“Behold yon miserable creature. That Point is a Being like ourselves, but confined to the non-dimensional Gulf. He is himself his own World, his own Universe; of any other than himself he can form no conception; he knows not Length, nor Breadth, nor Height, for he has had no experience of them; he has no cognizance even of the number Two; nor has he a thought of Plurality; for he is himself his One and All, being really Nothing. Yet mark his perfect self-contentment, and hence learn his lesson, that to be self-contented is to be vile and ignorant, and that to aspire is better than to be blindly and impotently happy. Now listen.”
– Edwin Abbott Abbott
Ever realize what makes something interesting? Have you ever looked at a piece of broccoli or a leaf and knew that there was something funny and beautiful about it, but didn’t quite understand why? Slow realizations building up to the bigger picture. Leonardo Da Vinci would analyze nature and record these types of observations as with many other alchemists throughout history. Their curiosity was sparked by a cumulative human knowledge base that we have been building since the beginning of language and writing as well as their own observations.
Some of my own observations from trips I’ve taken, music I’ve listened to and books I’ve read…
Music
(( mandel.wav – audio fractal loop, bach, Tool ))
The structure of Bach’s music resembles that of a classic type of fractal known as a Cantor set. Start with a line segment. Remove the middle third. Then remove the middle third from the remaining pieces, and so on. The result is a “Cantor comb.”
“The fact that Bach was born almost three centuries before the formal concept of fractals came into existence may well indicate that an intuitive affinity for fractal structure is, at least for some composers, an inherent motivational element in the compositional process.”
– Harlan Brothers
Current day – Tool, Fibbonacci sequence.
http://mathtourist.blogspot.com/2008/09/fractal-in-bachs-cello-suite.html
Flatland: A Romance of Many Dimensions (1884)
by: Edwin Abbott Abbott
Full e-Book online: http://www.ibiblio.org/eldritch/eaa/FL.HTM
Other sacred geometry, symbols in life (Masonry), jason’s jewelry, carl’s pinecone fractals & pineal gland…
—————–
I use fractals in much of my work. Mandelbulb. (link to Mandelbulb program & other fractal generators).
After a few dozen repetitions or ITERATIONS the shape we would recognize as a Perfect Fern appears from the abstract world of math. How and Why can this be?
Each section is a microcosm of a larger one. It is a glimpse into the divine when we are able to actually see these patterns with our own eyes. It allows us to see a system from a higher level, allowing us to imagine other levels higher than most people would think possible.
This leading up to recursive philosophy…
Giant loop on itself:
Gödel, Escher, Bach: An Eternal Golden Braid (commonly GEB) is a book by Douglas Hofstadter
http://en.wikipedia.org/wiki/Gödel,_Escher,_Bach
(Follow-up – I am a Strange Loop by Hofstadter)
—————–
Galaxy map hints at fractal universe:
http://www.newscientist.com/article/dn14200
——————–
Flash string theory / PBS documentary online (embed player?)
Leave a Reply