## Probability Analysis

PROBABILITY ANALYSIS of the JEWELED SPHINX

By Dr. Shih-Chuan Cheng Professor, Department of Mathematics Creighton University

Omaha NE 68178

This probability analysis will examine the possibilities that the coding of this jeweled sphinx can be explained by random chance or coincidence. These possibilities will be expressed mathematically as percentages or fractions of percentages as they relate to the Bernoulli distribution in the theory of probability.

There are at least 27 factors that point to this piece belonging to Napoleon Bonaparte. Let’s examine these 27 factors and assign a probability to each one.

Factor #1: One of Napoleon’s heroes, Augustus Caesar, had a signet ring with the image of a sphinx. We will disregard this factor.

Factor #2: This piece features open-backed jewelry settings (of the emeralds) which were not in use before 1800. Because of the high number of synchronous factors that we already have, we will not assign a probability to this factor, even though it does give us an absolute date range for the creation of this piece, i.e. 1800-present.

Factor #3: The coding of 21 and a “blank” is coded into the design in a deliberate and purposeful fashion. The odds of this being random are probably one in a thousand, but we will consider that perhaps this refers to “21 and a blank” of something else besides the Tarot code (even though no one has come up with anything else). For the skeptic’s sake, we will figure that this has a 75% chance of either being random or, more likely, that it refers to something else (that we can’t figure out); it is well known that both Napoleon and Josephine used the Tarot, and that Napoleon used Tarot coding in the coat-of-arms for the city of Paris.

Factor #4: “Four” repeats 21 times, the same as the number of face cards in the Tarot deck. “Four” is Tarot for Emperor, making this the dominant coding of the sphinx piece. The odds that this is coincidence are remote when combined with all the other factors, but, taken alone, we will be generous to the skeptic’s point of view and assign this a 95% chance of just being a coincidence.

Factor #5: The initials “JB” are coded into the design just below the sphinx. These happen to be Josephine Bonaparte’s initials and she is known to have had her initials on many of her personal items. And there is an “Empress” coded in before her name. Again, the odds of this being coincidental when combined with the other factors are astronomical, but we shall estimate that this factor, taken alone, represents a 99% chance of being coincidental.

Factor #6: The sphinx itself has a Tarot and numerical coding of “Empress Josephine” in the same fashion as factor #5. The odds of an instance of deliberate coding are increased by a factor of at least four when elements are coded in twice. But we will figure this is 90% likely to refer to something other than Josephine (even though we can’t figure out what that might be).

Factor #7: The initials “NB” are coded into the design. These are the initials of Napoleon Bonaparte. It is significant that this coding is derived from the total number of gems. This would most likely be either the designer’s or owner’s “signature.” Because of the already large number of strongly aligned factors, a very conservative probability of deliberate design will be assigned: 99% coincidental.

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Factor #8: The initials “NB” are coded into the design in the exact same pattern as the “JB” initials. This second instance of coding the same thing twice is striking and produces a dramatic tie-in that has a one-in- many thousands chance of being random when combined with factor #7, but for the skeptic’s sake, we will consider this factor independently from factor and assign a 95% chance that this refers to something other than the initials of Napoleon and Josephine (even though we do not know what that may be).

Factor #9: The Tarot code for “Emperor, Empress, Lovers” is coded into the design. The relationship of Napoleon and Josephine is considered one of the most iconic love affairs of all time. We shall continue on our conservative path and estimate that there is a 95% chance that this is either random or means something we can’t figure out.

Factor #10: There are two pearls; two is Tarot coding for “wisdom.” It appears that the saying “Pearls of Wisdom” is coded into the design. There is a one-in-22 chance that two pearls lines up with the number two, based on the 22 cards of the Tarot, and even less of a chance that these two pearls would be randomly associated with “wisdom.” But even though this coding is far more likely to be deliberate than random, we will choose a 90% chance of this being coincidental, just to be on the conservative side.

Factor #11: There are 10 sapphires in a partial circle below the reposing sphinx. The 10th Tarot deck card, “Fate,” depicts a wheel or circle below a reposing sphinx. The odds that the 10th Tarot deck card would be represented in this jeweled sphinx in such a striking match would have to be one-in-a-thousand, perhaps much more. Yet, for this subjective aspect of our analysis, let’s conservatively figure that there is a 90% chance of this just being coincidence.

Factor #12: There is a “fleur-de-lis” on the sphinx piece. This was a symbol of French royalty, also used by Napoleon in 1802. For the skeptic’s sake, we will figure that this has a 99% chance of just being coincidental.

Factor #13: Napoleon took great pride in pointing out that his name meant “Desert Lion.” Let’s just figure this has a 99% chance of having no relationship to this piece. (But this is truly an amazing “coincidence.”)

Factor #14: Napoleon personally visited Egypt, saw the sphinx & the pyramids, and was responsible for modern Egyptology and the “Empire Style” in art & architecture, including the many Egyptian-motif items that he personally commissioned on his return to France in 1799. We will estimate this has a 95% chance of being coincidental.

Factor #15: There is similar Tarot coding on French coins and in the coat-of-arms of the city of Paris commissioned by Napoleon. Again, we will figure this has a 95% chance of being coincidental or irrelevant.

Factor #16: The coat-of-arms for the city of Paris has many striking similarities to the sphinx piece. The chances of this are extremely remote. Yet, we will figure that there is a 95% chance that this, too, is coincidence or unrelated.

Factor #17: Napoleon was a Rosicrucian, his brother was a Mason, most of his Generals were Masons, and most of his close associates were Masons. Let’s say this has a 99% chance of being unrelated.

Factor #18: Josephine was the head of women’s Freemasonry in France and often used the Tarot to give readings to her friends. We’ll say this has a 95% chance of being unrelated, though when you consider this fact and factor #17, it can be seen as strong evidence of a close possible connection between Napoleon, Josephine, and the sphinx.

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Factor #19: The Mona Lisa, which Napoleon had hanging in his bedroom from 1800-1804, bears a striking resemblance to Josephine as well as to the crystal sphinx. We will figure that this has a 90% chance of just being coincidence.

Factor #20: Napoleon called the Mona Lisa “The Sphinx of the Occident.” This is another very interesting “coincidence.” Napoleon refers to the Mona Lisa as the “sphinx of the Occident” and we have Josephine sculpted in the form of a crystal sphinx---with Mona Lisa’s “expression.” We will estimate this has a 90% chance of just being coincidental.

Factor #21: There is a painting of Josephine that is posed in a very similar fashion to the Mona Lisa, with a very similar backround. Let’s just figure this is purely coincidental and not even assign any odds.

Factor #22: There is a Pavillion Josephine in Strasbourg, France, where Josephine is depicted as a reposing sphinx, very much like the sphinx piece. There is certainly an amazing resemblance to the Napoleon sphinx piece and the odds that these two are unrelated would have to be fairly high, yet we will figure that there is a 95% chance that this was just purely coincidental.

Factor #23: Napoleon gifted Josephine with Charlemagne’s talisman in 1804. It had been undisturbed for nearly a thousand years. This begs the question of whether Napoleon already had a talisman and wanted Josephine to have one of her own. We will take the conservative road and figure this has a 95% chance of being unrelated.

Factor #24: Napoleon produced other pieces of coded jewelry. Battlefield communications were coded as well. Coding things was a common practice in Napoleon’s day. We will figure this fact as 95% coincidental.

Factor #25: There are strong Napoleonic connections to the Netherlands, where the sphinx piece was found. We’ll say this is 99% coincidental. Applying the Bernoulli distribution method to the first 25 probability factors yields a maximum-likelihood estimation of 91% that these facts are not coincidental. There is only a 9% chance that coincidence can explain these factors. And, of course, this figure is attained using very conservative or “skeptical” percentages of coincidental possibility.

But the two strongest pieces of evidence are still to come:

Factor #26: The date coded into the sphinx, August 15, 1802 (Napoleon’s 33rd birthday) is the most significant date possible in the life of Napoleon as it relates to this sphinx. The mathematical likelihood of that is one chance in 36,525 (the number of days in a Century). Calculating the chances of all this being coincidence is now one chance in 328,725.

We have made a very conservative calculation with regard to our estimate of probability, the actual odds of coincidence are more likely to be much, much smaller.

But there is one last factor:

Factor #27: Of all the factors that could be considered, there is not one factor that lines up in opposition to the jeweled sphinx being Napoleon Bonaparte’s. This is akin to tossing a coin 27 times and having “heads” come up every single time. The odds of tossing a coin 27 times and having “heads” come up every single time, is one chance in 134,217,728.

Combining this calculation with our previous estimate yields our final tally for the chances that all these factors can be explained by coincidence or are unrelated. The odds of all these factors being unrelated or coincidental is now one chance in 44,100,722,636,800.