Scientific Method

The Greeks constructed a model in which the stars were lights fastened to the inside of a large, hollow sphere (the sky), and the sphere rotated about the Earth as a center. This model predicts that all of the stars will remain fixed in position relative to each other. But certain bright stars were found to wander about the sky. These stars were called planets (from the Greek word for wanderer). The model had to be modified to account for motion of the planets. In Ptolemy's (A.D. 90-168) model of the solar system, each planet moves in a small circular orbit, and the center of the small circle moves in a large circle around the Earth as center.

Copernicus (1473-1543) assumed the Sun was near the center of a system of circular orbits in which the Earth and planets moved with fair regularity. Like many new scientific ideas, Copernicus' idea was initially greeted as nonsense, but over time it eventually took hold. One of the factors that led astronomers to accept Copernicus' model was that Ptolemaic astronomy could not explain a number of astronomical discoveries.

In the case of Copernicus, the problems of calendar design and astrology evoked questions among contemporary scientists. In fact, Copernicus's theory did not lead directly to any improvement in the calendar. Copernicus's theory suggested that the planets should be like the earth, that Venus should show phases, and that the universe should be vastly larger than previously supposed. Sixty years after Copernicus's death, when the telescope suddenly displayed mountains on the moon, the phases of Venus, and an immense number of previously unsuspected stars, the new theory received a great many converts, particularly from non-astronomers.

The change from the Ptolemaic model to Copernicus's model is a particularly famous case of a paradigm change. As the Ptolemaic system evolved between 200 B.C. and 200 A.D., it eventually became highly successful in predicting changing positions of the stars and planets. No other ancient system had performed as well. In fact the Ptolemaic astronomy is still used today as an engineering approximation. Ptolemy's predictions for the planets were as good as Copernicus's. But with respect to planetary position and precession of the equinoxes, the predictions made with Ptolemy's model were not quite consistent with the best available observations. Given a particular inconsistency, astronomers for many centuries were satisfied to make minor adjustments in the Ptolemaic model to account for it. But eventually, it became apparent that the web of complexity resulting from the minor adjustments was increasing more rapidly than the accuracy, and a discrepancy corrected in one place was likely to show up in another place.

Tycho Brahe (1546-1601) made a lifelong study of the planets. In the course of doing so he acquired the data needed to demonstrate certain shortcomings in Copernicus's model. But it was left to Johannes Kepler (1571-1630), using Brahe's data after the latter's death, to come up with a set of laws consistent with the data. It is worth noting that the quantitative superiority of Kepler's astronomical tables to those computed from the Ptolemaic theory was a major factor in the conversion of many astronomers to Copernicanism.

In fact, simple quantitative telescopic observations indicate that the planets do not quite obey Kepler's laws, and Isaac Newton (1642-1727) proposed a theory that shows why they should not. To redefine Kepler's laws, Newton had to neglect all gravitational attraction except that between individual planets and the sun. Since planets also attract each other, only approximate agreement between Kepler's laws and telescopic observation could be expected.

Newton thus generalized Kepler's laws in the sense that they could now describe the motion of any object moving in any sort of path. It is now known that objects moving almost as fast as the speed of light require a modification of Newton's laws, but such objects were unknown in Newton's day.

Newton's first law asserts that a body at rest remains at rest unless acted upon by an external force. His second law states quantitatively what happens when a force is applied to an object. The third law states that if a body A exerts a force F on body B, then body B exerts on body A, a force that is equal in magnitude but opposite in direction to force F. Newton's fourth law is his law of gravitational attraction.

Newton's success in predicting quantitative astronomical observations was probably the single most important factor leading to acceptance of his theory over more reasonable but uniformly qualitative competitors.

It is often pointed out that Newton's model includes Kepler's laws as a special case. This permits scientists to say they understand Kepler's model as a special case of Newton's model. But when one considers the case of Newton's laws and relativistic theory, the special case argument does not hold up. Newton's laws can only be derived from Albert Einstein's (1876-1955) relativistic theory if the laws are reinterpreted in a way that would have only been possible after Einstein's work.

The variables and parameters that in Einstein's theory represent spatial position, time, mass, etc. appear in Newton's theory, and there still represent space, time, and mass. But the physical natures of the Einsteinian concepts differ from those of the Newtonian model. In Newtonian theory, mass is conserved; in Einstein's theory, mass is convertible with energy. The two ideas converge only at low velocities, but even then they are not exactly the same.

Scientific theories are often felt to be better than their predecessors because they are better instruments for solving puzzles and problems, but also for their superior abilities to represent what nature is really like. In this sense, it is often felt that successive theories come ever closer to representing truth, or what is "really there." Thomas Kuhn, the historian of science whose writings include the seminal book The Structure of Scientific Revolution (1962), found this idea implausible. He pointed out that although Newton's mechanics improve on Ptolemy's mechanics, and Einstein's mechanics improve on Newton's as instruments for puzzle-solving, there does not appear to be any coherent direction of development. In some important respects, Kuhn has argued, Einstein's general theory of relativity is closer to early Greek ideas than relativistic or ancient Greek ideas are to Newton's.