
professors of MIT endorse proof to arxiv Maxwell Equations derive Peano Axioms
Posted:
Jun 30, 2014 4:23 PM


Alright, the basic features of the Peano axioms which delivers the Naturals, the set 0, 1, 2, 3, . . . known as the counting numbers is the features of a unit metric which when added delivers all the numbers of the set. I call it the inductor unit. It is the metric of the distance from 0 to 1 and when we add 1 to that of 1 we get 2, and adding 1 to 2 we get 3 etc etc.
So basically we require three features in physics of the Maxwell Equations to give us the Peano axioms:
1) two items to form the inductor unit, in the case of Peano 0 and 1 2) the inductor unit as 1 3) successor adding of 1 gives all the set of counting numbers
So, do we have that in the Maxwell Equations? Well we can tackle that question from two viewpoints. One viewpoint is the flow of electric current such as the flow of either electrons or the flow of protons. A second viewpoint is that the chemical elements of chemistry is a succession of adding 1 more proton. So by increasing atomic number from element hydrogen as 1 to helium as 2 to lithium as 3 etc is also the Maxwell Equations.
Now a large list of the Peano axioms in books is shown as seven to nine axioms but most of those are concerning the properties of equality which we need not be concerned about in Physics because we can easily say a group of electrons obey equality or that a group of protons obey equality.
What we have to show is that 0 and 1 proton, either we have a proton or no proton. Then, this proton is an inductor unit, so that if I add 1 proton to 1 proton, we end up with 2 protons. And finally that by this adding of 1 more proton to previous protons we can have all proton arrangements.
Instead of protons I could easily switch to electrons in an electric current.
But I use protons because the chemical elements are based on a constant adding of one more proton to the nucleus of a previous atom to establish the next higher atom.
The reader should note that the inductor unit is the mathematics term for quantum in physics. That the distance of 0 to 1 for a metric of 1 as the inductor unit in mathematics, is the same as saying Planck's constant is the physics inductor unit, but in our case of Maxwell Equations the inductor unit is the metric unit charge of a proton or of a electron.
So, does the Maxwell Equations deliver to us these three:
1) two items to form the inductor unit, in the case of Peano 0 and 1 2) the inductor unit as 1 3) successor adding of 1 gives all the set of counting numbers
Well yes, as we translate numbers into either protons or electrons
1) two items to form the inductor unit, in the case of Maxwell Equations, the 0 unit charge of neutron and the +1 charge of proton 2) the inductor unit is thus a proton of +1 charge 3) successor adding of 1 more proton is a current of protons, larger from previous current which is seen in the table of chemical elements that lithium has 3 protons and beryllium has 1 more added proton and then comes boron with one more added proton, etc etc.
If the world had no atoms with the Maxwell Equations that builds the chemical elements but had some sort of other ordering of the world, then the set of Natural Numbers would not be the Peano axioms with mathematical induction but rather would be what this different ordering was.
Everything that Physics has, is reflected in mathematics and is the true math. If math veers away from what happens in physics, then that math is fakery.
Now there is a very interesting side note to this. As far as I know, there is only one case example of where science can duplicate mathematical induction of the Peano axioms, and that is the Maxwell Equations for atomic number of chemical elements and the electron or proton current.
Nowhere else in all of science do we duplicate the mathematical induction of mathematics. Biology has no mathematical induction. Thermodynamics has no mathematical induction. Quantum Mechanics has some of the Peano axioms but not the full set of mathematical induction.
What that tells us, or indicates is that the Maxwell Equations are the premiere set of axioms over all of physics and mathematics.
In biology, Darwin Evolution and DNA looks like it is math induction but there is a huge difference between Darwin Evolution and the chemical elements. For in chemistry we can start with neon, element 10 and remove a proton and end up with element 9, and remove another proton and end up with element 8 etc.
So the mathinductor can go either one way of adding +1 or go the other way of starting with a number and continually subtracting 1 until we cannot subtract anymore. Same thing with an electric or proton current we can either add more electrons (or protons) or we can subtract away until there is no current.
In biology the direction of reproduction is one way where a living organism adds one more living organism. In biology, we cannot start with a living organism and remove something to end up with another living organism.
So the difference is that in physics, in the Maxwell Equations, we can have a math inductor that is both adding or is subtracting. In the subtracting phase, it is called Fermat's infinite descent in Old Math. Biology as a reproduction mechanism is one direction only, ascending, not a descending mechanism. In mathematical induction, it is both ascending and descending. It is reversible.
So, the only place in all the sciences that we have mathematical induction is the Maxwell Equations of physics. Quantum Mechanics has no mathematical induction for it has no building mechanism such as adding one more proton builds the next element. QM has discreteness, the quantum but it lacks building of the quantum. The aufbau of chemistry is not QM but is rather the Maxwell Equations of how you have protons in the nucleus as a permanent current of protons and the surrounding electrons as a permanent current of electrons in a specific atom. QM focuses mostly on particle wave duality. But the larger duality is Electricity and Magnetism. So from that we instantly recognize QM is a subset of the Maxwell Equations. Everything in QM comes out of, or is derived from the Maxwell Equations.
Now it is interesting to note that in biology, they would have a mathematical induction provided they could go backwards in reproduction, where the offspring could reproduce to yield the parents. And one may think that with biotechnology that is feasible. But there is even more differences between math induction and biology reproduction, because math induction is reversible while biology reproduction is irreversible, for the offspring cannot yield the parent. Whereas a proton can be added to a iron atom to form a cobalt atom and a proton taken away from cobalt to reform back again into iron, and biology cannot simulate that buildup then builddown.
So in a sense, here we see the power of physics over biology, where the best that biology can do is go forwards with reproduction, while physics can go either forward or backwards with ease in either direction.
Now when I say that the Maxwell Equations of physics are the axioms over all of physics and over all of mathematics, is because anything in math is derived from the Maxwell Equations, and anything in physics is also derived out of the Maxwell Equations.
The world is but a reflection of the Maxwell Equations.
However, there are two more concepts in the Maxwell Equations which are even more powerful than mathematical induction, and which are only found in the Maxwell Equations. They are the concepts of perpetual motion and duality.
Perpetual Motion
What brings it about is the electrons moving around the nucleus of an atom. The electrons are in perpetual motion, never slowing down and never speeding up. How does that happen? Well it happens because of the Faraday law that a moving magnetic field causes electrons to flow in a wire loop. In the atom, the moving protons in the nucleus cause the electrons in orbit to always be in motion and the moving electrons in orbit cause the protons to always be in motion.
So, here I am turning the Maxwell Equations around and asking is there anything in mathematics to render a concept of "perpetual motion"? I doubt it, and is a prime reason why I say that mathematics is a subset of physics, for physics has so much more content in the Maxwell Equations, yet math cannot have many of those items of content.
Can mathematics have a concept of Perpetual Motion? Well it can come close with the idea of the golden log spiral, the equiangular spiral. That the angles are always the same hints of "perpetual constancy" but not really perpetual motion.
So, perpetual motion is an example of how much more rich is physics for it has concepts that math can never have.
Now of course, some will say that the Maxwell Equations are written by mathematics. But that is not what I am talking about. The mathematical induction is written in mathematics.
What I am talking about is whether mathematics has perpetual motion of its numbers and geometry. It does not and is beyond mathematics.
In this proof that the Maxwell Equations contain mathematical induction and thus Physics contains all of Number theory of mathematics, I should mention what Physics contains and Math can not contain.
Of course, I have to prove that the Maxwell Equations contains all of geometry of mathematics, not just Number theory. Here it is easy to show the Maxwell Equations contain the Pythagorean theorem for the theorem is equivalent to the Parallel Line Postulate of geometry.
Duality
But let me talk about what Physics contains in the Maxwell Equations which is above and superior to mathematics and which math can never deal with. In a sense, it is logic itself, of that of duality. The logic of Physics contains duality of a item having both properties of A and B wherein A is not equal to B.
Math cannot have this duality for it would be A = B, for it interferes with the concept of equality. And you cannot have math without equality.
In fact, we see duality in mathematics all the time, yet math itself cannot have duality, in that we can have the Pythagorean theorem as a geometry picture or we can have it as Numbers of m^2 + n^2 = z^2. We do not say that the number 9 is a square, for they are two different things, one is a number, the other is a geometry figure.
The Logic of mathematics is only Aristotelian logic and cannot possess a duality logic along with Aristotelian logic. As I said before, duality messes up equality in mathematics.
The Logic of Physics has both Aristotelian and Duality Logic. The logic of math has only Aristotelian.
Duality is what the 4 Maxwell Equations are 2 of them about electricity and 2 of them about magnetism. Electricity is the dual of magnetism, neither equal to each other but contained in every physical thing and physical interaction.
In Mathematics, we cannot write any axiom set that is both Aristotelian and Duality Logic.

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