How Science really works.
Even casual observation shows us that nature, as perceived by our senses, has reliable regularities and patterns of behavior. Through more precise and detailed study we found that many of these regularities can be modeled, often with mathematical models of great precision.
Sometimes these models break down when extended (extrapolated) beyond their original scope of validity. Sometimes extrapolation of a model beyond its original scope actually works. This warns us that we had better rigorously test each model for validity, and these tests should be capable of exposing any flaws in the modelflaws capable of demonstrating that the model isn't true.
Even when a model survives such testing, we should only grant it "provisional" acceptance, because cleverer people with more sophisticated measuring techniques may in the future expose some other deficiencies of the model.
When models are found to be incomplete or deficient, we often fix them by tweaking their details till they work well enough to agree with observations.
When rapid advances in experimental observations occur, a model may be found so seriously inadequate to accommodate the new data that we may scrap a large part of it and start over with a new model. Relativity and quantum mechanics are historical examples. These situations are often called "scientific revolutions."
When such upheavals occur, and old models are replaced with new ones, that doesn't mean the old ones were totally "wrong", nor does it mean their underlying concepts were invalid. They still work within their scope of applicability. Newton's physics wasn't suddenly wrong, nor were its predictions found unreliable or incorrect when we adopted Einstein's relativity. Relativity had greater scope than Newtonian physics, but it also rested on a different conceptual basis.
Past experience has shown that mathematical models of nature have tremendous advantages over the earlier, more appealing, models that use analogies to familiar everyday phenomena of our direct sensory experience. Mathematical models are less burdened with emotional baggage, being "pure" and abstract. Mathematics provides seemingly infinite adaptability and flexibility as a modeling structure. If some natural phenomena can't be modeled by known mathematics, we invent new forms of mathematics to deal with them.
The history of science has been a process of finding successful descriptive models of nature. First we found the easy ones. As science progressed, scientists were forced to tackle the more subtle and difficult problems. So powerful are our models by now that we often delude ourselves into thinking that we must be very clever to have been able to figure out how nature "really" works. We may even imagine that we have achieved "understanding". But on sober reflection we realize that we have simply devised a more sophisticated and detailed description.
Whatever models or theories we use, they usually include some details or concepts that do not relate directly to observed or measurable aspects of nature. If the theory is successful we may think that these details are matched in nature, and are "real" even though they are not experimentally verifiable. Their reality is supposed to be demonstrated by the fact that the theory "works" to predict things we can verify and continue to verify. This is not necessarily so. Scientists often speak of energy, momentum, wave functions and force fields as if they were on the same status as objects of everyday experience such as rocks, trees and water. In a practical sense (for getting answers) this may not matter. But on another level, a change of scientific model may do away with a force field as a conceptual entity, but it wouldn't do away with a forest, mountain or lake.
Science progresses through trial and error, mostly error. Every new theory or law must be skeptically and rigorously tested before acceptance. Most fail, and are swept under the rug, even before publication. Others, like the luminiferous ether, flourish for a while, and then their inadequacies accumulate till they are intolerable, and are quietly abandoned when something better comes along. Such mistakes will be found out. There's always someone who will delight in exposing them. Science progresses by making mistakes, correcting the mistakes, then moving on to make new mistakes. If we stopped making mistakes, scientific progress would stop.
What do scientists really think about 'reality'?
Scientists speak in a language that uses everyday colloquial words with specialized (and often different) meanings. When a scientist says something has been found to be 'true', what is meant isn't any form of absolute truth. Likewise scientists' use of 'reality' and 'belief' don't imply finality or dogmatism. But if we inquire whether a scientist believes in an underlying reality behind our sense impressions, we are compounding two tricky words into a philosophical question for which we have no way to arrive at a testable answer. I'd be inclined to dismiss the entire question as meaningless, and not waste time discussing it, or any other such questions. Yet a few scientists and philosophers disagree, and wax eloquent in writing and speaking about such questions.
The notion that we can find absolute and final truths is naive, but still appealing to many people, especially non-scientists. If there are any underlying "truths" of nature, our models are at best only close approximations to themuseful descriptions that "work" by correctly predicting nature's behavior. We are not in a position to answer the philosophical question "Are there any absolute truths?" We can't determine whether there is an underlying "reality" to be discovered. And, though our laws and models (theories) become better and better, we have no reason to expect they will ever be perfect. So we have no justification for absolute faith or belief in any of them. They may be replaced someday by something quite different in concept. At least they will be modified. But that won't make the old models "untrue". All this reservation and qualification about truth, reality, and belief, doesn't matter. It isn't relevant to doing science. We can do science quite well without 'answering' these questionsquestions that may not have any answers. Science limits itself to more finite questions for which we can arrive at practical answers.
Also, we've learned that not all questions we can ask have answers that we can find. Any question that is in principle or in practice untestable is not considered a valid scientific question. We like to think that scientists don't waste time on those, but they seem to pop up in discussion and in books quite often. (Many people think unanswerable questions are the most profound and important ones. Questions like "What is the meaning of it all," or "What jump-started the universe?" I think that scientists should set these aside for the philosophers to chew on, and get on with the business of answering more accessible questions.)
Aesthetic appeal of theories.
Many who write about science emphasize the "beauty" and aesthetic appeal of successful theories. I used to naively think that to achieve intellectually and emotionally appealing theories was a goal of science. Maybe it is, on the subconscious level, as a scientist may be more enthusiastic about developing an appealing theory than an "ugly" one. And if the appealing one "works" all the ugly alternatives are dropped and forgotten.
But there's no reason why nature's operations should be beautiful or appealing to us. There's no reason why nature's operations should even be fully comprehensible to us. It could be that when we achieve an even more successful theoretical description of nature it may turn out to be messy, difficult to understand and use, and totally devoid of emotional or aesthetic appeal. We may not be capable of devising more satisfying alternatives.
We've had a taste of this already. When quantum mechanics was being developed many physicists in the forefront of developing the theory didn't "like" it, and hoped that someday they'd find a different way to formulate the theoryone more to their liking. A couple of quotes illustrate this:
In spite of great efforts to find a more appealing theory, and ingenious attempts to show that such things as the Heisenberg uncertainty principle were "wrong", the effort to remove the ugliness of quantum mechanics has (so far) failed.
It seems almost inescapable that as physics becomes more successful and more powerful its theories become farther removed from the intuitive, simple, beautiful theories of earlier centuries. This shouldn't be surprising. As we unravel the mysteries of the universe our first successes are with those accessible to direct sensory experiencephenomena that occur in everyday life and are observable without specialized apparatus, phenomena that have simple enough behavior that we can grasp the explanation and feel we "understand" it. But now we have done all the simple stuff. So we must sweat the details of phenomena that can't be directly sensed, that can only be made to occur in the lab with expensive and sophisticated equipment, and which require us to invent new mathematics to describe what's happening. The fuel that motivates us to continue along these lines is the fact that so often it works remarkably well, resulting in both scientific and technological advances. The practical technological fall-out from science stimulates funding of further research. But inevitably the science upon which the technology of our daily lives operates becomes farther removed from everyday experience and farther from the understanding of non-scientists. Most people live in a world that they understand only in a superficial way. That has been so since the beginning of human history. Yet there was a time, in fairly recent history, that almost anyone could feel that with a bit of effort and study one could learn a lot more about science, and even have a feeling of understanding much of science, and finding it intellectually and emotionally satisfying. That is much harder to do today.
I think it was Von Neumann who said that if we ever make computers that can think, with the power of the human brain or better, we won't know how they do it. Future scientific advance may be carried out entirely by computers, predicting phenomena of nature better than any previous models and theories had. But the computers by that time will be evolving independently of us, designing and re-designing themselves, learning independently of our programmers, and finding their own algorithms for dealing with nature. These algorithms will be so complex (and probably ugly) that we won't know how they work, and won't be able to re-express them in ways we can comprehend. One bit of evidence to show how this could come about is the recent fuss over the Y2K (year-2000) problem. It's terribly difficult to reconstruct the logic of computer programs written years ago, for which documentation is fragmentary, and the original programmers retired or deceased. Yet this problem is a small one compared to the problem of debugging a computer program written, not by a human, but by a computer that is redesigning itself as it works, in order to solve problems that have frustrated the few greatest minds of humanity.
The symbiotic relation between mathematics and physics.
Students and laypersons seldom grasp the difference between mathematics and physics. Since math is the preferred modeling analogy for physics, any physics textbook is richly embellished with equations and mathematical reasoning. Yet to understand physics we must realize that math is not a science, and science is not merely mathematics.
In the early history of science, mathematics was considered a "science of measurement", and was supported because of its practical applications in land measurement, commerce, navigation, etc. But those who did math discovered that mathematics was a branch of logic, and certain important results (such as the Pythagorean theorem of right triangles) could be arrived at by purely logical means without recourse to experiment. Slowly there emerged a body of knowledge called "pure" mathematicstheorems that were derived by strictly logical means from a small set of axioms. Euclid's geometry was of this form.
Today science and mathematics are separate and independent disciplines. The physicist must learn a lot of mathematics, but the mathematician (unless working in an applied field) need not know science. In fact, most pure mathematicians seldom interact with scientists, and have no need to. Likewise, physicists generally are capable of doing mathematics without interaction with mathematicians, and have on a number of occasions, developed new mathematics to solve particularly knotty problems. One theoretical physicist I knew spent a lot of time reading the mathematics literature, saying "Those mathematicians are doing some stuff that might be really useful to us. I only wish they spoke our language." His point was that the language with which each discipline speaks of its own field has diverged to the point where special effort must be made to "cross over" into the technical literature of the other field. A similar situation exists today in philosophy, where the language of philosophy of science has become so specialized and technical that most scientists find great difficulty reading it. But as one philosopher put it, "Philosophers of science observe scientists from outside, trying to figure out what they are doing, how they are doing it, and what it all means. In this process we have no need to talk to them. It's like watching a game where you don't know the rules when you come in, but try to figure out the rules by watching what the players do. For philosophers, science is a spectator sport."
Geometers can define concepts such as "circle", "triangle", "parallel lines". Within pure mathematics, these can be "perfect". The mathematician's parallel lines are strictly and perfectly equidistant from each other, to a perfection unattainable by mundane measurement. All points of mathematician's circle are perfectly equidistant from its center, but no one could draw such a perfect circle even with the best instruments. The angles of a mathematician's triangle add to exactly 180°. But if you drew a triangle and measured the angles, each would have a finite precision and some experimental error, so the measured angles wouldn't add to exactly 180°, except accidentally.
By pure mathematics one can prove that the ratio of a circle's circumference to its diameter (called "pi") is approximately p = 3.1415927..., but we can also prove that one cannot express it exactly with a finite number of decimal places. Its value is an unending decimalan irrational number. No measurement of real circles can have such perfect precision, so the value of p cannot be determined by experiment on nature. This example illustrates that mathematics propositions cannot be proven by experiment, only by pure logic. On the other hand, no scientific law or theory can be proven by using only the methods of mathematics.
Mathematics is a handy analogy that can be used to model parts of nature. The mathematics can be carried out to whatever precision is needed, or "good enough" for a particular scientific purpose. Mathematics cannot discover new scientific truths, but as we develop science through hypothesis testing, mathematics can not only test the hypotheses against measurements, but help us refine (tinker) the hypothesis to bring them in closer agreement with experiment.
Logical deduction, including mathematical logic, is the language with which we frame our theories of physics. Mathematics is capable of far greater power and precision than mere words. In fact, it is the language in which may physicists do their creative thinking. It is also the tool we use to test our theories against the final (and unforgiving) arbiter of experiment and measurement. But mathematics is not a royal road to scientific truth.
Intelligent Design Creationism: Fraudulent Science.