hyperbolic crochet: Drawing is seeing

"Right angles don't attract me. Nor straight, hard and inflexible lines created by man," Oscar Niemayer, who recently died at the age of 104, wrote in his 1998 memoir, The Curves of Time. "What attracts me are free and sensual curves. The curves we find in mountains, in the waves of the sea, in the body of the woman we love." (Some pictures of his best works are here.)
Niemayer collaborated with Roberto Burle Marx who is best known for his amazing landscape designs, but he first thought of himself as a painter.

The painting and the garden - they both play with curves, they both have a drawing as their beginning.

Everything that one can imagine, one can draw, and indeed much better, because in drawing one has what is essential...It always begins with pictures. - Otto E. Rössler

This the very first quote which caught my attention in the exhibit I saw couple days ago in New York - The Islands of Benoit Mandelbrot: Fractals, Chaos, and the Materiality of Thinking. (NY Times review of it). This exhibition explores the role of images in scientific thinking, in this case, images produced by Mandelbrot to illustrate chaos theory and fractal geometry.

When seeking new insights, I look, look, look, and play with many pictures. (One picture is never enough.) - B. Mandelbrot

Mandelbrot's visual methodology challenged his era's accepted standards of mathematical thinking. There is a fascinating display of over 100 graphics from Mandelbrot's experiments that can be regarded as a predecessor of the Mandelbrot set. The guy at the admissions booth told me that this show has becoming like a cult show - many mathematicians and computer scientists are coming to see it. At the time I was there I was the only one in the room. It was actually a feeling of following somebody thoughts. Mandelbrot never tired of praising "the visual" as being crucial for thought.

Sketches on paper are often the first materialized traces of an idea. Intimately linked with the thinking process, they are highly ephemeral, mostly going unseen by the public. Sometimes hastily drawn on any available sheet, sketches document the process of intellection: the sudden urge of an emerging thought taking shape; the feedback loops created between data output, paper, writing utensil, and thought; the clumsy eloquence of the material; the way reasoning needs to materialize in various ways to be effective.- from the exhibit catalog (more about exhibit here)

This exhibit reminded me of one in Cornell - Jeni Wigtman "Visualizing Meaning" - here is a documentary about it. Before this exhibit in 2006 Jeni asked 1943 Cornell Faculty a question "Of the many charts (graphs, map, diagram, table and 'other'you have seen in your life, which has been the most important, remarkable, meaningful or valuable?" On the archival paper provided they were asked to create a copy of the chart and in the remaining space annotate notable attribute of the data and the image, describe what they remembered about first seeing this image and comment on why they choose this image. Of course, not all returned the answer to the question but I do remember the nice collection of the answers. Then some of them were reproduced large scale and were for a while on the wall across Mann Library but the whole collection was online. Unfortunately the link to it now is broken :-(.

Well, may be I do need to finally get into habit to have a notebook with me all times so that some of my ideas are caught as the sketches on paper....
I am not so good on making videos, so I really enjoy Vi Hart's ones - this latest one is very much for holiday season but also nice one about hands-on exploring various symetries:
<iframe width="560" height="315" src="http://www.youtube.com/embed/8EmhGOQ-DNQ" frameborder="0" allowfullscreen></iframe>

But for now - good bye, New York - till next year...