A New Dimension of Consciousness: Realizing and visualizing higher spaces

Beichler Academy of Spirituality and Paranormal Studies 2009 Proceedings

A New Dimension of Consciousness

Realizing and visualizing higher spaces

James E. Beichler, PhD

This workshop concentrates on understanding, experiencing and conceptualizing the

fourth dimension of space. The knowledge imparted will be helpful to understand any physical

theories based on higher-dimensional realities as well as expand an individual’s own

consciousness. This workshop deals directly with the intuitive geometrical notions that we all

use to perceive our commonly sensed world. Questions such as ‘What is the concept of space’,

‘Why only three dimensions’, ‘Why or why not more dimensions’, and ‘What is dimension?’ are

considered. Simple methods for the visualization a fourth spatial dimension are also discussed.

The ability to visualize the next higher dimension could well be enlightening if not the next

step in the ongoing evolution of human consciousness, while just trying to do so expands an

individual’s consciousness. If physical theories that use a higher dimension of space to explain

survival are accurate, then the conscious visualization of the fourth dimension will help prepare

each of us for what comes when our material bodies die. This knowledge should familiarize us

with the local environment ‘where’ we could end up when we die. Many people who have

experienced NDEs have reported that wherever they were during the event, the geometry was

different from the geometry that they were taught in school, which is a very good description

of how four-dimensional geometry relates to our commonly sensed three-dimensional

geometrical world.

Introduction

We commonly think of the physical world of our existence as three-dimensional with time,

however that view is very Newtonian. Not only is our space outwardly three-dimensional for

simple scientific considerations, it is Euclidean flat three-dimensional. In reality, there is no

guarantee that our world is three-dimensional or that it should even be three-dimensional, let

alone conform to the Euclidean flat geometry that we all learned in school. A three-

dimensional flat geometry is just the simplest geometry that fits our observations and

perceptions of nature, not necessarily the most accurate or even correct geometry. No one had

ever dreamed that the physical world could be anything but Euclidean until non-Euclidean

geometries were discovered in the 1820s and thereafter.

In fact, the idea that we could have other dimensions of space and other geometries was

so radical at that time that the new geometries were not publicized out of fear for the

repercussions and hardly anyone knew about the new geometries until the 1870s when they

finally became common knowledge. Scientists then spent the next few decades trying to

observe space-curvature in higher dimensions through astronomical observations. It was not

until Einstein made time the fourth dimension that the fervor over higher-dimensional spaces


began to subside. At least that was the story until just a few decades ago when a good number

of physicists began to speculate on the possibility that our commonly perceived space could

actually have more than three dimensions.

Before the 1970s, only a few scientists and science fiction writers dabbled in the possibility

that space could have more than three-dimensions. In fact the idea that any advanced alien

beings or extraterrestrial intelligences would automatically be able to think and communicate in

four or more dimensions of space seems fairly common in science fiction lore. Be that as it

may, the fiction writers and their audience have popularized some misleading if not outright

untrue generalities and myths about higher dimensions and how we might ‘sense’ or ‘cognize’

them. They commonly portray any higher dimension as a completely different place beyond

our common three-dimensional space. Living or just thinking in a higher-dimensional space

would certainly be different from our normal experience, but technically it is not a different

place than we now inhabit. If our world has higher dimensions, they would definitely not be

some other place. They would be point-by-point extensions of our normal space in a new un-

sensed direction, making our three-dimensional space of normal perception a smaller part of

the higher-dimensional space. However, this possibility raises serious questions about our

inability to perceive the higher dimension.

Some authors and scholars even believe that the next step of our own evolution is to

realize higher-dimensional spaces, i.e., learn of their existence and think within their context.

The notion is not that uncommon, but there is very little serious thought about the idea in

either the scientific or non-scientific literature. Undoubtedly, people have tried to realize or

mentally picture the higher dimensions, or even train themselves to think in higher-dimensional

spaces, but as far as we know all attempts to do so have failed. At least they seem to have failed

because we do not really know what thinking in a higher dimension would entail. Yet if we

could think in higher dimensions, it would surely enlighten us, so it should be beneficial to try

to mentally realize four or more dimensions of space. That attempt is the basis of this

workshop, to study the concept of a four-dimensional space and look at ways to think in the

higher dimension.

The fourth dimension of space

The whole concept of dimension is an abstract idea that has evolved in tandem with the

rest of science and mathematics. A few scholars have even attempted to place the whole

history of scientific thought within the context of developing the abstract nature of space, time

and dimension. In fact, the abstract concepts of space, time and dimension are fundamental to

physics, which is the most fundamental of all of the sciences. So the importance and relevance

of the dimensions of space or just space itself are beyond question. While the number of

dimensions that we perceive is not random, there is no reason to believe that the three-

dimensionality of space is absolute. In other words, the ultimate dimensionality of the universe

or even a pluriverse is open to debate.

The best that scientists, philosophers and scholars can do is observe how nature works

and try to develop the best theoretical and geometrical model to describe the nature of our

reality as experienced. At present, the nature of our reality is observed as a three-dimensional

space with time, or speaking more accurately a four-dimensional space-time continuum.


However, assuming that time is the fourth dimension does not preclude the possibility that still

other dimensions of space, time and/or a hybrid of both will never be discovered. There is

presently ample scientific evidence in physics and other areas of science to suggest the reality

of at least one such higher dimension of space, although most scientists do not accept this

interpretation of the evidence.

‘What is space?’

Space as an abstract physical concept suitable for either mathematical or scientific

investigation is hard to grasp and understand. We are not talking about how we think about

the world around us, but how do we abstract the idea or notion of space into something

that is reducible for use as a mathematical or scientific concept. The ancient Greeks did not

develop abstract notions of either space or time, yet they still formed the only philosophical

system that eventually developed these abstract ideas. Both of these concepts were originally

tied to the organic nature of the world as sensed and could not be abstracted into something

useful in science. If you perceive the world around you only as an organic whole, then the

abstract notions of space and dimensions make no sense whatsoever.

Even Aristotle never used a concept of space, but instead used a concept of ‘place’

whereby each and every material object had a natural place in the universe toward which it

would naturally strive. This conceptual system thus places Aristotle as a transitional figure

between the concept of an organic reality and our modern reductionist view of nature. Without

understanding the concept of space, neither Aristotle nor any Greek philosopher was able to

develop an abstract picture or concept of motion such as our modern concept of speed, which

is the first step to developing a ‘physics’ and the basis of theoretical science. This failure held

back the advance of science for hundreds of years.

It took western culture nearly two millennia from the birth of Natural Philosophy (with

Thales of Miletus about 650 BCE) in ancient Greece to break away from the organic

perception of reality and produce a simple and viable abstract concept of space. Throughout

the Middle Ages, space was equated to God: To try and cut up space into parts, even though

the philosophers and scholars were only talking about an abstract idea, was tantamount to

religious heresy and abstracting the measurement of a distance in space that was needed to

define a speed and acceleration was tantamount to cutting up God in reality. Under these

circumstances, developing the scientific concepts of the subjects of measurement and motion

through space were delayed for centuries while philosophers argued about how to express

space as an abstract idea rather than an organic measurement of a small part or bit of the

natural world.

This may seem strange or even funny to us today because we have grown up in a culture

where we can just pull out a ruler or yard stick (meter stick) and measure away as if there was

no problem while thinking of the measurement as an abstract idea for use in mathematics and

science. People could of course measure things thousands of years ago, but they could not

abstract the ideas to further mathematics and develop the conceptualized model of our world

called science. Newton was not the first to solve the problem, but became the most famous

when he distinguished between absolute and relative space. These were necessary precursors to

his development of the first successful laws of motion and gravity.


He overcame the religious obstacles by developing a dual notion of absolute and relative

space. Relative space was to be determined by the relative positions of material objects so it

was not, in itself, a separate ‘thing’. Relative space became the basic background principle of

science because physical measurements of objects in relative space could be thought of

abstractly for scientific analysis. But the concept of absolute space was altogether different.

Absolute space could not be broken down (mathematically reduced) into component parts,

even through a mental process of abstraction, measured in any way or observed and interacted

with. The very existence of absolute space was only implied through the measurement and

understanding of the physical intricacies of relative space. Absolute space was organic, an

undivided and undividable whole, and could only be considered as a whole. It was the

‘Sensorium’ of God; eternal, indivisible, indefinable and infinite. It was also the Euclidean flat

three-dimensional container into which our physical reality was placed. In other words, if all of

the material objects in the universe were to disappear, the three-dimensions of absolute space

would still remain.

Science no longer regards the concept of absolute space a reality. At least if it is a reality,

its existence would be irrelevant to the workings of science, which is now based completely on

relative space and time. Relative space is only relevant within the context of the material

objects by which it is determined, so relative space has no properties or characteristics of its

own other than those that are derived from the material objects from which it is determined.

All else is either scientific or metaphysical speculation, if not science fiction, or at least that is

the general attitude of the scientific and academic communities.

‘Why only three dimensions?’

There is absolutely nothing in science that demands or requires our physical reality be

limited to only three dimensions. The three dimensions of space are just what we observe and

perceive in nature. Perhaps at a different level of consciousness we will find it necessary to get

rid of our present notion of dimensions for some other abstract notion, but right now we

consciously perceive space to be three-dimensional. We do not even know if dimensions

actually exist in reality since they could just be how our material brains perceive physical reality.

However, we assume that our perceptions are accurate and true so we ‘assume’ that space is in

fact three-dimensional for all intents and purposes.

There could even be other universes with more than three and others with less than three

dimensions. In fact, our universe may have more than three dimensions. We only determine

the dimensionality of our space by the relative position of material objects. Since matter is

three dimensional (it is extended in height, width and depth), we judge space to also be three-

dimensional. However, there is no real guarantee that our space could not have more than

three dimensions. It is also possible that ultimate reality is infinite dimensional and that our

universe just occupies four dimensions within that infinite number with or without other

universes occupying other combinations of dimensions that are unconnected to our own.

Such a possibility has long been noted by scientists and sci-fi writers. The whole of reality

would then constitute a pluriverse (plural universes) of individual unconnected universes, but

there is no way to determine if this speculative idea is true or not.

A hundred years ago, it was argued that our space is three-dimensional because of the


inverse square law. All forms of waves (for example light and sound) spread out spherically

from their sources. In two dimensions they spread out circularly like the successive rings of

water across a surface that results from the drip, drip, drip of a faucet. This means that they

lose intensity much faster than they move away from their source because the intensity (energy

density) of a wave is spread out over the area of its spherical wave surface. The area of a

sphere is 4πr2, where ‘r’ is the radius or the distance from the source.

This means that if you go four times further away from the source of a sound, its intensity

would be reduced to 1/16 of its prior intensity. If you move twice as far away, the light’s

intensity at a point would be 1/4 as much because that intensity is spread over a four-times

greater surface area of the spherical surface of the progressing wave. It was once argued that

this inverse square law (intensity is proportional to 1/r2) could only be true if our space was

only and always three-dimensional. If our space were not three dimensional, then all of the

planets would plummet into the sun because gravity also follows the same inverse square law.

For example, if our common space were four-dimensional then gravity would follow an inverse

cube law (weight would be proportional to 1/r3) and planetary orbits would decay very rapidly.

However, this last argument need not be true since it contains a hidden or buried

assumption. The argument ‘assumes’ that any higher spatial dimensions would automatically

be the same as our normal three dimensions, or isotropic (all physical interactions are the same

with respect to any of the three dimensions) with them. A higher dimension of space would

not alter the inverse square law if it were not isotropic with the ordinary three dimensions. So it

is possible that our common space could have a higher number of dimensions, only they would

be different that the normal three dimensions of space by physical necessity. Since we know

that matter is three-dimensional, then any higher dimensions would not be like the ordinary

three or matter would itself have a higher dimensionality. Otherwise, matter could just be

limited to just three dimensions within a higher dimensioned space. So any arguments that a

fourth spatial dimension would change our physical laws and thus limit our world to just three

dimensions are not defensible.

‘Why or why not more dimensions?’

Under these circumstances, there is no reason to adopt a higher-dimensional space as our

real space unless nature forces us to do so by presenting science with problems that can ONLY

be solved by adopting the reality of a higher-dimensional space. According to the majority

opinion of science, there is so far no reason to do so. Science would only adopt a higher-

dimensional space if it could be demonstrated that there were physically testable or physically

observable phenomena that could only be explained by a higher dimension. This was not

always the case and could change again in the future as scientific opinions and attitudes, in the

form of paradigms, change.

Yet there are observable phenomena in science that have been confirmed and can be

explained by the hypothesis of a higher-dimensional space: Dark Matter and Dark Energy are

good examples, but not the only examples. There are also natural phenomena whose physical

existence science has not been confirmed, at least to the satisfaction of the vast majority of

scientists, but seem real none-the-less. These can also be explained by utilizing a higher

dimension hypothesis. Examples range from mind and consciousness to paranormal


phenomena, ‘spirits’ and the afterlife.

Twelve decades ago, astronomers were looking for evidence of space curvature in a fourth

dimension by using a triangulation method in parallax measurements with other stars. They

knew that if our space were anything other than three-dimensional Euclidean it must still be

very close to Euclidean flat for our physical laws to work so well. So they had to measure the

largest triangles possible to see if space curved in a higher dimension. If space were not

Euclidean flat, then the sum of the angles of a triangle could be less than 180 degrees (a

hyperbolic or saddle shaped open space) or greater than 180 degrees (a spherical or elliptical

closed space).

One famous scientist-mathematician by the name of Henri Poincaré stated that should

space curvature be detected in astronomical observations he would rather throw out the laws

of optics than accept the possibility that space was non-Euclidean curved or had a higher

number of dimensions than three. Many scientists, scholars and academicians still feel this way,

so it would take a very compelling argument or physical test rather than just a sufficient

example to sway the scientific community toward adopting the reality of a higher-dimensional

space. In the 1870s, Ernst Mach stated much the same attitude in that he would never accept

such a reality until material objects were shown to pop into and out of space, yet that is exactly

what now happens today at the quantum level of reality.

‘What is dimension?’

So we come to the question, what is dimension? We only know what dimension is by

experience and our experience is dependent upon our sensations of the external world. Other

than that, dimension is just a word. Some mathematicians even talk about ‘fractional

dimensions’ although natural scientists have little use other than speculation for that concept.

Dimension is just a name that we give to an abstract concept that will better help us

understand the nature of physical reality. A dimension would technically be the direction of

extension of movement of a material body or of the material existence of that body itself. It

is difficult to define dimension without using a circular argument which ultimately depends

on the word itself.

We do however normally accept the fact that the three directions of extension in space,

which we commonly call ‘dimensions’ exist at right angles to each other. So we could say that

the three dimensions of space are orthogonal or ‘normal’ to each other. Since this is how we

‘define’ the normal three dimensions of space, we would assume that any higher dimensions

of space are ‘orthogonal’ to the normal three dimensions of space. This fact seems to be true

in all cases tested and all of science is based on this assumption of ‘orthogonality’, so it

would be considered an established fact of nature.

The orthogonality of the three dimensions and the suspected orthogonality of higher

dimensions pose the most serious problem for any suspected higher dimensions. We cannot

imagine something that could exist at a right angle to the normal three dimensions of space.

For there to be a higher dimension, every point in our normal space would have to have

another component of direction, a fourth direction, with all four directions being at right

angles to one another. But we can only measure three directions in our space that fit or

display this property. So, a fourth spatial dimension would ‘appear’ to be internal to the point


itself from our perspective in three-dimensional space and it would seem as if the point in

three-dimensional space were infinitely dense with respect to three-dimensional space.

Yet to understand this we would have to postulate that space displayed the physical

property of density even while admitting that relative space is just an abstraction of the relative

positions of objects and could therefore not have any inherent physical properties of its own,

such as density. Relative space is not a ‘thing-in-itself’ so it cannot have a property such as

density variation.

From a higher-dimensional perspective, the three dimensions of our commonly-sensed

space would appear as an infinitesimally thin three-dimensional ‘sheet’ or ‘film’ cutting through

or across the greater four-dimensional space. While this explanation almost seems to defy

common logic, it also presents a completely logical (mathematical) explanation of the higher

dimension. This explanation also seems to fit the intuitive descriptions given by mystically

enlightened individuals of their mystical experiences. This logical anomaly implies that the

concept of a higher dimension is more of an exercise for a higher level of consciousness than it

is a mathematical or scientific speculation. It also implies that we cannot ‘sense’ the higher

dimension of space although there seems to be no reason why we still could not develop an

‘intuitive sense’ or even an ‘intuitive feel’ for a higher-dimensional space even ‘if’ we could not

physically measure (sense) anything in that direction.

The geometry of higher spaces

The science of measurement is in reality equivalent to the mathematical study of geometry.

In fact, simple geometry is very nearly a physical form of mathematics. The word geometry

literally means to measure (metry or metric) the earth (geos). That is why science can speak so

loosely about the geometry of space, which is another way of saying the way that we measure

the extension of objects and distances in space. In general, there are three classifications of

simple geometry and each changes how we measure, or rather the meaning of measurement

and motion, in space. We can have a Lobachevskian curved geometry, a Euclidean flat

geometry or a Riemannian curved geometry.

Lobachevskian geometry is the geometry of a saddle shaped surface. It is hard to imagine

in four or more dimensions, but easy to picture in two dimensions. In this space, parallel lines

actually diverge from each other as they get farther away from any starting point and the angles

of a triangle add up to less than 180 degrees. We are more familiar with a Euclidean geometry

because it is the geometry on a flat surface. Parallel lines are always equidistant from each other

no matter how far we extend them, even into infinity, and the three angles of a triangle add up

to exactly 180 degrees. With a Riemannian geometry, parallel lines actually diverge and

eventually come together at larger distances while the angles of a triangle actually add up to

anything between 180 and 270 degrees, depending on the type of Riemannian geometry

stipulated.

The surface of a sphere presents a two-dimensional Riemannian surface curved in a three-

dimensional space. On a sphere, like the Earth, longitude lines are parallel but they converge

and meet at the poles. If we draw a triangle with the first line running along the equator and

the other two lines starting one-quarter of the way around the world on the equator and both

terminating at the north pole, we will have a large triangle that extends around roughly one-


eighth of the globe. But that triangle will be made up of three right angels, so the sum of the

angles of that triangle will equal 270 degrees, not the 180 degrees of a triangle on a flat

Euclidean surface.

A Riemannian surface can also have one or two poles. Spheres, egg shapes, ellipsoids and

donut shapes are simple examples of double poled Riemannian surfaces; however a Möbius

strip is an example of a single polar Riemannian surface as is a Klein bottle.

A Klein bottle is a continuous two-dimensional surface curved in three dimensions, yet it has

no inside. The surface has only one pole and the surface is completely on the outside (or

inside) of the bottle. If you look at the surfaces of the Klein bottle and the Möbius strip, they

are continuous with only one side (Möbius) or one continuous inside or outside surface

(Klein), but not both.

Riemannian geometries are physically important because the theory of general relativity

that explains gravity posits that our three-dimensional universe is really a three-dimensional

Riemannian surface. Whether that surface is curved in a higher dimension (extrinsic curvature)

or not (intrinsic curvature) has not yet been decided. If the curvature is indeed extrinsic to the

three-dimensional surface, then a higher fourth dimension of space would be accepted and

become a scientific reality.

Hinton and the realization of the fourth dimension

During the late nineteenth century, shortly after the concepts of non-Euclidean and

higher-dimensional spaces were popularized, an English geometer by the name of Charles

Howard Hinton tried to develop a system to realize or cognize higher-dimensional spaces. His

system consisted of imagining how many constituent parts made up regular geometrical

figures in each of the different number of dimensions in which they could be drawn and then

extrapolating the mental picture into the next higher dimension above the normal three of our

world. The simplest figure would be the three-dimensional cube and its four-dimensional

equivalent the hyper-cube or tesseract. Hinton coined the term tesseract in this case.

If we look at the progression above from zero to four dimensions, we can pretty much

picture the different figures that represent each dimensional configuration. So we can

imagine what a hypercube or tesseract would look like. The tesseract is probably the easiest

polytope (a many or poly-sided figure) to picture in its four-dimensional incarnation, but this


same method can be used for any regular polytope (triangles, pentagons, hexagons and so

on) and that is exactly what Charles H. Hinton did in the 1880s and 90s.

He was never able to „realize’ a four-dimensional object, but his system and attempts inspired a

great deal of debate in popular scientific journals whether realizing higher-dimensional objects

was even possible or not. This discourse was part and parcel to the greater discourse on the

physical reality of mind and consciousness in the late nineteenth century.

It is much easier to draw a two-dimensional picture of a tesseract. You have to remember

that each section of the tesseract is a cube of equal size, which is hard to imagine from this

drawing. You may be able to logically or philosophically accept the tesseract as a four-

dimensional figure, but you can’t actually imagine it as it would appear in four dimensions. Or

in other words, you cannot directly experience its four-dimensionality in your mind.


We may accept that fact logically, but that does not make it easy to imagine what this tesseract

would really look like in its natural four-dimensional state. The best way to imagine it would be

to compare it to a Necker cube.

The Necker Cube

So now let’s play with these figures. If you really want to learn about a „thing’ it is quite

natural to play with it. Children don’t play with toys to have fun, although they have fun

playing with toys and things: They play to learn and just have fun doing it. That’s because life is

all about learning. The following is picture shows a Necker cube although it is nothing more

than a simple two-dimensional drawing of a three-dimensional cube. It is called a Necker cube

rather than simply a „cube’ because we can imagine it to be three-dimensional instead of a two-

dimensional drawing and doing so presents us with sort of an optical illusion.

Which side is in or out, forward or in the background, is controlled by your mind’s eye because

your mind sees all of the lines and squares of equal sizes except for the added depth to the

figure. That’s because your mind thinks in three dimensions and automatically adds in the third

dimension to the two-dimensional drawing. Your mind just interprets the two-dimensional

drawing as a three-dimensional object.


Now try and do the same with the tesseract. In your mind’s eye or your imagination, make

the tesseract sink in and out of the fourth dimension. When you did this with the Necker cube,

your mind just added a third dimension of depth to the two-dimensional drawing. It was easy

because your mind is expecting to receive three-dimensional sensations of a seen object and

you think in three dimensions. But why do you think in three dimensions? Is your mind limited

to three dimensions or is your mind just trained by experience to think in three dimensions by

your past history of sensations of our three-dimensional world and then just unnecessarily

limited in its mental abilities? No one can say for sure. Is three-dimensional space just a cage

that imprisons our minds from achieving a higher-dimensional greatness? We may only think

in three dimensions because of our experiential learning in a three-dimensional world. In other

words, it may be possible to think in four dimensions, or at least it may be possible to train our

minds to thinking in four dimensions.

Just as your mind’s eye added depth to the two-dimensional Necker cube, can you either learn

or train your mind’s eye to add another component of depth in the fourth dimension of space

to the tesseract? It is all the more difficult since this is a two-dimensional picture of the four-

dimensional figure, but even if you had a three-dimensional model of the four-dimensional

tesseract the task would be no easier, try as you may.

Notice that if you logically think of how a component of four-dimensional depth could be

added to the figure it would seem to go inward toward the center of the tesseract rather than

back into or behind the paper as was the case with the Necker cube. This fact is important

because it tells us, at least logically, where the fourth dimension is. Every point in space is

extended into the fourth dimension, so technically, from our three-dimensional perspective the

fourth dimension is inside us, or rather inside every point inside us. This means that if the

fourth dimension of space is real and it is as big as the other three dimensions in our universe,

each point inside of us is extended to a distance of nearly 13.7 billion light years inside of us.

My, how big we are!

However, from the four-dimensional perspective of our material world, which holds all

material objects in the universe or three-dimensional perceived world, would just amount to a


thin slice of the fourth dimension, just like a piece of two-dimensional paper is just a thin slice

of our three-dimensional universe. If you really think about this it is just like when the mystics

tell us that our ‘self’ and consciousness (material three-dimensional body) are individual things

at the same time that they are parts of a bigger whole. That is why mystics seek to find the

whole universe (13.7 billion light years of distance) within just our own small consciousness.

They say that consciousness is a reflection of the whole universe (they search for the universe

by turning inward toward consciousness rather than outward like science), just as the „sheet’

would be the reflection of the whole fourth dimension of the universe.

So now try another method and imagine that all of the lines in the tesseract are of the

same length, all of the surfaces in the tesseract are squares of the same size and the tesseract

is made of eight cubes all of which are the same size. It is only your mind’s eye that distorts

this figure, so add the depth in the fourth dimension that folds those eight cubes into the

four-dimensional tesseract with your mind’s eye. It is not so easy. Again, we can think it

logically, but we cannot picture it in our imaginations. However, if you now just take the

tesseract and break it apart and roll the cubes around in your mind destroying and

reconstructing the tesseract from them, maybe, just maybe, you can start to really imagine

that four-dimensional depth and finally learn how to think in four-dimensional space.

Rotate the tesseract around in your three-dimensional mind’s eye until you make it four-

dimensional. Is that impossible? No, not especially. If our three-dimensionality is just a learned

characteristic, instilled in our mind from a life time of seeing the world in that manner, rather

than a strict characteristic of the space in which we live and exist, then it should be possible at

some point to retrain our minds to think in four dimensions. Even if it were somehow shown

to be impossible, the practice would still be good mental training for your mind and

consciousness. However, if you can do this you will be thinking in a four-dimensional space

and will reach a new level of consciousness.

Other methods

Another method of imagining the tesseract would be to unfold the tesseract into its

component cubes and then refold the cubes into the tesseract. This operation falls under the

heading of playing with the figure. If we instead take a simple cube and unfold it we get a line

or cross of equal squares as pictured below. The cube was three-dimensional, but the resulting

cross of squares is two-dimensional.


Now take the two-dimensional cross, fold along the dividing lines and remake the cube. It is

easy. You can even do it in your imagination if you try. But you must realize one important

detail. When you fold the squares, which are two-dimensional, you must fold them through the

higher third dimension. It is impossible to fold the cross into the cube without moving into

and taking advantage of the next higher dimension.

So we can picture or imagine folding and unfolding the cube in our minds. Now try to do

the same thing with the tesseract. Or we can use an analogy with the cube as your guide, at

least that is how the mathematicians and scientists do it. Just work it through in your mind

logically. Take the tesseract and see how it unfolds and then refold it.

Unfolding the four-dimensional tesseract gives you a strip or cross of eight three-dimensional

cubes of equal size. Try and picture or imagine folding and unfolding the tesseract in your

mind. It’s not difficult to do; however, your mind automatically does it in three dimensions

so you have automatically distorted the cubes to fit into the three-dimensional perception of

reality in your mind.

Instead, try and picture folding the strip or cross of cubes into the tesseract while keeping

the cubes in an undistorted state (keeping them all the same size without „smashing’ them

together and distorting them) as if you are thinking at a four-dimensional level in your mind.

That procedure is very difficult if not impossible, but if you could master it you would be

thinking in a fourth dimension and should have just reached a new level of physical reality in

your thinking. It would be impossible to take eight cubes and physically fold them into a

tesseract because your action would have to take place in the higher fourth dimension even

though the matter in the cubes only exists in three dimensions or rather it is restricted to the

three-dimensional part of the four-dimensional space.

As difficult as all of this seems, the situation is not as bad as it was as short as three

decades ago. Today we have computers and we can design programs that simulate the folding

and unfolding of these figures to help us imagine how they would look in real space. All you

have to do is go to Google or some other search engine and type in keywords such as


‘tesseract’ or ‘tesseract + folding’ to find simple programs that you can play on your computer.

These could be very beneficial in helping you realize a higher-dimensional space and the

subsequent higher-dimensional reality that it represents.

Use as a form of meditation

The bottom line in this exercise is to grow or evolve your mind and consciousness. The

ability to visualize the next higher dimension would be an enlightening experience if not the

next step in the ongoing evolution of human consciousness, while just the effort of trying to

do so should expand an individual’s consciousness. If you could actually attain realization of

the higher dimension, you could end up Buddha-like as an enlightened human. Since the

characteristics and properties of the higher dimension sound vaguely like descriptions given by

people who have been enlightened, had enlightening experiences and visions or have had

NDEs, there is a great deal of circumstantial evidence that mystical enlightenment and NDEs

are nothing more nor less than the direct experience of a higher spatial dimension. So

meditating on these figures or these methods may well be as effective for rendering

enlightenment and ‘satori’ as chanting a mantra. The mental exercise certainly would be

beneficial even if you do not attain the desired enlightenment.

Evolution

It has been noted by many people that advanced intelligent beings would be expected to

be aware of this higher dimension and possibly even think within its context. If history is to be

believed, then it would also seem that trends lasting over the course of two and more centuries

imply that human consciousness is headed toward a new awareness of higher-dimensional

spatial characteristics. Both our physics and our mathematics seem headed in that direction,

which would indicate that our overall conscious evolution is also headed in that direction. If

the development of science and higher mathematics is part of the chain of evolution for

humans and other beings, then the evolution of higher-dimensional consciousness cannot be

far behind as a natural priority.

While many writers have written books forecasting that humans will someday if not

sooner be evolving a higher level of consciousness, the same can be said about the evolution

of higher-dimensional consciousness. Richard Maurice Bucke (1901) was one of the earliest

writers to address the issue of an evolving human consciousness. In his book Consciousness: A

Study in the Evolution of the Human Mind he developed the theory that consciousness evolved

through three states or levels: Simple animal consciousness, self-consciousness and cosmic

consciousness. The last, cosmic consciousness was an emerging mental faculty of the human

species although some individuals had already attained that state.

P.D. Ouspensky expanded on Bucke’s ideas and later claimed that humans can evolve into

higher states of consciousness, but they need a higher form of logic that he called the Tertium

Organum. This was also the title of his 1912 book on the subject. The subtitle of the book was

The Fourth Dimension as the Esoteric Nature of Reality. The subtitle tells it all, but the reading is far

more interesting. Humans need to understand the fourth dimension to evolve to a higher

consciousness. Ouspensky’s highest form of consciousness, equated to a cosmic

consciousness, was the fourth form and it included ‘the sense of four-dimensional space’ as


well as a ‘spatial sensation of time’.

Another author wrote a book directly claiming that the next step in human evolution

involved the awareness of a higher dimension to space. In his 1919 book, the Mystery of Space; a

study of the hyperspace movement in the light of the evolution of new psychic faculties and an inquiry into the

genesis and essential nature of space, Robert T. Browne first rendered a fair history of the

mathematical development of non-Euclidean geometries and hyper-spatial mathematics.

Browne then proposed the theory that humanity will one day develop to the point where

intuition overcomes logical intellect and humans will intuitively know the higher fourth

dimension. In the course of the book, Browne mentioned Albert Einstein’s special theory of

relativity, but he seemed unaware of the general theory, which was unfortunate because he

thought that the fourth dimension would not be Riemannian. Unfortunately his work came a

few years after Einstein’s general relativity was developed and Einstein based his theory on a

Riemannian geometry. However, Browne’s sentiment is still crystal clear, that human’s are

evolving the intellectual tools to be born aware of the fourth dimension of space, even if he got

the finer mathematical and scientific details wrong.

Survival theories

If physical theories that use a higher dimension of space to explain survival (Beichler,

Zöllner and others) are accurate, then the conscious visualization of the fourth dimension of

space will help prepare each of us for what comes when our material bodies die. This

knowledge should familiarize us with the local environment ‘where’ we could end up when we

die. Many people who have experienced NDEs have reported that wherever they were, the

geometry was different from the geometry that they were taught in school (geometry on a

Euclidean flat surface), which is a very good description of how four-dimensional geometry

relates to our commonly sensed three-dimensional geometrical world. There are many strange

peculiarities to higher-dimensional geometries that would appear mysterious, or magical, or

even miraculous to people with completely three-dimensional mindsets.

J.K.F. Zöllner seems to have been the first, but was surely the most vocal advocate of the

existence of spirits in a higher dimension of space after death during the latter decades of the

nineteenth century. His book on the subject, Die Transcendentale Physik, was published in 1878

and translated into English in a shorter version in 1881 by C.C. Massey. Zöllner chronicled his

experimental quest to verify his theory that spirits of the dead inhabited the fourth dimension

of space and were able to communicate with living mortals in the ordinary three dimensions of

space. He used well known mediums for his communication experiments, setting up all types

of challenging experiments for them to demonstrate their craft of communication. His primary

experimental subject was Henry Slade, an American medium. Although the experiments

Zöllner described in the book sound fool proof, Slade was caught cheating on one occasion

and Zöllner’s scientific career was ruined by association. If nothing else, Zöllner’s example

should act as a warning to any modern scientist who seeks to go too far in his claims of the

paranormal without adequate theoretical or experimental evidence.

Zöllner’s choice to place spirits in a higher dimension of space was not arbitrary. He

chose to pursue the four-dimensional hypothesis because the mathematical and physical

properties of a four-dimensional space fit what he and others witnessed with the mediums.


For example, if you have a sheet of paper (a two-dimensional surface) and draw a square on

it and place your pen point within the square, you cannot move the tip of your pen outside

the square without crossing the line. In order to move the pen point outside the square

without crossing the line, you must lift the pen up into the higher third dimension and put it

down again outside the square. Now, by analogy, think of a person locked in a jail cell with

no key and no other exit. The person couldn’t escape because the cell door couldn’t be

opened. However, if the person could somehow step into the fourth dimension, he could

just walk through the wall of the cell without going through it (in three-dimensions) and

escape.

Zöllner tested Slade in one instance by placing a piece of chalk between two small

blackboards. Then he sealed them with tape and tied them up. He then gave the sealed

package to Slade who concentrated for a while until scratching was heard inside the package.

When the scientists opened the package, they found writing on the chalk boards in different

languages where no writing had appeared before the package was sealed. They could only

explain this phenomenon by assuming that a four-dimensional spirit had reached inside the

closed and sealed package (it was only closed to three-dimensional beings in normal space)

from the higher fourth dimension and written on the chalk boards.

The test seemed foolproof, at least that was how Zöllner explained it, but Zöllner and his

friends were discredited for their experimental verifications of Slade and other mediums none-

the-less. One of Zöllner’s harshest critics, Mach, referred to this particular property of a four-

dimensional space when he stated that he would never accept the reality of the fourth

dimension until objects started popping into and out of common space. If material objects

could move into and out of four-dimensional space, to and from our three-dimensional space,

they would appear to pop into and out of our three-dimensional space without logical

explanation.

Sci-Fi

Over the years, Sci-Fi writers have gotten far more use out of the possibility of a higher-

dimensional space than any other group. While some stories might include monsters or

invaders coming from other dimensions (like the recent movie Knowing), the reference is

usually far more subtle. Many Sci-Fi movies use subspaces (such as Star Trek) or other forms

of hyperspaces to travel faster than light. In the movie Contact, an alien civilization sent a

radio message to Earth with instructions on how to build a transport to visit them. The

human scientists received thousands upon thousands of pages of instructions, but could not

read them without a primer to break the language barrier and translate the messages. None

of the sheets of data fit together until someone realized that the aliens think in many

dimensions, not three, and put the two-dimensional sheets of data together to form three-

dimensional cubic pages of writing - the aliens read and write in a higher-dimensional space.

Even what is seemingly magic in the Harry Potter movies can be logically explained using

a higher-dimensional space. When Harry and Ron go through the brick wall at the train

station in London to board the Hogwart’s Express on platform 2-3/4, they are just folding

themselves into a higher dimension. The mysteriously located Diagon Alley where Harry

buys all of his magical supplies and school books is nothing more than another three-


dimensional place that is attached to our normal Muggle space by the common four-

dimensional space, but this idea is not new to the Harry Potter movies. Dr. Who’s Tardis

(from the television series of the same name), which has an interior thousands of times larger

than its exterior, has been utilizing the same four-dimensional technique for several decades.

In these cases, you have a seemingly small volume of three-dimensional space on the outside

and a seemingly far larger volume on the inside. This discrepancy is just a simple matter in a

real four-dimensional space since each point within the three-dimensional volume of an

object is „stretched’ into a vastly larger fourth dimension.

However, one of the greatest Sci-Fi writers of all time was also one of the first to use a

fourth dimension of space. H.G. Wells wrote his famous novel The Time Machine in the 1890s.

In this story, he treated time as the fourth dimension which allowed the main character to

travel back and forth in time like normal people travel through space. Wells wrote this book a

decade before Einstein wrote his scientific paper on special relativity which unified space and

time as a four-dimensional space-time continuum. Wells was not smarter than Einstein,

although a very perceptive man, he was just reflecting some of the scientific ideas that were

being discussed in England at that time. Considering time as the fourth dimension of space was

well known among the best scientific and mathematical circles in Victorian England. However,

other short stories by Wells from the same decade are far more interesting.

In The Plattner Story, a boy’s school teacher finds a strange substance on the way to

school and begins testing it at school. It explodes and he disappears right before his student ’s

eyes in a puff of green smoke. The explosion sent him into an alternate part of our universe,

almost like a parallel three-dimensional sheet within our common four-dimensional extended

space. In this strange place, he could still dimly see his own universe and the people in it, but

could not communicate with them. There were strange floating head beings in his new

environment, mostly of dead people but some of the heads represented people still among

the living. The floating heads were more like four-dimensional embodied consciousnesses

than true spirits of just the dead. There was also a wall which he was drawn toward, but

would not cross because he felt that he would not be able to return to his own real world if

he did.

After some time in this parallel universe, he popped back into the normal world. To

everyone else, he had just popped out of and back into our three-dimensional space without

logical explanation. The only proof he had of ever having gone into another part of our four-

dimensional space is that his heart was later found to be located in the wrong side of his chest

and his right side had been exchanged or switched for his left. This reverse imaging is a

characteristic of a single polar Riemannian four-dimensional space, like the Klein bottle and

Möbius strip above.

William K. Clifford and other mathematicians in the late eighteenth century had argued

that the next higher dimension of space was single-polar Riemannian and Wells was merely

acknowledging their contributions to science by utilizing this geometrical feature of the fourth

dimension in his story. The strange land where he found himself was very similar to an afterlife

in a higher dimension from Wells’ point-of-view, but he never used the term „afterlife’ or

similar words. He allowed the reader to figure it out. Wells also used a four-dimensional

hypothesis for other stories, but these two are the most interesting. In both cases, Wells was


only extrapolating the consequences of applying scientific ideas that were commonly discussed

during the 1890s.

Conclusion

While the mathematical principle of higher-dimensional spaces is quite useful and their

popularity in physics has waxed and waned over the decades, actually visualizing them is quite

difficult. Einstein worked on a five-dimensional unified field theory in the 1930s, but eventually

abandoned the idea because he couldn’t understand how another dimension of space could

exist without our sensing or detecting it. Unfortunately, what he didn’t suspect is that we do

sense the higher-dimension with our ‘sixth sense’. Our normal five senses have evolved over

time as living organisms interacted within a four-dimensional space-time continuum, so they

are limited to three-dimensional space. If there were a fourth spatial dimension (a fifth

dimension of the space-time continuum) it would stand to reason that a special ‘sixth sense’

would have evolved or would presently be evolving to sense activity or interact within that

extra dimension.

Since the human consciousness is constantly growing and expanding and that growth may

well be a factor in our next evolutionary step, it would also seem probable that our knowledge

of the fourth dimension of space would play an important role in our next evolutionary step. It

is no accident that mathematicians discovered the abstract notion of a fourth dimension more

than a century ago and scientists are now beginning to take the concept seriously just as the

idea is becoming popular and even commonplace within our culture, as verified by the

popularity of the notion in SciFi stories. Human science evolves in step with human

consciousness and humans themselves, so why can’t consciousness evolve in lock step with

our knowledge of the true nature of physical reality? The ability to visualize objects in all four

dimensions of space in our minds could well help to force the next step in the evolution of

consciousness as well as human evolution.

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A New Dimension of Consciousness: Realizing and visualizing higher spaces

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