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### The Relativity of Wrong

– By Byron Jennings, Theorist and Project Coordinator

Isaac Asimov (1920 – 1992) was a prolific writer of science fiction and popular science books. Many people of my generation had their introduction to science through his writings. While not considered a philosopher of science, one of his articles should be required reading for anyone hoping to understand how science works. The article, with the same title as this blog, first appeared on The Skeptical Inquirer (p. 35, v. 14 1989) and later in a book of the same name.  The following is my take on his point.

To clarify the relativity of wrong concept, consider the value of π. A simple approximation is π = 3 (1 Kings 7:23). This is wrong but by less than 5%. A better approximation is π = 3.14. The error here is 0.05%. Strictly speaking both values are wrong. However, the second value is less wrong than the first. As a graduate student (in the olden days, as my daughter would say) I used π = 3.141592653589793 in my computer programs. This is still wrong but much less wrong than the previous approximations. There was no point using a more accurate value of π since the precision of the computer was 15 digits (single precision on a CDC computer). None of these values of π are absolutely correct. That would take an infinite number of digits, so all are wrong. However the initial values are more wrong than the latter values. They all are useful in the appropriate context.  Hence, the relativity of wrong.

The same logic applies to models. Consider the flat earth model. For the person who never travels farther that 100 km from his birthplace, the flat earth model is quite accurate. The curvature of the earth is too small to be detected. However when the person is a sailor, the question of the shape of the earth takes on more urgency. The flat earth model suggests questions like: Where is the edge of the earth? What will happen if I get too close? For the world traveler, the flat earth model is not sufficient. The spherical earth model is more useful, has greater predictive power and suggests a wider range of questions. Questions like: Does the earth rotate? Does it move around the sun or does the sun move around the earth? But it is a wrong statement that the earth is exactly spherical. Not as wrong as the statement the earth is flat but still wrong. However being not exactly correct does not make it useless. A spherical globe allows a much better understanding of airplane routes than a flat map. But the earth is not a perfect sphere. It is flattened at the poles (a quadrupole deformation). Smaller still is its octapole (pear shaped) deformation. The exact shape of earth will never be measured, as that would require, like π, an infinite number of digits but in an infinite number of parameters. It would also be useless. What is needed is a description sufficiently accurate for the purpose it is being used for. Science is the art of the appropriate approximation. While the flat earth model is usually spoken of with derision, it is still widely used. Flat maps, either in atlases or road maps, use the flat earth model (except for my road map it is a crinkled earth model) as an approximation to the more complicated shape.

Classical mechanics — Newton’s law of motion and Maxwell equations of electromagnetism — although superseded by relativity and quantum mechanics, are still useful and taught. The motion of the earth around the sun is still given by Newton’s laws and classical optics still works. However, quantum mechanics has a much wider realm of reliability. It can describe the properties of the atom and the atomic nucleus where classical mechanics fails completely.

Animals reproducing after their kind is the few generations limit of evolution. Thus over the time scale of few human generations we do not see new kinds arising. The offspring resemble their parents. Evolution keeps the successes of the previous model; cats do not give birth to dogs, nor monkeys to people, even in evolution. The continuity between animals-reproducing-after-their-kind and evolution is not sufficiently appreciated by the foes of evolution and perhaps not by its proponents either.

There is a general trend: new models reduce to the previous model for a restricted range of observations. Ideally the new model would contain all the successes of the old model but this is not always the case. But overall the new model must have more predictive power, otherwise its adoption is a mistake. Thus we have the view of science producing a succession of models, each less wrong (none are 100% correct) than the one it replaces. We see progress. Science progresses, new models are constructed with greater and greater predictive power. The ultimate aim is to have a model of everything with a strictly limited number of assumptions. This model would describe or predict all possible observations. Quantum indeterminacy suggests that such a model does not exist. However, progress in science is moving closer to this ultimate, probably-unreachable, yet still enticing goal.