10 December 2005

I dwell in Possibility--
A fairer House than Prose--
More numerous of Windows--
Superior--for Doors -

Of Chambers as the Cedars--
Impregnable of Eye--
And for an Everlasting Roof
The Gambrels of the Sky--

Of Visitors--the fairest--
For Occupation--This--
The spreading wide my narrow Hands
To gather Paradise--

~ Emily Dickinson, born this day in 1830

9 December 2005

"God has neither form nor shape under which we can know Him; when he speaks of Himself in metaphors and similes, He is adapting Himself to our foolishness, our limited capacity"

~ Christina of Sweden

"The Second Commandment, observed by Jews and Muslims alike, is not really a prohibition against making sculptures, it is a warning against the profound error of concretizing God, the profound error of thinking that you can possibly know what God is or looks like or wants."

~ Stephen Nachmanovich and Abdul Said

8 December 2005

"There is a star above us which unites souls of the first order, though worlds and ages separate them."

~ Queen Christina of Sweden, born this day in 1626.

As an orphaned child, destined to rule, she chose a life of physical discipline and intense study.  By the time she was 22, she was committed to peace among nations, and was instrumental in ending the Thirty Years' War.  At 28, she gave up the throne in order to pursue Catholic mysticism, travel and adventure. "Unconcerned with appearances, and daring to live a life of almost total freedom, Christina was one of the most highly independent, unconventional, and outrageously colorful women in history."

7 December 2005

"In the fight between you and the world...back the world."

~ Franz Kafka

6 December 2005

Those who would follow in steps of heroes
must heed clearly the voice of the people
and shape their dreams into visions.

For this is no journey of turning back,
no force that can be denied.

A culture of peace is dawning
and all will be changed in its light.

~ from The Dawning of Peace, by David Adams

5 December 2005

In Richard Feynman’s formulation of quantum physics, while you’re not looking, an object can and does do every possible thing. If you see a chair, turn your back, and find the chair where you left it, you would feel quite justified in concluding it had been there all along. How presumptuous of you! The correct quantum calculation would take an average over infinitely many things that the chair could have done during the seconds that your head was turned. It could have rocked on its legs. It could have turned upside down. It could have zoomed around the world and back again. Energy conservation is no obstacle in inventing these paths. They all must be considered part of the "in between" reality, in order to predict the simple probability that you’ll find the chair where you left it.

Two qualifiers: (1) "energy conservation is no obstacle". Actually, one thing that saves this schema from devolving into complete chaos is that the probability of each possible path is modified by the extent to which it departs from energy conservation. Those paths that involve the appearance or disappearance of large quantities of energy are proportionally less probable. (2) "...take an average over infinitely many paths" If you averaged the probabilities of all these paths, they would each contribute something positive to the overall probability. They would all be important. But in quantum physics the quantity that is averaged is a wave which can have positive or negative amplitudes, so some of the paths can cancel each other out. In fact, it turns out that all those probability waves for the chair going around the world have almost equal positive and negative amplitudes, so they tend to cancel, while some of the probability waves associated with the chair remaining in the same place tend to be in phase with each other, so that in the end these are the only ones that really matter.

"I think it is safe to say that no one understands Quantum Mechanics"
- Richard Feynman