(Cross-Posted at PowerUp)
Earlier on, PZ pointed to an article by some whack-job claiming to refute the theory of relativity. I'm not very familiar with relativity denial, so I didn't actually read the article. I picked it up again courtesy of Blake, and now I wish I hadn't. Take a look at his descriptions here:
MATHEMATICAL MODELS are abstract, idealized, imaginary models which contain characteristics and assumptions which cannot exist in reality (such as points, lines, triangles, spheres, etc.) These models can be purely logical, purely mathematical, geometric, kinematic, dynamic or electromagnetic. All of these models are based on the LAWS OF MATHEMATICS (symbols, equations, formulas etc.) which only approximate the physical LAWS OF NATURE. These mathematical models produce deductive conclusions which only apply to the idealized mathematical models.
PHYSICAL MODELS are real models composed of physical objects which are used in empirical experiments. By repeating identical (as far as possible) testing with these models, inductive conclusions can be made. These inductive conclusions, because they are the results of physical experiments, are the fundamental method used by science in an attempt to understand the LAWS OF NATURE. Knowledge about the real Universe must come from physics and not from mathematics. Experience has always been the primary guide in human reasoning concerning physical facts.
METAPHYSICAL MODELS are sophistic models which contain both mathematical characteristics and physical characteristics. These are mingled or mixed models. Neither mathematical deductions nor physical inductive conclusions can be produced from these models because they cannot exist in reality. These are pseudoscience models which result from “thought experiments”. These are purely imaginary mental creations. Any conclusions whatsoever that these models produce are completely irrelevant to anything. They cannot produce any valid understanding of reality. A sophist is someone who deceives people based on clever-sounding, but flawed arguments or explanations. However, these fallacious theories do produce popular imaginary science fiction tales about time travel (Back to the Future, motion picture) and spaceships that travel at the speed of light (Star Trek, motion picture).
We obviously lack a rigorous definition of what I'll call the "Pauli threshold", the point where an argument just gets so absurd that it's not even wrong. But I think it's clear that this particular nonsense is off the charts regardless of any metric we could possibly come up with.
For someone who is supposedly a "mathematics graduate" it is stunning how ignorant those three paragraphs alone manage to be. Even the most superficial look at the history of physics and it's relationship to math deflates his claims easily. The differential and integral calculus were developed in large part as a framework for early classical mechanics, in addition to providing the basis of analytic function theory. Successive developments in latter include Fourier analysis, which gave us the Fourier transform and allows physicists to use such idealized objects as phase-shifted sinusoids to describe otherwise inaccessible quantum behavior. Need we bring up super-abstract Group Theory, which is pretty much indispensible in describing spacetime symmetries? Need we point out that the complex vector space, which includes those seemingly perfectly abstract "imaginary numbers", is an essential notion in quantum physics? For some generic thing's sake, you have no physics without mathematics! Mathematics and physics, far from being "inherently different", are so conceptually intertwined and contiguous as to be inseparable.
In addition to being ignorant of the history of science, it appears that he's behind on every development in the philosophy of science since, uh...Bacon? Science isn't purely inductive, it employs a combination of hypothetical, deductive and axiomatic reasoning at multiple levels. And for another thing, constructing a physical model necessarily employs mathematical reasoning within an axiomatic framework. The purpose of tests is to see if these abstract models accurately predict reality.
I don't think I can bother with the rest of the article, the stupid is already burning through my skull. I'll leave to rest to other bloggers, Dave Bacon and "gg" have already tackled much of it.
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