Replaying the tape
The evolutionary biologist Stephen Jay Gould once proposed a thought experiment that he called “replaying life’s tape”. Suppose we press the rewind button and return to some point in the past, erasing all interim evolutionary developments. If we let the tape run again, will evolution occur in exactly the same way as before? Gould answered “no”, and used the thought experiment to challenge the assumption that biological evolution is a “ladder of progress” that drives life inevitably to the same advanced forms.
It is interesting to think what might happen if we carried out the same thought experiment, not for living things, but for equations. Would the equations develop in an unpredictable way, like the evolution of species? Or would it be inevitable? If we started all over again, would we still have F = ma? Indeed, would we have equations at all?
In the 19th century, the French philosopher Auguste Comte thought he could answer such questions. Comte advanced what he called “a great fundamental law” according to which each branch of human knowledge - as well as each person, state and civilization - passes through three different developmental stages: theological, metaphysical and scientific. In each stage, human beings try different approaches to securing stable and progressive relations with nature to make their surroundings peaceful and predictable. But inadequacies in each approach force human beings to make revisions, leading to the next stage.
The development of the concept of force nicely illustrates Comte’s law. In primitive times, Comte thought, humans saw the world as ruled by deities. This was natural and inevitable, for all humans acquire a notion of force from individual experiences of pushes and pulls in daily life. Projected into nature, this creates a theological picture in which everything from thunder and rain to the stars is the result of spirits behaving and misbehaving. The theological stage is indispensable because, in it, we learn how to explain, strive for consistency and overcome contradictions with new explanations.
But trying to control nature by pleasing the spirits through ritual and prayer (the earliest forms of technology) did not succeed in bringing about the desired predictability. A far more effective way of influencing nature turned out to be studying the changes that the spirits produced - the patterns in the seasons, tides and stars, in the behaviour of fire, and so on. This shift of attention moved humanity into the second, metaphysical stage. Here humans continued to attempt to explain the “why” of things through some ultimate cause or essence. But the supernatural agents were now replaced by what Comte called “abstract forces, real entities or personified abstractions”.
Force, for instance, was explained as operating through the medieval notion of “impetus”, which is passed from one body to another and causes motion. But these metaphysical agents, too, gradually became emptied of meaning, and reason itself did not provide a sufficient ground for understanding nature.
This led to the final - scientific - stage, which saw the maturation of the human intellect. Physics and astronomy, Comte thought, reached this stage in the 17th century. Human beings ceased to ask why phenomena happened and instead sought to answer how they happened by finding the appropriate laws. The number of such laws tends to decrease as science progresses. Gravitation, for example, was found to unify what had seemed to be myriads of forces into one.
Comte never considered the question of whether individual equations such as F = ma would reappear if the process recurred. But had this thought experiment been proposed to him, he would surely have held that the conceptual trajectory that led to F = ma would be more or less repeated, with theological concepts of force giving way to metaphysical concepts and then to mathematical laws governing abstract quantities.
摘自：http://physicsworld.com/cws/article/print/24291