Random Walk Bias
27 Jan 2010
Randomness can be biased in two fundamental ways :
1.Inside the same Order of Randomness
2.Between different Orders of Randomness.
The Randomwalk algorithm:
1.Take step d1 from start .
2.Take step d2 in a random direction .
3 Repeat .
4.See where you end up and have traveled .
See Appendix A
Inside the same Order of Randomness
From numerous other proofs , the Distance from center R = d*(n)^0.5
Where n is the number of beth(0) random steps .
This is the principle underpinning most of physics .
Between Orders of Randomness
See http://andreswhy.blogspot.com "Randomness" , Orders of Randomness 2" , "New Tools" et al
An extraordinary thing happens .
Because elements of beth(n) are infinitely more numerous than elements of beth(n-1) , there is an "osmotic" pressure between different orders of randomness .
An observer describing the system is statistically more inclined to describe an element as belonging to Beth(n+1) than Beth(n) , simply because Beth(n+1) is infinitely more numerous .
This can be calculated reasonably exactly .
Negative mass , dark matter and other beasties .
An obvious descriptive self-organization .
What does this mean ?
From the viewpoint of beth(0) , this looks like a compression . A particle .
Note that so-called Laws of conservation of Energy and Momentum only hold for beth(0) . The very existence of particles presupposes the axioms of finite information speed to enable beth(0) systems to clump together .
An infinite number of particles are possible . But not all particles are equal in terms of probabability of existence .
We can then define a particle as interacting elements that have a difference between beth(n) and beth(n-x) smaller than any other that can be found . Notice the infinity .
The whole of quantum physics falls out as result of this definition . This includes transluminals .( ie those pesky instantaneous –action-at-a-distance)
This can be seen as interactions between beth(n) and beth(n-x) systems. Ie self-organising clumping of energy .
We can then de-cohere matter (as previously discussed in Unpacking) .
Note that this will not release energy on the E=mc^2 model . (because most of the change(ie energy) is immediately repackaged .
I draw your attention to the ATP model of humans , where half of the body mass per day is created ATP , then immediately used . This is a beth(1) system .
All you need is chicken fat .
Beth(0) Random Walk
R^2 = (sigma(d*sin(cos(x)) )^2 + (sigma(d*sin(sin(x)) ))^2
R^2 = d^2 * (Sigma 1 + F(sin(x)) )
R= d *(n)^0.5 … the random walk at beth)0)
F(sin(x)) à 0 if n àinfinity . The Beth(0) definition .Another way of putting it is that we can always find F(sin(x)) à 0 for a x .
For higher orders of beth this would not be true (by definition) .
Note that if d = (n)^(-0.5) like in Riemann's theorem , the expression can evaluate to a finite value , including zero .
See Riemann's theorem in previous posts .
Any expression involving 1/n! (ie chopping things up )
See http://andreswhy.blogspot.com "Randomness" , Orders of Randomness 2"
are Beth(0) . This includes an expression like cos(ln(1/j))) . This would be an beth(0) expression as j->infinity . Which proves Riemann's Theorem .
Notice Riemann Orbitals
Surprisingly , they seem to be beth(0) . I would have thought at least beth(1) .
No wonder matter is so stable .