axioms for Physics 2012; axioms for geometry ancient Greeks; axioms for algebra 1860's
Now let us do some history lessons about a science and having the smarts and intelligence to ground the science in a axiom set.
Geometry started out in Ancient Greek times with the recognition that it needed a axiom set in order to prove things for that science of geometry, and by doing so, laying the axiomatic foundation of geometry so long ago, that geometry became the most advanced science in both mathematics and physics. So advanced was geometry that by 1830's the Euclidean axioms developed the Non-Euclidean geometry. In other words, if geometry had not been a science based on axioms, we would not have had Non-Euclidean geometry by 1830s.
Geometry is an example of a science that starts with a axiom set, but Algebra is an example of a science that had no axiom set until the axioms of the Natural Numbers of 1860s. So before 1860s, Algebra was mostly a loose collection of a lot of rules and topics not connected into a whole. Algebra before axioms was compartmental.
Now let us look at Physics. It has never had a axiom set over all of physics and it has suffered tremendously because it is today a vast array of unconnected compartmental vagaries and irrelevancies. Remember the saying that a "horse is a camel, designed by a committee". That is the state of affair of Physics by 2012. When Physics does not have a axiom set, then it has thousands of cranks and crackpots with their pet theory in our (your) face. Without axioms for physics, then Hawking can peddle his pet crankery of dense matter going into black-hole, or Bardeen Cooper Schrieffer can peddle their crankery of electrons joining up in pairs, or Peter Higgs can peddle his crankery of a boson that creates mass, or Gell- Mann and Weinberg can peddle crankery of quarks and Standard Model. And a huge list of so-called physicists peddling whatever it is they like and cherish at the moment and peddle it as if it is physics, when in truth, it is just they silly idiosyncratic like and pleasure, not science.
When you have a axiom set on the subject of physics, you are not allowed to violate or trespass beyond the tenets of those axioms.
Physics could have established the Maxwell Equations as the axioms of physics, just as Number theory started the axioms in the 1860s which ended up as the Peano axioms for the Natural Numbers and gave algebra a firm foundation.
But physicists were not bright enough, not clear nor logical enough in the 20th century, a century where any foolish crank and crackpot could bowl over the entire physics community with their silly and stupid ideas. They could do it because there was no axiom set to raise alarm that they were beyond true physics.
If the Maxwell Equations had been seen as the axiom set, then we would not have had a black hole theory, nor a Big Bang theory, nor quarks, strings, BCS theory, Standard Model, Higgs boson and numerous other nonsense. We would now be not burdened by all that worthless nonsense because all of those items violated the Maxwell Equations.
If geometry had never started with Euclid axioms and polished into the Hilbert axioms and the nonEuclidean geometries, then geometry would be similar to the state and condition that Physics finds itself in by 2013. In geometry without axioms we would have horoscopes as geometry, or we would have rapp-geometry (similar to rapp-music). And today's physics, because physics has no axiom set to control it, is best described as rapp-physics for it is so poor in truth content, that it is like being in music class, not physics class. "Let me sing you a song..."
Now it is not as bad of a picture as I painted above of Physics. Even though Physics has never had a axiom set, per se, plainly in view, that Physics as had a tacit, hidden, underlying axiom set. I speak of the "units measure" pervading physics. The units of force, acceleration, velocity, momentum, angular momentum, energy, distance, time, and other units.
Ever since Ancient Greek times to 2012, physics has had a hidden axiom set that imposed its logic upon physicists of "Units Measure", but that axiom set needs to be replaced by a far better axiom set. In year 2012, I realized as the first physicist, that the Maxwell Equations, the Symmetrical Maxwell Equations is the axiom set over all of Physics. We need to add a fifth axiom that says all the facts of Chemistry is the 5th axiom.
Now what a axiom set does for physics, is that it not only eliminates the shenanigans of nonsense of Standard Model, Higgs boson, quarks, strings, black holes and Big Bang etc etc. But a Maxwell Equations axioms instantly unifies all of physics and all the forces of physics.
So where early 1900s physicists were looking to unify the 4 forces and unify thermodynamics to other physics, that immediately all is unified since the Maxwell Equations derives all things of physics (along with the Chemistry axiom).
So my point in this post, is to paint the broad wide picture of the history of science. That a science without an axiom set, is a science that is riff with nonsense and polluted with crankery and crackpottery.
Google's archives are top-heavy in hate-spew from search-engine- bombing. Only Drexel's Math Forum has done a excellent, simple and fair archiving of AP posts for the past 15 years as seen here: