Tim Thompson

2005-Nov-04, 01:56 AM

It is my thesis here that mathematics, both pristine, and in the guise of theoretical physics (or theoretical science), is every bit as revealing of the natural world as is experimental observation.

In the Standard Solar Models (http://www.bautforum.com/showthread.php?t=33627) thread, I pointed out (http://www.bautforum.com/showpost.php?p=592472&postcount=67) that Eddington had applied fundamental physics, in a study of the opacity of the solar interior, and by comparing with the observed color, brightness & size of the sun, determined that its interior could not be made mostly of iron (or other heavy elements), and had to be made mostly of hydrogen. Upriver objected (http://www.bautforum.com/showpost.php?p=593044&postcount=69), commenting that "He calculated. He did not go to the suns interior.". I responded (http://www.bautforum.com/showpost.php?p=593379&postcount=71) with "Calculating is every bit as valid as going to the solar center, it is not a valid criticism of any science to say that a "calculation" is in any way weaker than an observation, as long as the calculation is based on principles derived from observation. This is exactly the case for Eddington, who used a calculational tool which, assuming it is properly derived, cannot be wrong, because it is derived from well established fundamental principles." And Upriver responded (http://www.bautforum.com/showpost.php?p=593518&postcount=72) in turn: "That is just so wrong. It is theory. Not reality."

With all that said, I am going to pick up the gauntlet here, and say that Upriver's response is so wrong.

One of the most fascinating things about the universe is that it is truly mathematical. It was that fascination which attracted me originally to physics. There are numerous examples of surprising & unintuitive realities, that were not discovered by experimental observation, but purely by mathematical research. The Uncertainty Principle in quantum mechanics was not discovered in a laboratory. Rather, it is purely mathematical in origin, actually stemming from Fourier theory (http://www.mathpages.com/home/kmath488/kmath488.htm). Chaos was discovered by Henri Poincare in 1903, long before it became an observational issue, by purely mathematical study. And Einstein deduced through logic & mathematics, that light would travel an altered path through a gravitational field. All of these things were discovered by mathematical & theoretical reasoning, not by "going there" and looking. I think that one of the weaknesses of many alternative views is that they fail to appreciate the real strength & value of mathematical reasoning.

Mathematics, after all, is really only a special case of symbolic logic. The scientific process of inference from observation is similar to the mathematical process, though not perhaps as formal. Nonetheless, just as the logical trail of deduction in mathematics leads to confident proof, so does the trail of inference from observation lead to an equally confident proof in the empirical sciences.

It is all built upon the single assumption that the laws of physics are equally valid throughout spacetime, and are the same. throughout spacetime. Certainly, astronomical observation makes it a virtual certainity that this assumption is true, as we see no reason to assume that physics as we know it is any different on the distant worlds that we observe.

The physics of opacity works just as well inside the sun, as it does inside a laboratory here on Earth. It is not necessary to go to the center of the sun. We can know, to the extent of that word in an empirical science, what's going on there by applying fundamental physics, mathematical physics, to that environment. After all, the fundamental physics we are talking about is all based on observation. So when we do a theoretical analysis of, say, the solar interior, then we are really engaged in the scientific pursuit of inference from observation. If the observations are by definition true, and the inference is logical, then the inference is very likely to be true as well (and in almost all cases experience bears this out).

So I maintain that mathematical (theoretical) reasoning & investigation, are as revealing as experimental observation, and is just as likely to provide valid insight. An over-reliance on observation alone stunts the scientific growth. Theory can be as real as observation.

And what do you think?

In the Standard Solar Models (http://www.bautforum.com/showthread.php?t=33627) thread, I pointed out (http://www.bautforum.com/showpost.php?p=592472&postcount=67) that Eddington had applied fundamental physics, in a study of the opacity of the solar interior, and by comparing with the observed color, brightness & size of the sun, determined that its interior could not be made mostly of iron (or other heavy elements), and had to be made mostly of hydrogen. Upriver objected (http://www.bautforum.com/showpost.php?p=593044&postcount=69), commenting that "He calculated. He did not go to the suns interior.". I responded (http://www.bautforum.com/showpost.php?p=593379&postcount=71) with "Calculating is every bit as valid as going to the solar center, it is not a valid criticism of any science to say that a "calculation" is in any way weaker than an observation, as long as the calculation is based on principles derived from observation. This is exactly the case for Eddington, who used a calculational tool which, assuming it is properly derived, cannot be wrong, because it is derived from well established fundamental principles." And Upriver responded (http://www.bautforum.com/showpost.php?p=593518&postcount=72) in turn: "That is just so wrong. It is theory. Not reality."

With all that said, I am going to pick up the gauntlet here, and say that Upriver's response is so wrong.

One of the most fascinating things about the universe is that it is truly mathematical. It was that fascination which attracted me originally to physics. There are numerous examples of surprising & unintuitive realities, that were not discovered by experimental observation, but purely by mathematical research. The Uncertainty Principle in quantum mechanics was not discovered in a laboratory. Rather, it is purely mathematical in origin, actually stemming from Fourier theory (http://www.mathpages.com/home/kmath488/kmath488.htm). Chaos was discovered by Henri Poincare in 1903, long before it became an observational issue, by purely mathematical study. And Einstein deduced through logic & mathematics, that light would travel an altered path through a gravitational field. All of these things were discovered by mathematical & theoretical reasoning, not by "going there" and looking. I think that one of the weaknesses of many alternative views is that they fail to appreciate the real strength & value of mathematical reasoning.

Mathematics, after all, is really only a special case of symbolic logic. The scientific process of inference from observation is similar to the mathematical process, though not perhaps as formal. Nonetheless, just as the logical trail of deduction in mathematics leads to confident proof, so does the trail of inference from observation lead to an equally confident proof in the empirical sciences.

It is all built upon the single assumption that the laws of physics are equally valid throughout spacetime, and are the same. throughout spacetime. Certainly, astronomical observation makes it a virtual certainity that this assumption is true, as we see no reason to assume that physics as we know it is any different on the distant worlds that we observe.

The physics of opacity works just as well inside the sun, as it does inside a laboratory here on Earth. It is not necessary to go to the center of the sun. We can know, to the extent of that word in an empirical science, what's going on there by applying fundamental physics, mathematical physics, to that environment. After all, the fundamental physics we are talking about is all based on observation. So when we do a theoretical analysis of, say, the solar interior, then we are really engaged in the scientific pursuit of inference from observation. If the observations are by definition true, and the inference is logical, then the inference is very likely to be true as well (and in almost all cases experience bears this out).

So I maintain that mathematical (theoretical) reasoning & investigation, are as revealing as experimental observation, and is just as likely to provide valid insight. An over-reliance on observation alone stunts the scientific growth. Theory can be as real as observation.

And what do you think?