## Friday, February 01, 2013

### Ramanujan’s smile

Andre Willers

1 Feb 2013

Synopsis:

Ramanujan proved the Four-colour Theorem via Mock Modular forms . He was amused .

Discussion :

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

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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 .

Z(1)=(1+x)(1+y)

Z(1)=1+x+y+xy

Z(2)=1+(-x)+(-y)+(-x)(-y)

Z(3)=z(2)+z(1)

=2(1+xy)

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 ."

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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 .

Andre

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