Thursday, December 29, 2005

Special Relativity

The first snow of the season has come and gone. Early in the morning of their treasured snow day, Barnacle Boy and Crash Kid made an expedition to the basement for their boots. The Boy's feet have grown since last winter -- the boots don't fit. The Math Man suggests that Crash wear my boots and Barnacle wear Crash's. I point out that this solution is unworkable, since the Boy's feet are a full size larger than mine and I haven't been able to wear Crash's shoes for several years. Math Man hadn't quite processed the new relative ordering!

New boots have been ordered!

Friday, December 02, 2005

Mechanical Miracles

Measured and restrained can easily become mechanical. Consider the candles. In medieval times, as now, you might light a candle for an intention. Then, you might truncate the candle to the measure of the saint who assistance you invoked. Now, at least in the Cathedral in Philadelphia, you drop a coin into a box and an electric light turns on. It is deeply unsatisfying -- but perhaps difficult to express why. I might say that we moved from one truncation error to another. The light is now utterly mechanical, we control its incandescence, the time it will "burn", the risk inherent in its burning.

Has this truncation of the expansion limited our ability to hear the communication of the unmeasured and unmeasurably abundant grace of God? The outward form appears much the same, but the res, the spiritual reality, has been irrevocably changed. Quantum chemists know that small changes in the functional form, to the point where two functions still appear identical, can lead to much larger changes in the expectation values of critical characteristics, such as the energy!