"You can't calculate probabilities with just algebra. The geometry must be taken into account."
Comte George Buffon, Essay on Moral Arithmetic
A PROOF OF STRING THEORY, PI AND MECHANICS
The original Needle has never recovered from its loss in 1812. Lost as well was its length of relative 1/4 pi as the universal random average. Significantly, relative 1/4 pi was also lost as the universal, random, gravitational unit of measure. This is one of the reasons why, until CRACKING PI CRACKING RANDOM, physicists could only theorize a string theory of physics and/or mechanics ...but not prove it.
String theory works with the random averages of the original Buffon Needle Problem. The key to string theory is the gravity bet with its geometric finesse through the Monte Carlo methodology of traditional random theory. The gravity bet is the organized form of "action at a distance" (see: What's Cracking).
This is also an organized form of the methodology of the quantum sciences. The results of that methodology contain the relativity that frustrated and eluded Albert Einstein (see: What's Cracking).
Every series of random measurements of a random table game --or any other random series-- tends to statistically deliver the proof of a string theory of physics/mechanics!
The heart of that proof is a geometric probability that contains a random flat bet advantage in contradiction of all traditional random theory. It is most fundamentally found in the relativity between the respective digits of the geometric divisions of pi.
That relativity is reflected in the geometric probability of any random series of ...anything and everything random.
In other words, as is the point of this entire website, the geometric probability --and flat bet advantage found in every random series of anything-- is already predictable. Just follow the relativity in the digits of pi's geometric divisions.
Yet again, every random series --of anything-- is already, in the first instance of randomness, just a predictable duplication, complete with a flat bet advantage, of the relativity in pi and its divisions.
These matters are easiest to understand with roulette. The critical first question: what's rotating?
The answer is a matter of relativity. It comes in three parts. Each represents one of the three parts of the structure of gravity's straight line pull along a field or object or game's pi-angle (or "diameter").
Each pi-angle has three poles. Each pole contains the relativity of gravity. The first part/pole of relativity is meaningless. This is traditional random theory and Einstein's relativity. The second and third parts contain the relativity that paves the path to geometric probability, including the relativity of quantum science.
First. Relative to the "game" and the players and traditional random theory and Simon Laplace and Albert Einstein, all that is rotating is a circle or wheel. The "relativity" of a random event on the circle is meaningless. The event is already part of the circle. With the exception of Quantum Mechanics, traditional science and education is stuck at this level.
Second. This is the relativity of the Center of Rotation. As the COR of the game or circle, it is also meaningless. However, the COR is also relative to 1/4 pi, relative to gravity's straight line pull through the circle or game object's pi-angle or "diameter."
No other length of Needle or unit of measure contains this dual random relativity. This is what was lost in the French Revolution. What's rotating is both a circle meaninglessly relative to the game of a circle ...and relative 1/4 pi, significantly relative to the circle's diameter (or to the Center of Rotation of a pi-angle).
Third. The third level of relativity is directly a part of gravity. It is only found with "action at a distance." Its relativity is meaningless relative to the pi-angle it is already a part of, but significantly relative to the circle we perceive. This is the magic of Quantum Mechanics.
The result of "action at a distance" is a predictable geometric event that should otherwise be "random" under traditional random theory but contains a flat bet advantage when sought with the relativity within the geometric finesse of "action at a distance." The event is meaninglessly relative to the pi-angle since it is already a part of the pi-angle ...but is simultaneously significantly relative to the circle it appears on in complete contradiction of traditional random theory. The significance is the "payoff." The significant relativity between the pi-angle and the circle of pi (the "game") is that the circle pays off the "action at a distance" geometric event of 1/6 pi ...as though it was 1/4 pi under traditional random theory?!
It is here that that theoretical physics meets the quantum sciences. The study of "physics" is the study of physical nature. No matter how small the particle, it is essentially a study of chemistry. The study of "mechanics" is the study of random motion. While it is readily assumed that mechanics is a study of how physical things move (the quadrature of traditional random theory) Rudjer Boskovic, the father of atom theory, had a profoundly different take.
Boskovic was a priest and Jesuit. He couldn't push his theories too far or hard since he knew he would be walking on religious thin ice if he used "actio in distans" and admitted the flat bet advantage. He could have been excommunicated. To Boskovic (and to Cracking Pi) the mechanics of an event were the movement of its probabilities, not the movement of the perceived object itself. That is, the random identification of an object's probability valued at 1/4 pi and its movement and transition to 1/6 pi (or 1/2 pi: the results are the same) with "action at a distance."
It is in the relativity between relative 1/4, relative to the diameter ...and relative 1/6 pi, relative to the circle (wheel or "game") that string theory unravels the tangled ball of quadrature.
Relative to the randomness of a game of quadrature (all "games" are games of quadrature) all that is rotating is a circle of quadrature.
Relative to the randomness of gravity, all that is rotating is a series of geometric probabilities that are as invisible as gravity itself. They may only be "seen" statistically.
The key to the string grail is the original Needle. The extension of the original Needle's formula with "action at a distance" (with critical focus on the inherent geometric finesse) combined with the factor of direction, randomly and geometrically delivers the mathematical proof of a string theory.
Each bead of the string is a fraction of geometric probability. Each bead is the average of two random events (the original Needle). Each bead has a random value: relative 1/4 pi. This is the proof of the original Needle. Each bead is a random event. Each event is a fraction that is the original Needle’s length. Each random event is the universal random average: relative 1/4 pi, relative to gravity's straight line pi-angle pull.
It is the relative nature of the three poles of pi-angle that holds the three pole matrix of geometric probability on which the relativity proof of string theory rests. To find and prove it requires the geometric finesse within "action at a distance." This gravitationally contrasts with the quadratic nature of the four pole matrix of algebra that would result without "action at a distance." Paradoxically, the same matrix of geometric probability (the mathematics of the original Needle and traditional random theory) is the perceptual algebraic foundation upon which "action at a distance" does its action.
Pi is a geometric event that we interpret as both the circle and the Center of Rotation. We perceive and describe them with the quadratic algebra of the decimal system.
With "action at a distance," gravity's random geometric probability rules over the random quadratic algebra of perception. The relative difference is the flat bet advantage: .16666.... .
On a roulette wheel, the difference is between the original Needle valued at relative 1/4 pi ...and the result of "action at a distance" which, at the third random trial, tends to change the expected relative 1/4 pi, relative to the diameter ...to relative 1/6 pi (or relative 1/2 pi) relative to the circle.
Since these matters of relativity are expressed entirely in a decimal (100 parts) description of pi, the same relativity must obtain, complete with a .16666.... flat bet advantage, between the first 100 digits of 1/4 pi and the first 100 relative digits of 1/6 pi (as well as between the first 100 digits of 1/4 pi and the first 100 relative digits of 1/2 pi). The digits of pi are ignored by the geometric finesse in "action at a distance."
The string of relativity between relative 1/4 pi and relative 1/6 pi leads to the odds of pi. At the end of the string of 100 relative digits is the flat bet mathematical gaming advantage: .16666.... (see below and within).
By the deductions and inferences of Einstein's EPR (Einstein/Podolsky/Rosen Paradox) challenge to Quantum theory, here is a complete description of physical reality insofar as Einstein's inference concerning the prediction of the geometric probability of gravity's random spin.
That is, in the very title of his EPR, Einstein said Quantum theory cannot be a complete description of physical reality. Roughly expressed, Einstein's argument and general reasoning was that otherwise Quantum Mechanics could predict the random time and place of a particle.
Since Bell's Theorem backfired the EPR on Einstein's relativity theories by successfully predicting random particle spin, it may be concluded that the successful prediction of random spin is, by Einstein's own reasoning, a complete description of physical reality.
As will be shown, this is probably not a complete description ...but it does appear to satisfy the present grail of randomness and mechanics ...and opens the door to a world of further wonders in this dimension of pi.
Here is a mathematical description of Einstein's vision, as expressed by the proof of a string theory. It uses the original Needle and its extension with "action at a distance" (that is: the geometric finesse). It also factors random direction.
Let it be understood and given that it is irrelevant how many pockets are on the wheel. These matters are dimensional. Relative to randomness, there are only two dimensions: the gravitational geometric probability of the pi-angle reality of a diameter ...and the perceptual algebraic quadratic reality of the mathematical perception of a cross diameter.
In other words, it is irrelevant how many pockets are on the "game" of any given wheel. Dimensionally, there are only 4. These are the two gravitationally real opposing poles of a diameter (or "pi-angle") and the two opposing cross diameter poles that lack gravitational reality and only exist as a perception of mathematical averages.
The gravitational reality of any "game" only exists as the two opposing diameter poles identified by the original Needle. They may be visualized as the diameter end poles of a circle subscribed by the parallel lines of the original Needle. The parallel lines are the limits of the field. The diameter is the shortest distance between any two adjacent lines. The circle touching two adjacent parallel lines is the "game."
THE MOST COMMON FORMULA FOR THE ORIGINAL NEEDLE: 2L / pi d = .50 .
This formula for the original Needle is the probability of the random drop of its length as the universal random average (relative 1/4 pi or 1/4 C) cutting any of several equidistant parallel lines. This exactly reflects the probability of a random Roulette ball landing in either of two opposing pockets on the pi-angle of a Roulette wheel. That is: .50 .
• Let “2” = the complete possibilities of two random measurements or drops of the Needle
• Let “L” = original Needle’s length = 1/4 C = relative 1/4 pi = universal random average
• Let pi = 3.14159....
• Let d = diameter (or pi-angle) = C / pi = (pi / pi) = “1.”.
THE ORIGINAL NEEDLE’S COMMON FORMULA MAY BE EXPRESSED ENTIRELY AS PI:
((pi + pi) (1/4 pi)) / ((pi) (pi / pi)) = .50
• Let “pi + pi” = two random measurements.
THE ORIGINAL NEEDLE’S FIRST EXTENSION FACTORS DIRECTION:
(2L / pi d) / 2 directions = .25 .
This is the random geometric probability of the Needle cutting a parallel line in a particular direction, exactly like the algebraic possibility of a Roulette ball landing in a particular pocket on a 4 pocket Roulette wheel.
THE ORIGINAL NEEDLE’S FIRST EXTENSION FACTORS DIRECTION AND MAY BE EXPRESSED ENTIRELY AS PI:
(((pi + pi) (1/4 pi)) / ((pi) (pi / pi))) / ((pi + pi) / (pi / pi)) = .25 .
• Let “(pi + pi) / (pi / pi)” = two directions = the possibility of two relative directions, on a field of two possible directions, over two random measurements, with the geometric certainty of one direction.
THE GRAVITY BET’S EXTENSION OF THE ORIGINAL NEEDLE, WITH BOTH DIRECTION AND THE GEOMETRIC FINESSE, FACTORS THREE RANDOM MEASUREMENTS OF A RELATIVE RADIUS, RELATIVE TO TWO RANDOM MEASUREMENTS OF THE FIELD'S DIAMETER:
(2L / pi d) (d / 3r)) / 2 directions = .16666.... .
• Let r = radius = 1/2 d.
THE GRAVITY BET’S EXTENSION OF THE ORIGINAL NEEDLE WITH BOTH DIRECTION AND THE GEOMETRIC FINESSE MAY BE EXPRESSED ENTIRELY AS PI:
(((pi + pi) (1/4 pi)) / ((pi) (pi / pi))) ((pi /pi) / ((pi + pi + pi) (( pi/pi) / (pi/ pi) + (pi / pi)))) / ((pi + pi) / (pi / pi)) = .16666.... .
[The numerator of the foregoing formula is continuous on a wider page. The only denominator is: the algebraic possibility of two directions factored by the geometric certainty of one direction: “((pi + pi) / (pi / pi))”.]
• Let 3 = three random measurements of all possibilities = (pi + pi + pi).
• Let r = a radius of the field = 1/2 a diameter = a diameter divided by two possibilities = (pi / pi) / ((pi / pi) + (pi / pi)) = .50 .
There is one fraction of relative 1/4 pi in the string formula for the gravity bet and 20 fractions of pi.
Since pi is only an algebraic statement of relative 1/4 pi multiplied by 4, the more correct geometric expression is a string structure of 81 fractions of: relative 1/4 pi.
When the pi-odds string of relative 1/4 pi, relative to gravity, is factored into gravity, the quotient is the DNA of that with which we both perceive and describe gravity and percentage.
That DNA consists of the decimal system and the 10 numbers (zero through nine) with which we express it. That is: 1/81 = .01234567890.... repeating to infinity.
Einstein was also almost correct that predicting random particle behavior would be a complete description of physical reality (or at least cross the threshold to a new dimension). The evidence is in the flat-bet advantage of .16666.... . It is universal and is found throughout these investigations into randomness using a finesse methodology.
Despite Einstein's inference that the success of Quantum Mechanics would not be a complete description of physical reality, the .16666.... advantage of Quantum theory and the "pi-odds" formula is only the mathematical difference, expressed as geometric probability, between perception and gravity. It allows perception to be defined as pi (more precisely: a string of relative 1/4 pi) and gravity defined: "1.".
The foregoing section, "Deconstructing Pi" puts this theory to the test.