Uncertain Principles: Two Cultures Within Science
[No equations in a paper] is almost completely inconceivable to me (at the risk of leaving myself open to the Vizzini joke). In my part of science, a paper without an equation is suspect, and I’m not exactly the world’s most mathematically inclined physicist. Physics is so intimately connected to math, and the business of doing physics is so inherently mathematical that its difficult to imagine a scientific paper about physics that doesn’t contain at least one equation. A press release or popular article, sure, but to a physicist, the equations aren’t some offal to be avoided en route to the science. The equations are the science. Objecting to the presence of an equation in a scientific paper is like objecting to the presence of meat in a steak sandwich.
I had the serendipity of reading another post just before reading Chad’s, related to the closing remarks concerning physicists sometime needing to learn some less “standard” math to do the physics they are interested in pursuing:
Medical researcher discovers integration, gets 75 citations
My more reasonable friends claim that this abstract isn’t really as amusing as I make it out to be. And to be sure, they’re right.
Murray Gell-Mann developed the “eight-fold way” to explain the spectrum of hadrons in the 1960s. It wasn’t until after he’d developed this formalism that he discussed his model with mathematicians, who then told him that he’d rediscovered group (representation) theory. This ushered ina new era in the history of particle physics where symmetry became our guiding light and group theory became a necessary tool for any particle theorist. Though, to be fair, in the 1960s group theory—unlike calculus—wasn’t something that physicists were expected to take during high school.
I’m also aware of a few instances of some of my colleagues struggling through some new way of analyzing clock performance, only to find out that the math is standard analysis of some other sort of problem. As they say, math is the language of physics.
There are physical observables that cannot be expressed as equations or even numerically approximated. Oh mama, that’s where the fun is!
Consider a stereocenter substituent (R)-C(H)(Cl)(CH=CH_2) and its enantiomorph (S)-C(Cl)(H)(CH=CH_2). (R) and (S) are Cahn-Ingold-Prelog notation for labeling chirality. Call them R and S respectively. Take an sp3-hybridized, undistorted, tetrahedral carbon atom with freely rotating substituents, C. Append four identical substitutents,
CR_4 versus CS_4.
Each of the two molecules obviously lacks a mirror plane, inversion point, and all higher order improper rotation axes. Write an equation to label the new optical center’s chirality or quantitate it. A tetrahedral core is too easy! Let’s make sp2-hybridized trigonal *planar* chiral carbons,
R_2 C=C R_2 and S_2 C=C S_2
Physics has no handle for atomic mass distribution chirality. Chirality is an emergent property. It is an external extrinsic property arising from aggregation. That the universe is chiral and derived physical theory is not is ex post facto jury rigged with manually inserted “symmetry breakings.” The whole of physics – classical and quantum gravitation, quantum field theory, SUSY – could fail for a footnote. Do opposite shoes violate the Equivalence Principle?
http://www.mazepath.com/uncleal/erotor1.jpg
There is no equation, only observation. The worst it can do is succeed.
There is no escape from the first example. Consider four different (R)-substituents arrayed about the central carbon in CIP (S)-configuration. CR_3S versus CS_3R also works to spec.
Present an undistorted tetrahedral carbon atom bearing four identical substituents yet being a fifth chiral centerl to your chemistry department. Enjoy the screams of outrage and agony.
i believe* that there was a Nobel prize in econ awarded for essentially “discovering” the derivative and applying it to economic theory.
it may be this one:
The Sveriges Riksbank Prize in Economic Sciences in Memory of Alfred Nobel 1969
Ragnar Frisch, Jan Tinbergen
*at least that is what one physics prof i had joked