TY!!
I’m not sure that I actually buy the idea that there is something radically different in Einsteins work as opposed to Newtonian principles.
If you take Newtons stuff, and you toss in the Lorentz equations, you basically end up with relativity.
I seem to recall that Einstein himself was quoted as saying that Hilbert was the most brilliant mind he had ever encountered.
I’m not sure that I actually buy the idea that there is something radically different in Einsteins work as opposed to Newtonian principles.
Einstein was thoroughly moored in Newtonian principles, so much so that he insisted on a direct correspondence between his relativity theory (Newtonian mechanics as he modified it for large-scale phenomena) and its verbal form of communication. And then Niels Bohr came along and made the correspondence principle among "domains" explicit: It doesn't matter how "strange" the "behavior" of the small-scale world of quantum mechanics might happen to be, it could finally only be described in Newtonian language.
From which I infer that the Newtonian formalism constitutes a kind of final, universal language by which "simple systems" in nature — which would be the particulate, inorganic, material systems — can be effectively described and reliably understood. Actually, I have little doubt about that these days, and pay homage to Newton for the magnificence of his achievement.
Yet the biological world does not seem to boil down to "simple" matter and mechanics. Newton can help with the "material basis" of life. But there's nothing in Newton that seems terribly useful to the study of biology beyond its physical basis.
People who say there is nothing beyond physical basis seem to be unqualified in the field of biology. Newton, for instance, cannot help us elucidate the causal relations/behavior of complex systems in nature. My main takeaway here: biology does not "reduce" to physics/mechanics.
If you take Newtons stuff, and you toss in the Lorentz equations, you basically end up with relativity.
I'm not an expert mathematician; but based on what I've read, your statement appears highly confirmable. Newton's formalism inspired amazingly effective mathematical derivatives, such as the Lagrangian and Hamiltonian formalisms, which are such important (and empirically effective) mathematical tools in physics today. One beauty leads to others....
But it seems to me such "beauties" refer to this day only to "simple" systems in nature — "particulate" matter of whatever scale, and the basic (Newtonian) mechanical laws. It seems to me biological studies require more than this.
I seem to recall that Einstein himself was quoted as saying that Hilbert was the most brilliant mind he had ever encountered.
Einstein was first and foremost one of the greatest mathematicians who ever lived. David Hilbert was yet another. It is no surprise to me that Einstein would admire him. Yet as Robert Rosen has pointed out, Hilbert's "pet project" of formalizing Number Theory ended up in total shipwreck — for reasons that Kurt Gödel later made manifest.
It kind of "hit the rocks" in the same way that Einstein's "cosmological constant" did. (Who knows, the CC might yet return in some fashion. But probably we'd have to get to the bottom of "dark energy" first.)
God bless all these men for what they imagine and try. They are all trying for Truth — or so it seems to me. FWIW