/\ The Quantum Pyramid /\

Quantum Pyramid
The Quantum Pyramid is another powerful aspect of our philosophy. The
understanding of the pyramid combined with our method of reproducing
this effect has led us to the realization that we create our own
realities.

Pyramid
The tree sorts randomly, and can start from any number on the pyramid.
Particles have a 50/50 chance of moving along either path in the tree.
If a particle continues to the next number down the tree then it
advances. Otherwise it reatreats back up the tree on the adjacanet
path. When it reaches 0 or 1, it can switch back over, and start
moving in the opposite direction.

This is the proportional version of the pyramid as seen with non-fixed
width fonts:

/\
/ \
/ \
1 0
/ |\ / | \
2 | \/ | -1
/ |\| |/ | \
3 | | -2
/ |\| |/| \
4 | | -3
/ |\| |/| \
5 | | -4
/ |\| |/| \
6 | | -5
/ |\| |/| \
7 | | -6
\ | | /
\ | | /
\| |/
^ ^



And here is how it looks if you have a fixed width font:


/\
/ v
1 0
/|^ /|\
2 | \/ |-1
/|\| |/|\
3 | ^ ^ |-2
/|\| |/|\
4 | ^ ^ |-3
/|\| |/|\
5 | ^ ^ |-4
/|\| |/|\
6 | ^ ^ |-5
/|\| |/|\
7 | ^ ^ |-6
\| |/
^ ^


Overview
In quantum physics everything functions through random reactions, and
we see this in traditional physics too within chaotic systems. But
when looking at the quantum pyramid there are two different ways we can
see it. We can let a particle fall through the pyramid completely at
random, or we can stop and *observe* the particle falling through the
pyramid at any given point.

If we just let the particle randomly start at either 1 or 0, it could
wind up at -6 or 7 next we look. But if we have a particular goal in
mind and we decide to observe the particle and start it off at 1. Then
the expectation that the particle will get to 7, instead of ending at
-6 is incredibly higher. And if we decide to observe the particle at 2
or 3 instead of one of the other numbers, then the odds increase even
more.

Because we are observing the pyramid, and by that I mean we are looking
at our particle at a given spot on the pyramid. We can actually
control where the particle will be in the future. Otherwise, when we
aren't observing the particle its future is entirely random, and it
could be literally anywhere on the pyramid.

But once we observe the pyramid we know where the particle will be in
the future, even though it is moving in a completely random pattern.

And by observe I mean we literally create. Because we can start the
particle off at a point in the pyramid ourselves, and let it operate
within the random chaos sphere.


Science
To calculate the average number of moves before we advance n steps
forward. The equation k( n-k ) will work, according to martingale
probability theory. k is equal to the absolute value of the number we
start at, and n is equal to our final goal. So if we start at 4, and
only try to advance to 6, the average number of moves it will take
before we get there is 4(6-4), which equals 8 moves.

To show the final proof of the quantum pyramid we only have to move
from the probability of winning the first game, and multiply it by the
probabilities of winning the following games.

For example, if we are at 3 and only try to advance one step, the odds
are 3/4 that we will advance one step before moving back to 0. And once
that step is reached there is now a 4/5th chance of advancing another
step forward.

We can easily calculate this by counting all the possible ways to
advance forward, which gives us the numerator. Then by adding 1 to
the numerator for every step we advance we have the denominator.
Because there is only one way we can go back to zero for every step
inside the tree.

To count all the possible ways we can win, just add the smaller
pyramids along the path to the direct route to our goal.

Source code to demonstrate the effects of the quantum pyramid can be
downloaded here: http://grimoire.genesismuds.com/martingale.cpp

.