Search All of the Math Forum:
Views expressed in these public forums are not endorsed by
Drexel University or The Math Forum.



Duality in Physics versus Duality in Math; and why most Series of math are fakeries #1537 Correcting Math
Posted:
Feb 10, 2014 2:32 AM


Duality in Physics versus Duality in Math; and why most Series of math are fakeries #1537 Correcting Math
Alright, I promised a post on this, where it comes up as a huge Fakery in Old Math, is when they equate Angles of Trigonometry with numbers of Algebra, so that they think they can graph sine and cosine as a function along with any other function on the same graph.
This is a huge mistake, because sine and cosine of Trigonometry requires its own special unique coordinate system and cannot be a function as are other functions. It cannot be a function, because the xaxis has numbers for which there are no angles to correspond to those numbers.
We see it very clearly and plainly in the Euler Identity of e^pi(i) = 1
Is pi a number or is pi an angle, or both?
If you insist pi is a number of 3.14... then 2.71..^3.14.. is about 23.14..
If you insist pi is a angle then e^(180 degree)i will give you the cos plus i sin relationship. So, which is it? If pi is an angle you can relate sine and cosine but not as numbers.
The problem here is quite dramatic and is seen in physics and mathematics that never does anyone produce answers of e^pi(i) itself, but rather they all turn to cos(t) + i(sin(t)) to do the computations and answers. As if the e^(t)(i) portion were some pathetic mannequin window dressing.
So here is where Old Math never learned about DUALITY and which physics learned duality in the last 200 years but mathematics never caught up. Mathematics still thinks angles can equal numbers as seen by the Euler identity and as seen by the idea that trigonometry has functions that coexist with other functions, when they do not. Trigonometry needs its own special Graph and coordinate system in order for sine and cosine to even be a function.
Duality in mathematics is best explained by the Regular Polyhedra where faces of one corresponds to vertices of another. So that the cube is a dual of the octahedron. Or, the icosahedron is a dual of the dodecahedron.
In physics, duality is best known by particle is a dual of wave. We can think of the wave as a cube and the particle as a octahedron. Another physics duality is momentum and position, or another is time and energy.
In physics, we never make the silly mistake of time = energy or momentum = position or particle = wave. We say a entity contains both a particle and a wave all simultaneously.
But in Old Math, they never learned Duality and so they made huge mistakes like that of e^(t)(i) = 1. Or they plotted the trigonometry functions as being functions with all the other functions. Or they said that pi was 1 for the unit circle. They were so silly, so very silly because what they were doing was tantamount to saying Cube = Octahedron.
More later, . .

Recently I reopened the old newsgroup of 1990s and there one can read my recent posts without the hassle of mockers and hatemongers.
https://groups.google.com/forum/?hl=en#!forum/plutoniumatomuniverse Archimedes Plutonium



