# Stepping into the Fourth Dimension

# Stepping into the Fourth Dimension

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More ↓Imagine going to a magic show, where the world’s top ranked magicians gather to

dazzle their wide-eyed crowd. Some would walk through jet turbines, others would

decapitate their assistants only to fuse them back together, and others would transform

pearls into tigers. However, with each of these seemingly impossible stunts, there is

always a catch. A curtain will fall momentarily; a door will shut; the lights will go out; a

large cloud of smoke will fill the room, or a screen will hide what is truly going on. Then,

a very different magician comes on, and performs stunts like entering a closed box without

opening any doors, and placing a mouse in a sealed bottle without removing the cork.

These do not seem very extravagant compared to the amazing feats other magicians pull

off, but what leaves the crowd completely baffled is the fact that he does these tricks

without placing a handkerchief over his hand, or doing it so fast the crowd misses what is

going on. To perform the mouse-in-the-bottle trick, he shows the mouse in his hand,

slowly twists it in a strange manner, and right before your eyes, his hand completely

disappears! A few instants later his hand reappears inside the bottle, holding the mouse.

There seem to be two parts of his arm; one in the bottle, and one out. His arm looks

severed, yet he has complete control of his fingers inside the bottle. The hand lets go of

the mouse, and again vanishes from inside the bottle, and reconstitutes itself on the

magicians arm. He pulled it off candidly, without the smoke and mirrors. Everything that

was seen actually happened. This magician, breaking the tradition of fooling the audience

with illusions, used cutting edge knowledge of higher-dimensional science to perform this

marvel. He sent his arm outside of 3-D space, twisted it in the fourth dimension, and

placed it back into the bottle. The fourth dimension is not time, but an extra direction, just

like left, right, up, down, forward, and backwards. This magician has used the fourth

dimension for entertainment purposes. However, the fourth dimension has other, more

practical uses and applications in the realm of mathematics, geometry, as well as

astrophysics, and holds the explanation to such natural phenomena as gravity and

electromagnetism.

To this day, many scientists and other people accept time as being the fourth

dimension. This notion is completely absurd. Time does play an important role in the

description of an object, but it is incorrect to perceive it as a dimension.

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### Related Searches

color, state, and frequency are all components used to describe an object, be it matter,

wave or energy, but they are not dimensions. The three spatial dimensions known to us

are used to describe where an object is in 3-D space, while mass, volume, color, etc.,

describe how it is. Describing when it is would be done using time, and saying time is a

dimension would be like saying that mass is a dimension, which is incorrect. Dimensions

are reserved to tell where an object is, and all other components of its description are

entirely separate. Time has been confused as being the fourth dimension for several

reasons. It seems to have first been referred to as such in H.G. Wells’ The Time Machine,

which came out in the late 19th Century. Equivalents to the 2-D ordered pair (x,y) have

been used to describe a point either in 2-D space (x,y,t), or in 3-D space (x,y,z,t). A

strange inconsistency is that the 1st, 2nd, and 3rd dimensions all need the dimension below

them, while time does not: a 3-D (3 axes) world cannot exist without first having a 2-D

plane (2 axes), and a 2-D plane cannot exist without first having a 1-D (1 axis) line; but a

point on a 1-D line can exist in time, which would make time 2-D. In this situation, time is

the second dimension, the t-axis. If it is well accepted that time is the fourth dimension,

the t-axis, how is it that in this situation time is the second dimension, which is well

confirmed as being the y-axis? How can time simultaneously be the t-axis and the y-axis?

It can’t. They are two separate aspects of the object and cannot be the same. Time is a

very important factor of an object’s description, but it cannot be considered a dimension.

If time is not a dimension, and more specifically, not the fourth dimension, then

what is? Understanding the fourth dimension to its full extent is beyond the power of the

human mind, but we can infer what the fourth dimension might be by drawing connections

between the three dimensions we are familiar with. When jumping from one dimension to

the next, we add an extra axis, or two new directions. Let’s examine the first dimension,

consisting of the x-axis. It has two directions: left and right. The basic infinite unit for the

first dimension is a line, its basic finite unit is a segment. When jumping to the second

dimension, we add another axis (y), thereby adding two new directions: up and down.

The basic infinite unit for the second dimension is a plane, its basic finite unit is a square.

Moving on to the third dimension, we add one more axis (z), creating two more

directions: forward and backward. The basic infinite unit for the third dimension is space,

and its basic finite unit is a cube. So far, the elements discussed have been easy for the

human mind to understand, since the standard of the universe is in three dimensions, and

concepts less than or equal to human capabilities can easily be understood; however, it is

difficult to deal with anything greater. As can be noticed, there are very distinct patterns

and steps that are constant when increasing the dimensional value: basically it is adding an

axis that is mutually perpendicular to all previous axes. By adding a z-axis, all three lines

join together at a single point, all forming right angles to each other. With this template,

describing the fourth dimension becomes easier. When progressing to the fourth

dimension, one more axis would be added (call it “w”); this will create two new directions

(call these w+ and w-), which are impossible for a 3-D mind to visualize. The basic infinite

unit of the fourth dimension is hyperspace (4-D space), and it’s basic finite unit is a

hypercube (a 4-D cube). In hyperspace, it is possible to have four axes joining at a single

point, all forming right angles to each other. This seems absolutely incredulous; four axes

can never meet perpendicularly! This is a 3-D mind speaking again. Two perpendicular

axes are impossible obtain on a line, and three perpendicular axes are impossible to obtain

on a plane. Four perpendicular axes are impossible to obtain in 3-D space, which is why it

can’t be visualized; but it is easily obtained in four-dimensional hyperspace.

Hyperspace seems extremely theoretical, without many solid facts with which to

back it up. But it is surprising how many factors and phenomena lean towards the fourth

dimension for an explanation. Mathematically, geometrically, and physically, hyperspace

mysteriously connects into a radiant harmony of completeness.

Geometrically, hyperspace makes sense; it all fits together. Going back to the

basic finite unite of the fourth dimension, the hypercube, let’s draw some connections with

the lower dimensions. To better understand the following paragraph, refer to appendix A

for a visualization of these concepts. Moving even before the first dimension, let’s

examine the zeroth: A point. It has no directions, meaning it has no infinite unit, just a

finite one: the point. To convert a point into a segment, (1-D finite unit) you would

duplicate the point (0-D unit) and project it into the added x-axis. Then, connect the

vertices; you get a segment, a 1-D finite unit. To convert a segment into a square, (2-D

finite unit) you would duplicate the segment (1-D unit) and project it into the added

y-axis. Then, connect the 4 vertices; you get a square, a 2-D finite unit, composed of four

segments all sharing common vertices (points) with their 2 perpendicular segments. To

convert a square into a cube, (3-D finite unit) you would duplicate the square (2-D unit)

and project it into the added z-axis. Then, connect the 8 vertices; you get a cube, a 3-D

finite unit composed of six squares all sharing common edges (segments) with their 4

perpendicular squares. Making the jump to the hypercube is no different. To convert a

cube into a hypercube, (4-D finite unit) you would duplicate the cube (3-D unit) and

project it into the added w-axis. Then, connect the 16 vertices; you get a hypercube, a

4-D finite unit composed of eight cubes all sharing common faces (squares) with their 6

perpendicular squares (Newbold). This boggles the mind. No 3-D human could ever see

a hypercube, because a hypercube cannot exist in a 3-D world just as a cube cannot exist

on a 2-D plane; a plane is missing two directions necessary to allow the cube to exist. Our

3-D world is missing two directions necessary to allow a hypercube to exist.

Another way to attempt to visualize the hypercube is by using tesseracts. Figure 1

in the diagram depicts six two-dimensional squares, arranged in a cross-shaped alignment.

The two outer squares can be folded up via the third dimension; next, the other squares

can also fold up, forming the fundamental finite unit of the third dimension: the cube.

Similarly, Figure 2 depicts the three-dimensional version of the cross, the tesseract, which

consists of eight cubes forming a cross-like object. Just like the cross was an unfolded

cube, the tesseract is an unfolded hypercube. The two outer cubes can be folded up via

the fourth dimension; next, the other cubes also fold up, forming the fundamental finite

unit of the fourth dimension: the hypercube (Kaku 71). This is of course impossible to

visualize, even imagine, with a three dimension mind. Imagine a two-dimensional person

living on a plane. He could see the six squares that form the cross, but he could never

even fathom having the squares fold up into a dimension greater than his own. It is

impossible for him to even imagine it. Visualizing this fold-up is very easy for us, with

3-D minds. However, visualizing a tesseract folding up into a hypercube defies human

comprehension.

The hypercube is probably the most easy four-dimensional concept to understand.

Yet it is not alone in 4-D geometry. In fact, discovering the fourth dimension opens up

possibilities for scores of new shapes and forms, that were never possible on a plane or in

space (Koch). The circle, triangle, and square are very familiar to us. They form nice,

simple equations when expressed mathematically, and are the basis of many natural objects

in today’s world. On a two-dimensional plane, a square and a circle must always be

separate. A merger of the two is impossible. Looking a step higher, through

three-dimensional eyes, combining a square and a circle is simple: the result is a three

dimensional cylinder. Thus we see that different two dimensional objects can combine in

the third dimension to create a unified shape. Other examples of merging shapes are: a

circle and a triangle form a cone, a triangle and a square form a pyramid, inversely, the

square and the triangle form a prism, the triangle and the circle form a three-cornered

dome, and the square and the circle form a four-cornered dome. From these examples

several conclusions can be drawn. Every two-dimensional shape needs two axes to exist.

By merging these shapes, one of them occupies the x-axis alone, one occupies the y-axis

alone, but they share positions on the z-axis. If this is true, then three two-dimensional

shapes can merge in the fourth dimension, or one 3-D object and one 2-D object can. For

example, a 3-D sphere and a 2-D triangle can merge in the fourth dimension, making it a

hypercone. It is simultaneously a sphere and a triangle, just as a cone is simultaneously a

circle and a triangle.

Another aspect of the fourth dimension is found in geometry’s roots: mathematics.

Using exponents, we can raise the dimensional value of a number. Take the number 3, for

example. The number 3, like any other number, is one-dimensional. It be made

two-dimensional by squaring it; 32 = 9. Thus we see that 9 is the one-dimensional value

for two-dimensional 3. A one-dimensional value can not only be squared (raised to the

second power), but it could just as easily be cubed. 33 = 27. From this we infer that 27 is

the one-dimensional value of three-dimensional 3. Any number can also be raised to the

fourth power; it would make just as much sense to call it “hypercubing” a number, just as

raising to the second or third powers is “squaring” or “cubing”. In math, multidimensional

reasoning is very easy and simple, since it doesn’t require visualization.

However, every mathematical equation can be expressed visually using a graph.

Most commonly, a two-dimensional graph is used to express equations that include two

variables, and x and a y. This draws a line on the graph, on which every points x and y

value can be inserted into the equation, and have both sides of the equation balance out.

For equations dealing with three variables, a three-dimensional graph can be used to

visualize it, using x, y, and z coordinates. Using this model, an equation sporting four

variables can easily be obtained (Guarino). It would only make sense to be able to visually

express this equation using a four-dimensional graph. But this leads to a great problem.

This is a three-dimensional world, and it lacks the two directions necessary to allow the

fourth axis to exist. Fortunately, there is a way to represent the fourth dimension using

just three. This is done by “faking” the fourth dimension using what is available in three

dimensions. To explain this, let’s have a look at the dimensions that we can understand.

just as a hypercube cannot exist in space, a cube cannot exist on a flat, two-dimensional

surface. However, using an artist’s trick called perspective, the third dimension can

“faked” on a flat piece of paper. Note the cube in figure 3. It appears very normal to us,

as we are used to seeing three-dimensional objects shown on two-dimensional medium. In

analyzing its structure, we note that a cube is composed of six squares. However, there

are not six squares on figure 3’s cube. There are only two: square ABDC and square

EFHG (see fig 4 A). The other four shapes that comprise this cube are actually

parallelograms that are representing full squares skewed through three-dimensional

perspective (see fig 4 B). In 3-space, angle EAB is 90o , however, in two-space, on this

flat representation, angle EAB is about 135o. Therefore, if a three-dimensional object can

be represented by faking in the second dimension, it would only be right that a

four-dimensional object could be faked in our 3-D world. This is done by first having

three lines joining at point all forming right angles to each other, then adding another line

going through that point. It wouldn’t really matter at what angle, either way it would be

right, or rather, wrong, since it is only faking an extra axis (see appendix B for a look at

faking the fourth dimension). With this, four-variable equations could be graphed on a

rotating four-dimensional graph emitting the same qualities as a two or three-dimensional

graph. All points on the graph would be expressed in terms of (x, y, z, w), meaning every

point has a four-dimensional value.

One might think about the fourth dimension, agree it is a good theoretical idea, and

acknowledge its practical use in math and geometry, but might wonder whether it exists in

the real world. Hyperspace makes sense in math, the numbers match up, so where is this

extra axis? Can we walk through it? Can we travel in hyperspace? How? Is it just a

pointless theory? Surprisingly, the four natural forces in the universe: gravity,

electromagnetism, and the nuclear forces “strong” and “weak” can only be explained

through the idea of hyperspace.

At a recent lecture, Kip Thorne, physics professor at Cal Tech and renowned

physical theorist, explained the nature of black holes. To give a visual idea, he held in his

hands a black rubber ball, a sphere. He announced that the circumference of the sphere

was about 30 cm. From this, you would expect that the radius of the sphere would be

30/p or about 10 cm. He continued to explain that it is not 10 cm, but that it was many

miles long. This seems impossible! To explain this, he made his audience imagine they

were blind ants living on the surface of a trampoline. By counting their steps, the ants

walk around the trampoline and determine that the circumference is about 20 meters.

Unknown to them, there is an extremely heavy rock lying in the center of the trampoline,

causing its surface to bend down to a great degree. Because of this, when the ants

attempt to discover the trampoline’s radius, the are surprised to find out that it is not 20/p

meters, but much more (see fig 5). In this situation we see that a two-dimensional circle

can have a radius more than diameter divided by p if and only if the circle is warped,

making occupy multiple coordinated on an extra axis, just like the curved trampoline’s

center had a greater z-axis value than its outer edge (Thorne Lecture). It was a 2-D circle

occupying 3-D space. If the ball that Thorne was holding had a radius more than its

diameter divided by p, then that 3-D sphere must be occupying multiple coordinates on an

extra axis: the fourth dimension. The center of the sphere would have a greater

four-dimensional value that its surface. This would mean that a black hole is

simultaneously a sphere and funnel shaped object, which will be simplified into a triangle;

and, just as a cone is a circle and a triangle, a black hole is a four-dimensional hypercone.

No longer is this fuzzy numbers and twisted math; it is an actual documented phenomenon

that can only be explained through the introduction of a new, four-dimensional axis. This

phenomenon of curving space is called space-time warpage. Einstein said that space-time

was warped by the presence of matter (Rothman 217). The density of the matter would

determine the degree of subsequent warpage. This means that large amounts of mass like

planets and stars warp space more so than a lost electron randomly drifting through space.

Back to the example of the trampoline, all objects on its surface would have a tendency to

slide toward the center, where the rock is. If a marble is on the trampoline, it is making a

slight dent in on the surface, but it is so small it is practically negligible. It will naturally

flow towards the rock, since the rock is creating the greater warpage. In this instance, the

attraction between the two objects is two-dimensional. Objects on the surface would slide

toward the rock, however, an object underneath it or hanging above it would feel no force

attracting it to the rock. On a planet, however, the attraction is three-dimensional,

meaning any object in 3-D space is attracted to the planet, because of it’s four-dimensional

warpage. This proves that the only way gravity can be explained is with the fourth

dimension. Einstein also stated that the greater gravity is in a field of reference, the slower

time will run (Encarta General...). As previously stated, large amounts of dense mass have

a greater gravitational pull, meaning the four-dimensional warpage is proportional to the

object’s gravity and mass (Gribbin 41). If this is true, than the speed of time in a given

gravitational reference is equal to the slope of space-time’s warpage (see figure 6), which

in turn can be measured by the specific object’s density. This raises two perplexing

questions: What happens when the slope is vertical? What happens when it is horizontal?

Einstein explained that time cannot exist without matter, and vice versa. If matter can be

expressed in amount of space-time warpage, the absence of matter would equate no

warpage, meaning no time. Time would completely stop when warpage’s slope was zero.

Strangely, when the most minute amount of matter is placed in space, and warpage’s slope

is infinitely close to zero, time would be running at maximum speed! As more mass is

added, warpage would increase, time would slow down, and come almost completely to a

stop, then, when warpage reaches no slope, or a vertical line, time would either run at an

infinitely fast rate, or it would cease to exist entirely. This eerie paradox is one of the

unsolved components of the four-dimensional explanation, along with one other: with the

trampoline example, the component that made the marble attracted to the rock was a) the

slope of the curvature and b) the force of gravity pulling it down. If space-time is warped

via the fourth dimension with the presence of mass, where is the four-dimensional force

that is actually causing the attraction? The warpage is merely funneling the direction of

the bond, but the original source of the force is yet to be discovered.

Along with gravity, other forces can be explained. When it comes to waves, we

have many examples to with which to relate. Waves create ripples in water, and compress

and decompress air molecules, creating sound. Almost all waves we know about need

matter to exist. A water wave cannot exist without water, and sound cannot exist without

air. But strangely, waves on the electromagnetic spectrum (including light, radio waves,

and X-rays) can travel through a vacuum: the absence of matter. This is breaks all known

laws! No other wave can exist in a vacuum, but somehow, electromagnetism can! There

have been several theories to explain this, such as the suggestion of aether, “which fill[s]

the vacuum and act[s] as a medium for light” (Kaku 8). This gives a shady explanation of

how light, proposed to be simultaneously a wave and a particle, can vibrate its own matter,

allowing it to travel through empty space. This theory, however, had many gaps and

paradoxes, and eventually was proven wrong in laboratories. In the early twenties, the

Kaluza-Klein theory was born, suggesting that electromagnetic waves were actually

vibrations in 3-D space itself (Kaku 8). This defies imagination, as this is only possible

through the acceptance of the fourth spatial dimension. Just like the two-dimensional

surface of water can ripple, causing it to occupy multiple coordinates in three-space,

three-dimensional space can ripple, causing it to occupy multiple coordinates in

four-space.

Another strange possibility opened with fourth dimension is the existence of

parallel universes. Using the third dimension, several two-dimensional planes can co-exist

in a parallel manner. Similarly, there could be multiple universes (3-D spaces) co-existing

in four-dimensional hyperspace. This of course is extremely theoretical, and could never

be proven. It can only be explained through thought experiments. Imagine an occurrence

of extreme space-time warpage happening in two parallel universes at identical XYZ

coordinates. They could possibly merge, creating a tunnel, or wormhole connecting

parallel universes via the fourth dimension (see fig. 7 B). If multiple universes do not

exist, or a trans-universal wormhole is impossible to obtain, there is still the possibility of a

universe connecting with itself (see fig. 7 A). Science fiction writers have often romanced

with the idea of shortcuts through space. The fourth dimension turns these dreams into

reality. It is impossible to exceed the speed of light, but it is possible to travel one light

year in less than one year (Encarta Special...). How? By traveling through a worm hole

that takes a shortcut through the fourth dimension.

With this information, keep your minds open about things that perhaps you cannot

fully understand. Furthering the research of higher dimensional science will surely amount

to many practical uses in our lives. Speaking of its uses, just how did that magician pull

off the mouse-in-the-bottle trick? It’s quite simple actually. In a two dimensional world,

an object can be placed an removed into and from a closed area by lifting it across the

third dimension (see fig. 8). Using this same concept, except one dimension higher, three

dimensional objects can be placed and removed into and from closed spaces by lifting it

across the fourth dimension. So how did the magician twist his arm and make it penetrate

the fourth dimension? Well, a good magician never tells his secret.

Works Cited

Kaku, Michio. Hyperspace. New York, New York: Oxford University Press, 1994.

Thorne, Kip. Black Holes and Time Warps: Einstein’s Outrageous Legacy. New York,

New York: W.W. Norton & Company, Inc, 1994.

Thorne, Kip. “Black Holes and Time Warps”. Lecture. University of Utah, Utah,

February 26, 2001.

Reichenbach, Hans. From Copernicus to Einstein. New York, New York: Dover

Publications, Inc., 1970.

Gribbin, Mary and John. Time and Space (Eyewitness Books). New York, New York:

Dorling Kindersley Limited, 2000.

Newbold, Mark. “Stereoscopic Animated Hypercube”. [Online] Available

http://www.dogfeathers.com/java/hyprcube.html, April 2, 2001.

Koch, Richard, Department of Mathematics, University of Oregon. “Java Examples of

3-D and 4-D Objects”. [Online] Available

http://darkwing.uoregon.edu/~koch/java/FourD.html, April 2, 2001.

Guarino, Michael, Physicist, Bachelor in Physics, Teacher. Personal Interview. March

30th, 2001.

Rothman, Tony, Ph.D. Instant Physics, From Aristotle to Einstein, And Beyond. Ney

York, New York, Byron Preiss Visual Publications, Inc, Ballantine Books, a

division of Random House, Inc. 1995.

Microsoft Encarta. “Eintein’s Special Relativity”. [Online] Available

http://encarta.msn.com/find/Concise.asp?z=1&pg=2&ti=761562147#s3

April 2, 2001.

Microsoft Encarta. “Eintein’s General Relativity”. [Online] Available

http://encarta.msn.com/find/Concise.asp?z=1&pg=2&ti=761562147#s5

April 2, 2001.