F= ma. You probably saw and used that equation in high school--or maybe you avoided the people who did. Quite a few philosophers also used that equation in philosophy's high school era, attempting to prove that everything can be explained with just those four symbols.
You have grown up, realizing there is more to life than physics: se, literature, politics, guns, butter, Steve's Ice Cream, and maybe one or two other things. Likewise, philosophers now see that you cannot quite figure out the cosmos by thinking of it as a lot of particles--unless maybe you add Murphy's Law to the standard rules of classical physics.
In The Open Universe, philosopher Karl Popper searches for that crucial ingredient whose absence keeps us from reducing the world's problems to perturbations in an atom's trajectory.
Written 25 years ago--though only published last year--The Open Universe attacks Einstein's theory of determinism, which holds that with a sophisticated enough scientific approach, man can explain and predict all occurences. But the argument only rarely appears dated. Popper proves that classical theory can never fulfill the objectives of the traditional philosophers--from Spinoza, Hobbes and Hume to Kant, Schopenhauer, and J.S. Mill--because it lends itself, through inaccuracy, to randomness and unpredictability. In this way, he buttresses quantum theory, which incorporates randomness as a principle. Einstein had often attacked this with his famous "God does not play dice with the Universe."
By breaking down a system into smaller, more easily solved physics problems, the proponents of determinism expected--in theory, anyway--that they could solve all of those equations and figure out what is going to happen next. Popper squarely attacks this view. First, he says we cannot know any initial conditions exactly--merely to some arbitrary precision. Since we have no way to tell how accurately we must know the measurements for a prediction of specified accuracy, we cannot always make the right prediction. Popper says a theory must be "accountable"--able to explain its shortcomings--to be completely deterministic. A theory which falls to explain one event automatically falls short of determinism.
Popper amplifies his position with numerous other arguments. Foremost of these is the famous "three-body problem" of classical physics: No exact solution exists for the equations describing the motion of systems which contain three or more particles--even if the initial conditions can be known exactly, our prediction must still be an estimate. Classical physics is not accountable and therefore does not imply determinism, Popper argues.
WHEN the philosopher shifts his attention to astronomy, he proves that velocity and position can be measured only to a maximum combined accuracy in celestial bodies. Thus he establishes a parallel in non-quantum mechanics to the Heisenberg Uncertainty Principle, which states that a particle's velocity and position cannot both be measured accurately at the same point in time. Later, Popper argues that because an observer is limited by the speed of light, he observes all initial conditions affecting the system only after the event has happened.
Here the thinker reveals his greatest weakness. By assuming that the observer is limited by the speed of light, he proves not that the future is not determined--only that we cannot tell what it is. Admitting this shortcoming, Popper explains that although he cannot prove that indeterminism is right, he can offer a number of arguments why it should be. This dilemma is the least satisfying element in an otherwise effective and successful study.
Popper is at his best in defining and delineating the various types of determinism. Through a careful study of scientific disciplines, he demonstrates that "scientific determinism" can be applied only to physics--all other disciplines must be reduced to F = ma. The first chapter, with a few modifications, could serve as a basic primer of holistic and reductionist thought, a boon for those intimidated by the concepts bandied about with such ease by those in the know.