Perfect opportunity to divert this discussion further. I love derailing threads. This dichotomy is something I find particularly interesting – apologies if this meanders a bit. The four pillars of the scientific method are…
1. Observation and description of a phenomenon or group of phenomena.
2. Formulation of a hypothesis to explain the phenomena. (In physics, the hypothesis often takes the form of a mathematical relationship.)
3. Use of the hypothesis to predict other phenomena or to predict quantitatively the results of new observations.
4. Performance of experimental tests of the predictions by several independent experimenters.
In physics, as in every experimental science, experimentation is paramount and experimental verification of hypothetical predictions is crucial. Science progresses through trial and error, mostly .... ups. Every new theory or law must be sceptically and rigorously tested before acceptance. Science progresses by screwing up, correcting the mistakes, then moving on to make more balls ups. If we stopped making mistakes, scientific progress would stop. When a scientist proclaims that something has been found to be 'true', what is meant isn't any form of absolute truth. Likewise, scientists' use of 'reality' and 'belief' shouldn’t imply finality or dogmatism.
In cosmology, to avoid the inference that the earth is near the centre of the cosmos, as implied by isotropy of redshift and of cosmic microwave background energy, a highly speculative and difficult-to-test hypothesis has been invoked known as the Copernican Principle. This posits that the entire cosmos is just like what we observe from the earth, at least at large scales. Through this gravity perfectly cancels at large scales and kept the cosmos from being inside a black hole during the early phases of a Big Bang. All Big Bang models depend critically on this hypothesis. The fact that the Copernican Principle up to now has been untestable means, strictly speaking, that Big Bang cosmology cannot be viewed as authentic science since it relies in a critical way on an untestable hypothesis. Ha ha!!!
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 of ‘scientific revolutions’. When such massive upheavals or paradigm shifts occur, and old models are superseded with new ones, that doesn't necessarily mean the old ones were completely fallacious nor does it mean their underlying concepts were invalid. They still work within their scope of their 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. I had always loved Newton’s declaration that if I have seen further than any man it is because “I have stood on the shoulders of giants”. A beautiful quote which encapsulated the scientific method. (Then it was completely ....... ruined for me by those Mancunian knuckle draggers Oasis naming an album after it.
I find this relationship – or symbiosis between mathematics and science that you refer to Vudu as fascinating. Mathematics is the preferred modelling analogy for physics. Any migraine inducing physics textbook is replete with byzantine equations and mathematical reasoning. Yet to understand physics we must appreciate that mathematics is not a science, and science is not merely mathematics. Today science and mathematics are separate and independent - yet cognate disciplines. The physicist must learn .... loads 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 their mathematics without interaction with mathematicians, and have on a number of occasions, developed new mathematics to solve particularly awkward problems.
My Father (we’ll call him Dad No.1) was originally a mathematician as an undergrad, but became an inorganic chemist by accident (and as a product very lucrative serendipitous stipend) but as an academic, his later body of work was as a physicist. (I have two Dad’s y’see – the other one was a rogue and a serial lothario who fled London back to Dublin not long after I was born and became a career hedonist. He probably listens to Oasis albums.) Those around Dad No.1 spent a lot of time reading the mathematics literature, saying things like "Those mathematicians are doing some stuff that might be really useful to us. I only wish they spoke our language." I remember that he always used to tell me about the complex arcane jargon with which each discipline had spawned within its own field had diverged to the point where special effort must be made to "cross over" into the technical literature of the other field.
By pure mathematics one can prove that the ratio of a circle's circumference to its diameter (called "pi") is approximately p = 3.141 etc etc..., but we can also prove that you cannot express it exactly with a finite number of decimal places. Its value is an unending decimal—an irrational number. No measurement of real circles can have such perfect precision, so the value of p cannot be determined by experiment on nature. The reason I’m saying this is because it illustrates that mathematical 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 adequate 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 tweak the hypothesis to bring them in closer agreement with experiment.
Logical deduction, including mathematical logic, is the language with which my old man framed his theories of physics. Mathematics is capable of far greater power and precision than mere words. In fact, it is the beautiful, elegant eloquence by 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 that I was referring to – as you say, the proof. But even mathematics should not be mistaken as a doorway to scientific truth.
What all this has to do with Rossi’s tyre allocation is most probably the subject of Jum’s next published thesis to be peer reviewed on powerslide.
Actually, what the .... does this have to do with speculation about Rossi’s rubber?
