1 Feb 2013
Ramanujan proved the Four-colour Theorem via Mock Modular forms . He was amused .
1.He saw a two-dim system as a complex number description
2. He then chopped it up infinitely .
3.He used Fourier transforms to delineate some areas (the colours)
4. He did this for the upper-half plane , then for the lower half plane (Google it)
5.Then he summed them . It came to 4 for the simplest case .
6. This is The Four Colour Theorem .
7. The Upper-half Plane is not a mirror of the Bottom-Half Plane
As previously described , there is a symmetry break .
"God's Snowball :
God is the ultimate snowball .
He put his thumb firmly on the scale through the Distributive Axiom of ArithII .
To recapitulate the Distributive Axiom of ArithII .
That xy term is the killer . If x and y are both negative , xy is positive . This breaks the symmetry . Any exchange rate is a multiplication of terms .Symmetry is broken in any exchange rate in an ArithII system .
The underlying system has a tendency to increase at any iteration . The snowball grows bigger . As described , if one integrates it over infinity of values it is 2/3 of basic value .
This is the added value of all the interactions.
This ties in with http://andreswhy.blogspot.com "Infinite Probes"
The basic observed value has a reserve of 1/3 of the value . This has immediate physical significance with quarks ."
8. Black holes .
This has obvious applications to Black Holes .
A surface black hole with a topological puncture (eg hawking radiation) can always be described in terms of the 4 Colour Theorem .
See Holographic black holes .
Since we are in a black hole with 3+1 dimensions , there must be a puncture to other branes . (for simple topologies)
9. That's macroscopically .
On Planck scales , things vacillate .
10 Any basic particle (call it a Preon) can only present 1/3 , 1/4 or 1/5 of it's surface for interaction with other similar particles . Sum this to infinity .
11. This is what Ramanujan saw . Simple .
12. it's a pretty simple Universe . Only humans have to complexify it for hierarchical reasons . .
A tribute to Ramanujan .