So the Maxwell Equations as a closed algebraic set of axioms does not allow for a 4th perpendicular to a given set of 3 perpendiculars. But does the Maxwell Equations, since it is closed algebraically prove anything else of huge importance to physics and mathematics?
Well, yes of course, for in mathematics when your axioms are closed set then they are immune to change. What I mean by that is that if someone comes along and wants to add a 5th equation to the 4 Maxwell Equations, then he is just wasting time, since you cannot make a closed set, more closed.
What can be done perhaps is to compress the 4 Maxwell Equations, although they are already compressed to their limit. What I mean is that in Geometry, they had a large list of axioms of say 24 of them at one time and someone saw that one of them was equivalent to another and so it was deleted making 23 axioms.
So the axioms of all of physics and thus all of mathematics since it is a subset of physics are these 5 axioms:
(1) all the facts and data of chemistry (2-5) the 4 Maxwell Equations
Now I am trying to think of another physical parameter such as dimensions, as to a proof from the fact that the Maxwell Equations are closed algebraically.
On Thursday, September 5, 2013 1:18:50 PM UTC-5, Archimedes Plutonium wrote: > Now what the description of the below proof is in mathematics, is called a "closed algebra set". The rationals in mathematics are a closed algebra set in that if we take any two rationals and add them, we do not arrive at a "new number" not already a rational. So that in the proof that the Maxwell Equations cannot have a 4th dimension because a 4th perpendicular cannot yield a new solution for the already preexisting solutions gained from 3 perpendiculars of 3rd dimension. > > > > Now the Natural Numbers: 0, 1, 2, 3, 4, 5, . . are not closed to division because we can take 1 and divide it by 5 and gain a new number not already existing. So that if the Maxwell Equations could take a 4th new perpendicular and arrive at a new solution not already existing with the 3 perpendiculars of 3rd dimension, then the 4th dimension exists, but it does not exist for the reasons stated above. > > > > I wrote in sci.physics, a few minutes ago: > > > > Maxwell Equations proof that 4th dimension is phony baloney #1461 New Physics #1811 ATOM TOTALITY 5th ed > > > > So how does the Maxwell Equations prevent the existence of 4th dimension or higher? > > > > It does so in the fact that the Maxwell Equations are linear and so the thought of a **new perpendicular** > > giving rise to a solution not already existing by the 3 perpendiculars of 3rd dimension is only wishful thinking. Every new perpendicular besides the existing 3 perpendiculars is a preexisting solution already contained in the Maxwell Equations. > > > > So that for example if we have a alleged 4th new perpendicular of a moving bar magnet of Faraday's law coming into a Ampere/Maxwell law set-up, that this new alleged 4th perpendicular is already covered by the existing Ampere/Maxwell law. > > > > In short, the Maxwell Equations cannot accommodate a new 4th perpendicular and that all solutions to the Maxwell Equations are handled by the existing 3 perpendiculars. > > > > What Ptolemy proved that only 3 dimensions can exist in mathematics could not be a general proof because Ptolemy could not bring in Physics and the human mind unable to perceive of a 4th dimension. But when we anchor the proof in the Maxwell Equations we get rid of that last objection, because the Maxwell Equations cannot fit a new 4th perpendicular. > > >