"You can't calculate probabilities with just algebra. The geometry must be taken into account."
Comte George Buffon, Essay on Moral Arithmetic
UNTANGLING THE QUANTUM ENTANGLEMENT
PARSING "ACTION AT A DISTANCE"
Cracking Pi Cracking Random delivers the geometry of randomness. This includes distinguishing between the randomness we perceive on two dimensions relative to our perceptions ...and the randomness that gravity is actually delivering on the single diameter dimension relative to gravity's straight line pull. The mathematical difference includes a fundamental flat bet advantage over traditional random theory: .16666.... .
This recovers, introduces and reintroduces, two long lost geometries: the original Buffon Needle Problem (1733) and its natural extension (although it appeared in first in history) the Vatican's long suppressed "actio in distans." Modernly, "action at a distance" is the methodology of Quantum Mechanics and Bell's Theorem.
The original Needle provides a matrix of random geometric probability. Its immutable relative length serves as gravity's own universal random unit of measure. That is: relative 1/4 pi.
Action at a distance is a natural extension of the original Needle. Together, they can apparently predict the geometric probability of any random series of anything, complete with a flat bet advantage.
These matters only make educational and mathematical sense with the solution of eight deeply interconnected mysteries spread over 4 centuries: randomness, relativity, "action at a distance," the original Buffon Needle Problem, pi, the French Revolution's Terror, the Terror's effect on public education, and the entanglement or "hidden variables" of Quantum Mechanics.
Action at a distance is the probability engine that drives Quantum Mechanics. Although it is little known, it is not new to science. The term is used as both a methodology and a result. It may be fairly said the world's technology is four centuries behind in development. That is when the Vatican first suppressed "actio in distans." It was never recovered until Werner Heisenberg's use of it in the 1920's. Even then --and now, almost a century later-- the recovery was (and remains) only partial.
Every random event (of anything of any kind whatsoever) is on one end of the diameter of the field, object or game. This applies regardless of the "shape" of the field, object or "game."
There is only one diameter.
Action at a distance is the methodology used to search for geometric probability on the diameter.
Geometric probability is found in relative positions on the diameter.
A randomly measured diameter has three poles: one end, the Center of Rotation (COR), the "other end."
The geometric truth of randomness and gravity may be demonstrated by predicting each relative pi-angle pole (opposing end pole of a straight line) in a series of random measurements.
Geometrically, the first random event in a series of three random events on a diameter of three poles ...is a diameter base.
The "other end" of a diameter is the relative pi-angle pole, relative to the diameter base. A relative pi-angle pole is an opposing pole. It is the third pole on a three pole diameter.
The methodology of "action at a distance" includes a geometric finesse. It is similar to, and simpler than, the common finesse in Bridge. It simply allows the middle or "second" event to happen, but does not give it statistical consideration.
On a randomly measured three pole diameter, the middle or "second" event is matched, as a matter of probability, with the Center of Rotation. This allows the third pole to be predicted at the third trial as the relative third pole on a three pole diameter.
In other words, the three part finesse methodology in "action at a distance" allows the three part geometric structure of the random prediction (or "bet") to automatically match the three part geometric structure of geometric probability, at the relative third trial, with the relative opposing third pole of a three pole diameter. This is in application on a wheel of two dimensions. With some other game "shapes" (ex: dice and RNGs) the finesse must account for the "game's" additional cross radii. The fundamental theory concerning the relative pi-angle pole remains unchanged since the fundamental theory is of geometric probability and the cross radii are the simple algebra of averages.
Traditional random theory doesn't recognize geometric probability. Therein is the flat bet advantage. Traditional random theory expects and "pays off" opposing poles as a .25 algebraic possibility.
The methodology of "action at a distance" uses a geometric finesse to eliminate the Center of Rotation from statistical consideration. On a randomly measured 3 pole diameter, as a matter of probability, the COR is the second (or "middle") of a series of three random measurements.
However, on the "game" of a randomly measured wheel or circle, after the third trial, the COR will appear once for each diameter end pole. After the 3rd trial, although only a three pole diameter is rotating and being randomly measured, this gives the statistical appearance of a circle of 4 poles. These are the Cardinal poles (N,S,E,W). Each end pole has a random .25 algebraic possibility. This is traditional random theory.
After eliminating the COR, the result of "action at a distance" becomes a matter of geometric probability on the diameter. On a three pole diameter, it allows the third of three random measurements to be predictable, as the relative third and opposing pole, relative to the first measurement. That is, the third and opposing pole on a 3 pole diameter is predictable, at each third trial, as a .33333.... geometric probability!
Therein, as a result of "action at a distance," is the flat bet random advantage. Traditional random theory expects and pays off an opposing quadrant pole as a .25 algebraic possibility on a circle of 4 quadrant poles?!
The essentials of these matters were known at the Paris Academy of Sciences in the 18th Century before being lost in the Terror. There are multiple reasons they have not been fully recovered. One reason is not because they are complicated. Rather, exactly the opposite. They are extraordinarily simple. This is the super simple grail envisioned by Albert Einstein. It also eluded him. However, he correctly predicted it would be simple, random, geometric and contain relativity.
There is nothing physical about the entanglement. Its nature is perceptual. It concerns our perception of gravity's randomness being delivered on two or more dimensions ...vs ...the gravitational reality that randomness is actually delivered on the single diameter dimension of a randomly measured field, object or "game."
Nothing is more fundamentally critical in understanding geometric probability. Every random event is on the diameter of the field, object or game.
There is nothing limiting the matter to small particles. Its first organized theory (if you don't count Francoise DuLaurens) came from Isaac Newton. He used it to predict the random orbit of comets.
The Vatican banned Newton's books.
In the late 18th Century, the leaders of the Paris Academy of Sciences conspired to end run the Vatican by having an atheist stooge proclaim himself the "greatest mathematician in France." By secretly handing him their own scientific work to present as his own, they would build his credibility. He could then proclaim the values of "action at a distance" with no one to contradict him. They already knew, of course, that its statistical truth cannot be reasonably contradicted anyway. However, France was a Catholic country by royal decree and the Academy was the King's Academy. To avoid religious/political conflict, they conspired a script that was all smoke to get around the Vatican. They had a good start.
However, just before their efforts could ripen, political circumstances forced them to completely reverse course and use the stooge to publicly disrespect Rudjer Boskovic and his use of "action at a distance." Boskovic was an ex jesuit but still a priest. He couldn't admit there was an advantage without risking excommunication. The infamous Laplace/Boskovic "debate" lasted over a year until the conspirator's unwelcome, but perceived as politically necessary, detour was complete. While the debate served the immediate political purpose of the detour, it was, unfortunately also an effective endorsement of the Vatican's suppression and so ended the conspirator's initial underlying purpose and means of introducing "action at a distance."
The "greatest mathematician in France" was given some sops, but he could only be left hanging. There was nothing anyone could do. As soon as somebody, somewhere, publicly proved the values of "action at a distance," Simon Laplace would look like a half baked cake layered with tiers of stupidity. First, for repeatedly bragging himself as the "greatest mathematician in France." Second, for academically attacking "action at a distance in the first place. Thirdly, for notoriously publicly and repeatedly attacking Boskovic and "action at a distance" in the rude manner that he did for as long as he did. That is, twice a month for almost a year and a half.
Two decades later, the French Revolution got underway. The remaining conspirators were among the foremost political leaders. During this period, the intent of the conspiracy may have died, but the secrecy of the conspiracy was still intact.
The conspirator's efforts then backfired into the French Revolution's Terror.
Laplace, still guised as the "greatest mathematician in France," now appears as the shadow puppet master behind the Terror. He brought with him the credibility of the Academy ...which he would control after certain men were eliminated. Laplace apparently used his undeserved reputation to covertly guide Robespierre with "mathematical certainties" of success for Robespierre's personal hopes and political aganda if he would introduce and lead the Terror as he did. The Terror and its increasingly absurd laws now appear to be the successful use of mass slaughter to serve as a coverup for the judicial murder of the remaining members of the conspiracy as well as Buffonet, the son of George Buffon. He held his father's papers in estate.
If Robespierre was Laplace's right hand, Joseph Fouche served as Laplace's left. He also effectively served as policeman/executioner ...first for Robespierre, then for Laplace.
The papers and records of all Terror victims associated with the Academy were immediately seized by Fouche and delivered to Laplace. Laplace's purpose now appears to have been to cleanse the records --archival, professional and personal-- of any and all mention of the original Buffon Needle Problem and "action at a distance." As well, of course, of any mention of the conspiracy.
Laplace was also the mentor of Napoleon Bonaparte. Laplace used his influence to have both Egypt and the Vatican's archives raided. Laplace also used his influence to effectively take control of France's newly introduced state run system of public education. Laplace kept particular control over the math and science curriculum and made certain the original Needle and "action at a distance" were omitted.
That model of education served as a model for the rest of the world. The math and science curriculae have generally remained unchanged. The original Needle and "action at a distance" remain omitted from public education.
In the 1920's, Werner Heisenberg introduced his theory of Quantum Mechanics. He used a 4 pole matrix ...just as does the original Needle. On this, he superimposed the methodology of "action at a distance." As ultimately proven by Bell's Theorem, out came a .08333.... flat bet advantage.
Until now, scientists could not resolve the advantage with traditional traditional random theory.
The difficulty for modern scientists does not appear to start with academic matters. Rather, the problem appears psychological.
The problem for scientists is that the utter simplicity of "action at a distance" comes with a price that few think they can afford. The cost is a mental admission that, relative to randomness, by the proof, deductions and inferences of the original Needle, we and our perceptions are the entanglement ...and the entanglement is pi. By clear deduction and inference of the original Needle, relative to a series of random measurements, we and our measurements and games and statistics and quantum theories and perceptions and entanglements are all ...just so much relative pi in rotation.
Concerning the grail of randomness, the original Needle holds both the lock and the key.
Measure something random one way and you get life's perception of traditional random expectations on the circle or circumference of the field, object or game. This considers each and every random event in a series of random events. It can be used to deliver reliable analytic results that match our perceptions. This method is called "Monte Carlo methodology." While the name "Monte Carlo" only appeared circa WWII, the first practical use of the methodology was introduced by the original Needle, 1733. One of its featured mathematical dynamics is quadrature. It proves the average random distance between two random events is .25 of the circle or field. That is: 1/4 C. That is a quadrant. Relative to randomness, a "circle" is simply the algebra of 1/4 C multiplied by 4. That is, relative to randomness, a circle is simply the algebra of 4 quadrants.
The random statistics of quadrature match life's perceptions of two dimensions: diameter and cross diameter. When measured randomly, with Monte Carlo, there is a statistical appearance of two equal dimensions (diameter and cross diameter) and four equal end poles (such as N,S,E,W). This is quadrature. It is a series of averages. This random theory is taught and used throughout the world. The perceptual icon is a randomly measured circle with two dimensions: diameter and cross diameter. This matches life's perceptions and expectations of randomness and comes complete with random statistical confirmation. Quadrature is the foundation of traditional random theory.
The original Needle's length relative to the circle is a quadrant and it is the lock on the grail. Its average length is inviolable. It statistically proves two dimensions. If the game is fair, it is impossible to find a flat bet advantage on a rotating or randomly measured circle or wheel or "game" of two (or more) dimensions and 4 quadrants.
The original Needle's simultaneous length 1/4 C is also relative 1/4 pi, relative to the diameter. This is the key. The original Needle's express and deductive and inferential proof is that, relative to a series of random measurements, "circles" and "games" and all other "shapes" do not gravitationally exist. The original Needle's length of relative 1/4 pi identifies the diameter with a random gravitational value of: "1." It identifies its own length as the average of two average random measurements. That is a percentage of the diameter. Therefore, by deduction, gravity values its own randomly measured straight line pull as: "1." ....
...While valuing the "circle" or "game" as just a gravitationally meaningless perception of the algebra of relative 1/4 "pi" in rotation.
The original Needle also deductively identifies both the Center of Rotation and the relative cross diameter as relative pi in rotation. Since it also identifies pi (and/or 1/4 pi and/or 1/4 C) as an average ...and since an average is just a perception ...and further, since gravity doesn't recognize perceptions or averages, it may be deduced and inferred that, relative to a series of random measurements, regardless of apparent "shape," only a diameter of three poles is rotating and/or being randomly measured in the first instance of randomness.
Since relative 1/4 pi is an average ...and since and average is just a mathematical perception of algebra, it may be legitimately eliminated from a statistical consideration of geometric probability. That elimination is executed by the geometric finesse in "action at a distance."
The original Needle sets up the matrix of geometric probability from which "action at a distance" is launched.
When randomness is measured with a geometric finesse, the geometric structure of the prediction or "bet" automatically matches the 3 pole geometric structure of the randomness that gravity is actually delivering on the three poles of the field, object or game's single diameter dimension. This methodology first requires Monte Carlo methodology. The geometric finesse is then overlaid upon the Monte Carlo stream of random events. In a long series, the finesse is the repeated omission of the middle measurement(s) in each series of three or more random measurements. As a methodology, this is often called "action at a distance."
Take three random measurements and eliminate the middle measurement from statistical consideration. This allows the third measurement to be geometrically predicted as the relative third pole on a randomly measured 3-pole diameter ...without mathematical interference from the algebra that randomly constitutes the COR (or middle pole of the diameter of the circle or game). Without the finesse, the Center of Rotation (or pi) statistically creates a fourth pole as an average.
Without a clear understanding of the differences between the methodology of Monte Carlo and the methodology of "action at a distance," everything appears tangled. The entanglement starts immediately with the value: "1." In a series of random measurements, should the radius or the diameter of the field be valued: "1."?
The answer must be first approached with a firm mental grasp. 1) In a series of random measurements, the relative cross diameter dimension is just a mathematical average ...just a perception. 2) Gravity doesn't recognize "perceptions."
By the proof, deductions and inferences of the original Needle, a relative "cross diameter dimension" is just the algebra of a series of random measurements. This understanding is inevitably followed by a necessary mental admission concerning pi.
By the proof, deductions and inferences of the original Buffon Needle Problem (1733) every "game" on a circle is of two dimensions. However, relative to gravity, the relative cross diameter dimension is just the algebra of random mathematical averages ...just relative pi in rotation.
Relative to the randomness of gravity, only the diameter dimension has random gravitational reality.
Let it be given that every randomly measured field, object or game has only one diameter. Let it be given that every random event is on a diameter.
Let it be given that every rotating or randomly measured diameter has three poles: one end, the Center of Rotation (COR), the "other end."
Let it be given that the COR averagely tends to randomly appear once for each end pole (otherwise the "game" isn't fair).
Such double random appearance by the COR gives the statistical result known as quadrature. That is: the statistical appearance of the four poles of two apparently equal dimensions. Let them be ready referenced as: North, South, East and West. Each pole is an equal possibility: .25 . This is traditional random theory. This matches life's perceptions of two dimensions: diameter and cross diameter.
Let a random event land anywhere. For easy reference, call it "South." It is given that it is at one end of a diameter of three poles that can be referenced: South, COR, North.
The mystery of quantum entanglement is relativity. It involves the apparent dual nature of relative probabilities on the single straight line dimension of a diameter.
On the one hand, it would appear obvious that random statistics on the three poles of a diameter would show the three poles of a diameter. On the other hand, on a circle, the same statistics can point to equal possibilities on the two dimensions (diameter and cross diameter) and four poles of a circle.
The key to the lock is the original Buffon Needle Problem. Its dual relativity mathematically denies the gravitational reality of a wheel or circle or "game" or any other shape. The dual relativity allows the set up of "action at a distance." That automatically opens the door to the prediction of randomness as the geometric probability of a relative pi-angle pole.
The original Needle's permanent length is a point of random convergence of the relativity of geometric probability, relative to the diameter ...meeting a point of algebraic possibility, meaninglessly relative to the circle or circumference of the field or "game."
The original Needle demonstrated its unvarying length as the average of two average random measurements. This is the universal random average. The Needle's length is a quadrant (1/4 C) of the circle subscribed by the rotating or randomly measured ends of a diameter. Relative to gravity's randomness, a "circle" is simply the algebra of the universal random average multiplied by 4. That is: C = 4 (1/4 C). Relative to the circle, the original Needle's relative length of 1/4 C is meaningless. It is already a part of the circle. This was Einstein's relativity. To him, all pockets on a wheel were equal.
Since an average is just a mathematical perception, the Needle's relative length is also just a relative perception.
However, the proof of the original Needle's length as 1/4 C, is also the proof of its length as relative 1/4 pi, relative to the diameter. That relativity is not meaningless. It is given life by its relativity to the COR of the diameter. That is, divide the metric "length" of the cross radius into the metric length of the quadrant. In all circles, the quotient is forever: relative 1/2 pi. If one cross radius is 1/2 pi, so is the other. Therefore, relative to the diameter, relative back to the circle and our perceptions, the COR is pi relative to the circle ... while the COR is also .50 relative to the diameter. The same results when it is understood a circle is just a series of end points of radii extending from the COR. Since a circle is pi, relative to a diameter, the COR is pi relative to the cross diameter. Relative to both the circle and diameter, the relative COR is still just a mathematical average. Just a perception!
Since the COR is only the perception of an average, it may be legitimately eliminated from statistical consideration in a series of random measurements seeking geometric probability. That elimination of the algebra opens the door to the geometric probability of "action at a distance." It is a geometric finesse in which the third pole of a diameter may be predicted as the geometric probability of the relative third pole, at the third random trial, of a three pole diameter ...without the statistical interference of the algebra of averages that statistically define the relative COR and/or circle or "game."
That is, take three random measurements. Only the third is predicted. Let the second event happen but eliminate it from statistical consideration. That clears out the COR from the "distance" between one end of the diameter to the other. The algebra of averages that define the COR and the "game" is simply eliminated. That opens the door for a clean prediction of geometric probability as the uninterrupted "distance" between one end of a diameter and the "other end."
This finesse methodology geometrically matches the structure of the prediction or "bet" to the geometric structure of relative probability between the diameter end poles. This is the "distance" in "action at a distance." It is the far side of gravity. It allows the "other end" of the diameter to be randomly predicted, at the third trial, as the relative and opposing third pole of a three pole diameter, with a predictable geometric probability of .33333.... .
Traditional random theory expects and "pays off" each opposing pole as though it was a quadrant pole with a .25 algebraic expectation.
The difference is a flat bet advantage (.33333.... - .25 = .08333....). That is the advantage in Quantum Mechanics. This is the "action" in "action at a distance."
There is no natural metric aspect of the "distance." It is distance from one end of a diameter to the relative other end. It is irrelevant what the metric distance is. The relative distance from one end of a diameter to the other is identical in all series of random measurements, whether the random measurements are of the diameter of an atomic particle or the diameter of a galaxy.
The "entanglement" is perceptual. Gravity doesn't recognize perceptions.
Monte Carlo methodology delivers an appearance of randomness on the perceived two or more dimensions of a circle or circumference of four equal poles.
Action at a distance delivers randomness on the single dimension of a pi-angle or "diameter" of three equal poles.
Monte Carlo methodology delivers traditional random theory.
Action at a distance delivers a flat bet advantage. Modernly, this is the methodology and flat bet advantage of Quantum Mechanics and Bell's Theorem.
Quantum physicists are nevertheless generally stuck in laboratories measuring the serial randomness of very small particles. They are using the right methodology of "action at a distance" ...but are still trying to understand --and impossibly resolve-- the magical flat bet advantage that comes on a single dimension ...with the multidimensional quadrature inherent to Monte Carlo methodology and the unrestrained use of the decimal system.
The recent success of China in demonstrating the quantum experiment of entanglement at 1,200 km into space is impressive as to technological ability but it is not a significant advance in quantum science. The distance is entirely irrelevant. It could be done from here to the far side of the solar system and the results would be the same. There is no physical "entanglement" at any stage of the process. It is entirely a matter of perception and the success is all in the measurement itself. As explained herein, we and our perceptions and outdated measurements are the only "entanglement."
It is not that traditional random theory is wrong. It is simply and dynamically incomplete.
This web site explains and instructs how to use the identical methodology of "action at a distance" to find the identical same flat bet advantage in the serial random measurement of any random series of roulette, cards, dice and random number generators. The foundations are explained herein. Ultimate applications will include examination of every random series of anything whatsoever: large, small; macro or micro; particles or gaming objects; random number generators or stock market or psychology, etc.. See WHAT'S CRACKING.
The mystery of the Terror is now exposed as a ruthless mass slaughter that was intended to cover up the murder of the handful of men already in the know of these matters. As well, to obtain their papers and thereby effectively conceal the original Buffon Needle Problem and its random proof of pi as well as the original Needle's natural extension: "action at a distance."
The Vatican must take responsibility for initiating the problem four centuries ago by suppressing the concept "actio in distans."
Simon Laplace, who falsely and knowingly bragged himself as the "greatest mathematician in France," must be assigned responsibility for effectively continuing the Vatican's suppression, although for his own reasons. Laplace was a mathematical fraud who encouraged Robespierre to initiate the Terror. Laplace's motive was to protect his undeserved reputation. He did so by using Robespierre and Joseph Fouche to promote terror tactics. The Terror was a cover for judicial murder. The Terror tactics of Laplace and Fouche were so repulsive that over a century later, they ultimately --and very specifically-- inspired the worst of Adolph Hitler and the Nazi regime. Laplace also used his mentor relationship with Napoleon Bonaparte to scour Europe to remove reports and studies of the original Needle and "action at a distance." Most especially, he had Fouche order one of Napoleon's generals to sack the Vatican's archives and transport them to Paris ...where they were burned. Disastrously, he also withheld the original Needle and "action at a distance" from the science and math curriculum introduced with the first state run system of public education. The world still follows that curriculum and Laplace's misdirection.
This grail is a flat bet (same amount or measurement taken each time) .16666.... advantage over traditional theories of random expectation. Many applications may be fine tuned with an additional .11111.... from centrifugal force. Relative to traditional random theory, the advantage only makes mathematical sense in the world of pi.
The advantage is found as a geometric probability on the single dimension of a diameter. This dramatically contrasts with the algebraic possibilities of traditional random theory on the two dimensions of a circle. The advantage statistically appears only with the methodology of "action at a distance." It only makes mathematical sense with the unchangeable length of the Needle in the original Buffon Needle Problem as the unit of measure.
These matters solidly belong in the actuarial sciences. There has been exhaustive testing, with 100% success, with gaming and random number generators. Other subjects have been lightly tested, with the partial coin exception noted below, with 100% success. The subjects range from the stock market to psychology to biological and geological distributions. Anyone may easily find and prove the advantage at home with dice, cards or a true random number generator (see: What's Cracking).
Waiting in the wings are studies in dynamic applications to such varied random matters as weather, inventory controls, sports and relationships including jury selection and terrorism.
Perhaps no word in the world's languages is more misused than "probability." Modernly, true "probability" only exists in the quantum sciences. It is only found with the use of the geometric finesse within "action at a distance." In a series of random measurements, the "finesse" is an omission of the middle measurement(s) from statistical consideration. The finesse is through the object, field or game's Center of Rotation (COR). This is the methodology of Quantum Mechanics.
Relative to the geometric randomness of gravity, all other applications of the word "probability" are actually the algebra of possibility. Traditional random expectations and theory are based only on the algebra of possibilities. Relative to gravity as randomly measured with "action at a distance," the algebra of traditional random theory is fundamentally only the equal possibility of one of two directions.
The difference is between the randomness of geometric probability that gravity always delivers on one dimension ...and life's inherent perception of randomness that the same event is delivered on two or more dimensions.
Within the "possibilities" found on two or more dimensions, such as a circle or any other shape, is the randomness of our common perceptions and traditional random theory. This is the "game."
However, by the proof of the original Needle, everything that is not geometric probability or the randomness of two directions is --paradoxically including two possible directions-- just pi.
Geometric probabilities are what gravity delivers in the single dimension of gravity's straight line pull along the pi-angle (or "diameter") of any randomly measured field, object or game. From any single measurement of gravity, there is only a straight line pull. The appearance of gravity as a warped field is only the result of several measurements in an ever changing field. It is also outside the scope of this study.
Such probabilities and the flat bet advantage are only found statistically and only with a geometric finesse.
The so called "probabilities" offered by the casino industry and traditional random theory are actually only algebraic possibilities. Their roots are based on the mathematical fraud executed by Simon Laplace in the early 19th century. His misconduct includes changing the fundamental nature of the original Needle. Laplace also controlled the curriculum of the world's first state run system of modern education. Disastrously, it has continued to serve as a model into the 21st century. By Laplace's intent, it does not contain geometric probability or the original Needle or "action at a distance." Laplace's conduct is discussed in depth in the history section of this site.
These matters are 8th grade simple concerning the geometry. They are 5th grade simple concerning the algebra.
Question: If the Vatican found "actio in distans" so threatening that it suppressed the concept ...and if it was so important that it was the subject of the longest debate in the history of the Paris Academy of Sciences ...why aren't we studying it today?
Question: If the simple original Buffon Needle Problem provides the matrix of geometric probability for "action at a distance" ...and if the Needle is so powerful that physicists had to throw it to determine the geometric probability of random neutron collision when they built the first atomic reactor ...why aren't we studying it today?
These matters are dimensional in nature. On one hand, we perceive randomness delivered in two or more dimensions. This perception may be idealized by a randomly measured circle of two dimensions: diameter and cross-diameter. The end poles of the two dimensions are the four quadrant poles often referred to as: North, South, East and West. Each pole is a random .25 possibility. This is quadrature. It is the foundation of traditional random theory. It is completely irrelevant how many possibilities are on the circle (or pockets on a wheel). Randomly, there are still only two dimensions and four poles.
The methodology of "action at a distance" mathematically separates gravity from perception. Gravity forever delivers its random events on one dimension only: the diameter of any randomly measured field, object or game. A randomly measured diameter has 3 poles: one end, the Center of Rotation, the "other end."
The third pole (relative "other end") is frequently called a pi-angle pole since the rotation of the diameter end poles describe the perfect arc of a circle of pi. The third pole on a three pole diameter appears to be a .33333.... geometric probability. However, the use of Monte Carlo methodology without a geometric finesse, leaves the relative third pole to statistically appear as a .25 algebraic possibility.
Here is where the entanglement gets gnarly.
The flat bet advantage comes from using the geometric finesse of "action at a distance" to predict and find the third pole (the relative pi-angle pole) on a 3 pole diameter as a .33333.... geometric probability that traditional random expects and "pays off" as a .25 algebraic possibility under quadrature. The difference is the flat bet advantage (.33333.... - .25 = .08333....) factored by two directions. That is: 2(.08333....) = .16666.... .
The geometric finesse is the omission of the second of three random measurements.
However ...the appearance of the COR (the second of three random measurements) as a dimension does not support traditional random theory until the fourth trial after a random entry into the series (see: What's Cracking: Beginner's Luck).
Knowledgeable entry into this world of geometric probability requires a mental admission. The price of the ticket is a psychological leap: relative to serial random measurements along the straight line of a diameter, we and our perceptions and dimensions and measurements and games and statistics are all ...just relative pi in rotation.
Cracking Pi Cracking Random resurrects and combines these two very old geometries of random probability: the original Buffon Needle Problem (1733) and the methodology of “action at a distance.” This geometric finesse sets up the geometric probability of the relative pi-angle pole ...and its delivery of a geometrically precise and predictable random flat bet advantage.
The original Needle is a matrix of geometric probability which is foundational. It naturally leads to "action at a distance." The original Needle provides the correct unit of measurement to make mathematical sense of both "action at a distance" and the resulting advantage of geometric probability. The unit of measurement is the original Needle's unchangeable length. It is the universal random average: relative 1/4 pi.
Both geometries have developmental roots traceable to Isaac Newton. Both geometries had a tortuous history throughout the 17th and 18th Century with the Vatican also banning the books of Newton and Buffon. Both geometries were lost in the French Revolution's Terror.
In 1812, Laplace effectively warped the original Needle.
The methodology of "action at a distance" was only partly recovered in Werner Heisenberg's theory of Quantum Mechanics. The original Needle has never fully recovered until this website. Reader's should very carefully note that what is offered in texts and on the web as the "Buffon Needle Problem" is NOT the original Buffon Needle Problem (see Exploring Random: Buffon Needle Problem)!
Only the original Needle supports the mathematical truth of "action at a distance" and the flat bet advantage.
CRACKING PI CRACKING RANDOM extends the methodology of the original Needle (and quantum theory) to every series of random measurements of anything. The original Needle provides its own length as the correct random unit of measure: relative 1/4 pi, relative to the object, field or game's pi-angle.
The flat bet advantage is gravitational, simple, random, geometric, contains relativity and is dimensional in nature. The pi-odds formula delivers it with the relativity that eluded Albert Einstein. He didn't believe in "action at a distance" and called it "spooky!"
In its most fundamental form, the flat bet advantage is doubled from quantum theory's .08333.... (because the particle or orbit or "field" is split) to .16666.... (when the "field" or circle is not split). In many random games, the advantage may be refined to include an additional .11111.... flat bet advantage from centrifugal force.
Of particular fascination, every series of random measurements --of anything-- inevitably tends to duplicate the relative geometric relationships between the relative digits of the geometric divisions of pi. This duplication includes the .16666…. advantage. Indeed, it is in and through the relativity of these geometric divisions that the advantage appears. It does so with predictable geometric precision. It is found with averages of geometric probability overlaid upon averages of geometric probability.
In other words, any random series of anything is already predictable with a flat bet advantage simply by looking at the relativity between the digits of the geometric divisions of pi?!
The inevitable conclusion is that every random series is already a predictable statement of pi in the first instance of gravity and randomness!!
Roulette with a dealer’s random release of the ball was used as the base model throughout this study. It is a near perfect universal model of randomness. Only the frets of a wheel hold back near absolute perfection. These matters have also been thoroughly and successfully tested with dice and cards and true Random Number Generators. So too, this has been lightly but 100% successfully tested with the randomness of the stock market and psychology as well as biological and geological distributions.
Far beyond gaming, the real nest of the gravity bet will be a statistical revolution in the actuarial sciences.
We --and our perceptions and measurements and quadrature-- are the mysterious "entanglements“ and/or "hidden variables” of quantum theory.
The inevitable startling mathematical conclusion is that "randomness" is only the possibility of 1 of 2 directions in a probability matrix of pi ...that is only mathematically realized with the geometric probability within "action at a distance."
We cannot see the forest for the trees. The reason is also a philosophical conclusion that was surely considered by the Vatican (no matter how the average geometric length was called): relative to serial random measurements of gravity, we and the forest and the trees …including our perceptions and beliefs and ideas and games and traditional random theories and measurements and statistics and quantum theories and descriptions and beliefs and histories and conclusions and averages are all ...just so much relative 1/4 pi in rotation!