Archive for the ‘Astronomy’ Category

Heroic Oversimplification for Modeling our World

October 20, 2007

The invention of deliberately oversimplified theories is one of the major techniques of science, particularly of the “exact” sciences. The biophysicist employs simplified models of the cell, the cosmologist uses simplified models of the universe, and so on.

It may be useful to examine one successful scientific abstraction, to see what it is like and for the sake of the hints it may give us. We choose one which is surely an example of a heroic oversimplification.

Let us assume that we may, in order to study their motions, replace each of the major bodies of the Solar System by a point; that each point experiences a mutual attraction; that we may estimate the attractive force by multiplying the mass of one point by the mass of the other, after which we divide that product by the square of the distance between the points; and that we may neglect all else.

The fact is that this theory, the Theory of Gravitation, has been adequate for predicting the motions of the planets for two and one-half centuries – and this in the face of constant checking by positional astronomers, who, it can fairly be said, carry precision to extremes. The worst strain has come from the orbit of Mercury, which unaccountably drifted from the predicted place by one-fifth of a mil (a foot, at a distance of a mile) per century, thus showing that the theory is rough after all, just as it looks. The improved theory, by Einstein, accounts for this discordance.

The Compleat Strategyst by J.D. Williams

Measuring Time

July 22, 2007

Time is defined by reference to astronomical phenomena. Astronomical recurrences mark out equal intervals of time:

– a year is defined as one trip of the earth around the sun

– a day is defined as one rotation of the earth

Relegation of the determination of the measure of time to the astronomer arises from the consistency[1] of the recurrences with which they deal. If such consistency had been noted among the recurrences characteristic of the human body, we would have looked to the doctors of medicine to determine the measure of time[2].

[1] Example of a “consistent” recurrence: the number of days it takes for the earth to orbit the sun is 365.25 days, year after year … the recurrences are consistent. For all ordinary purposes of life on earth, the various astronomical recurrences may be looked on as absolutely consistent.

[2] The heart beat is periodic, but not consistent; it beats quickly when we are active, slower when we are resting; such inconsistent recurrences would not be useful for measuring time.

— Alfred North Whitehead, An Introduction to Mathematics

Question: how is “hour” measured? Is there an astronomical recurrence that indicates an hour? An hour is one twenty-fourth of a day, of course, but how did the ancients realize that one twenty-fourth of a day has elapsed?