Visual Processing

I am a very visual person. I was raised by an artist and a computer programmer. This gave me access to artistic and flow-charting techniques. My dad used give my siblings and I flow chart templates to make art when we were young. When I became older, he explained what some of the shapes meant and then made a game for me. He'd give me a simple task and I would diagram the steps to do it, using those shapes properly.

As a family, we made almost weekly trips to the public library, bringing home art and music in addition to a multitude of books. Our home library sometimes had better references than my school's library. Arguments between myself and the sister just younger than me were usually solved by encyclopedias at ten paces. My mother made sure we had art classes. My dad made sure we had science lab kits. As a family, we made candles, leather and other crafts. Dad would also print out wall-size mazes which we kids and my mother would solved together. When I learned how to process information, it was not only through the verbal and mathematical means, but also visual and kinetic means.

I'm right handed, left eyed, and I have no dominant foot preference. I have taken math courses up to and including partial differential equations and I have about the same amount of credit hours in studio art as I do math. It probably follows without saying that my favorite math class was analytical geometry. I feel that this makes me qualified to make the follow statement:

Calculations can be done visually as well as mathematically.

Anecdotal evidence: When I was in high school, my mother took one of my classmates and I to an UIL science competition. Between the tests, the contestant schools could work on brain teasers. One of them was a word problem about how much material a sculptor would need if they made a bust twice as large in every dimension. While my extremely intelligent classmate began to do the mathematical calculations, my mother read the problem and immediately gave the correct answer. After verifying it with math, my shocked classmate asked my mother how she did the calculation. She used pictures and hand gestures to explain her thought process. He was totally lost by her explanation, so I gave him an interpretation he could understand. For the rest of the problems, my classmate and mother answered them with their own methods, while I translated between the two of them. In every case, both methods gave the same answers.

Historical evidence: All those wonderful geometry and trignometry relationships started out as a function of the relationships between visual elements such as lines, points, angles, planes and solids. M. C. Escher discovered several crystallography relationships years before the mathematical models, through purely graphical means. While many mathematicians hold Escher in the highest regard and consider him to have had an exceptional mathematical mind, he actually did very poorly with math in school and struggled to understand the mathematical treatises sent to him when he was older.

So, having made put that pet peeve to rest, I will share with you a diagram I made a few months ago showing visual processing as part of the problem solving process. While I do not detail how to do math visually (perhaps I will do that in another post), the diagram does show some of the ways visual processing has brought about solutions -> http://cosmicsiren.blogspot.com/p/diagram-of-visual-processing.html



O’Connor, J. J. & Robertson, E. F. (2000). Maurits Cornelius Escher. MacTutor History of Mathematicians. Retrieved February 28, 2010, from http://www.gap-system.org/~history/Printonly/Escher.html

Interesting math history facts

According to Wikipedia...

1) The oldest known mathematical object is the Lebombo bone, discovered in the Lebombo mountains of Swaziland and dated to approximately 35,000 BC.[10] It consists of 29 distinct notches deliberately cut into a baboon's fibula.[11] There is evidence that women used counting to keep track of their menstrual cycles; 28 to 30 scratches on bone or stone, followed by a distinctive marker.[12]

2) The majority of recovered clay tablets date from 1800 to 1600 BC, and cover topics which include fractions, algebra, quadratic and cubic equations, and the calculation of regular reciprocal pairs (see Plimpton 322).[20] The tablets also include multiplication tables and methods for solving linear and quadratic equations. The Babylonian tablet YBC 7289 gives an approximation to √2 accurate to five decimal places.

3) The Babylonians had a true place-value system, where digits written in the left column represented larger values, much as in the decimal system. They lacked, however, an equivalent of the decimal point, and so the place value of a symbol often had to be inferred from the context.

4) The oldest mathematical text discovered so far is the Moscow papyrus, which is an Egyptian Middle Kingdom papyrus dated c. 2000–1800 BC.[citation needed] Like many ancient mathematical texts, it consists of what are today called word problems or story problems, which were apparently intended as entertainment.

5) In China, the Emperor Qin Shi Huang (Shi Huang-ti) commanded in 212 BC that all books in Qin Empire other than officially sanctioned ones should be burned. This decree was not universally obeyed, but as a consequence of this order little is known about ancient Chinese mathematics. From the Western Zhou Dynasty (from 1046 BC), the oldest mathematical work to survive the book burning is the I Ching, which uses the 8 binary 3-tuples (trigrams) and 64 binary 6-tuples (hexagrams) for philosophical, mathematical, and mystical purposes. The binary tuples are composed of broken and solid lines, called yin (female) and yang (male), respectively (see King Wen sequence).

6) The earliest civilization on the Indian subcontinent is the Indus Valley Civilization that flourished between 2600 and 1900 BC in the Indus river basin. Their cities were laid out with geometric regularity, but no known mathematical documents survive from this civilization.[27]

7) The Surya Siddhanta (c. 400) introduced the trigonometric functions of sine, cosine, and inverse sine, and laid down rules to determine the true motions of the luminaries, which conforms to their actual positions in the sky. The cosmological time cycles explained in the text, which was copied from an earlier work, correspond to an average sidereal year of 365.2563627 days, which is only 1.4 seconds longer than the modern value of 365.25636305 days. This work was translated into to Arabic and Latin during the Middle Ages.

8) In the 12th century, Bhaskara first conceived differential calculus, along with the concepts of the derivative, differential coefficient, and differentiation. He also stated Rolle's theorem (a special case of the mean value theorem), studied Pell's equation, and investigated the derivative of the sine function. From the 14th century, Madhava and other Kerala School mathematicians further developed his ideas. They developed the concepts of mathematical analysis and floating point numbers, and concepts fundamental to the overall development of calculus, including the mean value theorem, term by term integration, the relationship of an area under a curve and its antiderivative or integral, the integral test for convergence, iterative methods for solutions to non-linear equations, and a number of infinite series, power series, Taylor series, and trigonometric series. In the 16th century, Jyeshtadeva consolidated many of the Kerala School's developments and theorems in the Yuktibhasa, the world's first differential calculus text, which also introduced concepts of integral calculus.

Symmetry, Math, Life and Art

After watching this video a few times, I have decided that the Japanese had some good insight into the creative process with their Essays In Idleness:

"In everything . . . uniformity is undesirable. Leaving something incomplete makes it interesting, and gives one the feeling that there is room for growth..."

Following what was said in the video, I think this is another feature of art that engages the viewer in conversation.

I'm going to apologize here. I was going to go ahead and write up some of the things I read about humanity's need for balance and such, but I think I will save that for another post.