I agree with yours, and Tim Thompson’s, assessment that mathematics is logic. And within this logical construct expressed in mathematical relationships, and their interrelationships, when applied to scientific observations we can conclude certain fundamental truths of how these relationships fit logically into a framework of ideas, what we call ‘scientific theory’. We now have some four centuries of scientific theories of how works the universe to give credence to what we have come to believe as true. Ergo, the computer on which I read and write this is proof that we have gotten some things right. Good science also demands a continuum of inquiry, or open mindedness, to test and retest and we had come to believe, based upon these fundamental truths, so there really is not safe island of rest when it comes to science. Such as evidenced on these BAUT discussions, especially ATM, there is always room for some form of reasonable speculation, that we may not have the whole story right, and so need to keep challenging our knowledge with falsifiable tests, if we are to avoid the label of dogma. This is elementary, logical, and true. However, what sets astronomy separate from all other sciences, including those not easily quantifiable (except through use of statistics, such as bio-sciences), is that while we can perform tests here on Earth in a laboratory type setting, except for where we had sent spaceprobes within the very small radius of our solar system, we are not able to falsifiably test scientific theories at very great distances in space. We may crosscheck ideas, quantifiably, through a whole web of scientific theories across disciplines, i.e., Quantum physics with astrophysics, or General Relativity with gravitational lensing, but we cannot crosscheck the entire spectrum of General Relativity with Quantum physics, for now, so there are holes in our fundamental knowledge, holes we hope future scientific research can fill in. So while the logic of a whole web of interrelated knowledge may fit together into a whole scientific theory, with quantitative and mathematical support, there is still the need to falsifiably test the theory; since we do not as yet have a wholly unified theory of how all the pieces fit together, as a Grand Theory, where all things are explainable by this logic, we cannot be certain. In essence, until such time that the Grand Theory is complete, our whole web of knowledge still rests on our ‘fundamental truths’ that nevertheless need additional research and testing.

I think this is the conundrum we encounter in Astronomy, versus all other science, in that our ‘tests’ for astronomical scientific theories are always at a distance, sometimes very great distances, so we do not have the benefit of falsifiable tests up close. How do we measure the speed of light, for example, in vicinity of our nearest stellar neighbors, such as Alpha Centaury? Or how do we know that implied Dark Energy, that which explains space expansion, exists at all? If we assume Doppler space expansion, something we cannot test for here on Earth, then the whole web of knowledge, even mathematically quantifiable knowledge, is only within the parameters of the logic constructed around this assumption. (Einstein assumed a homogenous and isotropic universe, but this is merely an assumption and not testable at present; in fact, we hope this is right to make it all fit mathematically!) But have we found other evidence to collaborate this logic? Is there evidence, for example, of space expansion tangentially? We only know of space expansion via ‘line of sight’, what we see in our instruments delving progressively deeper into space, and there the logic holds. But we cannot falsifiably test for it in any other way, except within the parameters of the web of mathematics we created to explain (assumed) Doppler space expansion. Is there any evidence of space expanding on Earth? No. So without such a collateral test, we are forced to fall back upon the logical explanations based upon our assumptions. But what if cosmic light redshifts for some other reason, perhaps something not yet considered (not counting tired light here), which would explain this redshift from another cause so that our observations of redshifts, consistent that they are for all distance as calculated, are actually no more than an optical illusion? Good science demands that we know the answer to this with some degree of falsifiable tests, and not merely accept that the logical calculations all work, so it must be right. Do you see my point? Of course, you know my position on the (variable) value of G in deep space…

Therefore, the fact that we can make electromagnetic energy work for us, and have a whole body of science and physics to explain this phenomenon (why I can write this on my computer) is still not the same as explaining astronomical observations made over great distances, where it is virtually impossible to test for what is observed. Except as these observations coincide logically within our structure of theories to explain what is observed, we still do not know, since we cannot find collaboration from other sources. Have we ever found evidence of tangential space expansion, for example? Our physics should be able to find some other evidence, something local, to collaborate with what we think is physics at a distance, quantitatively proven here with falsifiable tests (especially if the universe is homogenous and isotropic, which is a philosophical assumption). If we cannot do that, whether or not the math is logical and true, still leaves holes in our knowledge that speculators, such as those who challenge accepted theories of the mainstream, have grounds on which to challenge accepted doctrine, no matter how logical it is. The final proof, short of a Unified Theory of Everything, is to test falsifiably. Actually, now that I think of it, even if we had a Grand Unified Theory, we would still need to test and verify regardless of how great is the consistency factor. Science demands no less, if it is to avoid the "holy writ" of dogma. Would you agree?

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Credibility is simply incredible... sometimes even to me.
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