What would happen if we rewound the tape and let science develop again from scratch? Robert P Crease looks at some results of this thought experiment
The equation F=ma, shorthand for Newton’s second law of motion, is the 1+1=2 of classical mechanics. The equation seems obvious and straightforward. It appears simply to translate an ordinary experience into measurable terms: push something and it moves.
Yet like 1+1=2, F=ma grows mysterious when looked at closely. It does not refer to ordinary experience, but to an abstract world of zero resistance; in reality, we must continue pushing things to keep them moving at the same speed. The equation also says nothing about mass-energy exchange. And it gives centre stage to force – a concept absent from most formulations of contemporary theories like relativity and quantum mechanics.
How can such an elementary equation about something as ordinary as motion conceal so much? The answer lies in the historical process leading from ancient times to the formulation of F=ma in the 17th century. This conceptual journey shows that when we learn this equation, we master (and inherit) more than we think. The fact that an equation such as F=ma arose out of a developmental process, however, invites the question of whether the process would happen the same way twice.
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.
The critical point
But so what if our thought experiment tells us that we would end up with something like Newton’s second law again? In his recent book, Comte After Positivism, the US philosopher Robert Scharff tries to explain why this conclusion is important.
As Scharff points out, the main function of Comte’s law is to express and articulate his dissatisfaction with the state of science around him. Comte sought to bring to light again the often-forgotten background of science – why we do it, what has been tried and failed, and how it affects the atmosphere of human life. By describing and propounding the law, Comte wanted to improve our understanding of why we do science this way and thus help usher humanity from the metaphysical to the scientific stage.
In fact, Comte’s ideas about thought experiments are still relevant today, given that science is now being challenged theologically by a new brand of creationism, in the form of intelligent design. It is also being challenged politically by an attempt to use it as a pliable instrument for accomplishing ideological ends. And it is challenged even by promoters who are unable to recognize their own tunnel vision. Though our situation differs from that of Comte, his goal of achieving self-consciousness with respect to science and how we inhabit the world it has shaped is more urgent than ever.
