To know that
we know what we know, and to know that we do not know what we do not know, that
is true knowledge.
Nicolaus
Copernicus
With Nicolaus
Copernicus being featured in today’s Google doodle to celebrate his
540th birthday, it leads all of us to
think more carefully about every supposed fact, and admire those who question
the rules or challenge the authority, as Copernicus’s iconoclastic success in
discovering that the Earth is actually circling the Sun, and what had been
thought–that the Earth was at the center of the Universe–was wrong.
Though we may understand more about Universe than five
centuries ago, still, what we know, compare to what we don’t know is a tip of
iceberg. How hard could it be to solve a giant jigsaw puzzle of nature? Most complex ideas before they become
scientifically validated, they appear in abstraction. There is some
mystical-ness when they first appear.
The art or science, what is the nature of our universe, here
are a tale of another two contemporary geniuses:
Authenticating
Pollock Paintings Using Fractal Geometry: his masterpiece Blue Poles:
Number 11, 1952 by rolling a large canvas across the floor of his windswept
barn and dripping fluid paint from an old can with a wooden stick. Given that
Pollock's paintings are often described as 'organic', the obvious step towards
identifying the 'hand' of Pollock is to take the pattern analysis techniques
used to identify fractals in Nature's scenery and apply the same process to
Pollock's canvases.
But if Pollock's swirls of paint are indeed a celebration of
Nature's organic shapes, what shapes would these be? What geometry do organic
shapes belong to? Do objects of Nature,
such as trees and clouds, have an underlying pattern, or are they 'patternless'
- a disordered mess of randomness?
Although natural systems appeared to be disordered, hidden underneath
was a remarkably subtle form of order. This behavior was labeled as chaotic and
an area of study called chaos theory was born to understand Nature's dynamics.
Mandelbrot’ fractal theory :
Pollock's work had huge influence on Mandelbrot (great mathematician). Benoit
B. Mandelbrot (November 1924 – 14 October 2010) was a Polish-born, French
and American mathematician, noted for developing a "theory of
roughness" in nature and the field of fractal
geometry to help prove it, which included coining the word
"fractal". He later created the Mandelbrot
set of intricate, never-ending fractal shapes, named in his honor. In
1975, Mandelbrot coined the term fractal to
describe these structures and first published his ideas in 1975, and later
translated, Fractals: Form, Chance and Dimension.
Mandelbrot ended up doing a great piece of science and
identifying a much stronger and more fundamental idea—put simply, that there
are some geometric shapes, which he called "fractals", that are
equally "rough" at all scales. No matter how close you look, they
never get simpler, much as the section of a rocky coastline you can see at your
feet looks just as jagged as the stretch you can see from space.Many of
Nature's patterns have been shown to be fractal. Examples include coastlines,
clouds, flames, lightning, trees and mountain profiles. Fractals are referred
to as a new geometry because the patterns look nothing like traditional
Euclidean shapes. In contrast to the smoothness of artificial shapes, fractals
consist of patterns that recur on finer and finer magnifications, building up shapes of immense complexity.
So both the artist and scientist observed how the
pluralistic world would - emerge (by generative design, pattern) - that can
only be defined by fractals, in which cartesian approaches fails. Will the
growing interplay of art and science transcend to the next level of cognizant
of the world, the nature, and our infinite Universe?
We are all the bits and bytes, signals and notes of our Universe, we may also discover or co-paint the information masterpiece we can or
can’t understand, may Copernicus’s spirit of questioning inspire our curiosity
and encourage us to think differently.
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