Archive for the ‘week_2_math_perspective_time_space’ Category

Week 2: Math<3art

Sunday, January 18th, 2009

           Math is everywhere, it is in everything, and it is used every day; therefore it is not mystery that math and art go hand in hand. As it was expressed in lecture math plays many parts in art especially with the concept of zero, perspective, the Golden Ration, and dimensionality. Mathematics is used by artist and scientist alike to further expand their perspective of life.

A very important mathematical and scientific feat, thought of by Albert Einstein that greatly affected the artistic world is that of the fourth dimension; this idea as expressed in “The Fourth Dimension” was a “liberation for artist.” The Fourth dimension allowed artist to move away from basic linear and realistic drawing done on canvas and it moved them into more of sculpting and physical art forms. The idea of the fourth dimension allowed artist to elaborate on things they believed belonged in the fourth dimension such as: gravity, non-gravity, spiral, airlessness, synthetic forms, shadows, mirrors, and etcetera.  The fourth dimension is expressed in various art forms such as writing and sculpting. Writers such as H.G. Wells, Edwin Abbot, and Charles Hitton dabbled with the Fourth dimension. H.G. Wells’s The Invisible Man and Charles Hitton’s writings are the best expressions of the idea of the Fourth Dimension.  The fourth dimension is also expressed in paintings and sculpting. Kazimir Malevich’s “Suprematism: Soccer player in fourth dimension” is a painting of various different color squares in which one is looking at a soccer player (in all honesty I don’t see it but it’s a good example because he was one of the founding artist). malevich97Moreover Adam Chou’s “Fourth Dimension” is a stone nose looking sculpture that is different in every single direction you see it and that is supposed to represent the fourth dimension. Einstein’s theory of relativity translated into the fourth dimension which greatly impacted the artistic and scientific world; however there were other discoveries that helped the artistic world develop new artwork.4th-dimension

The Golden Ration and the number or non-number zero.  The Golden Ratio can be expressed as 1.6180339887498948482 or as phi. The Golden ratio is a natural ratio that is seen in nature and is the most appealing to the eye. Because the golden ratio is the most appealing to the eye it has been naturally included in art. In architecture the golden mean has served to make the Parthenon in Athens and even the great pyramids of Egypt by creating structurally and decorative proportions of these structures. Moreover, the Golden Mean has been used in some of the most famous paintings of all time such as “Dance at Bougivial” by Pierre-Auguste Renoir, or “House of Parliament” by Monet, and Salvador Dali’s “Persistence of Memory.” dali1houseofprenoirNot only is the Golden Ration a revolutionary mathematical concept for art but so is the number zero. The number zero is a fairly new number considering it was just taken into consideration in the sixteen hundreds but in the beginning when it was just becoming well known artist considered this number a new art project. The idea of zero is very similar to infinity and sometimes they are even used interchangeably by people, therefore Helaman Ferguson took this knowledge and created this sculpture “Zero to Infinity in Nothing Flat.” ferguson21Moreover, this new art of Fractals also considers the number zero in its makings as is expressed by Pollock’s Fractals. The Golden Ratio and Zero are two well known mathematical concepts that are amazingly being mixed into art when it would seem that neither should blend together.

Math is a subject that relates to almost everything in the world, but what is more amazing that this subject can be translated into beautiful art work when it is mere logic and patterns. The idea of the Fourth dimension, the Golden Ratio, and Zero are all very strong influences for art work of various different forms such as architecture, literature, painting, and sculpting. This just goes to show that two things such as water and oil can mix.


Dafne Luna


Sunday, January 18th, 2009

This week Professor Vesna talked about the number zero. She described it as inciting a revolution in the world of mathematics. The kind of revolution that tested the mettle of math adherent. One slide in particular caught my eye, because it said (0=infinity) which would explain how a simple number such as zero could be such a revolutionary new concept in math. The number zero is very simple to explain and understand, but its inverse - infinity - is an intangible number and that is what complicates matters.

This weeks assigned reading dealt with the fourth dimension - an equally abstract concept, when you think of it as a spatial dimension and not as time. Abstract concepts are where art and science meet. Thinking about these concepts got me thinking about the two cultures again. Last week we discussed the two cultures and how there is a divide between the people in the art world and the people in the scientific community. I agreed that such a divide did exist and, in my head, I had a clear mental picture of the two cultures and the divide between them. I imagined a wheel with the root of knowledge at the middle and various fields were spokes on that wheel. As one progressed down the spoke of a given specialization, be it art or science, the distance between the spoke on which one found one’s self and the adjascent spoke grew. Ironically, visualizations - of abstract concepts, more specifically - is where, I believe, art and science begin to rejoin.

At the forefront of science, researches are often confronted with very abstract concepts. From ephemeral nano-scale particles to dizzying numbers of dimensions, scientists are tasked with making these abstract concepts tangible to the layman using media. This is important, because scientist rely on the discoveries of the scientists before them, by making a discovery accessible and easily understandable through effective communication, it creates a solid foundation for tomorrow’s discoveries. Effective communication is also a cornerstone for art, as most artists, especially modern artists, have always sought to express the intangible through media. It is the artists who find or develop a technique or medium to effectively communicate their message, that are remembered as being luminary artists. The scientist and the artist are no longer divided, but rather share a very similar quest. The scientist strives to achieve better science through the use of art. The artist strives to achieve better art through science.

Enrico Mills

Week 2 - The Fourth Dimension and Other Unknowns by S. Mercier

Sunday, January 18th, 2009

Reading this week’s article I was completely confused. I’m not an art, science, or math major; I am a psychology major. The words fourth dimension, non-Euclidean geometry, and many of the other words used in this article don’t mean much to me if anything. I had never heard of most of the people mentioned in the article so when the author tried to explain art inspired by non-Euclidean geometry in terms of Kadinsky and Picabia confusion ensued.

And so I sought the help of google. Wikipedia says (not the greatest source, I know, but good enough for this purpose):

Such a space differs from the familiar 3-dimensional space that we live in, in that it has an extra dimension, an extra degree of freedom. This extra dimension may be interpreted either as time, or as a literal fourth dimension of space, a fourth spatial dimension.

Reading back on the article, the author refers to the fourth dimension as both a spatial dimension (mostly in the beginning) and time (more at the end). But what does this look like? The article doesn’t explain what exactly a fourth dimension is or looks like. The only dimensions I can think of are depth, length, and width or X, Y, and Z on a plane. But according to Tetraspace, a website dedicated to the fourth dimension, “The fourth dimension is all space that one can get to by travelling in a direction perpendicular to three-dimensional space.” Still, this explanation doesn’t do much good for the visualization of a fourth dimension. So I searched for a good example of a 4-dimensional object and found the tesseract (see below).



It looks like a cube with a smaller cube projected inside of it and it kind of reminds me of those squishy things filled with water that when you grabbed them they fell out of your hand (water wiggler or water snake). But of course, how did the fourth dimension figure into art?

I found a website dedicated to the fourth dimension and art and stumbled upon a painting by Duchamp, an artist mentioned in the article. I remembered it from one of the TA’s presentations on Thursday.

Nude Descending a Staircase, Duchamp, 1912.

Nude Descending a Staircase, Duchamp, 1912.

The painting is meant to depict a body going down a stairs in various stages. In the article, there is a good quote by Oscar Dominguez that I think helps explain this painting:

“Let us imagine for a minute any three-dimensional body, an African lion for example, between any two moments of his existence. Between the lion L0, or lion at the moment t=0, and the lion L1 or final lion, is located an infinity of African lions, of diverse aspects and forms. Now if we consider the ensemble formed by all the points of lion to all its instants and in all its position, and then if we trace the enveloping surface, we will obtain an enveloping super-lion endowed with extremely delicate and nuanced morphological characteristics.” -P.208

Applying this quote to the Duchamp’s painting, we can say that the first image of the nude is N0, or the nude at t=0 and the second image of the nude is N2, or the nude at t=0, and so on. The depiction of all N images results in the painting above. From this quote, I also began to understand the fascination behind sculpting the movement of a falling leaf.  However, as the article asserts, this view refers to the fourth dimension as mostly time and not the spatial dimension that is referred to in the beginning of the article.

There was a quote on The Fourth Dimension, a website dedicated to The Fourth Dimension in Art, which I found interesting:

Some have defined the elusive fourth direction as time, but even though time is a direction of sorts, time is more of a function of the fourth dimension as opposed to its definition. Because of the nature of a ‘new space’, we may be able to see it only as a time-based phenomenon.

It suggests that the fourth dimension is in actuality a spatial dimension that can only be perceived through time. This quote clarified helped me visualize, along with the examples above, the notion of the fourth dimension. It is a dimension beyond our three-dimensional reality. It is as the author contends, subversive to our notions of perspective.

-Stephanie Mercier


Sunday, January 18th, 2009

In this week lecture, it was clear to see that science and art cannot exist without one another.  Both are intertwined at the beginning.  When science is broken down, it is seen as a series of mathematical equations, or chemical reactions but little do one notice that it is all art.  Science describes the existence of art, and science cannot be pictured without art. One day I am going to be studying medicine and as I think about the medicine it takes to keep one alive, I realize that medicine is an art but medicine has always been a science.  This site helped me do some extra reading on different perspectives on the two views and one of the references that I used was the Brittanica Encyopedia.


During the European bubonic plague epidemics of the 14th century, the art practiced was “bleeding” the plague victims. Not every one could bleed the patients, some could bleed them too much or too little. The rationale for this was based primarily on the teachings of the Greeks Hippocratus. It was felt that the human body had four humors — blood, phlegm, yellow bile, and black bile. Each humor came from a specific organ — blood from the heart, phlegm from the brain, yellow bile from the liver, and black bile from the spleen. As long as one’s bodily humors were in equilibrium, one was in good health. Illness occurred if one’s bodily humors reached a state of dysequilibrium. The medieval physician’s role was to restore this equilibrium and he did so by recommending rest and diet, and if this failed, he would proceed with various forms of bloodletting. Medicine at the time was based on Greek theory and philosophy rather than scientific observation. Physicians seemed to make no connection between the abnormally large number of dead rodents and the subsequent development of the bubonic plague and were ill prepared to have any effective impact on the recurring plague epidemics.

One effect of these repeated bubonic plague outbreaks was the development of the “scientific method” which began at the University of Padua in the 15th century. Human dissection was occurring and, as a result, human anatomy was becoming both more accurate and important, as was surgery. The emphasis in medicine was changing from philosophy to practical physical science and anatomy. It is felt that practical surgery and anatomy were, at least in part, an important component in the development of the scientific method. The scientific method consisted of identifying a problem, postulating a hypothesis, testing the hypothesis by (most importantly) observing and experimenting, and then interpreting the data and drawing a conclusion. This became the basis for modern experimental science and in turn the basis for modern accurate medical science.

During the late 19th and early 20th centuries, Sir William Osler was recognized as one of the greatest medical teachers of all time. He strongly influenced the organization of the clinic at Johns Hopkins Hospital in Baltimore and perfected teaching medical students at the patient’s bedside. He taught them the art of medicine utilizing the stethoscope, physical exam, and patient history with “the patient as his text.” This possibly was the art of medicine at its finest. The medical pendulum is swinging from the art to the science side. However, in my opinion, the best clinician is one that uses both art and science, armed with his scientific knowledge, practices using excellent clinical judgment (which of course is his art). Compassion and understanding are a large part of this art.

By Julie Pham

Nicolas Nelson Sec1A, Week 2

Sunday, January 18th, 2009

Nicolas Nelson Sec1A, Week 2

Math is fundamentally known as the purest science and the scalpel of technology, but in my opinion, from the third culture’s viewpoint, also an unmistakable art. A disciplined study it may be, but isn’t nomenclature and convention a kind of art, and it’s the unique uniformity that make linguistics an art. Aspiring transcendentalists may claim that it’s also representative of our many worldviews and one underlying truth (and according to Emily Dickinson, truth = beauty)—several methods, one answer (as Adam put it). Or more; many mathematical issues are still up for debate. There is something intrinsically artistic about representing practical applications with axes and origins, representative of an ideal situation with certainty against chaos. The universe is nothing but trajectories and probabilities—four forces in constant interaction that drive all things exactly how each moment in the known and speculated history of everything. In fact, the fourth perceivable dimension (mathematically, the t-axis) determines the existence of derived “moments” in the first place. And isn’t there beauty in a complicated sheet of integrals and radicals? Or even more in understanding the diverse jumble? There are many names for one thing i.e. log 1 = 0x = y – y = zero = nothing. And though 0 isn’t a “natural number,” its properties still permeate the real world i.e. 10^0 times anything will yield the same intensity, no matter how many sponsors you have if none contribute anything you raise no money, equal credits and debits negate one another.
Perspective is science that enhances art, or was it art that enhanced science? Though al-Haytham was a scientist, the first truly accurate usages of the equations now used to aim laser beams and reflect images of different planets were for the realism of paintings. One master of perspective—also of science, art, and technology—was Leonardo da Vinci, one of my few heroes as far as accomplishments go. He was a true and literal Renaissance man—“the” one—and he enlightened the world of another aspect of aesthetic beauty buried beneath mathematical mysteries—the splendor of space.
The golden ratio determines all from what’s attractive in a human face to the radial and standard symmetric growth of trees. Phi = φ = (1 + √5)/2 determines a lot in nature, as an understatement. Isn’t that beautiful enough—a common denominator that’s actually a number (albeit—or maybe, especially—an irrational one)? Of the eleven suggested dimensions in this universe, it’s fascinating that one number has such an influence over living material across the first three.
As for the fourth, time is an especially exquisite creation, if you believe in any sort of intelligent design. Regardless, we mortals get to enjoy this dimension in a way that we cannot the others; time and the circumscriptions it mandates not only allows us to experience different parts of the same reality while being the same “self”—rather, a dynamic self—but also challenges us to appreciate what we have for its brevity. Art may be an attempt to eternalize something abstract and fleeting, but all things, even physics, is bound to end sometime. Time and deterioration is truth. Life implies death implies art, science, and technology to make a splash while we’re here. There’s an edge we have on any God who is out there.
P.S.: Sorry for my blogs’ link-less-ness; I still need to ask my TA or someone how to do it again. Technology apparently isn’t my forte.


Sunday, January 18th, 2009

The Fourth Dimension

The notion of a fourth dimension is extremely interesting, but it may be awfully mindboggling as well. Having lived our lives with the knowledge that only three dimensions exist, and thinking that we only interact with three dimensions, trying to comprehend a fourth dimension is no small task and will take much getting used to. There are two prominent, leading schools of thought spearheading the search for the fourth dimension. One side advocates time as the fourth dimension, whereas the other proposes that the fourth dimension is also spatial.

Personally, I believe the fourth dimension is time, because as time goes on, people and events change. For example, consider two people setting up a meeting to discuss a project for school. In order for the meeting to take place smoothly, they must specify a location and time. This demonstrates that time is an important parameter in describing events. We incorporate this fourth dimension into our everyday lives without even realizing that we are doing so. This is simply because we have never thought of time as a fourth dimension since it is an abstract concept. But once I started thinking about time as a fourth dimension, it made perfect sense to me. After all, for one thing, I have known this fourth dimension all my life without realizing it. For another thing, time plays such an important role in our lives and governs almost everything that we do.

However, there is another branch of science called Euclidean geometry that claims the fourth dimension is spatial. In this branch of thinking something called a tesseract is introduced. A tesseract is a four dimensional cube capable of manipulating space so that it changes into another shape or form. This means that space may change into four dimensions. This idea of a fourth dimension is much more difficult to comprehend because we have never thought of space in this way. It is much harder to imagine space having four dimensions because we are accustomed to looking at three-dimensional objects. Tesseracts and higher dimensions have been explored and discussed even in children’s books such as “A Wrinkle in Time,” in which there are tesseracts of the fifth dimension. Clearly, the concept of higher dimensions is not a new field or idea, and many people have been very interested in pursuing it.

Another concept of higher dimensions is that of bounding volumes. This means that everything has a lower dimension bounding and containing it. A square is contained by four edges, which are lines of a lower dimension. A cube is contained by six squares, which are shapes of a lower dimension. In order to imagine a fourth dimension, one would have to imagine something contained by three dimension objects. Now this is nearly impossible to do for someone like me, because I already have problems trying to visualize three dimension objects in space, but for something with better spatial capabilities, this might be more feasible for them to do.

Whichever the fourth dimension really is, whether it be time or space, chances are that it will soon be discovered and proven. Until then, one can only speculate and indulge in his or her own conceptions about the fourth dimension.

Wen Wu

Week_2 - Art and Mathematics & Science as One

Sunday, January 18th, 2009

In Victoria’s lecture on Monday, people such as Escher were really interesting to me. He never even considered himself a scientist or mathematician, yet he was convincingly able to create art with a brilliant sense of perspective. Escher’s art consists of pictures that consist of physical impossibilities that are somehow possible in his artwork. One example was of the two hands that are drawing each other, breaking the fourth wall. Another example is his works with transmutation, such as the one with ducks turning into triangles turning into fish. Another one of Escher’s work that I thought was interesting was this one where he is looking into an mirror-esque orb and the reflections seem to be really precise.


I’ve always thought of math and science as separate entities from art. Sure some artist could use mathematics to create art, but I’ve had a pretty clear distinction and mental image of a scientist from an artist. After week 2 and the discussion of “Mathematics, Perspective, Time & Space”, and especially after all the TA’s presented their works to the class, I don’t really know why I always felt the need to separate scientist from artists. There are many scientists that have an artistic side as well as artist that find the sciences interesting. After hearing about the history of the TAs, I’ve learned that computer scientist are now working in architecture, John studying biology in undergrad and now working with digital design in grad school, and Rangan who is now making Wii-related games to help people with Parkinson’s disease. It is really nice when people combine different focus of studies and make something useful for others to use.

One of the links I looked at was about pavement drawings by Julian Beever. What struck me the most about the artwork is how pavement is an everyday two dimensional surface that people spend no time thinking about. And yet Julian Beever, through his chalk drawings, has somehow turned pavement into a medium through which the second dimension intersects both the third dimension, as well as the intersection between artwork and reality. For example, one of the drawings consists of a lily pad pool with a real-life girl standing in the middle. The striking thing is that angle through which the picture was taken; the girl looks as if she has become a part of the artwork, despite the fact that the lily pad pool is only in two dimensions (more on this artwork can be seen at: The final link I looked at was called algorithmic mathematical art by Xah Lee. I liked how he used computerized graphs to create his artwork. Although they were just mere graphs, they looked very appealing to the eyes. This just further shows how mathematics and science can also be art (more on this at:


About the reading, I thought the introduction of the fourth dimension was really interesting as it gave artist more ways to create art and express themselves. From what I’ve learned, the 4th dimension can be seen as time and artist have their own interpretations on how to express this fourth dimension. The art form relied on a mathematical and scientific approach and could be considered very abstract. These “pioneers” were considered very “avant-garde”.

My experience at UCLA so far with respect to art and science is pretty much my major versus GE classes I want to take. If I wasn’t required to take GE classes, I doubt I would have ever taken desma9. It is interesting to study art though because I’ve always considered art to be more of an subjective thing while science to be objective. Thinking back to my high school days where I took 2 years of art classes, it was actually one of my favorite classes because it was the least stressful and just time to relax and just draw, paint and many other art related things. Many of the things that were done in high school art were loosely math related such as working with vanishing points and linear perspective. After we got perspective down, we were able to convincingly draw a street with buildings that were realistic.


By Arthur To

Week 2: Art derived from Science and the Significance of Interconnectivty

Sunday, January 18th, 2009

In my post last week I discussed my art’s dependence on technology. I use scientifically developed and engineered tools to make my designs a reality, without which I would have nothing. Victoria’s lecture exemplified several similar cases where the creation of art was invariably aided by science, or more specifically, mathematics. Ironically enough, it was an eye-opening experience to learn about other artists who similarly depend on science to create their art. However, I had never been directly exposed to the concept of art being derived from science. In my art, science is just a means of expressing what I’ve already created in my mind. However in the examples she presented, such as “Process 6” created by C.E.B. Reas, they find their content and, in my opinion, partially their meaning in science. I see this meaning being directly rooted in the flow of logic found within many scientific structures such as mathematics.

Image derived from "Process 6" by C.E.B Reas

The concepts I had previously been introduced to, concepts such as the golden mean, found significant value in the creation of my designs, but I never really considered the implications of using a mathematic ratio to determine perspective and scale in my designs. It was just kind of a rule that had been given with no attention paid to its origins. Now looking back at its source, found in Phi and the Fibonacci Sequence, I can see a truly significant connection between the laws that govern science and the principles that govern art. The correlation between the innate design found in nature and the created design found within an artist or scientist’s work is undeniable and according to Henderson’s article, can also be traced through history. I was pleasantly surprised to learn that at the same time as Einstein and the scientific community were searching for the answer to the fourth dimension, the artistic community was also following and being influenced by these same pursuits.

With regards to my own experiences within the theatre department at UCLA, I have found a much juxtaposed world. On one hand, there are countless examples where art is very isolated from technology, seemingly on purpose as if to maintain a sense of purity within the art. Certain professors feel that no amount of 3-D CAD animation can ever truly equal a skilled hand watercolor rendering. At other times as I mentioned before, technology and science are the only way things can happen in my work. There are classes where we are taught CAD for example, classes that would parallel, though on a simpler plane, those found in the engineering school. There are also classes specializing in structural dynamics and simple mechanical engineering, such as for scenery design and construction.

However even with these divisions, I know that my department is much better connected than most. I have friends in the engineering school who mention people who never come in contact with any sort of art outside of their few required GEs. One only does what is necessary for success when a specific goal is desired. I think that this narrow perspective may be our greatest challenge in the arts and science, one which the individuals we have discussed in the class thus far have sought to overcome. They seek connections in that which seems unconnected and express that which is known in new unpredicted ways. I believe this level of unconventional analytical thought is crucial to all substantial progress.

By Sohail e. Najafi

Week2 - The Failure of Math/Science and Art - Simon Wiscombe

Sunday, January 18th, 2009

Something has been pestering me about the entire conversation we’ve been having about Math/Science and its influence in art, something which, until now, I’ve been unable to place my finger on. We are constantly shown examples of artists who have used science and its influence to further their work and, likewise, some scientists who have used art to influence themselves; this is precisely the problem.

Slightly referring back to the two cultures, the class has been shown numerous examples of art and science influencing each other, and how such an event is marvelous because it blends the math/sciences and the arts, but I argue that it doesn’t. In fact, this does nothing to further the separation between the two. Simply having knowledge in the one or the other doesn’t tie the cultures together. It doesn’t open communications effectively, nor does it eliminate the problem between the two. Deriving art from knowledge of math/science and, likewise, deriving science from knowledge of art has been happening for decades and it has not furthered the relationship between the two. Rather, I would argue that USING art to CREATE science, or USING science to CREATE art, is the true blending of the two, and the direction in which both fields must strive toward.

To illustrate my point, I will use some examples. In class, we have been shown the idea of perspective coming, slowly, to paintings. This is not a blending of the two. Rather, artists simply used the discoveries of physics to further their art.

Not blended cultures.

Not blended cultures.

But what, then, is an example of a complete blend of the two cultures? I would argue that recently developments in CGI, for example, are such an example. Specifically, an Associate Professor at UCLA, Joseph Teran, has used algorithms he has developed in numerous special effects, including the tentacle beard of Davy Jones in the recently Pirate’s of the Caribbean movie trilogy. His work is also constantly used by George Lucas’ Industrial Light and Magic for their special effects [link].

It's all mathematics!

It's all mathematics!

It’s work like this that must be the future of both science and mathematics if they wish to blend the two cultures.

Simon Wiscombe

Week2_Math and Art

Sunday, January 18th, 2009

The reason why people may see math and art as polar opposites is probably because they are expressed in different ways.  While art is expressed through colorful strokes of a paintbrush, math is articulated through numbers and formulas.   Regardless, they are, in actuality, very codependent of each other. 


Throughout history, math has commonly been the source of inspiration for artists.  One major example of this is the Golden Ratio (also known as the “extreme and mean ratio”) German psychologist Adolf Zeising, who was one of the first to notice it’s frequent manifestations in nature, such as the arrangement of branches in the veins, stems and leaves of plants and the geometry of crystals fell in close proportion, described the Golden Ratio to be the “ground-principle of all formative striving for beauty and completeness in the realms of both nature and art… which permeates… all structures, forms and proportions”.   It is also apparent in some of history’s greatest and most-well known structures, such as the Parthenon and the Great Pyramid. 


Likewise, art has been used as a way to visually communicate mathematical concepts and formulas, as can be shown by Edwin Abbott’s 1884 book, “Flatland”.   In the story, A Square is the main character who lives in a two-dimensional world.  Because he is limited to only two dimensions of movement and reality, he does not know and cannot know what a three-dimensional shape looks like.  In example, whenever a sphere crosses by his world, he merely sees a circle that is increasing and decreasing in shape. Abbot’s story, which puts readers in the shoes of a character of a lower dimension attempting to grasp the concept of a third dimension, allows readers to grasp the notion of a Fourth Dimension more easily.   Abbot explains:

It is true that we have really in Flatland a Third unrecognised Dimension called ‘height,’ just as it also is true that you have really in Spaceland a Fourth unrecognised Dimension, called by no name at present, but which I will call ‘extra-height.’ But we can no more take cognisance of our ‘height’ than you can of your ‘extra-height.’ …

While many may say that mathematics is an objective field, I really do not think it is.  I think it’s more subjective, because the people who do the math are subjective human beings.  Who is to decide that certain rules in math are or aren’t valid?  Who’s to say that 1 + 2 = 3?  Mathematics is a merely an objective way to view a very subjective reality. 


After hearing Professor’s Vesna lecture regarding Mathematics, Science and Arts, I am beginning to see math as an art form, one consisting of numbers and symbols and hidden meanings.  It aims to accomplish the same thing that art does and that is to discover the world around us.  In this case, however, the artistic achievement lies in the mathematician’s ability to conceive a formula or concept to explain nature’s patterns and laws.


Michie Cao