Re: The Quantum Pyramid
- From: The Thing <tthing@xxxxxxxxxxxxx>
- Date: Sat, 28 Oct 2006 06:38:59 -0700
On Fri, 27 Oct 2006 21:26:53 -0700, CoreyWhite wrote:
I spent quite a bit of work trying to get this to format on google
groups, so let me know if it needs explination. Basicly the tree sorts
randomly, and can start from any number on the pyramid. It has a 50/50
chance of moving down either tree. If it continues to the next number
down the tree 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
/\
/ \
/ \
1 0
/ |\ / | \
2 | \/ | -1
/ |\| |/ | \
3 | | -2
/ |\| |/| \
4 | | -3
/ |\| |/| \
5 | | -4
/ |\| |/| \
6 | | -5
/ |\| |/| \
7 | | -6
\ | | /
\ | | /
\| |/
^ ^
Here is how the pyramid looks if you have a universal font installed in
your usenet or e-mail client.
/\
/ v
1 0
/|^ /|\
2 | \/ |-1
/|\| |/|\
3 | ^ ^ |-2
/|\| |/|\
4 | ^ ^ |-3
/|\| |/|\
5 | ^ ^ |-4
/|\| |/|\
6 | ^ ^ |-5
/|\| |/|\
7 | ^ ^ |-6
\| |/
^ ^
In quantum physics everything functions on 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 you can see
it. You can let a particle fall through the pyramid completely at
random, or you can stop and *observe* the ball 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 allow it to start at 1
instead of 0. Then the expectation the particle will get to 7, instead
of ending at -6 are incredibly higher. And if we decide to observe the
ball at 2 or 3 instead of one of the other numbers, then the odds
increase even more.
What I am trying to say is that 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.
8)
And by observe I mean we actually create, literally. Because we can
start the particle off at a point in the pyramid ourselves, and let it
operate within the random chaos sphere.
Now here is the math:
To calculate the average number of moves before you advance n steps
forward. The equation k( n-k ) will
works according to martingale probabilitytheory. k is equal to the
absolute value of the number you start at and n is equal to your 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 you 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. And once that
penny is collected there is now a 4/5th chance of winning another
penny.
You calculate this easily by counting all the possible ways you can
advance a step, to get the numerator, and adding 1 to it to get the
denominator. Because there is only one way you can lose. To count all
the possible ways you can win, just count how many smaller pyramids
there are along the path, and add those to the direct route.
Here is the source code that proves the quantum pyramid's results:
. #include <stdio.h>
. #include <stdlib.h>
.
.
. main ()
. {
. double r;
. long int M;
. double x;
. int y;
. int z;
. int count;
.
.
. int seed = 10000;
. srand (seed);
. M = 2;
.
.
. int score = 0;
.
. //Score keeps track of the number of beans won every game
.
.
. int games = 0;
.
. // games keeps track of the number of games we have played before
. //losing all of the beans, which is equal to score.
.
.
. int beans1 = 0;
.
. // Initial value set to zero and defined within the loop
.
. int wins = 0;
. int lost = 0;
. int quit = 0;
. int init = 0;
.
. printf ("Initial Beans: ");
. scanf ("%d", &init);
. printf ("Stop after winning X number of beans: ");
. scanf ("%d", &quit);
.
. for (int cnt = 0; cnt < 10000; cnt++)
. {
. // We play 10,000 rounds
.
.
. int count = 0;
. beans1 = init + score;
.
. // Beans gets defined here, as starting with 3 beans
. // and having a 0 bonus score (It changes as you
. // win more beans per round)
.
.
. int beans2 = 1;
.
. // The program attempts to win just one
. // bean for every game.
.
.
. while (beans1 != 0 && beans2 != 0)
.
. // The battle begins
.
.
. {
. r = ((double) rand () / ((double) (RAND_MAX) + (double)
(1)));
.
.
. x = (r * M);
. y = (int) x;
.
. z = y + 1;
.
. // A coin is flipped and is either 1 or 2 in value
.
. if (z == 1)
. {
. // Heads wins.
.
. beans1++;
.
. // Beans1 gains one bean from Beans2
.
. beans2--;
. }
. if (z == 2)
. {
. // Tails loses
.
. beans1--;
.
. // Beans2 gains one bean from Beans1
.
. beans2++;
. }
.
. count++;
.
. // We keep track of the number of rounds in the battle
.
. }
.
.
. if (beans1 > score + init)
. {
. // If beans1 is greater than the initial value
. // of beans plus the total number of beans
. // that have been won so far in this game, then
. // the score goes up, and we go on to the next
. // game. We check this at the end of every game.
.
. score++;
.
. games++;
. }
.
. if (beans1 <= 0)
. {
. //If beans1 has lost the game and doesn't
. //have anymore beans then we know the
. //game is over, so we reset score, and reset
. //games.
.
.
. printf ("Lost at: %d beans , %d games.\n", score + init,
games);
.
. // And we print out the total number of
. // games played on this trial and show the
. // total score plus the initial value of beans.
.
. lost++;
. score = 0;
. games = 0;
.
. }
.
. if (score >= quit)
. {
. wins++;.
.
. printf ("Won at: %d beans , %d games.\n", score + init,
games);
.
. beans1 == 0;
. score = 0;
. games = 0;
.
. }
.
. }
.
. printf ("Total Won: %d/%d\n", wins, wins + lost);
.
. }
Cool, why do you call this a Quantum Pyramid?
.
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