therefore, the passing of time in a three-dimensional world of ours is possibly due, to the continues three-dimensional expansion of space together with the influence of time as a separate dimension, represented by the constant motions of all existing matters, big and small (even by particles smaller than the quarks), in the Universe. This notion implies that there is really no absolute point in space that is at rest or to state it in another way, any assigned reference point in space is itself at motion. Therefore, the four-dimensional space-time itself, could be, in an expanding mode. William Clifford*1, who first suggested that gravitation might be due to an underlying geometry, could be correct and the geometry involved here is not that simple.
This informal hypothesis also suggests that if the dimension of time is in the fourth dimension, gravity could also be a kind of dimension and it is in the fifth.
The Existence of the Fifth Dimension
There is a lot of opposition to the idea that the “earth could be expanding along with the rest of the universe”. The idea of a man standing on the earth, feeling the effect of gravity as a downward pull and the same man standing in a very smooth elevator that is accelerating upward at just the right rate of exactly 9.8 meters per second squared feeling no difference is not new, it was already known as the basic postulate of the Theory of General Relativity. It states that a uniform gravitational field (like that near the earth) is equivalent to a uniform acceleration. But Einstein hypothesized that gravitation is a property of space rather than a "force" acting upon bodies. According to this view, space itself curves as a result of the presence of matter. The world as we perceive it is full of irregularities. Space-time is not flat but precisely "warped”. Einstein even believed that his space-time has the tendency to expand due his first impression that the universe is static so he introduced the “cosmological constant” as he admitted later, as his greatest mistake. Further more, the equations of relativity predict that gravity, or the curvature of space-time by matter, not only stretches or shrinks distances (depending on their direction with respect to the gravitational field) but will also appear, to slow down or "dilate" the flow of time. While special relativity indicates that at near speed of light, matter will shrink and increase in mass tremendously only give the impression that matter in motion also affects space-time.Stephen Hawking, started from 1975, developed “quantum gravity” based on Feynman’s sum over histories. He suggested that using the Euclidean space-times, in which the direction of time is at the same “footing” as to the direction of space, there exist a possibility that space-time become finite and have no singularities that formed a boundary or edge. Visualizing that the reason why a man standing on the surface of the earth feels gravity as due to the earth’s surface moving in an accelerated motion as the earth expands in a geometrical rate is the physical way of flattening the curves of space-time.
Projecting one self to a fifth dimension is like being left behind at that point of singularity at the very instance of the creation of the universe and viewing everything getting larger as the passing of time and not part or bounded by Einstein’s four-dimensional space-time.But viewing things in a fifth dimension is not that easy to grasp and it may take time for others (people who are more authorized in this field of science), to accept the validity of this idea. But consider the following reasons based on the stories told;1) The idea of an expanding earth along w/ the rest of the universe is similar to Tom’s story, perceiving a cube as three different quadrilaterals that are strangely connected to each other2) Fitting the mathematical relation of the rate of the earth’s expansion to the moon and the natural phenomenon of tides is similar to Jack’s story, sensing a vertical line that suddenly appears as two separate dots.Therefore, there are two groups of people who may deal this idea in opposite perspectives. The first group who are more “open minded” to consider and give it a try and those who thinks that this idea is as crazy and ridiculous as to a certain Adam’s idea. But the impression that the world as we perceive it is full of irregularities means the mathematical approach involved here is not that simple and there are many other factors that need to be considered such as the expansion of the sun, the outward spiral revolution of the earth, the outward spiral motion of the man standing on the earth's surface as the earth rotates on its axis, the moon's outward spiral revolution to the earth and others, etc .
Modified Euclidean Geometry
In General Relativity, space itself is not actually flat but ”curved” or warped by the presence of matter and energy in the Universe. It also suggested that gravity is not a force but a consequence of bodies trying to follow straight paths in a four-dimensional space-time but perfectly appear to move along curved paths in a three-dimensional space. Does this mean that such a body like the earth is not really circling around the sun (elliptic orbit), but more possibly, moving in a straight path in a four-dimensional space-time? How about Stephen Hawking’s suggestion in his proposal of a theory of quantum gravity that Einstein’s “curved space-time” must be taken Euclidean…does this mean to make the curved space to re-appear as perfectly flat? The idea of the earth expanding along with the rest of the universe fits Hawking’s idea of taking (or dealing), Einstein’s curved space-time as Euclidean.
Maybe, through a computer-generated animation, it is possible to physically view Hawking’s version of a “curved space” this way: “Imagine the earth circling around the sun. Now, make it appear that the sun and the earth gradually getting larger while the distance between them increases (the space-in-between bodies getting wider). In doing that, the earth’s path as a curved orbit would then appear to be a straight path in space (Note: original idea of fmjr).” General relativity was introduced by Einstein in 1915 at the time he thought that the universe was static. Maybe, he realized that the idea of the expanding bodies would not match that kind of a static universe, so he assumed that space-time to be curved. Only in 1924 that Edwin Hubble gave that revelation that the Universe is expanding. But recent studies, suggest that the Universe is not only expanding but racing out at an ever-faster pace.
This suggestive idea that “all bodies and spaces-in-between them in the universe are expanding in a three-dimensional fashion” could be a good starting point to consider that might shed light to the mysteries behind “dark matter” and “dark energy”.
REFERENCES
a)English Mathematicians, “World Famous Mathematicians”, ProStyleGrafix, Phil, 2005
b) Stephen Hawkings, “A Brief History of Time", Bantam Books, 1988
c) Thread, “Existence of a Fifth Dimension”, BAUT science forum
d)Sub-topic, The Gen, Theory of Relativity, “Theory of Relativity”
www.marxist.com/science_old/relativitytheory_html
e)Robert R. Britt, “Dark Matter and Dark Energy: one andtheSame? www.space.com/scienceastronomy/mystery_monday_049712.html
f)Andrew Chaikin, “Dark Energy: Astronomy Still Clueless About the Mystery Force Pushing Galaxies Apart” www.space.com/scienceastronomy/astronomy/cosmic_darknrg_0201151.html
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