Archive for the ‘week2_math’ Category

Week2/Math and Art/ James Martin

Sunday, January 18th, 2009

Art and math are not always combined, but I think the best art comes with a combination of both aspects.  Personally, I do not usually understand the “hidden meanings” behind some art and how all of the art critics see these ideas.  But to me, when math and geometry is involved, it seems to take art to a whole new level and I really enjoy it.  Math adds life to art and gives it a little more flavor.  Since I am a first year south campus major, my classes have all been math and science up t this point.  I decided to take Desma 9 in order to broaden my horizons in art and other subjects offered.  I first noticed the connection between the two subject my freshman year in high school when I took geometry.  Geometry was always my favorite math class since it allowed me to visualize the problem.  The combination of shapes and art creates a true beauty that cannot be beat.

In this weeks lecture, the golden ratio really caught my interest and I wanted to research it more.  Before this class, I had actually never heard of the golden ration so when I saw the video of how it worked I became much more interested.  The golden ratio is the ratio between the sums of two quantities and the larger is the same as the larger one and the smaller one.  Ancient Greek mathematicians, who saw and used it in geometry, first saw the golden ratio.  Most usually give credit for the discovery of it to Pythagoras.  Euclid gave the first true definition of the golden ratio and stated “straight line is said to have been cut in extreme and mean ratio when, as the whole line is to the greater segment, so is the greater to the less.”  In his book Elements, Euclid goes into detail about the golden ratio.  But as we saw in lecture, the golden ratio is not only used in art. It is also used in architecture and everyday life.  The Parthenon is one of the most famous buildings and it is observed to be extremely close to the golden ratio.  Also as we learned from lecture, the golden ratio can be used to show whom what our society classifies as beautiful.  The you tube video showed used a program in which we can apply the ratio directly to faces and mold them to “perfection”.  Piers Brosnan and Angelina Jolie are both some of the most beautiful people according to the golden ratio.  The golden ratio works for a very wide variety of things including art, architecture and many, many other uses.

http://library.thinkquest.org/trio/TTQ05063/phihistory.htm

Right now, I am leaning toward an engineering career with automobiles.  This would probably be my dream job right now and this weeks topic fits perfectly in what I want to do.  Cars, art, and math all go together.  With the economy and the depletion of fossil fuels, many people see the need for math and science to help create more efficient cars.  This is a passion of mine but I also love the art aspect of cars.  With hybrid and other types of fuels progressing, the math aspect of cars is blooming and in full force.  However with the new Prius, it is a hybrid but to me it is ugly.  I wish to incorporate math science and art to create what I believe is the perfect car.  Math and art are extremely close; it just may be hard to recognize it at first sight.

http://www.wisil.recumbents.com/car_aerodynamics/

http://www.youtube.com/watch?v=suiDK61jAc8

James Martin

Week 2/Fourth Dimensional Art/Kelly Tseng

Sunday, January 18th, 2009

In this week’s discussion on the math, perspective, time and space, the fourth dimension and non-Euclidean geometry represent influential aspects in mathematics and art that paved way for historical movements such as Surrealism. Last winter, I took a course in Arts and Architecture and studied prominent abstract artists whose works had lasting impacts on society. In Henderson’s work, “The Fourth Dimension and Non-Euclidean Geometry in Modern Art: Conclusion,” she notes that non-Euclidean geometry “signified a new freedom from the tyranny of established laws.” When artists escape the rules of visual reality they are liberating themselves from visual reality and the perspective system that for many centuries was used to portray the world as three dimensional. At this point, they have reached the fourth dimension, which may be represented in abstract art. The sculptures of Robert Longhurst (http://www.cs.berkeley.edu/~sequin/SCULPTS/LONGHURST/) convey an abstract nature of art. When looking at the second sculpture from the top left (Arabesque XXIX), I feel that this work transcends the three dimension of space and achieves the fourth dimension, time. Although I am still not quite certain how the fourth dimension actually looks like in art, going by what Hoffmann stated in the 1930 Art Digest: “All profound content in life originates from the highest phenomenon of the soul: from intuition, and thereby is found the fourth dimension.” As a result, I believe that anything that abides by this statement may be considered fourth dimension. This piece by Longhurst is quite abstract and when I look at it, I feel that it can represent anything belonging to or beyond the lines of imagination. The qualities of this work are independent from the visual references in the world. I feel that it encompasses the realms of math, perspective, time and space.

Another piece of work, not mentioned in class, is the “Sculpture and Glass” by Christopher Ries (http://www.susqu.edu/Art_Gallery/Exhibitions/Ries-Sep1999/Ries.jpg). I really like this great artwork because it is very creative and beautiful. Ries utilizes the surfaces of the glass to create an illusory image of three sunflowers instead of just one. Although the creation of such a fine, flawless piece required the cutting, slicing, heating, grinding, and the blowing of glass, the final product looks perfect, as if it did not undergo such cumbersome and mechanical processes. “Sculpture and Glass” transcends visual reality, employing illusive techniques that follow alternative kinds of space.

Week 2: Linking Math and Art; Jasmine Huynh

Sunday, January 18th, 2009

This week’s article, “The Fourth Dimension and Non-Euclidean Geometry in Modern Art,” was very informative about the fourth dimension movement. The article was interesting on many levels. First, it discussed a unique connection between art and science. I had previously thought that Einstein’s Theory of Relativity only had great significance to physicists and engineers of the time. However, it appears that artists readily incorporated his discovery as well: La Vie de L’espace discussed how the theory was a component of the fourth dimension. The article also showed a political aspect as well. The beginning of the article discussed how the “fourth dimension was a symbol of liberation for the artists” and “non-Euclidean geometry signified a new freedom from the tyranny of established laws.” The article managed to cover many grounds.

My favorite part of this week’s article was the section that discussed Oscar Dominguez’s work. The article mentioned that his writing was highly scientific. He successfully related physics/mathematical terms to a bigger, artistic concept. I especially liked how he said “Between the lion L0 , or the lion at the moment t=0 and the lion at L1…” because these are terms that I am familiar with and can easily understand. It was interesting to see how he could relate two seemingly unrelated topics.

The piece of works that most peaked my interest was Xah Lee’s Algorithmic Mathematical Art. I really liked his work because he seemed to come from a similar background as me: a science major who views mathematical models as an aid in solving problems. He managed to see the models in a different light. His use of mathematical algorithms to create art is very interesting. I particularly like his compilation because each of the pieces can be interpreted in two ways: first as a mathematical model, second as a piece of art. I was surprised to see how some of the pieces appeared as freeform artwork that was not generated by mathematical algorithms. Good examples of this would be the “density plot of the equation “equation Sin[x*Sin[y]]-Cos[y*Cos[x]]==0” and the “nested inversion of circles” by William Gilbert.

Inspired by the links on the class website, I wanted to see more examples of fourth dimension art. I found that there is an artist by the name of Tony Robbin who specializes in fourth dimension art, specifically the hypercube. I particularly like his piece titled “Lobofour, 1982″ because it is both definitive and undefined. Up close, the piece looks very geometric and made of only cubes and triangles. It looks as if each cube was placed in a particular spot for a reason. Further away, the piece looks very abstract. The piece is no longer full of cubes, but rather, it is a backdrop with many colors and the white lines make a variety of geometric shapes. It is a very interesting piece.

http://tonyrobbin.home.att.net/work.htm

(Scroll to piece titled “Lobofour”)

Week 2 Fourth Dimension by Marie De Austria

Sunday, January 18th, 2009

                According to Henderson’s “The Fourth Dimension and Non-Euclidean Geometry in Modern Art: Conclusion,” the fourth dimension is characterized by “total abstraction,” “bold experimentation,” and is “deliciously subversive.”  It was a major symbol of liberation of artists.  It is interesting to see the history of how art, not so much as moved, but branched off into different respects.  There are those who stick with the classical way of expressing their creativity and then some, a growing few, who challenges what is already there and creates their own sense of creativity.  The more I read the article, the more I can see parallel events between what was happening to the world of Modern Art and to the onset of conceptual maturity in a person.

                Classical and traditional Art focused on patterns, proportion, symmetry, perfection as illustrated by Greek structures such as the Parthenon and the Last Supper.  There is simplicity in their surface appearance but you can feel the dignity behind the artist’s rendition.  These pieces of art respect the rule of one vanishing point, shadowing techniques, and most of all, plausibility.  In comparison, “Escher’s Endless Stairs” and the “U and Bar,” purports significant deviations from the techniques that classical artists respect and maintain in their work.  In the U and bar, there are two light sources.  Escher’s stairs implies two light sources to create the illusion of depth in more than one area.  Both, however, are simply impossible to recreate in real life unlike the classical pieces.  These modern art pieces are far more simplistic in its appearance than those of classical art but its majesty lies not behind the artist’s rendition but in the way it confuses and deceives the audience’s vision.  As the youtube video that Professor Vesna showed in class, fascination for modern art can go on endlessly because, I think, our brains cannot comprehend the impossibility of the pieces.  There is something to be said about the power of curiosity to influence human action.  It is also this curiosity that draws people to these implausible masterpieces.

                As Duchamp said, there is something “deliciously subversive” about breaking all the rules of classical art and idealist visions.  Like a person whose rebelliousness begins when he can no longer put up with the rules that he thinks do not follow his own beliefs, modern artists “rebelled” against the commonly held rule.  It is when a person begins to create his own path that his creativity, as was discussed last week, flourishes.  Like a college student who is bound to bounce his ideologies with those of his colleagues and then dig their own path to lead, modern artists look into themselves to bring out their own sense of creativity bound by no rule, no common perspective, no one light source, and not even the bounds of possibility. 

http://www.christcenteredmall.com/stores/art/zabateri/last-supper-zoom.jpg

http://en.wikipedia.org/wiki/File:Parthenon-2008.jpg

http://www.simplex.t.u-tokyo.ac.jp/~sugihara/hobby/esher.jpg

week2/Fourth Dimension in Math and Art/Jillian Cross

Saturday, January 17th, 2009

Week Two: Math, Perspective, Time and Space

            When looking at this week’s topic, I immediately thought of the book Einstein’s Dreams by Alan Lightman. The fictional novel follows Einstein as he “dreams” up different possibilities of time, relativity and the fourth dimension. Einstein dreams up about 30 different scenarios during his quest to figure out mysteries of time, space and relativity (some excerpts from the novel are found here: http://www.cc.gatech.edu/home/idris/Stories/Einsteins_Dreams.htm).

 The book was given to me by a friend who thought I may enjoy the nerdy mathematical side of it. While I have always appreciated this novel from a math and science point of view (the different ideas about a fourth dimension and its mathematical implications are fascinating), after this week’s lectures I began to see its impact on the art world as well.

Only now have I been able to look at the novel and appreciate the role of time and the fourth dimension from the creative artistic side. By adding the fourth dimension to art, one is able to gain a whole new perspective on the world. Picasso and Braque argued in the beginning of the twentieth century that “we see with two eyes, and our eyes move to understand a scene.” To them, understanding the scene meant creating a new perspective. The fourth dimension was essential in adding time and space into that perspective. Cubism was a result of this new perspective.

I was surprised to learn that artists had been using a time and space perspective years before Einstein published his theory of relativity. While Einstein was trying to logically figure out this phenomenon, artists were already using it to gain a new take on their art. For example, Marcel Duchamp created a four-dimensional cubism work called “Nude Descending a Staircase No. 2” four years before Einstein published his work (work and facts can be found: http://www.strangehorizons.com/2002/20020916/fourth_dimension.shtml). Duchamp did not understand the physics of relativity; he just saw it as being able to enhance his work.

When Einstein finally published his theory, many believed that he “killed the romance between the public and the fourth dimension of space.” To much of the public at this time, the fourth dimension was a beautiful new perspective on their world. I find the description of Einstein killing that romance a little far-fetched. As a scientist, I find my passion (and therefore romance) in actually understanding these things in our world. I would rather learn about the many amazing things that are present in our world and our lives than fantasize about what they could mean.

This website describes perspective and time and space in a very unique way to different groups of people: http://www.dartmouth.edu/~matc/math5.geometry/unit16/unit16.html. “There seemed to be a lot of fascination with the fourth dimension early in this century, but it meant different things to different people:

  • Time is often considered the fourth dimension in the space-time continuum with three space dimensions and one time dimension.
  • Color has been described as a dimension.
  • For some artists the fourth dimension appears to have been a metaphor for liberation from the conventions of linear perspective.
  • To some philosophers it was a physical reality to which we have limited access.
  • To many mathematicians, the fourth dimension simply means an abstract space described in terms of four mutually perpendicular axes.”

This article also shows several different pictures of perspective from both the math and art point of view. Artistically, the fourth dimension is very evident in cubism and geometrical art. On the other hand, the ideas of time and space have changed the views of scientists everywhere by adding substance to many abstract calculations. Overall, I find the incorporation of time and space into both math and art fascinating. It is incredibly interesting to see that both artists and scientists were “discovering” this phenomenon at a similar time in history through very different means.

 

week2 \ assignment \ Alberto Pepe

Friday, January 16th, 2009

This week’s blogs should be about Mathematics, Perspective, Time & Space. Have a look at the list of links on the class website, here. Browse the links, select a piece of work or project, and discuss it in the context of the topics discussed in class. Of course, you are encouraged to do a little research and find new related projects (I will count this as extra credit). Limit your discussion to 1 or 2 projects.

P.S. I also added a link to the right on How to blog. Check it out for blogging guidelines.