CRACKING PI CRACKING RANDOM
"YOU CAN'T CALCULATE PROBABILITIES WITH JUST ALGEBRA. THE GEOMETRY MUST BE TAKEN INTO ACCOUNT."
Comte George Buffon, Essay on Moral Arithmetic
INTRODUCTION GEOMETRIC PROBABILITY
Pi and Wheels and Cards and Cubes and Random Number Generators ...and a Random Flat Bet Advantage: .16666....
Geometric probability may be found in all series of random measurements. It statistically appears with a natural advantage over the expectations of traditional random theory. It is grade school simple at an easy level of gravity. While roulette most readily illustrates these matters, cards, cubes and random number generators are more readily available.
The flat bet advantage is demonstrated below. Anyone may duplicate it with their own dice and/or online random number generator.
Geometric probability and the random advantage are found embedded in the widest applications of actuarial science. Beyond gaming, this has been successfully tested with the stock market, psychology, random number generators and biological and geological distributions. All with a proximate .16666.... flat bet advantage. Cards, cubes and random number generators are illustrated here.
The search for geometric probability essentially turns every random series into a “game.” It is between the randomness that gravity delivers as geometric probability on the single dimension of a straight line diameter of three poles ...and life’s perception of randomness occurring as the algebra of averages on a perceived matrix of a circle of two dimensions and four poles of possibility.
The original Buffon Needle Problem (1733, 1777) demonstrated every random series to statistically appear as a “circle” of two dimensions and four quadrant possibilities. Each quadrant is an end pole of the two dimensions. Each quadrant is a .25 random possibility. If the long run average of any random series is other than (or closely proximate to) a quadrant of the field, the “game” is not fair.
However, the original Needle also proved that despite life’s perceptions, measurements and statistics, the two dimensions of a circle were not equal. The randomly measured diameter has a random value “1.” The relative cross diameter is relative pi in rotation. That is, relative to any random event as the pole of a quadrant (call it South for convenience) the opposing pole (North in this example) has a diameter distance with a random value: "1." The deductions and inferences of the original Needle’s length is that the relative cross diameter distance between relative East and West has a random value of relative pi in rotation.
The original Needle proved its length as the average of two average random measurements. That is: .07853.... diameter. That is: relative 1/4 pi, relative to the diameter. Since an average is just a perception relative to gravity, the only random connection between gravity and perception (and “games” of two or more dimensions) is the universal random average of 1/4 pi as the universal random unit of measure. It is a matter of geometric probability.
The original Needle’s length as the average of two measurements naturally invites a third measurement. The original Needle’s deductions and inferences point to the third measurement of a random series as reflecting the geometric probability of the opposing third pole on a single diameter dimension of three poles: .33333.... .
The first event of a random series is at one end of a diameter. The third event of a random series is the other end of the diameter. The second event only exists as a statistical average. It appears as the middle pole.
The perception of randomness occurring on two dimensions is the basis of traditional random theory. It is called "quadrature." However, traditional random theory has no gravitational basis other than the algebra of averages relative to perception. By the proof of the original Needle, relative to a series of random measurements, all relative cross dimensions are just perceptions of mathematical averages. That is, random pi in rotation.
In a series of random measurements, gravity doesn’t recognize perceptions or algebra or averages or cross dimensions. Gravity only statistically recognizes its own straight line pull along a single diameter dimension. Straight up and down down geometry!
The old adage “the wheel has no memory” is a red herring. Relative to a series of random measurements, “wheels” and “circles” and the 4 poles of quadrature and cross diameters that make up traditional random theory ...do not gravitationally exist other than as mathematical perceptions. Just averages. Such averages comprise the Center of Rotation (hereafter: COR). Since, gravitationally and relative to randomness, a "circle" is just a series of end points of radii extending from the COR ...and since a "circle" is pi ...so too, the COR is pi. This too is a deduction and inference of the original Needle.
It may be said everything is relative to gravity. By the proof of the original Needle, in a series of random measurements, everything relative to gravity that isn’t gravity ...is just relative pi, relative to a series of random measurements relative to gravity. Relative to gravity, a game is just a perception. Relative to gravity, and a series of random measurements of a “wheel” ...both the “game” and the “wheel” are just perceptions. Just the averages of relative 1/4 pi in rotation.
However, relative to the “game” (as opposed to relative to random gravity) both the “wheel” and the “game” are real. However, they are only real relative to perception.
There is only one diameter. Every random event is on the diameter. In whatever form the field or object or game’s “shape” appears, there is only one diameter. Every series of random events --of any random series of anything-- randomly and gravitationally occurs on the single dimension of a diameter.
A diameter has two gravitational poles. They may be described as the two opposing end poles of a straight line.
When it is measured randomly, a diameter statistically appears to have a third pole. It is the statistical average. It statistically appears as a “middle” pole. It appears statistically as the second or middle pole. It statistically tends to averagely appear again at the fourth measurement of a series. This is the heart of quadrature. Since each pole is the average of a quadrant, every series of four random measurements tends to statistically appear as a circle of four quadrants.
Quadrature is the basis of traditional random theory. It appears to measure four equal poles. However, relative to a series of random measurements, two of the four poles defining quadrature are gravitationally real and two are just mathematical perceptions.
Quadrature also contains an automatic red herring relative to perception. The two perceptual poles statistically make the two gravitational poles appear as quadratic poles of 90 degrees of arc each.
When the perceptual poles are statistically eliminated by the geometric finesse of “action at a distance,” the two gravitational poles take their proper gravitational place.
The relative opposing pole (the “other end” of a randomly measured straight line) is the third pole on a diameter of three poles. It statistically appears as a geometric arc of 120 degrees. That geometric probability is algebraically factored by one of the two possible directions that constitute a “game.” This fundamentally contradicts quadrature and traditional random theory.
In the circumstance of quadrature, the randomly measured diameter statistically appears to describe a circle.
In the circumstance of "action at a distance," a randomly measured diameter statistically appears as a diameter.
Since a circle is pi, a rotating or randomly measured diameter is also called a “pi-angle” since the arcs of the rotating ends describe pi. A pi-angle is sometimes also called a straight angle or 180 degree angle.
For the averages of four poles and two cross diameters to effectuate and become statistically real so as to hold the mathematical justification necessary to become the quadrature of traditional random theory ...the average of four poles must have the opportunity to appear and average. That average contains the heart of relativity. For an average to appear statistically, it must be recognized as the average of two poles (South and North in the continuing example) relative to one pole (South) ...and statistically appear yet again as the average of two poles (South and North) relative to the opposing pole (North). That is: for an average to have mathematical validity, it must appear twice: once for each of the two end poles being averaged.
Again! For a random mathematical average to appear with a mathematical claim of gravitational legitimacy, it must appear once each for each of the two geometric end poles it is averaging. That is a total of four random events. It gives the statistical appearance of four random poles of a circle ...when in gravitational fact, all that is being randomly measured are the three poles of a diameter. This appearance is due to the middle pole (the average) appearing twice. That is: once for each end pole. That is: the average appears at the second event of a series and the fourth event of a series.
Without demonstration with --by and from-- the fourth random event in a series, quadrature can have no legitimate mathematical claim as an average. The random process for establishing the average of four possibilities must necessarily be ...four opportunities to do so. In other words, the quadrature (four random events) of traditional random theory can only legitimately come into play after a series of four random measurements.
The application of quadrature to fewer than 4 random events is simple a shortcut convenience. It is also a disingenuous red herring that allows the gaming industry to thrive and survive.
Traditional random theory says all random events in a series --including the first, second, third and fourth-- have the same random values.... .
They do not!
The so called random “odds” propagated by the gaming industry are mathematically correct as to quadratic averages They are mathematically incorrect as to geometric probability.
Before the fourth trial of a series can deliver the randomness of quadrature with a circle of four poles, the first three trials of the same series already contains the geometric probability of a diameter of three poles. The geometric probability of the third pole appearing at the third of three random trials is .33333.... . This result is what is searched for with “action at a distance.”
The geometric probability of the third pole appearing at the third random trial of a diameter of three poles is untouched by the interference of averages.
This process is automatic with every random series ...of anything!
This is called "Beginner's Luck."
When a random series extends beyond three events --to four or more events-- it becomes quadrature.
To overcome quadrature, action at a distance may be used to eliminate traditional random theory and its supporting quadrature.
Uninterrupted geometric probability is automatically found in every series of three random events. This is “Beginner’s Luck.” Every person entering a random series --gaming or anything else-- is automatically in a circumstance of “Beginner’s Luck” at the third of the first three events.
Action at a distance simply predicts the third random event in a series of three. Action at a distance never predicts the fourth random event in a series.
The problem for traditional science is incestuous analytic reasoning. The traditional presumption is that, relative to our observations of randomness, our observations (visual or telescopic or microscopic or statistical) are presumed to hold the gravitational truth of randomness relative to our observations of randomness. It is an issue of being unable to see the forest through the trees.
The original Needle proved our observations of randomness hold no gravitational reality. Gravity simply doesn’t recognize observations or measurements or quadrature or games or circles or multiple dimensions or statistics or forests or trees.
By the proof of the original Needle, relative to the randomness of gravity, the diameter has a value “1.” ...and everything else, including ourselves and our perceptions and theories measurements and statistics and quadrature and trees and forests are all ...just relative pi in rotation.
The metric length of relative 1/4 pi, relative to the diameter ...is also the metric length of a quadrant of the field, circle or “game” relative to the circle of averages created by a series of random measurements.
Action at a distance superficially appears as a series of ever-differing random events. In fact, it is a precise relative geometric structure repeated over and over. If a random series extends beyond three, the three part geometric structure of "action at a distance" is simply repeated over and over with each successive prediction being of each next successive third event.
The random geometric completion of a straight line is found by predicting the relative opposing pole --the “other end” of the straight line-- at the third trial. Such opposing pole tends to appear with .33333.... geometric probability. This is factored by the possibility of two directions (the real “game”). This is “action at a distance.” When "action at a distance" is successively repeated and repeated over and over ...it is also simply organized "Beginner's Luck."
There is a caveat!
It concerns pi and the relative cross diameter and its COR.
The “circle” that contains “game.” It is a dimension of relative perception, relative only to perception.
However, even with "action at a distance" the COR must be allowed to occur. The key to successful prediction of randomness is allowing the quadratic events to occur ...but not statistically valuing them. The lack of assigned value to the second and fourth random events of a series is the "geometric finesse" of "action at a distance."
While "action at a distance" is grade school simple, the key to its success is correctly identifying the COR and its game nature. The COR and the nature of the game are defined by the radii that define the relative cross diameter.
If the field has a fixed COR like a roulette wheel or game of two dimensions, and the ball is released randomly, the geometric finesse looks for the relative pi-angle pole at each third trial.
If the field has a fixed axis like a tumbling six sided cube of three dimensions, the geometric finesse looks for the relative opposing pi-angle pole at each thirteenth trial.
If the field does not have a fixed COR, such as lacking in random number generators, the geometric finesse looks for the relative pi-angle pole at each 4th trial subject to variations (described below) from the generator brand's unique algorithm. That is, the quadratic nature of the game without a fixed COR will automatically allow both relative lateral poles of averages. That is, the geometric finesse is of both relative cross radii. For example whereas a fixed COR such as the field of roulette finds the third diameter pole at the third trial such as S, COR, N ...a field without a fixed COR finds the third pole of a three pole diameter at the fourth trial such as S, COR, COR, N.
If the field is a deck of cards of 4 suits, two entire suits must be valued as the COR. In the circumstance of four suits, not only is the relative pi-angle pole to be found at the fourth trial ...it is found at multiple depths of finesse.
Such apparent suspension of probability is the “magic” of “action at a distance” ...and the quantum sciences.
These are simultaneous parallel dimensions. The question is not whether there is a parallel dimension to us ...the issue is not realizing we and our perceptions are a parallel dimension that only exists as a relative perception relative to our perception ...relative to the more fundamental natural dimension of gravity!
The COR is more than it appears. The COR has no gravitational reality relative to a series of random measurements to which it is only a perception of relative pi....
...However, relative to the “game,” the COR has statistical reality. The success at roulette with three random trials is that relative to the “game,” the fixed nature of the two relative cross radii are fused into a single cross diameter. So too, the “game’s” diameter is also the fusion of two radii. In other words, in roulette, half the structure of the “game” (the fused radii constituting a diameter of game’s quadrature of two diameters) already geometrically matches the geometric structure of gravity’s single diameter.
If each of the four quadrant radii that comprise the “game” of roulette were independent, a spinning wheel would essentially have four randomly flapping quadrant radii wings. It would also be a very different “game” relative to a series of random measurements. That would require a “finesse” through more measurements of the COR.
The gravitational geometric probability of a relative pi-angle pole at the third trial cannot be denied....
...But the incessant statistical nature of the “game” also cannot be denied.
The astounding answer is statistically demonstrated with pi, cubes and random number generators. Relative to a series of random events, the probabilities of gravity with one dimension on one hand ...and the possibilities of the “game” with two dimensions on the other hand, occur simultaneously.
The relative opposing pi-angle pole will always tend to appear as though it was a .33333.... geometric probability at the third trial regardless of how many intervening finesses are necessary to eliminate the “game’s” radii from statistical consideration!
The advantage will tend to appear if the number of finesses are equal to the number of quadrants that define the game relative to the game!
In all fair cases, a .16666.... flat bet advantage of geometric probability tends to be averagely found between opposing poles such as S and N.
The unit of measure is a quadrant (or relative 1/4 pi).
Relative to South without the finesse of “action at a distance,” both the diameter and the circle will tend to statistically appear equally as a series of quadrants.
That is: S W N E; S W N E; S W N E; S W N E; appears statistically the same as: S C N C; S C N C; S C N C; S C N C. This is traditional random theory. This is quadrature. In each case, the COR is the average of a quadrant that statistically tends to appear once for each end pole. In each case, relative N appears (and “pays off”) as a .25 algebraic possibility.
Quadrature is a natural grouping of four. For example, let a roulette series be: 4,27,18,16,22,34,3,28,25,12,20,23.... etc.. Under quadrature, these are automatically grouped: 4,27,18,16; ...22,34,3,28; ...25,12,20,23. Each number will tend to appear as the proportion of a quadrant. If every number is predicted or “bet,” an advantage is impossible.
With “action at a distance,” the same numbers would be grouped in threes: 4,27,18; ...16,22,34; ...3,28,25: ...12,20,23. Each number is a proportion of a pi-angle. By only predicting each relative third number, the flat bet advantage appears.
Action at a distance uses one geometric finesse to eliminate one average radius (or one average diameter if the radii are fused). Theoretically, with “action at a distance” the averages of a random series will tend to statistically look like this: S C N; S C N; S C N; S C N.... .
Action at a distance with a dice cube looks like this: S C C C C C C C C C C C C N.
With the unfused quadratic radii of FOREX and the stock market, “action at a distance” tends to dimensionally deliver this: S C C C N. [Work in progress with compound geometry indicates significant quadratic bonus beyond the geometric probability of .16666.... .]
Compound geometry is geometric probability ...within geometric probability ...within geometric probability ...etc.. In a study of random roulette trials a relative pi-angle pole was found at every ninth trial (three sets of three). [Work in progress with compound geometry again indicates significant quadratic bonus beyond .16666.... .]
The relative pi-angle is forever found as an arc of 60 degrees. That is: 1/6 pi. In a field of twelve equal possibilities, that would be two numbers. An RNG delivers one number at a time. The circumstance is not too dissimilar to forcing a square peg of geometric probability into a round hole of algebra.
Geometric probability will prevail.
RANDOM NUMBER GENERATORS
There are two basic types of RNGs: True and psuedo. True RNGs deliver numbers from outside sources of randomness such as atmospheric noise or radiation. Pseudo RNGs program their algorithims to generate their own numbers. Here are the test results of two of each type.
The test model for each RNG was set up as a twelve pocket roulette wheel. For easy reference, the numbers are arranged in order like a clock. The theoretical model of randomness on the numbers of a twelve pocket wheel are the naturally opposing poles of the decimal system with twelve numbers: 1 opposite 7; 2 opposite 8; 3 opposite 9; 4 opposite 10; 5 opposite 11; 6 opposite 12 (or 6 opposite “0“ if the RNG insists on including or starting with “0”).
Each successful prediction "pays off" 12 - 1.
In theory, in a series of three random trials, at each third trial, each number is a .33333.... geometric probability relative to its opposite number. This will be factored by the algebra of two possible directions. That is: .16666.... .Each opposing number will --in theory relative to gravity-- appear as a relative pi-angle pole with geometric probability: .16666.... .
The depth of finesse for each of the RNGs differed slightly but significantly. In the two pseudo RNGs, the geometric probability of a relative pi-angle pole --North relative to South adjusted for direction-- was found at every third measurement. In one true RNG, it was found at every fourth measurement. In the fourth RNG (also true) it was found at every fifth measurement.
In this chart, the characters “+” and “-” refer to the direction in which geometric probability is found relative to the theoretical pi-angle pole. The “+” indicates Clockwise. The “-” indicates Counterclockwise. The @ character and attached number refer to the depth of finesse for the algorithm of that RNG. For example, the term “Pi-angle+1@4“ would refer to the first Clockwise number/pocket to the right of the theoretical pi-angle pocket ...at a depth of four random trials.
Continuing the example, if the first random number of a series is “8,” the theoretical true opposing pi-angle number/pocket is “2.” However, the probability pocket for that model RNG is identified by “+1.” This indicates geometric probability will be found at the first pocket in a Clockwise direction from the theoretical true pi-angle pole/pocket. In this example, that would be “3."
The depth of the finesse is indicated by the “@” sign. The case example, “@3“ indicates the geometric probability will be found at each third trial. The case example, @4 indicates each fourth trial. The case example @5 indicates each fifth trial.
The Far Side of Gravity
These are zero sum games. Traditional random theory says there should be no random advantage. That is: 0.0000.... subject to an unpredictable random deviation. Expected long run random deviation is approximately plus or minus a little over one and one half percent. That is: .015.... .
Action at a distance says there should be a random flat bet advantage of geometric probability. That is: .16666.... .
Randomnumbers.info: Quantum true random number generator.
Position: Pi-angle: +1@5
Success: %: +.15....
Random.org: True random number generator using atmospheric noise.
Position: Pi-angle: +2@4
Success: %: +.13888....
Appzaza.com: Cryptographically secure pseudo random number generator.
Position: Pi-angle: -1@3
Success: %: +.13194....
Mersenne Twister: Popular pseudo random number generator.
Position: Pi-angle: +1@3
Success: %: +.11458.... .
TOTAL TRIALS: 8,766
TARGET: .16666.... FLAT BET ADVANTAGE OVER ZERO SUM GAME.
SUCCESS: .1351.... FLAT BET AVERAGE ADVANTAGE OVER ZERO SUM GAME.
The question is predicting the random pi-angle of a single cube. That is, the relative opposing number or facet) of any randomly appearing number or facet.
The test dice pits were comprised of U and V shaped stacks of books on a bar room pool table. The table (the floor of the pit) was the thick padding cover usually used to protect the table when not in use.
The criteria for randomness was that the cubes be thrown randomly with variations of force and direction including left to right, right to left, right hand, left hand, backhand, forehand, overhand and underhand. The cubes were to be thrown with sufficient force to strike at least two walls of the pit. This criterion for randomness is twice as stringent as casinos which only require cubes to strike one wall of a pit.
How the cubes are picked up between throws is absolutely critical! They must be picked up exactly how they landed face up. If they are in any way “tumbled” in the handling between throws, the statistical thread of geometric probability is lost since the cube doesn’t know if it is tumbled for the record or for fun or from carelessness.
A total of 33 dice were tested using different people in separate sessions over a period of three years. Twenty four of the dice used were casino quality sent directly from the world’s leading major manufacturer. Two versions of casino quality dice were used: “Feather Edge” and “Razor Edge.” Two other dice were casino quality that had previously had actual casino use. As well, six cubes were inexpensive dice from board games. Another tested cube was from a pair of very expensive board game dice that were promoted as cut to perfection by laser.
A total of over ten thousand dice trials can now be pointed to as delivering a closely proximate random flat bet advantage: .16666.... .
The most perfect results were obtained by the “Feather Edge" cubes. These rang in a flat bet advantage just under .16666.... . Feather Edge cubes are simply “Razor Edge” cubes with the razor edges smoothed out.
Razor Edge cubes are mandated for use in Nevada casinos and most casinos in other jurisdictions. They deliver a non random effect not dissimilar to illegal dice called “flats.” A “flat” is a shaved cube that tends to deliver certain numbers. Razor Edge dice are not shaved but they are cut individually from a pressure formed bar. Regardless of how well the cube is balanced, this results in a mechanical difference between the four razor sharp edges on two facets of the cube where the bar was cut ...and two razor sharp edges and two rounded edges on the four remaining facets.
The numbers on “Razor Edge” cubes are applied randomly but the 2 - 1 difference in the mechanical construction of “Razor Edge” over “Feather Edge” allows a casino to pick and choose which numbers they prefer their "Razor Edge" cubes to deliver.
The 2 - 1 difference was precisely reflected in the results tested here by delivering a one third loss of geometric probability. The Razor Edges delivered a flat bet advantage that was predictably just under .33333 less than expected. That is: 2/3 of .16666.... . That is: .11111.... .
The legal mandate of Razor Edges is outdated and undoubtedly a holdover from an early time when gaming was more openly controlled by the mob. The modern excuse is offered that Razor Edges give more grip and therefore “more randomness.” This is disingenuous. The excuse does not address the issue. Differing edges on the same cube automatically destroys randomness by automatically favoring certain facets over others. If the intent of a gaming commission is fairness, then gaming laws should require all facets and edges of a cube be equal.
The six common board game dice averaged just over five percent flat bet advantage. The expensive laser cut board game cube gave the worst percentages of all. Its losing result is apparently from both a “laser edge” and lack of balance regardless of the edge differences. This would not be unexpected from a small company that has a laser but not the expensive precision equipment needed to mark and balance it.
This theory of geometric probability and cubes was tested by a reporter in Santa Barbara, California. Richie Demaria organized three sessions over a two year period using friends, associates and teachers. The dice pits were set up on a padded pool table at the Cliff Room, a respected sports bar in Santa Barbara. The books comprising the walls of the “pits” were provided by the popular nearby Mesa Book Store. The cube series started with stutter steps. An early article in the Santa Barbara Independent: https://www.independent.com/news/2017/mar/09/arnoldis-chef-cracking-pi/.
A Touch of History
The concept and methodology were suppressed by the Vatican four centuries ago: “actio in distans.” Isaac Newton avoided the name but nevertheless used the methodology in his Principia to predict the random orbit of comets. The Vatican banned his books. The methodology proves its value when 1/4 pi is used as the unit of measure. That delivers a .08333.... advantage over traditional random theories of expectation for the random orbits of comets.
Rudjer Boskovic was a prominent priest and mathematician. He used Newton’s methodology and published it with discretion, also avoiding the name: “action at a distance.” Like Newton, he could not admit an advantage. In 1776, for political reasons (rather than the Vatican’s religious reasons) Boskovic was called out by Simon Laplace at an infamous year-long “debate” at the Paris Academy of Sciences. Laplace was a front for Jean Condorcet and George Buffon. The “debate” was fraudulent since Boskovic and his assailants knew there was an advantage to the methodology. However, his assailants also knew Boskovic couldn’t admit there was an advantage without risking excommunication. Boskovic could only say it was just another way of measuring something. Boskovic appeared to somehow publicly “lose” the “debate.” The reputation of “action at a distance” was further buried.
Jean Condorcet is the father of actuarial science. He was also Permanent Secretary of the Paris Academy of Sciences and a prime mover in the politics behind Laplace and the attack on Boskovic. Paradoxically, like Boskovic, Condorcet could not openly admit the geometric truth of “action at a distance.” In 1784, his use of the methodology was mathematically subtle and did not appear to be associated with “action at a distance.” The Condorcet Paradox remains one of the best ways to assess the random values of multiple electoral votes that have a complexity of at least three issues. It delivers a seemingly satisfactory advantage over traditional attempts to resolve such complex matters. The results appear relative to three random measurements of a rotating “diameter.” The “diameter” is comprised of a ballot reflecting shifting political interests in differing districts. The resulting value and advantage of Condorcet’s Paradox may be demonstrated with 1/4 pi as the unit of measure. That is: .08333.... .
Simon Laplace was the mentor of Napoleon Bonaparte. Laplace used the relationship to seize control of education in France. He intentionally omitted “action at a distance” and the original Needle from the curricula of the world’s first model system of state run public education. Nothing has changed in the past two centuries. In 1812, Laplace disingenuously changed the length of the original Needle so that it was no longer a geometric probability of relative 1/4 pi. His intent was to destroy all traces of geometric probability. His motive was to avoid the embarrassment that would follow when “action at a distance” was finally accepted. If that occurred in his lifetime, Laplace would be faced with the blushing fact that he publicly and rudely attacked Boskovic ...when he otherwise knew the truth. He succeeded in his machinations beyond his wildest dreams. Action at a distance and the original Needle remain out of public education.
The effect of Laplace and his fraudulent nature continues ...even into the quantum sciences.
Quantum mechanics and Bell’s Theorem predict the random spin of a split particle. They use the same methodology as Newton, Boskovic and Condorcet ...and get the same flat bet advantage: .08333.... .
From Laplace’s negative legacy, the name “action at a distance” is seldom used in quantum science. To do so immediately invites a profound and statistically apparent truth concerning pi that would is disturbing and unacceptable for many. The original Needle and its remarkable truth of geometric probability have effectively never appeared in education or science.
What is presented on the web as the “Buffon Needle Problem” is the result of Laplace’s fraudulent machinations and his warp of the Needle in 1812. Laplace’s alteration of the original Needle rendered it into its exact opposite so that it cannot deliver geometric probability.
Gravity delivers its random truth though the geometric probability of “action at a distance.” It is only substantiated through the original Needle's universal random average length: relative 1/4/pi. The geometric truth that emerges exists entirely in a world of relative pi!
Throughout all of actuarial science, every series of random measurements delivers a flat bet random advantage: .16666.... .
The methodology of “action at a distance” has a natural complement in the codons that define the chromosomes holding life’s DNA. These are the most fundamental structures of life. Each codon consists of three of four possible compounds. Each third compound in the selection is a natural relative pi-angle pole. Like the natural difference of .08333.... in the randomness of gaming, codon compounds hold the same mathematical difference in their selections as well: .08333.... . The difference appears to be in the pi. Between the perceptions of life and the randomness of nature, it also appears we are the pi.