28 January 2007
Those whose accomplishments on a global scale are deep and long-lasting are seldom the ones whose self-importance drives them to disdain people of lesser ambition. Emulate Mother Theresa and Ghandi.
– Josh Mitteldorf
27 January 2007
26 January 2007
O vast Rondure, swimming in space,
Now first it seems my thought begins to span thee.
25 January 2007
Joseph Lagrange, born this day in 1736, invented a mathematical procedure for global optimization. A century earlier, Isaac Newton had come up with a technique for finding the maximum or minimum value of a function. It was Lagrange’s genius to apply the same principle to the more abstract notion of finding the function or shape that best satisfies some mathematical criterion. For example, what shape wing provides the most lift to an airplane?
Lagrange re-formulated the physical mechanics of Newton. In Newton’s way of thinking, the state of a system at any moment is derived from the state a moment before by a differential process. But Lagrange conceived of the entire history all at once, and showed that one could derive an equivalent set of equations from on optimization principle: Every particle follows a trajectory that minimizes its action, defined as the time integral of the difference between kinetic and potential energy.
In the twentieth century, it was found that Newtonian thinking did not generalize easily to quantum mechanics, but simple and elegant ways were found to formulate QM in terms of Lagrangian optimization. It was Richard Feynman who took this idea to its denouement in formulating quantum electrodynamics as one big Lagrangian optimization problem.
There is a life lesson from Lagrange’s insight: We perceive ourselves as poised on a cusp in time, concerned about the immediate future and what we might do to affect it. But there is another perspective, in which an entire trajectory in time is seen as a whole. Our life journey – its struggle, its disappointments, its lessons, and its triumphs – constitutes a whole with an integrity and a beauty which can be appreciated from a perspective outside time.
24 January 2007
“How can I be optimistic without knowing what direction science will take? This is exactly the point. There are two kinds of optimism, the optimism of people who think they know the future and the optimism of people who believe the future will be more interesting and, if always imperfect, more wonderful than they can imagine. I am of the second kind. The first kind sometimes comes along with a belief that time and change are illusions, and that the world is evolving towards an eternal timeless state of perfection. This is the optimism of religious fundamentalists and orthodox Marxists, and one sees it reflected also in the cosmologies in which our evolving universe is just a transient fluctuation in an otherwise permanent state of thermal equilibrium. The opposite kind of optimism lies behind the evolutionary theorists who believe the world is so intricate that the simplest mechanism that could predict the future of life and the cosmos is the universe itself. If we are the first kind of optimist we seek to transcend the complexities of life to discover something eternal behind it, something like the imagined view of God. If we are the second, we seek to live and think within the swirl of life; we aim for comprehension and wisdom but have no illusions of transcendence or control.”
23 January 2007
The Giver of Stars
Hold your soul open for my welcoming.
Let the quiet of your spirit bathe me
With its clear and rippled coolness,
That, loose-limbed and weary, I find rest,
Outstretched upon your peace, as on a bed of ivory.
Let the flickering flame of your soul play all about me,
That into my limbs may come the keenness of fire,
The life and joy of tongues of flame,
And, going out from you, tightly strung and in tune,
I may rouse the blear-eyed world,
And pour into it the beauty which you have begotten.
~ Amy Lowell ~
22 January 2007
“Those who have taken upon them to lay down the law of nature as a thing already searched out and understood, whether they have spoken in simple assurance or professional affectation, have therein done philosophy and the sciences great injury. For as they have been successful in inducing belief, so they have been effective in quenching and stopping inquiry; and have done more harm by spoiling and putting an end to other men's efforts than good by their own. Those on the other hand who have taken a contrary course, and asserted that absolutely nothing can be known — whether it were from hatred of the ancient sophists, or from uncertainty and fluctuation of mind, or even from a kind of fullness of learning, that they fell upon this opinion — have certainly advanced reasons for it that are not to be despised; but yet they have neither started from true principles nor rested in the just conclusion, zeal and affectation having carried them much too far....
“Now my method, though hard to practice, is easy to explain; and it is this. I propose to establish progressive stages of certainty. The evidence of the sense, helped and guarded by a certain process of correction, I retain. But the mental operation which follows the act of sense I for the most part reject; and instead of it I open and lay out a new and certain path for the mind to proceed in, starting directly from the simple sensuous perception.”