Written by G. T. Hushion. Posted in Exploring Random

"You can't calculate probabilities with just algebra. The geometry must be taken into account."

Comte George Buffon, Essay on Moral Arithmetic



Successful prediction of the random future is entirely possible as a geometric probability. The gravity bet may be applied to any series of random events. Success critically depends on how the field and COR is defined and measured.

Essentially, each randomly measured field can be loosely understood as a roulette wheel, however uneven and irregular the field's shape may be, even if it is a list. Randomness will automatically and statistically treat it like a "circle" or roulette wheel, with any necessary modification such as if the wheel suddenly had an odd shape or one or more odd colored pockets.

The gravity bet's application in the world of sports, including game action and sports betting, will be mind boggling. In team sports, offering opponents a series of yes/no decisions will set up the gravity bet with dynamics never before considered.

So too, there will be necessary adjustments with actuarial tables and weather predictions.

Predicting the random future will inevitably include personal matters such as health and relationships. This can include predicting a significantly higher probability of meeting the right mate.

The predictable geometric future will allow the recognition and prediction of certain physical or psychological characteristics of a person or group or “type.” Under traditional random theory, these appear simply as random distribution of percentages in the general (or specific) population like the percentages of a roulette wheel. So too, when one particular event randomly occurs and the the geometric finesse is properly applied, the next several random appearances may be geometrically predicted, with an allowance for the relevant percentages, with the flat bet advantage. This is addressed in CRACKING PI CRACKING RANDOM.

Biological and geological applications have been lightly but successfully tested.

Biologically, a report of random biological distributions (various species of grasshoppers in a Central American pasture) have also been tested and predicted with the same .16666 advantage over traditional expectations of random distribution. Genetically, the .16666.... advantage has been found in the DNA of a double helix.

Geologically, an underwater obstruction was predicted and found in a sea floor cable laying operation.

Weather predictions, including earthquakes have yet to be tested. Certainly they hold exciting promise.

The gravity bet also has application to random human psychology and decisions with wide promising application from jury selection to terrorism.

A fascinating study of random human psychology and pi, centered on anti-social behavior, was successfully tested along a 10 mile section of road in California (Rt. 154) outside Santa Barbara. That stretch is a “Daytime Headlights On” section with prominent signs. Until the late 1990’s, before a new enforcement policy was announced in the local paper, it was a state requirement that regular commuters knew wasn’t enforced. Since tourists tend to take the Rt 101 scenic coastal route, the inland route of 154 is mainly used by local commuters. A study of 460 passing vehicles, over a period of several days, gave a remarkable result. The ratio of those who did not follow the social contract and did not turn their lights on those who voluntarily did follow the social contract and turn their lights on was, with near precision, the ratio of 1 to pi. More specifically: 1 to 3.19.... .

The Stock Market also fits into the classification of psychology. As previously noted, a five week study of the "Twelve Most Active Stocks" in the Wall Street Journal was particularly satisfying. The stocks were theoretically bought and sold as often as possible at a particular time and day relative to a previous particular time and day. The gravity bet delivered up a .145 flat bet advantage. The only question was not of the stock's "value" but only if it would predictable go up or down.

The phenomenon of using geometric probability to predict random psychological phenomena appears applicable regardless of whether the field is a circle or line of people! This also means, since a series of random psychological decisions is geometrically predictable, the gravity bet may also apply to otherwise apparently unpredictable political decisions!

Perhaps on battlefields, the geometric finesse may prove shockingly accurate in predicting "random" matters. While geometric probability certainly can't replace hard intelligence, it may obviously be an invaluable tactical and strategic adjunct.

As well, the gravity bet will have application in creating and cracking security codes that incorporate randomness.

Two important areas invite special attention. The first is the distinct possibility of a fundamentally new type of efficient engine which can utilize the geometric finesse and its geometrically probable gravitational advantages with super efficiency.

The second area of interest is a new look at "random" radio emissions from outer space. To date, such emissions are checked for regularity ...and for pi.

The biggest question is whether there is life in other solar systems as intelligent as we are. That question may need to be reformed. Perhaps --by just merely looking for pi (especially with the decimal system)-- we are really asking if there is intelligence out there as dumb as we are. We probably won’t get an answer. But if we are looking for radio signals pulsing pi, perhaps we should also start looking for the more fundamental universal values of relative 1/4 pi, 1/2 pi, 1/6 pi, and the geometric relationships between them, including the .08333 and .16666... and .27777.... advantage!

Equally important is a new examination of pi itself with a unit measurement based on something other than the decimal or binary systems. For example, dropping the zero from the decimal system (using nine figures instead of ten) might deliver a fresh look at both random radio emissions and pi. So too, with mathematical systems based on 3 or 4 or 6 or 9 or 16, etc..

Besides roulette and dice, the gravity bet's application to cards has been well demonstrated with thousand of turnovers in the simple game of "guess the next card." It has also been demonstrated in casinos with the table game of Baccarat. It only awaits more sophisticated development into the more complex games of Bridge, Poker and Blackjack!

The use in actuarial statistics will enormously benefit health insurance and risk management as well as everything random from inventory controls to structural failures, from market analysis to system deliveries. In short, to every aspect of business that is touched by randomness.



Written by G. T. Hushion. Posted in Exploring Random

"You can't calculate possibilities with just algebra. The geometry must be taken into account."

Comte George Buffon, Essay on Moral Arithmetic.


Various terms and words used by mathematicians to describe the Needle have included: "unique", "charming", "quaint", "arresting" and "of the greatest notoriety."

The Needle was the first means to statistically determine pi (Snell, J. Laurie, Introduction to Probability. p.57 Dartmouth College. Random House/Birkhauser Mathematic Series, 1988).

From his Needle, Buffon is credited with an independent discovery of the binomial theorem (Gillespie, Charles Coulston, ed. dictionary of Scientific Biography. Vol ii, p.577, Scribner, 1970).

Buffon and his Needle are also credited with the first practical use of the "Monte Carlo Method" of probability analysis (Buslenko, N.P., D.I. Golenko, Yu. A. Shreider, I.M. Sobol, and V.G. Sragovich. The Monte Carlo Method. The Method of Statistical Trials. p.4,  Ed. Yu. A. Shreiver. Trans. G.J. Tee. Pergamon Press, 1966).

As well. from the composition of his Needle, Buffomd is credited with the first use of calculus to determine probabilities (Levin, S., Mng. ed. Lecture Notes in Biomathematics: Geometrical Probability and Biological Structures: Buffon's 200th Anniversary, Proceedings. Ed. by R.E. Miles and J. Serra. Proceedings. Paris, 1977).

Buffon's Needle Problem is considered history's first mathematical statement of geometric probability (see: Levin, above, p.29).

The Needle was the introduction of local geometric probability (Cajori, Florian. A History of Mathematics. Chelsea. 3rd ed., p.244, 1980).

The original Buffon Needle Problem cannot generally be found in modern scientific literature other than in this web site and the book cited above: "Geometrical Probability and Biological Structures: Buffon's 200th Anniversary, Springer-Verlag."

Even in Springer-Verlag, other than a quick look at the original Needle, the numerous studies of the Needle that are presented there do not reflect the original Needle, but rather Simon Laplace's warp of the Needle.

The numerous variations of the original Needle that are widely available and promoted on the web as the "Buffon Needle Problem" are the antithesis of the original Needle. They are based on the mathematical fraud perpetrated by Simon Laplace in 1812. In his intentionally misnamed book on "probabilities," Laplace disrespected the original Needle's random length. He disingenuously and maliciously substituted in a needle with the geometrically meaningless length of: any arbitrary given length.

The original Needle's length of relative 1/4 pi, relative to the diameter of the field being randomly measured, is gravity's own statement of geometric probability relative to the randomness of gravity. It is an immutable universal average measurement.

On the other hand, Laplace's variation is without random geometry. It is simply "random" algebra. It is simply an algebraic statement describing any arbitrary length of needle. It is pure algebra for its own sake. It is meaninglessly relative to life's perceptions and is without regard to the geometry of the universal random average.

Laplace is most famous for the "Laplace Transform." It is simply the reverse of his warp of the original Needle.

Laplace kept the original Needle out of public education. That effectively buried the original Needle. Why did Laplace effectively conceal the original Needle and replace it with a fraud?

The answer is simple but deeply buried in the circumstances leading to the French Revolution's Terror ...of which Laplace now appears to have been the architect. The reason Laplace needed the original Needle out of sight was because the history of its truth would have exposed him as a fraud. To avoid that embarrassment, he used Robespierre and Joseph Fouche to murder four specific men. The coverups were the mass killings that constituted the "Terror." There is a more detailed discussion in the History Sections of this site.

Georges Buffon (1707 – 1788) initially presented his Needle Problem to the Paris Academy of Sciences in 1733. In 1734, it was first published in a minor journal intended for worthy work of non Academy members. It was published again in a minor journal in 1776. Its first major popular publication was in 1777, in supplement (4) to Buffon's Histoire Naturelle.

The original Needle introduced geometric probability as it delivered the first random proof of pi. The geometric nature came from proving relative 1/4 pi, relative to the field's diameter, as both 1/4 of a circle (that is: 1/4 C) and, simultaneously, the universal random average: relative 1/4 pi.

The original Needle proved 1/4 pi to be a percentage of the diameter: .78539.... . Therefore, a randomly measured diameter has a random gravitational value: "1."

In delivering the universal random average, the original Needle introduced geometric probability. It also introduced the methodology of serial random measurements. Since WWII, this methodology has generally been known as: "Monte Carlo Methodology."

Buffon originally used a baguette (French loaf) on a plank floor. He suggested a needle on a checkerboard would be more convenient. The name understandably stuck.

The original Needle asks: on a series of equidistant parallel lines, if two players want an even chance a randomly dropped needle will cross a line, how long must the needle be?

“Je suppose que dans une chambre, dont le parquet est simplement divise par des joints paralleles, on jette en l’air une baguette, & que l’un des joucurs parie que la baguette ne croisera aucune des paralleles du parquet, & que l’autre au contraire parie que la baguette croisera quelques-unes de ces paralleles; on demande le sort de ces deux joucurs.”

Buffon concluded that the needle must be approximately 3/4 of the diameter distance (shortest possible distance) between the lines. More precisely, that percentage: .78539.... . That is: relative 1/4 pi, relative to the diameter.

“...que la longueur de la baguette doit saire a peu-pres les trios quarts de la distance des joints du parquet.”

Buffon also identified that percentage as one fourth of the circle described between and just touching two adjacent lines. That is: 1/4 C.

“...quart de la circonference du cercle don’t la longue de la baguette est le diameter...”

A unique and fascinating feature of the original Needle is that it readily and deductively demonstrates that, in the first instance, every series of random measurements --of anything-- automatically turns the circle or field or game or object (of any shape) into a dimensional game of relative pi in rotation. More specifically, into a series of random measurements tending to average 1/4 pi each (see: A Proof of String Theory, Pi and Mechanics).

The original Needle proves a field or circle or game’s diameter (or "pi-angle") has a random mathematical value: “1.”. Therefore, deductively, the radius of the diameter has a random mathematical value: .50 .

It is here that the original Needle makes its random point. It deductively and inferentially proves the relative cross diameter (the dimension of relative “width”) has a random mathematical value of relative pi in rotation. An examination of the relativity is found by making 1/4 pi relative to the Center of Rotation. This is effectuated by dividing 1/4 pi into the cross radius of 1/2 pi. This may also be found by dividing the metric length of a quadrant (the original Needle) by the metric length of the cross radius. The makes the universal random average relative to the COR of the game or field being measured.

By dividing the radius into the quadrant, the outcome is the mathematical value of the relative cross radius for every series of random measurements: relative 1/2 pi. This appears to hold true for any randomly measured field.

The original Needle coincidentally (since it apparently appeared a year before Boskovic's first apparent use of "action at a distance") supports Boskovic’s methodology of a geometric finesse for predicting the orbits of comets. Since the original Needle’s deductions and inferences invite the finesse, it is quite possible the original Needle inspired Boskovic. As noted in the history section, in 1733, Boskovic was teaching mathematics in the educational hierarchy of the Colegio Romano. He may have been asked to evaluate the Needle for the Jesuit's consideration. Both the original Needle and "action at a distance" are traceable to Newton. In 1733, "actio in distans" was already suppressed by the church.

The heart and soul of Laplace’s work was based on the random quadrature he usurped from the original Needle. It appears he may have been quietly handed the Needle by Buffon and Condorcet in 1770. It appears Laplace just as quietly used the Needle’s point (without mention or reference of the Needle or Buffon) in 1772, when he announced he had “discovered” that the “second degree of every equation lies in quadrature.” That, of course, is the point of the original Needle. This history indicates Laplace's announcement concerning quadrature was almost surely part of the set up to use him. That is, quadrature is fairly easy to understand. Having him make the announcement would help establish his credibility. With credibility established as the "greatest mathematician in France," Laplace could introduce "action at a distance" and make it credible. His professed status as an atheist would leave him immune from religious discipline. Since all close examinations of the original Needle naturally lead to "action at a distance," Buffon could then reintroduce his Needle Problem and it could be exposed to open examination.

It is a point of this history that Laplace never discovered anything. Virtually everything he published, with the possible exception of a minor (and disastrous) study of tides, appears to have arguably been stolen from others, mainly from the scientists he had murdered in the Terror.

“Amongst the minor discoveries of Laplace in pure mathematics I may mention his discussion (simultaneously with Vandermonde) of the general theory of determinants in 1772; his proof that every equation of an even degree must have at least one real quadratic factor….” (Ball, Rouse. A Short History of Mathematics. Macmillan, 1908. p.419).

When Buffon unexpectedly published the Needle, in both 1776 and 1777, in the middle of the Laplace/Boskovic “debate” over “action at a distance,” the geometric truth surely started its inexorable atomic fizz. It is here worth noting that Boskovic is the father of atom theory. Buffon, who was the driving force behind Laplace, was the first to conceptualize "quantum."

There for the taking was a .08333 flat bet advantage (or .16666 depending on the "game") over the very traditional random theory of quadrature that Laplace was advocating …and that would appear two centuries later as the same flat bet advantage in and of the Quantum sciences.

The flat bet advantage is the randomly measured geometric difference between a circle and diameter. In the Boskovic/Laplace debate, relative to the mean inclination of comets, relative to the totality of the field (360 possible degrees) it is also the difference between 45 degrees and 60 degrees, factored by two possible directions. That is: 60 – 45 = 15. Next: 15 /360 = .08333…. . Next: 2 (.08333) = .16666 .

It is the difference between our perception of randomly finding one of four algebraic poles on a circle or orbit, each with a .25 algebraic possibility …and gravity's eternal random delivery of one of three geometric poles on the circle or orbit’s diameter, each with a geometric probability of .33333, factored by two directions.

That is: 2 (.33333 - .25) = .16666 .

The same random advantage is found on a semi circle as discussed within.

As is the subject of this book, an arc of 60 degrees is not only .16666 of a circle, it is the geometric probability, over three random measurements, of a randomly measured field’s relative pi angle pole. Therein is the flat bet advantage: .16666.... . Again, it is only found with the methodology of "action at a distance."

In short, the original Needle structures the algebra of a randomly measured circle as the average of four Cardinal poles of 90 degrees each. To define the circle, just multiply a quadrant (length of the original Needle or Cardinal pole) by 4. This is the fundamental algebra on which the odds of every random table game are based.

Shorter yet, with a few fresh words to help out, when the original Needle is extended with “action at a distance,” the algebra of a randomly measured circle of four poles is geometrically changed to six poles of 60 degrees each. Each pole is .16666 of circle or "game." To mathematically define a circle (which is just a random statement of algebraic possibilities) after using "action at a distance," just algebraically multiply the randomly found arc of a geometric pi angle pole by 6.

That too, is just an appearance of the circle relative to the pi-angle pole.

Shortest of all, with some additional necessary explanation: ...when the same series of random events is made relative to the complete pi-angle pole (or: "diameter") with "action at a distance," relative random values change again. Deductively, the first random event in the series is geometrically structured in a pole of 1/12 of the wheel. On a 38 pocket wheel, that would be 3.16666.... pockets. Let a randomly released ball land anywhere. Let it be pocket 23 for example.

Relative to the game of and on a circle, the ball just landed in pocket 23.

As this entire website and discussion indicates, pocket 23 was an event on one of three pole/pockets of geometric probability on the circle or game's diameter. In the first instance of randomness a diameter has three poles: one end/Center of Rotation/other end. That gives pocket 23 an apparent initial random value of geometric probability: .33333.... .

Since it is the first in a series and the relativity cannot yet be established in the first of a series, pocket 23 also retains its random value on a circle: .25 as a quadratic pole. As well, since the circle has yet to be mathematically eliminated by the geometric finesse of "action at a distance," the circle statistically retains its algebraic influence.

Therefore, relative to perception relative to the randomness of gravity, the first random event in a series has a random geometric value: 1/12 C. That is: (.33333) .25 = .08333. Or, just as accurately, 1/12 pi.

Relative to the geometric probabilities delivered by "action at a distance," a random roulette ball lands in a "pole/pocket" that is 3.16666 units wide. This is the first ball in a series of three. It is not predictable since, mathematically, it is not yet geometrically identified by relativity ...and it is only through relativity (the relativity only found with "action at a distance") that prediction of randomness is possible. However, just because it was not mathematically (through relativity) identified as an event on the diameter, doesn't mean it wasn't a geometric event happening on the diameter. Therefore, without the geometric finesse of "action at a distance" (yet to be applied in events 2 and 3 of the series) the random event of a ball landing in pocket 23 simply appears as part of the circle. By the proof of the original Needle, pocket 23 is part of the circle as a continuing series of events of relative 1/4 C each. Therefore, by proof of the original Needle, pocket 23 has a dual random average value: .25 on the circle and .33333 on the diameter. That is: .08333 of the circle. Since a circle is pi relative to the randomness of gravity, that is: 1/12 pi.

The second event in the series has an inferential value: .25 C or .75 C. (that is: 1/4 pi or 3/4 pi) on a circle. That is: E or W relative to a first random event in, for example, S. Geometrically, it matches the middle pole of a three pole pi-angle (or "diameter"). This value may only be inferred and may not be directly statistically proven ....since it is the very Center of Rotation (that is: pi) that is eliminated from mathematical consideration through the geometric finesse in "action at a distance."

It is the third event that holds the flat bet advantage. It is predictable --with action at a distance-- as the geometric probability of the third pole on a diameter of three poles. Relative to both the "game" and our perceptions (they are one and the same since the "game" only exists in and of our "perceptions") the geometric probability is factored by the possibility of two directions on the circle of the "game." That is: .33333 / 2 = .16666 .

None of this game analysis is possible without the original Needle as the universal random unit of measure.

The underlying nature of these matters was apparently known both in the Vatican and the Paris Academy of Sciences in the 18th century. All was lost in the French Revolution. This occurred under the control of Laplace who was protected during the iron-fist 15 year tyranny of Napoleon ...who was in turn, mentored by Laplace.

As discussed within, geometrically, the use of "action at a distance" only makes mathematical sense when it is an extension of the original Needle. This is due to the requirement of "action at a distance" that Monte Carlo methodology be used to form the underlying mathematical matrix upon which "action at a distance geometrically feasts.

The original Needle also introduced the methodology of serial random measurements (it only acquired the name "Monte Carlo methodology" circa WWII). The original Needle introduced geometric probability. Since the original Needle proved random geometric probability to be a statement of relative 1/4 pi ...and since the original Needle was the first random proof of pi ..."action at a distance" is best understood in terms of pi (using relative 1/4 pi as the unit of measure and 1/2 pi or 1/6 pi as the predictive goal.

The flat bet advantage appears to shatter traditional random theory.

Did Laplace see it?

Of course!

Every indication is that it was given to him by Buffon between 1770 and 1773. As well, Laplace obtaining Buffon's papers held in estate after Laplace had Buffon's son guillotined (see History). Today, the Needle often bears Laplace's name and is sometimes referenced as the Buffon/Laplace Needle Problem.

In 1812, Laplace published the Needle under his own name without crediting or mentioning Buffon.

“Imaginons un plan divise par des lignes paralleles, equidistantes de la quantitie a; concevons de plus un cylindre tres-etroit don’t 2r soit la longueur, supposee eqale ou moindre que a. On demande la probabilite qu’en le projetant, il rencontrera une divisions du plan.” (Theorie Analytique des Probabilities, Simon Laplace, p. 569).

["Let us imagine a plane divided by equally spaced parallel lines of the distance a; and a cylinder of the length 2r and suppose the cylinder to be equal or less than the distance a. Give the probability of a toss touching a line of the plane."]

Buffon’s original take on the Needle left a clear inference that the value of a randomly measured field’s radius is: .50 .

When Laplace changed the Needle’s ("cylinder’s") length from .78539 (that is: the universal random average) of the field’s diameter to the complete length of the field’s diameter (or any other length) he eliminated the universal random average!

That ended geometric probability relative to the randomness of gravity. It left intact the appearance of geometric probability relative to life's perceptions ...but that was just unpredictable algebra. Laplace made the point stick by  controlled the roots of modern science and education That ended any effective study of relativity and gravity for the next two hundred years. Laplace's perfidy continues to this day as science continues to be without the original Needle and the geometric truth of "action at a distance." (The correct use of "action at a distance" requires a unit of measure that is: the  relative 1/4 pi of the original needle).

In his analysis, Laplace fundamentally changed the original Needle while discrediting its original length. He also, without giving reason or discussion, arbitrarily and casually mentioned that his calculated result (without mention of “pi angles” or the Needle or Boskovic or “action at a distance” or any other reason) must be multiplied by 16 ...?!  

The only reason to multiply the result of Laplace’s calculations of the Needle by “16” is if the randomly found arc on the Needle’s circle of 360 degrees is a relative geometric probability of 60 degrees (that is: 1/6 of a circle) without going through three random measurements and the finesse of “action at a distance.” This seemingly impossible mathematical phenomenon is the result of Laplace’s disingenuous convolutions (see History).

If this history of pi and gaming is correct, then it was precisely for this reason Laplace was brought into the Paris Academy of Sciences. Buffon needed someone to be a front for his Needle's geometric probability. Buffon's reason was that in its original form, his Needle inevitably leads to "action at a distance." The scenarios aren't hard to imagine.

Question: "If the two average random measurements of Buffon's Needle give the universal random average ...what do three give?"

Answer: "By the proof of the original Needle, two random measurements tend to give a universal random average that is only a mathematical perception. Three random measurements of "action at a distance" gives a flat bet advantage on the diameter of gravity's pull. This advantage is only found with when the middle measurement of perception is eliminated from consideration by the finesse. The elimination is geometrically legitimate since it is just a mathematical perception in the first instance of randomness.

When measuring the randomness of gravity, eliminating the middle measurement is a legitimate action. By the proof of the original Needle, the middle measurement is just a perception --just a mathematical average.

The original Needle --and only the original Needle-- naturally sets up a mathematical matrix for the geometric probability of "action at a distance." The basis of the matrix is the straight line of gravity with a value of "1." and the circle of pi that is subscribed by the rotating (randomly measured) diameter. The quadrants of he circle are just mathematical perceptions.

Sixty degrees of arc is 1/6 of a circle. However, when found randomly with “action at a distance,” its relativity to a diameter comes with a unique directional factor. Like a circle, the random measurements of a diameter are also subject to the possibility of two directions ...but with a difference.

Two possible algebraic directions on a diameter come with a geometric certainty of one direction.

Two possible algebraic directions on a circle come without geometry or geometric certainty. They are just two algebraic possibilities.

With “action at a distance,” all four directional factors come into play, but not equally. The randomness of gaming relative to a diameter is different from the randomness of gaming relative to a circle. This difference iis what this study is all about in the first place.

When two possibilities are factored into the Needle’s quadrant arc of 90 degrees (or into the average gaming quadrant) they also contain the two possible directions transferred from the diameter, through 1/2 pi (comes automatically with "action at a distance") with a unit of measure of relative 1/4 pi. This reduces a Quadrant to 45 degrees of inclination relative to a diameter base or, relative to the COR 22.5 degrees of inclination.

When 22.5 degrees is made relative to a circle of 360 degrees (the “game”) the result is .08333 . This result (Laplace’s result ((and also the advantage of the Quantum Sciences))) must be multiplied by 16 to order to define the circle (or game or field or orbit or particle or randomly measured circumference of anything). That is: 16 (22.5) = 360. This completes the field (or "game") of 360 degrees, to which the result of a random measurement is relative. However, it is only relative as an algebraic statement relative to the circle being measured. Since a circle (or "game") is already only a statement of algebra ...this incestuously renders it meaninglessly relative to the quadrature that Laplace was promoting as well as to the geometry he was ostensibly looking for.  

That is what Laplace necessarily did to obtain the 60 degrees he needed to be able to multiply 22.5 degrees by 16 to obtain the results in degrees (or 60 degrees by 6 if the results are expressed as percentages). He simply changed the Needle’s length.  

The problem for Laplace and his take on the Needle is that he couldn’t use “action at distance” over three random measurements to get the result of 60 degrees that is delivered by the randomness of “action at a distance” and the original Needle. That would have exposed the sham of both his apparent acceptance/usurpation of the original Needle in 1770, and of his fraudulent "discovery" of quadrature (the Needle’s quadrature) in 1772, and his use of it to attack Boskovic’s finesse methodology of three random measurements in 1776.

To protect his plagiarism of the Needle, Laplace had to start with 60 degrees instead of the original Needle’s 45 degrees (straight line connecting the ends of a 90 degree arc which is the original Needle’s length) because otherwise, in 1812, he would have been right back where he was in 1776 …where he was ultimately proved wrong in the Boskovic debate although no one could admit it (to do so would invite the wrath of the Vatican). Laplace’s solution was to arbitrarily lengthen the Needle. This intentionally lost the unique geometry of the original Needle’s random length. It made the original Needle’s length geometrically meaningless and no more than algebraically equal with any or all other lengths.  

Without the original Needle and its insistence on relative 1/4 pi, Laplace could use the original Needle’s paradox of quadrature and twist it into an appearance of randomness without going through “action at a distance” and pi....  

...All Laplace had to do was make his "cylindre" longer than the original Needle’s random length.

Laplace made his "cylindre" the entire length of the diameter distance between the lines. Laplace claimed there were fewer “errors” when using his length. By that he meant his longer length crossed a line more often than a shorter length (such as --by implication-- Buffon’s length of the original Needle). Therefore, according to Laplace, pi could be calculated faster.

Instead of recognizing the original Needle’s relative valuation being relative to a field’s complete diameter (which is random “1.” and to which everything random is gravitationally relative) Laplace left the muddled inference that the value of a randomly measured field’s radius is “1.” ...from which it may be algebraically deduced that the complete diameter therefore has a random value of: "2." ...and therefore a circle is deductively valued: "2pi."

History has since interpreted Laplace's disingenuous comment to mean that Buffon made an “error” that Laplace somehow “corrected.”

Nothing could be further from the truth!

Ever since Laplace's malicious warp, the original Needle has been considered as no more that a quaint way of calculating pi. It is now sometimes called the "Buffon/Laplace Needle Problem" or the "Laplace/Buffon Needle Problem" or even the "Laplace Needle Problem."

In point of fact, there is no error in the original Needle and no one has ever found or identified one. The "error" was entirely Laplace’s.

Laplace did not make an error of algebraic calculation. Rather, it appears a malicious error in which Laplace was concealing the original Needle's random geometric truth of pi and his twisted usurpation of it.

Laplace's alteration of the original Needle is perhaps the greatest disaster in the history of commerce and science and education. It even derailed Albert Einstein's quest for the grail!

Laplace's change made the random geometry of relative 1/4 pi algebraically equal to any other length of Needle or "cylindre." In doing so, he dismissed and disdained the unique geometric values of the original Needle. That lost the unique fundamental geometric values of “1.” and pi that are only found with the random circumstances of the original Needle.

History, including Einstein, followed Laplace's lead. "One complete revolution corresponds to the angle 2pi in the absolute angular measure customary in physics...." (Einstein, Albert, tr. Lawson. Relativity. Crown, 1961. p.125). Like Laplace, Einstein also valued a radius as: "1.".

The original random values of "1." and pi ...are restored and explored here. As previously noted, even after it was altered, the power of the Needle is such that when physicists built the first atomic reactor they had to use the needle by randomly tossing nails on a grid floor to determine the probability of random particle collision so as to know how thick to build the walls.

The formula for the gravity bet is the formula for the original Needle, extended with the geometric finesse ("action at a distance") factored by two directions. This delivers the random flat bet advantage: .16666 !

In the world of science and education, the original Needle has never fully recovered since its loss through the Paris Academy of Sciences and Laplace. In short, the original Needle never had a chance to develop beyond its original introduction.

Laplace’s conduct and cover up was surely the most colossal fraud in history. Disastrously, it has been the basis of science ever since, including the stock market and the insurance and gaming industries!

It may be fairly said that any deep understanding of randomness and geometric probability and "action at a distance," must start with the original Needle.



Written by G. T. Hushion. Posted in Exploring Random

"You can't calculate probabilities with just algebra. The geometry must be taken into account."

Comte George Buffon, Essay on Moral Arithmetic



Wheels and circles and games have four poles and no memory. Relative to gravity, they only exist as algebra in our perceptions.

Diameters (or "pi-angles") have three poles. They do not need a memory. Relative to gravity, they have a gravitationally real structure of geometric probability.

These random matters concern the different geometric realities between the two fundamental dimensions: gravity's straight line pull on the diameter dimension (or “length”) of a circle or game or field ...and life's perception of a relative cross-diameter dimension (relative “width”).

The fundamental dimensions appear equal ...but it is only an appearance. A circle or any other "shape" appears to have two dimensions of length and width. However, gravity doesn't recognize "shapes." Relative to gravity, the "shape" of a circle or game or field is only an appearance unique to life's perceptions.

When an apparent multidimensional object is measured randomly with the geometric finesse in "action at a distance," there is, statistically, a fundamental dimensional change.

By the proof of the original Needle, only one dimension is physically real and rotating. It is the diameter or, more accurately, a "pi-angle."

The problem for the world of contemporary science is not that science has yet to discover and solve the difficult complexities of the universe and its dimensions. The problem is that we are the problem. We and our perceptions and experiments and measurements are the greatest complexity. The real problem is threshold: how to eliminate ourselves and our perceptions from our experiments.

The solution is the methodology of the geometric finesse. The mechanics of the finesse are exactly like the mechanics of the common finesse in the card game of Bridge. The geometric finesse is the heart of "action at a distance." This methodology statistically changes the apparent "shape" of whatever it is used to randomly measure. It statistically expresses the geometry of a diameter rather than the algebra of a circle or wheel or game or list or any other "shape."

As also discussed below, experimenting with gravity and the geometric finesse could, until fairly recently, get the user excommunicated. Only four centuries ago, Giordano Bruno was burned at the stake for supporting the ideas and gravitational theories of Copernicus. The church suppressed the concept of "action at a distance." After Newton used the methodology to predict the random orbits of comets, the Vatican banned his books.

Traditional random theory accurately states the “wheel has no memory.” However, it is only accurate because, relative to randomness and gravity, “wheels” and other “shapes” do not gravitationally exist in the first instance of randomness. They only exist statistically relative to life’s perceptions and random measurements. This was the proof, by deduction and inference, of the original Needle.

The unit of measurement of the original Needle is its length. It is the universal random average: relative 1/4 pi, relative to the diameter.

Relative to the randomness of gravity, only a diameter dimension is physically real. More accurately, its reality is found as probability. By the mathematical proof of the original Needle, gravity expresses its geometric probability through the single dimension of a diameter.

Through the original Needle, gravity randomly values itself: "1."

Simultaneously, the deductions and inferences of the original Needle randomly value the relative cross-diameter dimension as just relative pi in rotation ...just a mathematical average ...just a perception expressed by the algebraic possibilities of a circle or "game" ...or pi.

In the first instance, the net pull of gravity is on, and/or along or from, an object’s diameter.

When a field or circle or object or game is randomly measured ...all that are physically “rotating” in the first instance, relative to the random event, are the geometric probability poles of the object’s diameter. This was a deduction of the original Needle. The proof came with the original Needle's extension with "action at a distance." 

The original Needle used relative 1/4 pi to prove that, relative to a "game" or circle, "pi" was just an algebraic expression of relative 1/4 pi multiplied by 4 ...and so was a circle ...and so too was a "wheel" or "game" or any other randomly measured field.

The deeper geometric significance of pi is found in its prominence as the COR of a rotating diameter (any random table game or other randomly measured field). The threshold significance of pi is that it has a dual nature depending on how and whether its random nature as the COR is counted.

A series of random measurements will statistically display a circle or "wheel" if each random outcome (which automatically includes the COR) is counted or measured or predicted. This is traditional random theory. This is Monte Carlo methodology. The COR is simply "counted," or allowed to averagely randomly appear twice in a series of four random measurements: once for each end pole. This gives the random statistical appearance of four Cardinal poles (NSEW). This is how a 3 pole diameter of geometric probability statistically appears as the quadrature of a 4 pole circle. This is the proof of the original Needle (without an extension with "action at a distance"). This is the foundation of traditional random theory ...without the dynamic of relative 1/4 pi, relative to the diameter.

The result of the geometric finesse is paradoxical and defies all traditional random theory. The COR statistically displays itself, by default, as a diameter pole. This can only occur if the COR (or the second random event in a series of three) is finessed through and not counted or measured! Otherwise, the COR ...and pi ...appear as two poles and as a circle. Why...?

...For the reason that by taking four measurements (quadrature) on a three pole diameter, the COR necessarily averagely appears twice. Geometrically, that gives the statistical appearance of four equal poles: South, COR, North, COR. That gives the statistical appearance of an unpredictable circle of four equal poles. South, West, North and East.

The simple finesse methodology eliminates the "middle" of three random measurements or cards played. This eliminates the algebraic dual nature of the COR. The dual nature is that the COR is .50 diameter ...while simultaneously is both 1/4 pi, 1/2 pi and pi (depending on perception and how it is measured) relative to the cross diameter. Getting rid of a randomly measured object's COR is the geometric finesse methodology of "action at a distance."

Diameters do not need a memory. Geometrically, when measured randomly with the gravity bet (or the "action at a distance" of Boskovic's methodology for predicting the orbits of comets ...or the "action at a distance" of the Quantum sciences for predicting random particle spin) ...all randomly measured diameters statistically display a gravitational structure of three probability poles: one end, the Center of Rotation (as a single pole since it is finessed through), the "other end."

In the first instance, physically, relative to the random measurement itself, with all series of random measurements that are made with the methodology of a geometric finesse, the statistical proof appears clear. All that is rotating in a series of random measurements is the geometric probability of a single dimension. It is a diameter or "pi-angle" of three poles ...not the algebraic possibilities of a circle or wheel with two dimensions and four poles.

In the first instance of randomness, relative to randomness and/or gravity, every random roulette ball, and every turn of a randomly shuffled card, are random geometric events on a diameter... whether of a circle or suit.

Geometrically, the algebra and traditional "odds" of a "wheel" or "circle" is the "game." It is a far distant second rate random event compared to the random geometric probability of the diameter.

The geometry of a diameter doesn't need a memory. It has a gravitationally real structure of a single dimension and three poles.

Inherent in a diameter's random geometry is the simple, fundamental, flat-bet advantage of .16666 . In a series of three random events, it is the difference between the third event being a pi-angle pole of geometric probability on a diameter of three poles ...but appearing through our traditional measurements and traditional random theory and in our perceptions a Cardinal pole on a circle of four Cardinal poles.

In short, the geometric finesse delivers the third pole on a diameter of three poles ...which traditional random theory expects and "pays off" as the 4th Cardinal pole on a wheel or circle or “game” of 4 Cardinal poles.

The difference is factored by the possibility of two directions. That is: 2 (.33333 - .25) = .16666.... .

A “wheel” only exists relative to a “game.” Wheels have no memory because, when measured randomly, they simply do not gravitationally exist. They only "exist" in the measurements of our perceptions

Gravitationally, relative to the geometry of randomness (as opposed to relative to the algebra of a “game” or “wheel”) all the real random geometric gaming action --the geometric action with the flat-bet advantage-- is on the three poles of a field or game object’s relative diameter!

Diameters do not need a memory. Relative to the underlying random gravitational events of roulette or any other randomly measured game or field, all that is gravitationally rotating in the first instance is the straight line, single dimension, 3-pole geometric probability structure of the wheel or field or game’s diameter!

The gravity bet succeeds because the three pole geometric structure of the prediction or bet matches the three pole geometric structure of that which is being predicted or bet.

In every case, that structure is not a round circle. It is the straight line of a diameter or "pi-angle."



Written by G. T. Hushion. Posted in Exploring Random


"You can't calculate probabilities with just algebra. The geometry must be taken into account."

Comte George Buffon, Essay on Moral Arithmetic



The methodology of "action at a distance" is a geometric finesse. The mechanics of the basic finesse are identical with the mechanics of the common finesse in the card game of Bridge. The application is even easier since the "game" values are not considered. That is: take three random measurements and eliminate the second while predicting the third to be relative to the first.

By the proof of the original Needle, every random table "game" is a "game" of 4 equal possibilities on a circle. Each possibility is a Cardinal pole. That is a quadrant. Each quadrant Cardinal pole is a .25 algebraic possibility. This matches life's perceptions and expectations of a 4 pocket wheel. Since these matters are dimensional, this is also the basis of quadrature and traditional random theory.

It doesn't matter how many "pockets" are in the "game." There are still only two dimensions: diameter and perceived relative cross diameter. It doesn't matter how many "pockets" are in the "game," half the random events will land on one side of the diameter and half on the other. Similarly, with the perceived relative cross diameter. It doesn't matter how many "pockets" are in the "game," half will land on one side of the perceived relative cross diameter and half on the other side. This is quadrature. Relative to a series of random measurements, gravity dosn't recognize "shapes." Gravity only recognizes its own straight line pull along the diameter of the randomly measured field, circle, "shape" or "game." It doesn't matter what the "shape" of the "game" is. The entire matter is dimensional. This is the basis of traditional random theory.

The statistical results of traditional random theory on a 4 pocket wheel match our perceptions and expectations. Each Cardinal pole (or "pocket") tends to appear with .25 of the total measurements taken. Traditional random theory relies on Monte Carlo methodology. That is: count all measurements and take an average. It is worth noting again that this methodology was introduced by the original Needle in 1733, while the name "Monte Carlo" was only attached circa WWII.

The original Needle also proved each Cardinal pole was a geometric probability of relative 1/4 pi, relative to the circle or "game's" diameter....

...And that....

...Sets up "action at a distance" and makes mathematical sense of the flat bet advantage: .16666.... .

Action at a distance changes traditional random theory by geometrically matching the structure of the measure or prediction or bet the geometric structure of the diameter of that which is being randomly measured or predicted or bet. That is: at the third random trial, predict the relative pi-angle pole (the opposing diameter "end pole") relative to gravity's straight line pi-angle pull from the first random trial.

In other words, if the first random event is in "South," predict the third random event to be "North."

In the first instance of randomness, the relative pi-angle pole delivers a .08333.... mathematical difference between an event on gravity's pi-angle and the same random event on the pi-angle's circle. Geometrically, a relative pi-angle pole is the third and opposing pole on gravity's geometric structure of a pi-angle of three poles.

While the quadratic structure of the "game" or COR may require a deeper finesse (such as the 9th trial for an RNG or the 13th trial with a cube) to reach the relative pi-angle pole, it is still fundamentally the third pole on a structure of three poles.

Gravity's relative pi-angle pole is an arc of 60 degrees of geometric probability. Traditional random theory expects, and pays off, an opposing pole as though it is quadrant Cardinal pole with an arc of 90 degrees. The difference is the foundational part of the flat bet advantage. That is: .08333.... . The difference must then be factored by two possible directions which, constitute the "game." This doubles the flat bet advantage: .16666.... .

This, of course, makes no sense under traditional random theory. For the identical reasons, this is why Quantum Mechanics also makes no sense under traditional random theory.

To make mathematical sense of "action at a distance," it is first necessary to make a mental jump and agree with the original Needle's inferences of pi. Relative to randomness, we and our games and the game's Center of Rotation, are all just pi. The threshold question then becomes a very limited piece of mathematics. What geometric structure is to be assigned the random value: “1.”?

A diameter is the straight line that cuts a circle in half. A radius is one half of a diameter.

The idea of "action at a distance" is to predict the randomness of an opposing pole, such as North relative to South (or the reverse) or East relative to West (or the reverse) as one of three poles on a diameter of three poles. That is: South, Center of Rotation, North (or the reverse) ...or ...East, Center of Rotation, West (or the reverse).

This geometric structure of 3 poles does not coincide with the algebraic structure of 4 poles on a circle or "game." The methodology of "action at a distance" only makes mathematical sense if the randomness of "1." is valued correctly.

However, if "1." is valued correctly so as to make mathematical sense, it must use the correct unit of measure. That unit is the length of the original Needle: relative 1/4 pi.

The most fundamental problem in physics starts with traditional random theory. The problem starts with traditional random theory valuing a random field or game radius as: “1.”

The original Needle was randomly and gravitationally correct when it valued a randomly measured field's diameter as: "1.". By simple deduction, a radius therefore has a random value: ".50".

This random geometric truth is from the original Needle.

Any attempt to apply the algebra of traditional mathematics and/or random quadrature to reconcile the differences with geometric probability is useless if the purpose is to understand randomness. This is the "spookiness" of "action at a distance." The attempted reconciliation inevitably leads to an all-encompassing world of pi.

Apparently, the more scientific education a reader has, the more difficult this is to understand.

Simon Laplace changed the fundamental dimensional nature of random values when he took the Needle (without mention of Buffon) and changed its length. His changes were more than a mere proportional change of the original Needle's length. Laplace fundamentally changed the original Needle's random nature. It was no longer random geometry relative to gravity. It became just a meaningless algebraic search for pi, relative to the quadrature that Laplace used to make the alteration.

Disastrously, Laplace also disingenuously and wrongfully implied the original Needle contained "errors."

The historical damage caused by changing and disregarding and disrespecting the original Needle's random geometric length is evidenced by the fact that tens of thousands of highly trained mathematicians and scientists have tried to break randomness over the centuries. Other than Quantum theory, none have succeeded.

This is also evidenced by the fact that “action at a distance” is the very heart and pulse of Quantum theory. It contains the very grail that is the subject of this study ...but Quantum physicists still cannot mathematically understand their own success....

....The reason is that they are starting with the wrong random value of: “1.”.

....The problem is that the correct value of "1." comes with an inference on the price tag. That is, relative to a series of random measurements, gravity has a random value: "1." ...and everything else, including ourselves and our perceptions and measurements and statistics and "games" are all ...just relative pi in rotation.

To understand the mathematical values of randomness relative to gravity as opposed to randomness relative to our perceptions, it is necessary to start with the original Needle's correct random geometric value of: “1.” It is the value that gravity itself, by virtue of the original Needle's genius, assigns to gravity's own straight line pull on the diameter of a randomly measured field.

The problem Quantum physicists have is using and applying the same algebraic value of “1.” to geometric randomness as they --and we all-- apply the value of “1.” to the everyday world of non-randomness. This is the mathematical disaster we perceive and know from our education and experience.

The algebraic value of “1.” used in traditional random game theory ...and the geometric value of “1.” as gravity randomly defines its own randomness ...are fundamentally different. They exist in entirely different dimensions.

The random, gravitational, geometric nature of pi (every random table game or series of random measurements) is fundamentally different from life's perceptions of its algebraic nature and "shape."

Geometrically, dimensionally and gravitationally, the randomness of "games" is not what it seems!

Relative pi (or relative 1/4 pi multiplied by 4) is perceived as a circle. The randomness and relativity we perceive is only relative to a circle and "games" and life's perceptions. That makes the relativity we perceive (Einstein's relativity) meaningless since what we perceive on a circle is already part of the circle.

By the proof and deductions and inferences of the original Needle, relative pi is also, geometrically, the Center of Rotation relative to an object's diameter. When pi is understood geometrically as the COR, it may be made geometrically relative to randomness and gravity....

Paradoxically, to find the flat bet advantage in pi, the COR (that is: pi) must be eliminated (finessed through) so that pi doesn't statistically appear in the random equation. This is what "action at a distance" does. It forms an equation using the divisions of pi eliminate pi from the equation.

It is here that the entire world of Quantum theory runs into the brick wall that comes from starting with the wrong measurement. In this case, it is starting with the wrong value of "1.". When something is measured randomly in Quantum theory, it appears to change by the very fact of measuring it.

Here's why.

It is the dimensional results of our measurements that change with the geometric finesse. The statistical results that come from eliminating the COR proves the randomness that we are measuring does not mathematically agree with the mathematical randomness we perceive. The brick wall instantly melts with the realization that it is just a wall of pi in the first instance. We ...and our excessive perceptions and unnecessary measurements of the COR ...are the pi. Eliminate the middle measurement with the geometric finesse ...and the problems of pi and perception go away. This is the dynamic value of "action at a distance."

All the random geometric action, including the flat bet advantage, is in the predictable interaction between relative 1/4 pi, relative to the circle or "game" ...and relative 1/2 pi (and/or relative 1/6 pi) relative to circle or game's diameter.

The same advantage is found between the relative digits of relative 1/4 pi and relative 1/2 pi, but the relationship between relative 1/4 pi and relative 1/6 pi is more theoretically accurate for the reasons given herein.

It is the diameter of a wheel or shuffled card suit or cube that randomness and gravity are acting on. Relative to gravity, the value “1.” must be applied to the randomly measured field or game’s entire diameter.

However, relative to life’s perceptions, and by common agreement and education (following the lead of Laplace) we assign (as do Quantum physicists in error) the value “1.” to a randomly measured field or game’s radius.

Laplace's alteration kicked pi out of gravity's diameter where it is naturally, randomly and geometrically, positioned as the COR. Laplace's change left pi as merely a circle (or COR) be counted with every random measurement. Laplace's alteration also leaves room for the COR to be redefined as: "1.". This fits life's perceptions but has little to do with random geometric probability. It makes the random geometric truth a mathematical impossibility.

The algebraic and geometric differences of "1." should have evolved side by side. Laplace had history's richest opportunity to make that happen. Instead, he used his political power to make certain they did not evolve at all. Rather than embracing these new random geometries, Laplace, the "father of modern game theory," inexcusably dismissed them. He made his questionable academic point stick by lack of integrity (Laplace's lack of integrity is historically well known and documented). His outrageous conduct was protected by the men he mentored: Robespierre, Napoleon and Fouche, rather than by reasoning and academic ability.

This is not a mathematical matter in the first instance. Nor does it fall and under any other traditional science or academic discipline. It is a matter of recognizing the single dimension of gravity and its relationship to the world of relative pi an entirely new dimension.

For the past two centuries, Laplacian mathematics have been harvested in quadrature and effectively welded in bronze and sealed in cement. It is now virtually useless to ask a mathematician to understand or confirm these matters. No "physicist" or “mathematician” or "statistician" can do it without apparently surrendering, at least psychologically, the basis of his or her education.

It will surely be a mass of naturally inquisitive students who will ultimately confirm these random matters of pi and geometry. It will undoubtedly occur first across the internet.

The use of "action at a distance" must be modified with "games" other than roulette with a dealer's random release. Such other games generally require a deeper finesse. This is discussed elsewhere in this site. It must be noted again that reliable published roulette outcomes with a dealer's random release are virtually non extinct except as found and referenced in this site.

Those without access to a Roulette wheels, or books of Roulette outcomes (problematic in themselves) can easily find and prove the random flat bet geometric advantage with dice.

This is a matter of perception and analysis in the first instance. It is worth noting that this is probably why, in all of history, the only common thread of academic discipline concerning the fundamental evolution of “action at a distance” is by three men trained as lawyers: Buffon, Boskovic and this author.

Buffon is considered a non-mathematician. He also studied law. He also came up with the calculus of the original Needle.

Boskovic was recognized as one of the greatest mathematicians in Europe. He also held advanced law degrees. He came up with the methodology.

This author is also researcher and forensic analyst and independently came to the same conclusions as Buffon and Boskovic.

The gravity bet mathematically unites the work of Buffon and Boskovic. This author adds the factor of direction. This delivers the gravity bet.

The world of “action at a distance” simply cannot be understood with traditional mathematics and geometry. Action at a distance exists in an entirely separate dimension of relative pi and its geometric divisions. This is not a matter of becoming more educated with additional new dimensions. It is a singular matter of simply eliminating the familiar old dimension of our perception of a relative cross diameter.

The perceived cross dimension of "width" simply doesn't exist relative to randomness and gravity. Relative to gravity, relative "width" is simply just relative pi (that is: relative 1/4 pi multiplied by 4) in rotation. That is: relative to serial random measurements, the dimension of "width" is just a mathematical average ...just a perception.

It is the super simplicity of perception that is life's common stumbling block. It is similar to being unable to see the forest because of all the trees. Relative to randomness and gravity, we and the forest and the trees are all pi in the first instance.

These are matter of perception and analysis in the first instance. Not mathematics. By the proof of the original Needle, it is simply a perceptual matter of mathematically accepting the totality of gravity --including the complete diameter of a game or gravity field-- as: “1.”

It is the mathematical consequence of geometrically defining a diameter as "1." that appears, as Einstein put it, "spooky."

Relative to a diameter valued as: "1." ...everything else, including ourselves and our perceptions, has a relative random value of relative 1/4 pi in rotation. This conclusion comes from the proof and deductions and inferences of the original Needle. Relative 1/4 pi is just an average. However, unlike other averages, it is directly relative to gravity's straight line pull.

No special knowledge is necessary to use the gravity bet and its "action at a distance." For those who wish to mathematically understand it ...the only arithmetic concerns appropriately dividing pi by 2 or 3 or 4 or 5 or 6, etc... Any middle grade student can do it. Anyone can do it with a calculator.

The flat bet advantage is the difference between 1/6 pi (the geometric probability of a pi-angle pole factored by two directions) and 1/4 pi (the foundational Cardinal pole of traditional random game theory). The difference is made relative by the mathematical relationships between 1/4 pi and 1/6 pi (same identical results as found between 1/4 pi and 1/2 pi). Therein is the flat bet advantage, divided by two directions. That is: .78539 - .52398 = .26179 . Next: (.26179) / .78539 = .33333. Finally: (.33333) / 2 = .16666 .

As detailed herein, anyone can most easily prove it with a true RNG from the web or a near perfect cube or deck of cards. It may be noted here that the advantage in cards starts with 1/3 of the inverse of pi. It should be noted again that a deeper finesse is necessary than three trials. That is: a finesse 9 deep for RNG's and 5 deep for cards.

The original Needle was the first and only random bridge between the dimension of perception and the dimension of gravity. The bridge is comprised of the original Needle’s own length of relative 1/4 pi at one end of a cross radius and of 1/2 pi at the COR at the other end of the cross radius.

The geometric uniqueness is that the unit of measurement of relative 1/4 pi is just a mathematical average while relative 1/2 pi (and/or 1/6 pi) contains the physical geometric reality of a randomly measured diameter's end poles.

The uniqueness is that 1/2 pi contains a physically real geometry that is also comprised of two algebraic measurements of relative 1/4 pi. Finding it with “action at a distance" completely shatters traditional random theory.

Relative 1/4 pi is gravity's translation of the randomness between perception (everything we perceive and are taught and believe including traditional random theory) and gravity (what randomness and gravity actually deliver).

The original Needle deductively and inferentially proves that, relative to randomness ...perception is just a dimension of relative pi in rotation. By the mathematical proof and deductions and inferences of the original Needle ...relative to the diameter dimension of “length” ...relative "pi in rotation" replaces the perceived dimension of relative “width.”

The original Needle also proved that, relative to randomness, relative pi was just an algebraic statement of relative 1/4 pi multiplied by 4.

When measured serially and randomly, relative to perception, relative to gravity, it is relative 1/4 pi that is relative to the diameter in the first instance ...not relative pi that is relative to the diameter in the first instance!

Pi is only relative to the diameter in the first instance under traditional random theory in which pi is relative to perception. This is Euclidean geometry.

In the pi-odds theory, relative to randomness, in the first instance of randomness, pi is the COR as the middle pole of a three pole diameter. The gravity bet and "action at a distance" insists pi must be first understood through relative 1/4 pi over two random measurements ...before pi may be secondarily perceived as the ratio between a circle and diameter.

Since, by the random proof of the original Needle, pi is only an algebraic average of the cross dimension ...just a perception (like relative 1/4 pi) too, relative to gravity, the perceived cross dimension of relative “width” is just that ...only a mathematical perception. More specifically, it is relative pi in rotation. More specifically yet, it is relative 1/4 pi in rotation, multiplied by 4, with the dynamics of two possible directions. This is the "game." This is also the COR.

Every random table "game" is of two dimensions: length and width. Only length is "physically real." Relative width is just an algebraic average. Together they are the "game." Dimensionally, every random "game" is of 4 poles: the end poles of the two dimensions. Again, this is also the COR.

The original Needle proved each pole on a circle to be equal as well as the universal random average of relative 1/4 pi.

By gravity's own random proof of itself through the original Needle ...the relativity principles of pi in the original Needle appear as the only logical bridge between the randomness of gravity and the randomness of our perceptions.

Traditional random theory is on one side of the issue. In it, all is relative to a circle or "game" or COR before being secondarily relative to gravity's more fundamental structure of a rotating diameter. This means the "game" is always a game of perception and relative pi. Playing the "game" makes the search for geometric probability an impossibility. Geometric probability is only found with "action at a distance." Playing the "game" makes "action at a distance" an impossibility.

1) gravity along the diameter dimension of an object’s (including all gaming objects) “length” and inherently having a value of: “1.”

2) perception as the relative cross-diameter dimension of relative “width” with an inherent relative value of relative 1/4 pi in rotation (or 1/2 pi or pi depending on orientation of perception) relative to the diameter of the gravity field. In traditional random theory, the dimension of "width" is inevitably measured with a metric value such as inches or millimeters or miles or light years.

This allows a flat bet random advantage to become a reality when the random measurements are made with "action at a distance" and the dimension of"width" is eliminated from statistical consideration.

When "action at a distance" is couched in the geometric probability of the original Needle, the flat bet advantage appears. The mathematical sense also becomes clear as Pi and its digits become geometrically meaningless.

The real random geometric action is between a diameter base of relative 1/4 pi and --through "action at a distance"-- relative 1/6 pi (or 1/2 pi ((dealer's choice))) as a relative pi-angle pole. This is what spooked Einstein. This is the flat bet advantage of Quantum science. This is the advantage that comes with "action at a distance."



Written by G. T. Hushion. Posted in Exploring Random

"You can't calculate probabilities with just algebra. The geometry must be taken into account."

Comte George Buffon, Essay on Moral Arithmetic


3.14159265358979323846264338327950288419716939937510582097494459230781640628620899862803482534211706798.... .
For interest and reference purposes, the ten digits continuing after the one hundred and second digit (that is: “8”) are: 2148086513.... .

1/2 PI
1.57079632679489661923132169163975144209858469968755291048747229615390820314310449931401741267105853399.... .
For interest and reference purposes, the ten digits continuing after the one hundred and second digit (that is: “9”) are: 1074043256.... .

1/4 PI
.785398163397448309615660845819875721049292349843776455243736148076954101571552249657008706335529266995.... .
For interest and reference purposes, the ten digits continuing after the one hundred and second digit (that is “5”) are: 5370216283.... .

THE FIRST 106 RELATIVE DIGITS OF RELATIVE ONE SIXTH PI: .5235987755982988730771072305465838140328615665625176368291574320513027343810348331046724708903528446636913.... .
For interest and reference purposes, the ten digits continuing after the one hundred and sixth digit (that is: “3”) are: 4775221371.... .