Archive for the ‘Week2_Mathematics, Perspective, Time & Space’ Category

Week 2 - to KNOW, by Jonathan Diamond

Monday, January 19th, 2009

                Before I begin, I would you like you to consider this story I put together: Imagine you’re an astronaut en-route to a far away planet never before visited by humans, when suddenly your ship crashes on another planet that was hidden in the shadow of an immense object, rendering it ‘invisible’.  You and your crew survive the crash, and find the atmospheric conditions of the planet able to support human life.  There exists only one problem, the planet has no moons or sources of light—it’s pitch black.  As you scavenge around the wreckage you find a flashlight and begin to search for intelligent life to possibly help you return to earth.  Suddenly, you come across a moving object that appears more like a blob with tentacles than anything else.  As you approach it you suddenly ‘hear’ someone greeting you.  After some inquiry and conversation you find out that it is this blob that is conversing with you.  As you come closer to this ‘alien’ you see it has no eyes, ears or mouth.  You ask, “How can you see in this darkness?”  The alien replies, “What is seeing, and what is darkness?” You explain, and it replies, “We on this planet have no eyes, we ‘know’.  There are no sounds or sights to interpret, we only “know” what is there and what isn’t.”


                Linda Henderson’s conclusion about the fourth dimension and the idea that art is ideal for the expression of what science essentially cannot express, is extremely appealing.  What does it mean to know? Humans see, hear, taste, smell and feel, but realistically, these senses are nothing more than different neurological sequences interpreted by our brain to produce the world we have come to accept around us.  But no one should be so bold as to say we ‘know’.  The fire truck that drives by only appears a certain color because our eyes interpret the electromagnetic energy that bounces off of it in a certain way.  The floor we stand on only feels as it does because the nerves in our feet feel something we consider pressure.  With this idea in mind, how do we know anything?  The answer simply is that we don’t.  Carrying this idea further, we as a species should never be haughty enough to say that just because we can’t sense/understand an idea, it doesn’t exit.  If a jelly fish were asked what exists outside the edge of the water (the land), it would reply that obviously nothing exists, it is just edge of the world.  Clearly the jellyfish, given its physical limitations, could never understand what lies beyond the edge of that water.  Humans need to apply this ideology to our existence.  What exists beyond the limitations of our perceivable world?  The first three dimensions are easily described, however, how can we possibly understand the many following dimensions?  Many describe the fourth dimension as space-time.  Clearly through our technological and physical limitations we cannot scientifically prove anything, however through art, the expression of this fourth dimension is much more easily conveyed.



These pictures help pictorially describe the first five dimensions:


This is a 3D projection of an 8-cell performing a simple rotation about a plane which bisects the figure from front-left to back-right and top to bottom—a tesseract rotating around a plane in 4D:


This is another method for an illustrative depiction of different dimensions.  Consider an ant that crawls on a piece of paper.  Relative to its position and its conscious understanding of the world it lives in the piece of paper is flat.  But from an outside perspective we know it is moving through much more than the first two dimensions. 

[I couldn't get these pictures to work, I intended to attach the two different pictures of ants crawling that appear near the top of the page]


To carry this idea further, assuming that space-time is the fourth dimension how can we possibly express the fourth dimension?  In the two previous pictures, there is generally only one perspective from a viewer.  Granted, the ant would have a different 2D perspective depending upon where it physically lies.  Yet, from a third person view, there is only one position—in other words time is held still.  Now consider the following piece.

This website describes finding dimensions very well:


                When considering history and the immense curiosity of human kind, it makes logical sense that when the idea of the fourth dimension was introduced, new genres of art surfaced.  Art did something that science could not—it took the curiosity of the mind, combined aesthetics and created a synesthetic experience that could not be attained any other way.  It satisfied the mind in ways that science could not.



Week2_In Four Dimensions This Blog is a Giant Cat by Eric Debbold

Monday, January 19th, 2009

Before I dive into multidimensional diction, I would first like to admit that I had no idea that art and science have been so vigorously intertwined over the last century.  I never would have guessed that there was such a scientific debate among artists and surrealists about the nature of the fourth dimension, incorporating the (at the time) cutting edge Einstein theories and conceptual mathematics.  I was surprised to learn that Dali was actively engaged in the struggle to depict the fourth dimension, but this article reshaped my view of many works, notably Dali’s Persistence of Time.
The melting clocks in aforementioned painting symbolize to me the struggle with a distorted view of the physical world along with a new perception of time.

Many people view art as a stagnant recycling of ideas, but when artists reinterpret their worlds by examining new scientific discoveries, this idea of art must be thrown out.  When the entire artistic community can be greatly influenced by Einstein’s Theory of Relativity, or by the introduction of new technology (illustrated by the new influx of graphic art and digital art) art will forever have new things to say and new ways to say it.

On to dimensions.  Like most people, I initially rejected the idea behind a forth spatial dimension, after all, what would that even look like?  After reading the assigned reading and many wikipedia articles on the subject, however, I felt like I was getting a grasp of the subject.  Think of a two-dimensional character, like Mickey Mouse.  To Mickey, the three-dimensional world is almost impossible to comprehend.  Lines that appear to intersect in Mickey’s world do not intersect in ours, as they can also move through the z-axis.  Thus an object that appeared to be on top of another in Mickey’s world would in fact not even be touching in 3D space.  An example of a four dimensional equivilant is the Klien bottle, shown here:

Thinking in multiple dimensions is also absolutely necessary in String Theory, because it allows certain physical freedoms that three dimensions prohibit.

The best way to explain the idea of a forth dimension is through analogy. Analogy is also the most useful way to think about quantum physics.  I learned last week that though electrons are not waves, they exhibit wave-like behavior, and by thinking of them as waves science has taken many steps in explaining how the world of the very small works.  Quantum physics, unlike string theory so far, has yeilded an exorbant amount of technical advances, most notably computing technology.  A family friend was recently telling me how he uses the concept of quantum tunnelling to devlope better flash-drives for your computer.  In this way analogies serve to create tangible results, not just semantic questioning.  In the quest to develope new and more useful analogies, art can play a huge role in science, as artists are masters of anaolgy.

Although this next link has a questionable connection to the reading, I thought it too cool and interesting to not share.  It helps to create what I think is yet another dimension of the human reality, what we call our inner eye or imagination.  In the physical sense there is no Imaginationland, but it plays a huge role in how we percieve our universe, not only in our sleep but in our interpetation of the raw electrical data sent to our brains.

Ok, so I know it might be a pain to pull out the headphones and close your eyes, but its quite cool if you give it a chance:

-Eric Debbold

Week 2: Mathematics Perspective Time and Space by Carmin Pelayo

Monday, January 19th, 2009

Whenever someone speaks to me of art, my first idea is the most archetypical one,  a medium sized canvas with a two dimensional picture painted on it; however, as I’ve come to learn, the concept of art has evolved way past that and according to Linda Henderson, it’s not a recent occurrence.  Her article about the fourth dimension is greater proof of the integration of science and art.   She speaks of the original idea of the fourth dimension as being spatial and consisting of non-euclidian geometry.



It was the paramount of most art because it gave artists the liberty to experiment with different ideas and have a crutch to lean on if questioned.  However, with the greater acceptance of Einstein’s claim of the fourth dimension being space was greatly debated and a manifesto was written in order to clear any misinterpretations.  I believe that this is one of the greatest things that could’ve happened;  it assimilated not only the idea of a temporal fourth dimension but the ability to incorporate even more “scientific ways” of doing art.  Whereas sculptures used to be still images of events, they began to overflow with fluidity, an illusion of movement, and movement can only be conceivable if there is time.  This gave many modern artists a new medium to work with.  For example instead of a simple exhibition of paintings or sculptures,  some artists such as Kenneth Huff use time-based projects to illustrate patterns in nature and many other different things.  A more famous example of these evolving time-based projects are animated fractals; objects that continuously spilt in which the pieces can be a smaller copy of the whole thing.

                These new methods also gave way for the use of math in art and the combination of all three.  In my own personal experience, in my calculus class we used the function of any graph and rotated it around the x-axis to make an object completely out of layered circles.  After finding the correct equation, you could break up the number of breaks, so pretty much just saying how thick they would be, and then plugged in the corresponding x value, solved the equation, and you got the radius of the circle you needed to make.  A way that this could be used is exemplified in Brent Collins “Vox Solis”

Another form in which mathematics is related to art is the golden ratio.  Ever since the Renaissance artists have created there paintings in trying to keep with this ratio, assigned the Greek letter phi (ϕ) with the numerical value of approximately 1.61803398… Leonardo da Vinci is probably best known for the continuous reoccurrence of this in his work such as The Vitruvian Man

 and the Mona Lisa.

  Apart from the fact that many believed it to be aesthetically pleasing, it is something that relates art back to something which naturally occurs in nature, most easily seen in the layout of sunflower seeds, as well as in something as ancient as the Great Pyramid of Giza. 

Week 2 - Dimensions by tung dao

Sunday, January 18th, 2009

The dimensions, something we all take either for granted or, as Otto Bretscher writes in his text, Linear Algebra, “is often poorly understood in popular culture, where some mysticism still surrounds higher-dimensional spaces.” Since we are trained to think of the world we live in as three dimensional, we have difficulty imagining the other dimensions, if there are indeed more. For everyday imagining, there appears to be no need for anything more than we perceive. Einstein brought forth the idea of time as a fourth dimension that we live in, but since that dimension is only a one way path (so far), we tend to ignore it as a dimension since we cannot freely move through it. As it turns out, dimensions are rather arbitrary and can be assigned to represent any number of things. The artists have their interpretation of it, as do mathematicians and physicists.

Artists in the 20th century have come up with novel interpretations of what this mysterious fourth dimension is. Dali, with his Persistence of Memory, portrayed time as clocks that have been melted away, freely along the surface that it rests upon. As Linda Henderson writes in “The Fourth Dimension and Non-Euclidean Geometry in Modern Art”, “…the fourth dimension was primarily a symbol of liberation for artists.” It provides an idea that can be represented in ways that has not been applied so far. The fourth dimension, in a way, was used as justification to enable artists to portray the surrealist world that is completely different from the one we live in.

In math, dimensions are not particularly as mystical as most people think. Most would be baffled by the higher dimensions when they are encountered for the first time. Questions such as “how does one graph something in a dimension higher than three on paper?” will arise. As it turns out, the dimensions are nothing more than variables, which are like inputs into a function to produce some number of outputs. Take for instance a function that will graph the average percentage grade of all the students in a class. If there is only one student in the class, the input variable will equal the output variable, producing a graph that is a line that is forty-five degrees to the horizontal. For two students, imagine a horizontal plane that defines the two grades of the students and above every point on that plane is another point that has the data churned through some function. The end result is a surface above (or maybe even below, but we would hope not in this case) the two input variables. However, graphing a function is only a way to help understand the nature of a function. In application, it is usually not necessary to graph all the variables since only the end result is usually what matters.

Physicists, the ones responsible for reifying higher dimensions to the common people, have come up with a plethora of what the higher dimensions are. Rob Bryanton’s interpretation of 10 dimensions is neatly presented in his video “Imagining the Tenth Dimension”. In short, dimension number four is time, beyond that are all the different possibilities of the universe and all the different possible universes, and the tenth dimension itself is all the possibilities that can happen. But he stops there. The ten dimensions of his make sense, but it is arbitrarily chosen to make sense for his purpose. Brian Green, in the PBS Special The Elegant Universe, explains there are a number of working theories of String Theory, and that the number of dimensions each theory predicts is different from one another.

It seems as though the number of dimensions that exist depend on the application and how dimension is defined. For most of us, we can safely live in our three dimensional world and know that we’re moving through an irreversible dimension we call time. Higher dimensions are nothing to be afraid of until some day in the future when the situation of the universe calls for it.

Tung X. Dao.

Two independent variables and a dependent variable can be represented with a 3-D graph

Two independent variables and a dependent variable can be represented with a 3-D graph

Week 2_Eyes of Salvador Dali by Cheng-Kuang Liu

Sunday, January 18th, 2009

I talked about golden ratio in my blog post last week, and it came up in this week’s lecture. It looks like I will have to talk about something else this week. (But golden ratio will also be briefly mentioned.)

I find it very interesting to learn about the development of depth perception in paintings through out history. Before the discovery of the vanishing point, paintings look awkwardly “flat.” ( The limbs of human figures seem to overlap and jam together and it looks really unnatural. Eventually artists intuitively started depicting depth, but not in a rigorous way. Their drawings show some depth but still seem skewed. This is because the artists have not fully realized how the human vision physically works, and the resulting paintings are not rigorously mathematically defined. It is not until the application of “single vanishing point” when paintings look “3-D” and realistic. For example, “the last supper” by Leonardo da Vinci is both a timeless classic and a perfect demonstration of “single vanishing point.” One of my most admired artists, Salvador Dali, is also a master with depth perception. His eyes seem to be able to even penetrate the objects so see their depths, and many of his works show such penetration (

In fact, Salvador Dali redrew “the last supper” himself (, also with extremely accurate depth perception. In a sense, he out-did Leonardo da Vinci in that Salvador Dali painted the room in which the last supper took place to be a hollow dodecahedron. When artists studied depth perception, this special spatial geometric object, dodecahedron, was of special interest. It appeared in Escher’s works ( It was further developed by Fuller. Actually, it is quite interesting even how one pentagon came about and that it contains the golden ratio. From a pentagon, with several additional simple dots and lines, one can draw the 3-D view of a dodecahedron. This solid is so particular that some find in it metaphysical interest and it even has mythological connections (note 1). Salvador Dali was able to reproduce this particular geometry, or in this case a fraction of it, very accurately. It shows his mastery with the depth of the structure. Such particular portrayal of the scene of the last supper definitely adds to the “3-D-ness” of the entire painting, and it looks very convincing. The room’s being a dodecahedron rather than a rectangular box also enhances the otherworldly flavor of the scene, and it made the room seem a lot brighter, as if it is glowing with mystic glory. Finally, many of the objects in the painting are semi-transparent, as if many dimensions blend together, thus adding even more of the mystic feel to the whole scene.

Fractal art is also found in Dali’s work ( In this nightmarish piece of work, “Visage of War,” Dali portrays the never ending and ever repeating pain and torment of war. The usage of fractal fits very well with this idea: when you zoom in, it is the same horror, and when you zoom out, it is still the same horror. This piece of work is not geometrically rigorous to be called a fractal, but perhaps its distortion and its deviation from rigorous geometry conveys the distorting torture all the better.

Note 1:

Week 2: The Fourth Dimension in Modern Art by Roger Call

Sunday, January 18th, 2009

Since the 1930’s, modern art has evolved and transformed as the social norms of society have become more liberal and accepting towards extreme abstract thinking.  During the early 20th century, Einstein’s Theory of Relativity lead to a general dissaproval of the exploration of the fourth dimension.  Even the artists of this era did not push the presence of “deep space” as  Henderson claims.  Clearly, this “deep space” was like uncharted territory and surprisingly this subject was left untouched until the later 20th century.  Modern art seeks to explore and utilize this “deep space” to a great extent, pushing the limits of imagination and perspective.

What is this “deep space?”  Henderson describes it as the boundary that which the artists of the early 1900’s would not cross, but what really is this “deep space?”  Deep space could be a synonym for the fourth dimension, which could be described as the exploration of time and space.  In my opinion, deep space is the depths of the human imagination.  These depths do not necessarily relate to any aspect of society, nor must they make sense, but rather as close to raw imagination as possible.  These thoughts do not have to be even coherent, but just bits and pieces, even color or patterns.  These thoughts can be either emotional or intellectual, even combined with physical memories of the senses.  All of these combined create this “deep space” each and every one of us have within us.  Artists such as the cubists and surrealists and dadaists of the past expressed some of these thoughts and thier works.  Modern works such as this piece, which resembles that of fractal art, explore the depths of deep space.


Not only did Einstein’s creation of the Theory of Relativity dampen the imaginations of the early 20th century artists, but it was one of the first occasions in which science directly affected art.  As we have been exploring in class, as science and art become more advanced, they eventually become the same as scientists discover their experimentation and theories resemble artwork, and artists work tend to incorporate ares of science.  This fractal art of the modern age shows this trend in action, and as we continue to progress as a race, art and science, evolving for centuries, from the days of the dinosaurs and throughout the 2oth century and into the future will ever approach the art as art approaches science.

Week 2

Roger Call

Section C

Week 2 _A Fourth Dimension? by Joseph Duy Nguyen

Sunday, January 18th, 2009

The article “The Fourth Dimension and Non-Euclidean Geometry in Modern Art: Conclusion” by Linda Dalrymple Henderson brings up the intriguing idea of what constitutes the fourth dimension. After Einstein’s Theory of Relativity was published, many people came to accept the idea that time is the fourth dimension. However, there are many others who still think that time is only a part of the larger idea of a fourth spatial dimension. This notion of a fourth dimension may never be solved due to human’s limited ability to comprehend something that cannot be seen such as time. Scientific calculation has proven Einstein’s Theory of Relativity to be correct. But once again, it is only a theory and can be disproven with further facts such as with Newtonian physics.

The idea of time being the fourth dimension brings up a lot of speculation on what is possible. If time was the fourth dimension, then time traveling would no longer be an impossible dream to mankind. Just like going forward and backward is possible for the three spatial dimension, going forward and backward should be possible too if time was to be the fourth dimension. This idea of time jumping brings up a problem that makes time seem unlikely to be the fourth dimension. Suppose a person named James goes back in time to kill his grandfather before he married his grandmother. In a logical sense, James’s father would not exist, and neither would James. Therefore, James could not have gone back to kill his grandfather. This is just one of many paradoxes that exist if time was actually the fourth dimension. These impossible situations can only be solved if the theoretically alternate dimension exist and could be proven. Another theoretical thought is that humans will be able to travel to a distant planet such as Neptune if Einstein is indeed totally correct with his Theory of Relativity. Since space is curved according to Einstein, then distances are really longer than they really are in reality. The fastest way to get from point A to point B is to go from point A to point B in a straight line. Therefore, humans can travel to distant planets by figuring out a straight route from Earth to the planet. Below is an illustration to make this concept easier to understand.

The idea of a fourth spatial dimension is somewhat incomprehensible as well. Interestingly, if the fourth spatial dimension is to follow the guideline according to the other three dimensions, then the 4-D figure would be otherworldly as discussed by Cliff Pickover (1). For example, a 2-D figure is a sheet of paper and a 3-D figure would be a human. The 2-D figure would only see cross-section of the 3-D human. Similarly, if human, a 3-D figure, views a 4-D figure, we would only see cross-section of the 4-D figure. We would not be able to comprehend the 4-D figure because we are constrained to only 3 dimensions. Another radical thought would be that the fourth dimension figure would be able to remove body organs from our body without ever making an incision on our body. Suppose a marble is bound within a 2-D square. From the square perspective, there is no way for the marble to be removed from the square without making a break in the square itself. However, a 3-D figure like us, could easily move the marble into the third dimension by pulling it upward out of the square into the third dimension. Thus, from this idea, a 4-D object could possibly remove body organs from within our body without ever making an incision on our body. This idea is not necessarily impossible but difficult to perceive because of our limited imagination. Our perspective is confined to our senses. Only by removing the restrictions on our human senses can we possibly understand the fourth dimension.


-Joseph Duy Nguyen

Week_2_Art and Mathematics_by Nikolaos Mouchtouris

Sunday, January 18th, 2009

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Math and art are the basis of two different worlds, the scientific and the artistic one respectively, which when combined, they can generate a more accurate representation of life. Even though, I am a science major, learning endless equations and theorems have no real-world application. I truly admire Albert Einstein and I am fond of his theory of relativity, but I doubt that anybody has ever realized a time dilation in his life. Perhaps for a common person who does not have any interest in learning scientific theories, the theory of relativity and the time being the fourth dimension is as abstract as a Picasso painting. However, their combination into something that actually attracts people and influences them is what makes pure science and fine arts, because that way they actually influence the people. A simple example from the lecture to simplify this is M. C Escher’s work which really impressed me as he integrated perspective in his paintings in a way that is very scientific. His work “Circle Limit III” is accurate to the millimeter and his other work, shown in class, “Ascending and Descending”, he presents his own “artistic theory” of relativity, indicating how perplexed and mind-boggling the theory of relativity is.

Personally, I find Escher’s quote, “I have often felt closer to people who work scientifically (though I certainly do not do so myself) than to my fellow artists.” very significant because he is a distinguished artist, dedicated his life in art, yet he realizes the importance of respecting and co-operating with the other “side”, science. For him, science is a different way of looking at life, a contradicting point of view, yet he admires the way scientists work and think, because it perhaps complements him. Moreover, going back to the first week’s topic, this quote brings up the necessity for a third culture, one that combines both art and science, resulting in a more clear view of how things work.

Believing in the union of mathematics and art and not admiring Leonardo da Vinci is impossible. Da Vinci is the first example of an individual who with his work proved the importance of this fusion of these two different aspects into one. He compromised art, science and technology of the time into his works, resulting into revolutionary paintings, structure and devices. Not only being a perfect example of the third culture, he used science in his work in a way that both impresses the viewer but also manages to convey a deeper message.

It has become apparent that knowing about math and art regardless of the major each individual decides to follow is imperative because what we see around us, life in general, is not just black and white; let’s not forget of what is in between. Besides, most people have a single approach in life which they use to interpret the world around them, but the individuals who distinguish are the ones who not only have one approach, but two, trying to see the world from two different perspectives at the same time.

Today, it is surprising what man can do with technology; Da Vinci’s most famous painting is Mona Lisa, which probably took him a lot of effort and time to create it, while now it is possible to recreate it in a bit more than two hours.


Nikolaos Mouchtouris

The Golden Ratio in Music & Beyond - by Ricky Irwin

Sunday, January 18th, 2009

Of the variety of mathematical concepts of time and perspective discussed by Professor Vesna this past week, the theory of the golden ratio captivated my interest. If I hadn’t ever been exposed to the ratio, phi or the Fibonacci series before the lecture, the ideas presented by Ms. Vesna would appear extraordinary and on the verge of implausibility. Such an idea of a golden ratio ubiquitous throughout art and science over all time seems more suited to the plot of trite Hollywood blockbusters like The Number 23, The DaVinci Code or National Treasure instead of actual mathematical studies. From architecture like the Taj Mahal or the CN Tower, the usage of the Divine Proportion by Renaissance artists like Leonardo da Vinci, human anatomy such as faces or even the heartbeat, down to the minutiae of phi integration such as the shape of credit cards, the golden ratio seemingly surrounds humans in almost every aspect of beauty, perfection and aesthetic.

Often I take interest in transposing the rules and structures of science and art to the methodology of music and seeing how the three interrelate. In this case, Professor Vesna’s insight on the golden ratio led me to investigate as to whether such a far-reaching ideal has its roots within the sense of perfection within sound and music as well. As I expected, much of western music is founded on phi as well.

Through several charts, it was explained that musical scales are based on the Fibonacci numbers, and that musical frequencies are based on Fibonacci ratios, and that pure Fibonacci relationships can be explored through plucking and touching strings on a guitar without touching the frets. The compositions of music can also be dissected to find phi, as the climax section of songs can on average be found at the phi spot, about 61.8%. There have been theories that composers of classical music such as Mozart also integrated the golden ratio in the composition and arrangement of his sonatas.

Additionally, it has been hypothesized by H.E. Huntley in his book The Divine Proportion that the golden ratio goes even further in music into appearing in certain intervals of notes. When two notes of the same frequency are played at the same time, or in unison, it is perfectly consonant and its period of time in its rhythm is the same proportion as the period of time the human eye takes in viewing a pefect square. Also, the major 6th interval is supposedly the most pleasing, since it reflects a ratio of 8:5, or a golden ratio of 1.6. Even musical instruments are constructed with the golden ratio in mind, such as this violin:

It is easy and automatic in art or music to analyze beauty and style through an artistic mindset, through critiques based on influence, genre and innovation. However, as I’ve seen through this exploration of the golden ratio, math may be often forgotten in analyis but is an intrinsic foundation for all art, music and beyond.

Week 2 Blog on Where the “Fourth Dimension” Came From by Sara Captain

Sunday, January 18th, 2009

For every action, there is a direct and deliberate reaction. So, as long as society drifts toward one trend, an opposing and reactionary trend is bound to develop, whether it be big or small, abandoned or extended, correct or incorrect. The example that comes to mind at the moment is that of two nationalisms in Middle Eastern history; as the Zionist movement gained momentum, the native inhabitants of that region of the world was forced to have an opinion on the issue because it inherently involved them and their homeland. For this reason, Arab nationalism was created in response to Jewish nationalism in the area. Another and perhaps more relevant example is the invention of the number zero; when civilization began assigning numbers to quantify, there eventually needed to exist the opposite of quantification, which is null, or zero. Before the institution of religion, there was polytheism in its undefined form, which was simply a spiritual and traditional way of life and recognition of higher entities human beings felt; then, when monotheism appeared, this feeling became known as the contemporarily controversial and troublesome issue we call religion. In this same way, the pattern society has been taking toward a world where everything is more defined, labeled, and categorized by words and artwork, there naturally needed to be an opposing view in which no object is necessarily defined or even there. This view is now known as the Fourth Dimension, and it is as revolutionary in its context as in its limitless content.
The 19th century birth of the Fourth Dimensional perspective was revolutionary because of the definitions -or lack thereof- that it proposed. But at the same time, could we simply be assigning words and artwork again in order to express the opposite of an idea already well-known to society, which is this practice of assigning specific material definitions itself? As human language strives to keep up with human progress, we are constantly attempting to identify each idea and express it so that we can communicate it to others, whether it be via words or artwork.