Physicists and Philosophers Debate the Boundaries of Science

Some theories are so easy to test, a 4th grader in her science class can test it conclusively in half an hour. We don't even question these theories anymore, because they've been set in stone for centuries.

Some theories take millions of dollars and several years to test, but they're manageable by large research universities and governments. At the very edge of this range, we have things like the Large Hadron Collider testing the existence of the Higgs boson. That one actually cost a few billion dollars and several decades, but we could live with that.

Some theories will take trillions of dollars and several centuries to test. Perhaps it will be quadrillions of dollars and several millennia instead, or even several million years. Right now, we don't even know what kind of technology we will need to test string theory. Perhaps we'll need to evolve into something else before our brains can even imagine what it would take to test it. But eventually we'll get there, if we learn to accept that science is bigger than all of us and stop being so impatient.

The difference between these three kinds of "testable" are quantitative, not qualitative. It just looks qualitative because the quantities involved are so huge. But if someone cannot grasp the idea of a theory that takes aeons to develop and test, I don't think they're qualified to judge the merits of theoretical physics.

jwmerrill's razor: points in the plane should be considered to be close to the origin unless there is evidence otherwise.

Is this a reasonable law? As reasonable as Occam's razor? I think probably not, but I don't have a strong opinion. One interesting thing to note is that the law doesn't say where the origin is (similarly, Occam's razor is vague about what exactly is meant by "simple" and "complex").

Finite asymptotic form: for any finite point set, there is a distance D such that no point in the set is further from the origin than D.

Continuous asymptotic form: given any function from points in the plane to non-negative numbers which has a finite integral, there is a distance D such that the integral of the function over the region that is further from the origin than D is less than any epsilon_1, and such that the function is everywhere less than any epsilon_2 on this region except perhaps on a set of measure 0.

The asymptotic forms are provable mathematical statements, but I think it would be a mistake to say that either of them is a very compelling argument for the original statement of "jwmerrill's razor."

Without intending to call you out in particular (I don't know what opinions you hold), I think people sometimes accept some odd logic in probability theory that they would be less likely to accept in other contexts. Bayesian probability theory provides practical solutions to a lot of interesting problems, and I personally wish people would emphasize those cases more, and make fewer sweeping statements about it being a consistent theory of all of the scientific method.

"In this revolution, research has become central; it also becomes more formalized, complex, and costly. A steadily increasing share is conducted for, by, or at the direction of, the Federal government. Today, the solitary inventor, tinkering in his shop, has been overshadowed by task forces of scientists in laboratories and testing fields. In the same fashion, the free university, historically the fountainhead of free ideas and scientific discovery, has experienced a revolution in the conduct of research. Partly because of the huge costs involved, a government contract becomes virtually a substitute for intellectual curiosity. For every old blackboard there are now hundreds of new electronic computers. The prospect of domination of the nation's scholars by Federal employment, project allocations, and the power of money is ever present and is gravely to be regarded. Yet, in holding scientific research and discovery in respect, as we should, we must also be alert to the equal and opposite danger that public policy could itself become the captive of a scientifictechnological elite."