A few years ago the city council of Monza, Italy, barred pet owners from keeping goldfish in curved bowls. The measure’s sponsor explained the measure in part by saying that it is cruel to keep a fish in a bowl with curved sides because, gazing out, the fish would have a distorted view of reality. But how do we know we have the true, undistorted picture of reality?
The goldfish view is not the same as our own, but goldfish could still formulate scientific laws governing the motion of the objects they observe outside their bowl. For example, due to the distortion, a freely moving object would be observed by the goldfish to move along a curved path. Nevertheless, the goldfish could formulate laws from their distorted frame of reference that would always hold true. Their laws would be more complicated than the laws in our frame, but simplicity is a matter of taste.
A famous example of different pictures of reality is the model introduced around A.D. 150 by Ptolemy to describe the motion of the celestial bodies. Ptolemy published his work in a treatise explaining reasons for thinking that the earth is spherical, motionless, positioned at the center of the universe, and negligibly small in comparison to the distance of the heavens.
This model seemed natural because we don’t feel the earth under our feet moving . Ptolemy’s model of the cosmos was adopted by the Catholic Church and held as official doctrine for fourteen hundred years. It was not until 1543 that an alternative model was put forward by Copernicus. So which is real? Although it is not uncommon for people to say Copernicus proved Ptolemy wrong, that is not true. As in the case of the goldfish, one can use either picture as a model of the universe. The real advantage of the Copernican system is that the mathematics is much simpler in the frame of reference in which the sun is at rest.
