Archive for the ‘week_2_math_perspective_time_space’ Category

Week 9 Blog _ Nanoart _ Sarah Van Cleve

Sunday, March 8th, 2009

Christian Orfescu is a material scientist who runs the analytical laboratory at Caleb Technology in Torrance, California. By day he researches nanotechnology looking for ways to create more efficient lithium batteries, yet in his time off the job he uses art to inform people about the new technologies of the Twenty-First Century. The inspiration for Cris Orfescu’s art comes from the molecular landscapes, measured on the nanometer scale, of various materials. He is so inspired by these images that he calls his work “nanoart” and in 2006 he started organizing competitions for artists with similar ideas.

These nanoart artists are confronted with quite a hurdle when trying to illustrate the realm of nanotechnology (defined as materials that have dimensions of one hundred nanometers or less). Because nanomaterials can be more than one hundred thousandth of the size of the head of a pin, these materials are impossible to photograph. The image below exemplifies the size of the smaller than microscopic nanomaterials, which the artists are trying to recreate. To get any sort of image of these tiny substances one must use scanning electron microscopes. Even with this technology the images can only be portrayed in the color gray. While some see this as a limitation, Cris Orfescu believes this allows the nanoart artists to let their creativity shape how we see science. Mr. Orfescu admits that his interpretations of nanotechnology are not works of science but he believes they can do a better job at attracting attention to the subject: “With more than 70 percent of the people in the U.S. using products incorporating nanotechnology, I want people to know about it and I hope my art stirs their curiosity to find out more.”


For an example of nanoart see the image below. In this work called “Black Eye NanoOctopus” the artist created a nanosculpture by hydrolyzing a tiny drop of a titanium organometallic compound and coating the structure with gold so that it could be best visualized with a scanning electron microscope. The gray colored electron scan was then painted and digitally manipulated before the final image was put on canvas.


Like Cris Orfescu most nanoartists have a strong passion for the field of nanotechnology itself, but they simply use “the other culture” of art to get through to the public. As put by another nanoart artist, Darcy Lewis, “Nanotechnology will dramatically reshape our lives, with amazing medical and economic benefits, however, we must strive to focus on its unimaginable positive benefits, and curtail the weapons and negative applications it can also be used for.” It’s clear that the development of the new science of nanotechnology will undoubtedly lead to great new technologies—nanoarts are simply trying to spread this message with an innovative mix of science and vision.

By: Sarah Van Cleve

Week 9_Nanotechnology: Proceeding with Caution

Sunday, March 8th, 2009

Nanotechnology in the blood stream

Nanotechnology in the blood stream

Week 9_ Nanotechnology: Proceeding with Caution

Nanotechnology is the head of forward progress.  When we think of the future of sciencefiction movies, we see a plethora of shiny metal structures, flying cars, and everything is automated for us.  Most of these automated objects will probably happen through nanotechnology.  This week’s letures, especaiallyt he guest lecture on Thursday, were quite insightful and informative about explaining the details and backgrounds of nanotechnology, such as the Buckminsterfullerene.  Examples of nanotechnology influences include progress with minuscule surgery, advanced production of specific items, creation of medicines and energy, and so on and on.  However, nanotechnology may not necessarily be all peachy and cheery.  Nanotechnology could cause unsuspected toxicity and may potentially harm global economics.  This article ( explores the potential increase of pollution with nanotech’s miniscule size.  While our human bodies are well adapted against ash, dust, and other natural particles, our bodies’ skin and immune system are unsuitable to combat the size of nanotechnology.  Humans that deal with nanotechnology are essentially putting themselves in an environment that could cause lung damage and other damage to the circulatory, lymphatic, and nervous system. Recent studies have shown that lungs and mucus have difficulty removing inhaled nanoparticles.  Adverse effects of nanoparticles on human health depends on physical shape and level of exposure, however, the general consensus is that these miniature sized particles are smaller than cells so they can penetrate basic biological structures and disrupt normal functions.  Nanotechnology can also potentially cause a lot of privacy invasion.  Dan Brown, the author of the Da Vinci code, wrote Deception Point, where nanotechnology was frequently used to assassinate enemies and infiltrate enemy lines.  These were used to take incriminating pictures and provide constant surveillance.  While I don’t know how realistic these nanobugs are, the idea of someday reaching these stages are frightening and enraging.  The right to privacy would be repeatedly violated, and in the wrong hands, these nanobugs would repeatedly rape people’s unalienable rights.  How far is too far then?
I am not saying we should halt the progress of nanotechnology.  This would not only be foolhardy, but it would halt a lot of medical and technological advances.  However, I believe the progress of nanotechnology should be taken with an extra ounce of care.  As the lectures states, nanotechnology is bringing forth a paradigm shift and society is never going to return to a society without nanotechnology.  Because there is a new market for nanotechnology, there will be entrepreneurs eager to capitalize.  Furthermore, nanotechnology may be the answer to some of the biggest of mankind’s problems.  This article,, discusses how nanotechnology may remedy our energy crisis.  Nanomaterial may be used to harness the energy of splitting water and can be used to store hydrogen, usually very flammable, may be stored with a certain type of carbon nanotube.  Nanoparticles may also be used to more efficiently capture solar energy.  Nanotechnology may yet be the answer to many of our problems, but researching this material and using nanotechnology should be handled with a lot of care and precaution.



Nanotechnology and Medicine

Nanotechnology and Medicine

By: Jason Kwok

Week 2_The Fourth Dimension

Sunday, February 1st, 2009

Nowhere do art and science come into play more than in painting; considering aspects of geometry, perspective, and perception, mathematics and science are some of the greatest considerations made by artists. Henderson describes artists making the leap into the fourth dimension, freeing themselves from the confines upon them for centuries. Calling the fourth dimension “a symbol of liberation for artists,” this aspect of painting combined the scientific and mathematical backgrounds required to create such a viewpoint with the artistic skill needed to adapt this knowledge to the canvas (205).

With the implementation of science into art, the presence of the fourth dimension paved the way for the creation of abstract art. The fourth dimension gradually made its way into other art forms; artists working in literature and music found themselves experimenting with new kinds of language and methods, creating art that was altogether innovative and unique. Sculpture progressed from traditional forms, to hollow forms, to open forms, and finally to the clearest way to represent the fourth dimension: cosmic art. Taking into account a different phase of matter altogether, sculptures were pulverized, taking on a new form: a gaseous state. Artists using cosmic art to present their works had truly implemented the ideas of science, embodying the fourth dimension throughout (206).

Henderson, Linda Dalrymple. “The Fourth Dimension and Non-
Euclidian Geometry in Modern Art: Conclusion.”

- Junki Chae

Week 2: “Opposites” Attract- Math and Art Working as One by Leslie Grant

Sunday, January 25th, 2009


This week’s lecture stimulated my thought process on many issues, one of them being the potential that math has to enhance artists’ works and perceptions. I was fascinated by M.C Escher’s ability to use perfect mathematical precision in his use of repetitive shapes and figures in artwork, and thought that it must be impossible to accomplish such a task. As I further contemplated this feat I made a surprising realization- I too had done the same thing for an art project that I completed during middle school. Obviously I most likely had more discrepancies in my measurements than Escher did, but I still managed to create a stencil of a creature that would be symmetrical and fit into itself when traced on paper, a sort of puzzle piece for itself. The task seemed daunting at the time, and still seems like it would be extremely difficult to attempt again from scratch. The fact that this project, which was perfected by an artistic and mathematical genius, was clearly proven to be doable by a group of seventh grade students six years ago, proves that anyone is capable of creating their own forms of art, even if they feel that they are not naturally adept at the task they have set out to accomplish, even if they are having difficulty initially grasping the idea that inspires their work, or even if the art that they are attempting to recreate is based on a concept that is unorthodox. Originally I planned to incorporate one of Escher’s symmetrical drawings to illustrate this concept, but upon searching and finding this modern 3D lego rendition of one of his most famous sketches, I figured that the ingenuity of it captured the idea even better. 



This project shows just how much can be done when imagination is put to use.

This project shows just how much can be done when imagination is put to use.



On that note, I lead into my theories on the fourth dimension and how they have affected the world of art. Linda Henderson’s article, “The Fourth Dimension and Non-Euclidean Geometry in Modern Art,” presents an interesting history of its introduction into society, and there is one statement in particular which I find to be extremely important and worth pondering, and which I would like to expand on. Henderson states that “like non-Euclidean geometry, the fourth dimension was primarily a symbol of liberation for artists.” It is interesting to think of the fourth dimension as a novel idea which artists were, at one time, just beginning to consider and explore. I feel like this sums up the entire concept of art. I see art not only being able to look upon something tangible and depict it with feeling, but also as having the ability to imagine something in a way that no one else does and effectively portray your personal visualizations and ideas to the outside world through a creative outlet of some sort. Interestingly enough, I have always seen Salvador Dali as a prime example of one who felt comfortable expressing abstract visualizations on canvas, and it was merely his thought process which brought to life some of his more famous paintings. It is only upon doing more recent research, at this site in particular (, that I discovered that it was not Dali’s mind alone that inspired these images, but that hallucinogenic drugs had a great deal to do with it. One of my more recent displays of naivete, I suppose. I suppose my point, before I got sidetracked with this interesting tidbit of information which depicts Dali as somewhat playing into the stereotype of artists, is that I feel that if everyone contemplated this all-encompassing definition of art it would be more clear to some why technological advancements can fit into the category of artwork.

Solely based on the previous ideas and theories that have been floating around since what seems to be the beginning of time, I am quite curious to see what theories about the fourth and fifth dimensions will surface as time and research continue. I am certain it will be a topic of interest for quite some time, and am glad that I will be around to see what unfolds.


Leslie Grant

Week 2 - The Fourth Dimension - Miki Koga

Monday, January 19th, 2009

Introduction of the fourth dimension in the 1900s enabled artists to reject laws of perspective and formalist art theory and experiment with an extra degree of freedom. What I found interesting in Linda Henderson’s “The Fourth Dimension and Non-Euclidean Geometry in Modern Art” is how different artists had their own take on the fourth dimension. Many artists interpreted the extra dimension in abstract art. Sculptors incorporated the time element of motion into their figures. The artist Sirato even proposed ‘cosmic art’ made entirely of gaseous material. Idealists came up with a utopian concept of the fourth dimension as a higher reality. Others saw it as a “new language” for the future. Strangely enough, although I am a science major and typically identify more with scientific explanations, the artists’ idea of the dimension as a new medium of expression resonates most with me. My sense of the fourth dimension also lies in Pablo Picasso’s description of Cubism: “It’s not a reality you can take in your hand. It’s more like a perfume. The scent is everywhere but you don’t quite know where it comes from.”

In all honesty, the article was a little confusing to follow. I didn’t come out with an explicit definition of the fourth dimension. But maybe that’s just it. Scientists speculate that it is time or another spatial dimension. For artists, it’s more of a symbol or rationale: a symbol of liberation, a rationale for new exploration of reality. The more vague the definition, the more freedom and possibilities there are in interpreting it. One thing that may be certain is that the mathematician, scientist, and artist’s correlative sense of intuition, innovation, and intelligence are instrumental in dealing with the fourth dimension.

Lastly, I wanted to touch on the whole idea of objective versus subjective, and quantitative versus qualitative as it relates to me. As a second year chemistry major, I’ve spent over a year now taking classes in the physical science and engineering series. In high school I was under the impression that science and math were strictly objective and quantitative. You solve a math problem to find a definitive answer. The answer is black and white, right or wrong. However, taking more advanced college courses, I’ve discovered that while the answer or equation may be objective and quantitative, the derivation process and theories used may not be so clear-cut. Furthermore, science and math involve a lot more gray areas and abstract exploration that call for visualization. Out of the box, visual thinkers excel. For example, picturing the geometry of molecules in organic chemistry helps make sense of what happens when they interact at the microscopic level. You’ll often find me fiddling with my model kit like a little kid playing with Tinkertoys. I draw mechanisms out or look up images in my textbook for a deeper understanding. Likewise, computerized images of various surfaces and scalar fields were essential when I took multivariable calculus. While the need for visualization does not constitute math and science as subjective or qualitative, what I’m trying to say is that the labels ‘objective and quantitative’ are constricting. The two subjects involve more than just number crunching and stoichiometry. There is theorizing that is subject to interpretation, as well as visualizing a microscopic world that involves a sense of intuition. Science may also be as objective as the assumptions being made, the established facts at that time, or the scientist behind an experiment. We shouldn’t be so quick to categorize or label things.

By: Miki Koga

All Part of the Same

Monday, January 19th, 2009

Art can exist on its own, and math can, also exist by itself. However that does not mean they are no related or cannot overlap with significant meaning.  Math can be used to draw perspective.  This brings up the idea of Escher’s art works.  He creates drawings with different perspectives especially of different buildings. However, they are impossible to be made in real life.  The picture of the stair case that is always going up is an example of this.  The drawing is all based on perspective that could never exist in real life. 

In one of my math classes in high school, the students were forced to relate math and art.  I had to draw a picture and write mathematical equations that graphed the picture.  This showed a direct correlation between math and art.  The math equations I wrote actually drew a picture.  Art could be created directly from mathematical equations. 

This reminds me of the idea of chaos theory. Chaos theory is the idea that nothing is random or chaotic.  There is a mathematical equation to explain everything.  It makes me wonder if all art could be written in mathematical equations.  With this idea, the line between math and art would be completely blurred.  There would be no difference between math and art because they would be one in the same, just as my math class in high school.

It is amazing how nature can be so related to math.  The in class demonstration on people’s faces and the golden ratio shows how the math is part of nature.  It is also amazing how the golden ratio was discovered so long ago by humans. The ancient Greeks used it in building designs such as the Parthenon.  Art, science, math, and nature are not just related, but really part of the same.  They are just different perspectives on the same idea.

Week2_by Heeseok Lee_Interlinking between Art and Mathematics in Pyramid

Monday, January 19th, 2009

As an engineer, I have taken so many mathematics classes from Algebra to Calculus in college, and I have realized that math brings numerous artistic characteristics. Especially, for problem-solving, Mathematics always requires to bring up some imagination or creative thought to reach the answer. In addition, Mathematician also has creativity as much as Artist does. Personally, I think that Both Art and Mathematic are oriented in the same motivation, in terms of seeking and trying to explain how the nature works. Only differences are that Art takes more advantages of not having limit on appealing their thought or idea while mathematic is outlined and has boundaries under some rules and principles.
From historical piece of art or architecture, It is easily seen how math and art are interlinked and enables each other to be more expressive and completed. Most of all, pyramids shows a good example of how ancient Egyptian used mathematical concept on designing of it and constructing process. Pyramids shows golden ration as pantheon shows, as mentioned in lecture. If you take a cross-section through a pyramid, you would get a triangle. If the pyramid is the Great Pyramid, we get the so-called Egyptian Triangle. It is also called the Triangle of Price, and the Kepler triangle. The ratio of the slant height(S) to half the base(B) is said to be the golden ratio. From my high school’s trigonometry class , I was supposed to verify this golden ratio in pyramids by computation of Slant Height.

*Here is my computation to verify existence of Golden ratio in pyramid.
height = 146.515 m,   and    base = 230.363 m
(These values are determined by various expeditions.)
Half the base is      230.363   ÷   2 = 115.182 m
So,  S^2 = 146.515 + 115.182 2 = 34,733 m2
S = 18636.9 mm
Dividing slant height s by half base gives
186.369   ÷   115.182 = 1.61804
The Egyptian triangle thus has a base of 1 and it equals to hypothetical value. Its height h,
h^ 2=  Φ^2 – 1^2  as solving for h, value of Φ^1/2 is determined.
By Computing the value for the height of the Egyptian triangle to verify the ratio .
1: Φ^1/2: Φ
Therefore, the sides of the Egyptian triangle are in the golden ratio

In addition, pyramids contains not only mathematical concept used but also full of symbolism.
“If flooding of the Nile symbolized the annual return of watery chaos, then geometry, used to reestablish the boundaries, was perhaps seen as restoring law and order on earth. We’ll see this notion again of geometry being sacred because it represents order, especially in the Middle Ages. The rope stretchers triangle when opened out gives a zodiac circle, with the number of knots the most important of the astrological numbers. The square, with its four corners like the corners of a house, represents earthly things, while the circle, perfect, endless, infinite, has often been taken to represent the divine or godly. So squaring the circle is a universal symbol of bringing the earthly and mundane into a proper relationship with the divine, and the Golden Ratio reverberates with the idea of the Golden Mean, the principle of moderation, defined by Aristotle as the mean between the two extremes of excess and insufficiency, as generosity is the mean between prodigality and stinginess, and by Horace, called the philosopher of the golden mean, advocated moderation even in the pursuit of virtue.” (Heroditus Book II, Paragraphs 124, 135)
I was very impressed that Egyptian artists used mathematical concept and ratio to reflect their values and thoughts. Although it is modern scholars’ interpretation and assumption, but it is really amazing to see how ancient people put art and math/science in one masterpiece. It is very unpleasant to see how Art and Science fields are divided and generally do not put effort to interlink and collaborate with each other to seek more accurate way to express and explain our thoughts, values, and the principles of world where we are living.


Merging Math and Art: by Jessica Young

Sunday, January 18th, 2009

The merging of math in art and art in math is an idea of antiquity that has become radically popularized over the last couple years with the improvement of technological machinery.  Ancient peoples of Greek and Babylon tradition used mathematical sciences to improve not only the structure of their architecture, but also the aesthetic appeal. The Greek construction of temples was something that used precise angles to maximize the stability of the structure, ensuring that it would be lasting.  Even now, thousands of years after the construction of the first temples, many structures remain standing, almost perfectly intact, despite the wear and tear caused by severe weather and heavy human traffic during religious ceremony.  The Babylonians likewise used mathematical means to maximize the space and load bearing capacity of the palace at Babylon.  The Queen Semiramis and Nebuchadnezzar were said to have commissioned the building of the hanging gardens, and did so using the idea of maximizing efficiency of space through squares. The structure was supposedly built up by constructing square upon square in decreasing size from top to bottom, as displayed in this reconstruction:


Also utilizing science and technology, the architects were able to irrigate the gardens by using water lifted from the Euphrates River.

Week 2: Math and Art by Jessica Amaya

Sunday, January 18th, 2009

                Math, for many people, represents a dark and mysterious world, where many sleepless nights are played out in order to find the proof of some theorem. They believe the people involved in such a world are dull and serious, or crazy even. However, when thinking of art, they imagine lively characters full of life and glee. How shocking it must be, for those who posse those thoughts, to find out that art and math are intertwined. 

                The truth of the matter is that mathematical shapes are found in the most beautiful flowers, that painters find so delicious to paint. The Golden Ratio, introduced in Tuesday’s lecture, also falls under both the math and art categories.  Everything can be broken down into shapes, which makes drawing, painting, sculpting, architecture and other forms of visual art possible. Of course having creativity to make those works is crucial but so is thinking of proofs to theorems.  In this day and age the division between math and art has grown but during the surrealist period (and many other modern art time periods) that division was much less solid.

                Non-Euclidean geometry opened a door for so many artist to explore their talents in different levels. One of the most well known artists that was affected by this new geometry was Salvador Dali. He was interesting in expression his thoughts through a new dimension, the fourth dimension, which was what the Non-Euclidean geometry offered. Math influence on painting did not start with this however. Perspective was a huge thing that revolutionized art and  how scenes were drawn. Although many artists today use perspective just as a technique and do not understand the math behind it, they can’t change the fact that they are still doing math unconsciously.

                There exist people, however, that do know that math is an essential, but not the only component, of art.  For example, there is Kenneth A. Huff who finds the mathematical shapes in nature to create prints and other visual art works. His works have a clean and intriguing beauty to them that draw the viewer in. 200512

There is an interesting proffessor in the University of Colorado who believes that math is very much art itself and that art can help explain and create an easier understanding of math. You can read about her, Carla Farsi, on the following link.

Similarly, there are courses that try to teach about art and math as one to get more people to see that math is hard, but it can be simplified with art. Such a course can be found in the following link.

There is a division between math and art, but I am sure that more people and more courses like the ones above will change that soon.

Beautiful math art

Beautiful math art



-Jessica Amaya

Week2_Personal Perspective

Sunday, January 18th, 2009

“The difference between a mountain and a molehill is your perspective.”
- Al Neuharth

Does the mathematics of perspective govern art? This is a question that I found myself asking when presented with this week’s lecture topic of perspective. It’s all very mathematical indeed, giving precise, functional instructions for creating a work of art. It’s a societal influence, too. In real-life art we are conditioned to expect certain things from our surroundings. Architecture, for example. Sure there are deviations and artistic embellishments but do we ever see such innovation as we see in abstract art brought to life on the streets?

Not your typical apartment complex.

Not your typical apartment complex.

I came across a few examples and they range from extremely dramatic to subtle but effective. These are the same kinds of tricks that M.C. Escher played on his audience with his sketches. At first glance his drawings seem to have great depth and flawless dimensions until, after careful review, it seems that the dimensions are skewed. Often times the staircase will run in horizontal loops or water will run uphill in a way that is quite unexpected. This used the principles of perspective while betraying those very same principles. Much like these two buildings:

They employ all principles of a sturdy structure and yet they betray those very same rules that govern much of today’s architecture.

In much the same sense, a lot of art is about the unexpected. One does not expect a building to be turned on it’s head, and one does not expect to find a Golden Ratio or a Fibonacci Sequence that governs the growth patterns and visual qualities of most things in our natural world.A more mainstream but just as fresh look on architecture.

A more mainstream but just as fresh look on architecture.

A triangle is the strongest, most efficient geometrical shape. A circle is the only shape that will not collapse upon itself. Mathematics explains these.

A fresh perspective can lead to a new form of art. Cubism and minimalism can be governed by mathematics, as can ballet and architecture.

This coincides with last week’s focus on the separation of two cultures. They truly are not as polarized as we may think. It simply takes perspective to appreciate the ways that art and science complement each other.

Photography would be considered by most to be an art form. However, some may not realize how much photography obeys the laws of mathematics and perspectives. Perspective can change a plain picture of a fence to an intriguing display of point of view and symmetrical design.

Just a fence.

Just a fence.

In a nutshell, how we view the world is absolutely individual. It’s subjective. It is much the same as our individual capacity to understand thermodynamics and our personal appreciation for aesthetics and passionate arts.

Is it a molehill or a mountain? Depends how tall you are.

-Lindsey Dawson