BEAUTY: More Thoughts on Symmetries and Beauty
A previous entry, “BEAUTY: The Mathematical Idea of Symmetry,” presented a passage from the book THE UNIVERSE AND THE TEACUP: THE MATHEMATICS OF TRUTH AND BEAUTY by K.C. Cole. Here is some more from that same work:
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“Symmetries…show up in transformations involving context or scale or shape. Mountains and molehills share roughly the same shape, as do swirling stars in galaxies and the swirling cream in coffee. Snail shells and sunflowers repeat the same patterns over and over because their genetic instructions encode a symmetry of proportion: The next row of petals or twist of shell always grows so that it remains in exactly the same proportion to the one that follows and the one that proceeds. ‘This notion of symmetry…,’ writes Rothstein, ‘is close to what we call, in other contexts, harmony.’
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“All of these are symmetries, and all speak of deep connections that lie buried underneath the superficial differences. They are the same kinds of symmetries, Rothstein argues, that create the emotional responses we ‘feel’ in the presence of beauty– in math or music. ‘What we ‘feel’ in such moments is the analogy of the part and the whole, object and other object, relation and relation.’…
“A variation of this equation lies at the heart of the Golden Rule, which tells us to do unto others as we would like others to do unto us.”
(pp. 178-179)
February 5th, 2010 at 7:37 pm
At last! some official recognition of symmetry – the same as in Chaos Theory. The iteration points all have an opposing sides of symmetry. The whole universe (or multiverses) is formed the same way…down to our very cells..to the farthest horizon.
February 6th, 2010 at 7:37 am
Multiple interesting thoughts in such a short quote! Equating the whorl of stirred coffee with the multiverses (of Lee). That we respond to the described gradients when experienced as beauty….
I read and reread thhis and find more within the statements to expand the mind as a series of gradients…and so experience delight in learning as beauty.
February 6th, 2010 at 11:13 am
While we’re on the subject of swirls/whorls, see cosmologist Andrei Linde’s sequence of snapshots of the evolution of scalar field “choices” of the three potential energy minima (represented by red, blue, and green) in domains where the inflaton field is small.
http://www.stanford.edu/~alinde/kandin.gif
Even if you have a high-speed internet connection you will have to wait a while for the GIF file to load. If you have a low-speed connection you can try one image at
http://www.stanford.edu/~alinde/kand20.jpg
Linde dubbed these visualizations examples of the “Kandinsky universe” after the famous Russian abstract artist.