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Sunday, February 13, 2011

Unavoidable symmetry

Here are two bits of symmetry appreciation:

Can you see (with the eyes of imagination) the double reflections generating the icon (of the Publican and the Pharisee) below?

As such, the images of the Publican and the Pharisee form two distinct symmetry orbits generated by double reflections, introduced earlier here.




Now enjoy one a poem of J.L. Borges, where he (as often) plays with reflections, mirrors, and more:

We are the time. We are the famous
Jorge Luis Borges 

We are the time. We are the famous
metaphor from Heraclitus the Obscure.
    We are the water, not the hard diamond,
    the one that is lost, not the one that stands still.
We are the river and we are that greek
that looks himself into the river. His reflection
changes into the waters of the changing mirror,
into the crystal that changes like the fire.
   We are the vain predetermined river,
   in his travel to his sea.
The shadows have surrounded him.
Everything said goodbye to us, everything goes away.
   Memory does not stamp his own coin.
However, there is something that stays
however, there is something that bemoans. 


And here, perhaps Borges brings us an image of a single-point orbit when the colors of its element are erased:


"Denying temporal succession, denying the self, denying the astronomical universe, are apparent desperations and secret consolations. Our destiny is not frightful by being unreal; it is frightful because it is irreversible and iron-clad. Time is the substance I am made of. Time is a river, which sweeps me along, but I am the river; it is a tiger, which destroys me. But I am the tiger, it is a fire, which consumes me, but I am the fire. The world, unfortunately, is real. I, unfortunately, am Borges"

Jorge Luis Borges. Essay: A New Refutation of Time in Labyrinths. Ed Donald A Yates and James E Irby. Penguin Books 1987.


Revisions 02/25/2011
06/06/11
These  postings are based on "Symmetry Studies An  Introduction to the Analysis of Structured Data in Applications"  Cambridge Press (2008)



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