Golden Ratio Everywhere
We have made this discourse just to arrive to the number that is the most suitable to be checked as a key to the code-breaking. If the key is just a number, it hardly could be found a better candidate.
I prepared a matrix containing all three items. What I recognized at first glance was the striking similarity of the line containing them to the drawing shown above. Indeed, if we place the column containing the date to cut the line, the lengths of the segments to the right and to the left of it contain 60 and 37 columns (that is, unit lengths) respectively! See Figure 6.
Calculations yield 60/37 = 1.621621... and
97/60 = 1.616666....
The latter value differs with less than 0.1 % from the Golden Ratio. Moreover, 37, 60 and 97 form a series that fits the best a series of numbers containing 60, where the ratio of the last member to the next-to the last one approaches the Golden Ratio. This series is formed in the following way: choose any two numbers and add them. The sum is the third number of the series. Proceed in the same way taking the second and the third number to get the fourth member of the series, and so on. The series in which the first two numbers are two units is called Fibonacci numbers after a medieval Italian mathematician (see the Appendix).
Then I suddenly realized the link with the pentagon. The number that was the result of the multiplication of 60 with the number of the letters mene mene tekel, which is also the number of the letters of the number 2006, i.e. 9, is 60?9 = 540. But 540 is the sum of the interior angles, in degrees, of a regular pentagon.
Then I noticed that the number of the letters in 2006, 9, the number of the letters in the writing of the wall, 15, and their sum, 24, can be reduced to members of the Fibonacci sequence (red)
15/9 = 5/3 = 1.66666...
and
24/15 = 8/5 = 1.6
3, 5 and 8 are successive Fibonacci numbers and therefore their ratio is close to the Golden Ratio. The latter ratio differs with about 1.1 % but the fact that these numbers belong to this sequence could be suggestive for further exploration.
Meanwhile, I noticed that the number of columns of the left section, 37, which ends with the name of Joshua, multiplied by the sum found above, 24, yields 888. 888 is the number of Jesus Christ according to the Greek numerology. We just mention this fact. The subject itself is outside the scope of our study.
Having come so far, we should look for more places where the Golden Ratio is hidden. It surely is to be found somewhere else. The most disputable term at this point certainly is Joshua. So let us check whether the Golden Ratio has something to do with this name. Evidently, no other parameters or values are to be monitored except number(s) of appearance. The decisive characteristic that we required beforehand was that the term should be used with the conjunction ‘and’. And we examine the name in the plain text only. So let us check how many times the name Joshua appears in the Torah and how many of these occurrences are in the form and Joshua.
While doing this I ran across an interesting fact. Joshua occurs 26 times as ע ש ו ה י but also once as ע ו ש ו ה י . Interestingly, this single case when the spelling differs is in Deut. 3:21, in the only occasion when Moses uses it in direct speech to Israel, when speaking from himself. In the narration, even in direct speech but when the information comes from the Lord and is only conveyed by Moses, the spelling is uniform! So let us check how many of these 26 occurrences are in the form ‘and Joshua’ (ע ש ו ה י ו ). The number turned out to be 10. Therefore, the number of occurrences when the name Joshua is used without the conjunction ‘and’ is 16. Now, all three numbers 10, 16 and 26 may be divided by 2 and produce the sequence
5, 8, 13.
So they are three of the Fibonacci numbers. And the ratio 13/8 = 1.625 is only about 0.4 % larger than the Golden Ratio.
It appears as if Moses changed the spelling by adding an extra vav (ו ) especially to fit the number of the uniformly spelled name to 26. Indeed, the number of the Name of the Lord (ה ו ה י ) according to the Hebrew numerology is exactly 26: י = 10; ה = 5; ו = 6; ה = 5. Therefore, 10 + 5 + 6 + 5 = 26.
Now I felt that even the original third term of the writing on the wall, Upharsin, (ן י ס ר פ ו ) must somehow support our findings. It occurs 57 times encoded in the Torah. We have already confirmed that it cannot be found even within a very large matrix containing all the other items. The experiment, therefore, will be to find the nearest intersection with the line starting with the first mem (מ ) in mene and ending with the last letter of Joshua (ע ). The program Torah4U.2, which I use, gave as result an intersection at 226 places to the left of the ע in Joshua. The letter of upharsin that lay in the intersection point – that is, the letter in the line extended to the left, was pe (פ ). What appeared to be most interesting, however, was that the skip was -9,151. I immediately compared it with the skip of the number 2006 (ו ק ר ש ת ק ר ש ת ), which is 14, 965 (as absolute values). The ratio turned out to be
14,965/9,151 = 1.63534
It is just 1 % larger than the Golden Ratio. I checked for all the skips of upharsin. Among the 56 remaining occurrences, there was no other skip to fit better the Golden Ratio with the number 14,965!
But this was not all. The number of letters between ע and פ , i.e. the number of letters that were to be leaped over, is 225. And 225 is exactly 15, the number of the letters in the writing on the wall, squared: 152 = 225!
But there is even more. The period of the orbital rotation of the planet Venus around the Sun is 224.72 Earth day-and-nights. Notice that 225 is the best whole number approximation of 224.72. Now by dividing the period of rotation of the Earth, 365.28 days by the period of Venus, 224.72 days, we obtain
365.28/224.72 = 1.6255
It differs with less than 0.5 % from the Golden Ratio. Although amazing at first glance, this result reflects the properties of the regular pentagon. The apparent movement of the planet on the sky is a direct effect of the ratio between the diagonal and the side of a regular pentagon. In the perfect case, this ratio is the Golden Ratio. The actual difference is due to the slight eccentricities of both orbits.
Conclusive Reflections
Imagine we are in the palace of Belshazzar in that fatal night. Suddenly a text appears on a wall. All astrologers, sorcerers and magicians are called to solve the problem of reading and interpretation. Did they possess the means for solution and could not solve the problem just because they didn’t use it properly? I don’t know. The Biblical record says that they were unable even to read the message. Then enters Daniel and not only reads but also interprets it. Did he use mathematical or astrological means to do it? I don’t know. So much strange seems therefore the fact that we had to use a mathematical code that was known in principle to the Babylonians at the time of this event to find the writing encoded in the Torah.
There is an even more interesting question. Did Daniel interpret the writing in such way that to give a hint to the code-breakers in the Latter Days? I dare answer positively to this question. Daniel’s weird interpretation of the third item helped me very much to find the proper answer.
We have used purely mathematical method for our code-breaking. However, this method has been ‘clothed’ in astrological meanings since the dawn of the post-Flood civilizations. Is there any astrological allusion in the Bible? I believe, yes. Star is used several times in the New Testament. We find it in the beginning of Matthew where the Gentile Magi say: We saw his star in the East (2:2). But it is in the book of Revelation where we find specific references to Venus as the Morning Star: in 2:28 I will also give him the morning star and almost in the end, 22:16 I am ... the Bright Morning Star. In my opinion, Venus is the only celestial object that could be referred to as the Bright Morning Star. Is this additional evidence that it is the Lord Jesus, Yeshuah the Messiah, Who will put an end to Babylon the Great (Rev. 17:5)? The proper meaning of I am the Morning Star is dubious due to the role of the emphasis. In the light of our findings, we can realize the implication. It is not the claim of the impostors I am a Good One but the assertion of the authentic King of Kings:
I am the Bright Morning Star,
i.e. I am those who you must glorify instead of what you do now to a wrong object.
Many Christians claim that no time limit could be found either in the plain text or hidden as a code in the whole Scripture. Their opinion is based on what the Lord Jesus said to his disciples: that He will come as a thief and that no one, even He Himself knew the day and the hour...
We may object on the following grounds: 1. No particular date can be derived from what we have found. It is just a year, which nobody knows if it belongs to the ending eon or to the new one; and 2. Even if we state that AD 2006 will be the most fateful year in the human history, it is a historical fact that the start of the Christian era, though claimed to be fixed to the birth date of Jesus of Nazareth, does not correspond to the actual year of His birth. Jesus was born earlier than 1 AD. He was born at latest in 4 BC, but most probably even earlier. Therefore, He may not knew when speaking to His listeners that some 5 centuries later a monk will set a wrong year as His birth date.
There is something unusual with the fall of Babylon. It was a great city surrounded by high walls. Four chariots could pass each other on their top. When Cyrus besieged it in the summer of 539 BC, the citizens ridiculed him because they had enough provisions and water to resist for years. The water was provided by the river Euphrates, which ran right through the city. But at inlet and outlet openings in the wall, there were grids going down enough into the water to prevent penetration of enemy. So when the autumn came, Cyrus was driven to despair. Meanwhile, he ordered his soldiers to dig a ditch that was many miles long, which had to surround Babylon. This ditch remained dry. Suddenly, one of his officers suggested that it would be better to fill it with water. The only source that could provide the required quantity of water was Euphrates. Cyrus agreed and diverted the river waters to the ditch. Xenophon and Herodotus, who wrote the records, say that even at that time Cyrus did not know what to do next. The solution flashed in his mind when he saw the water receding...
By coincidence, this happened when the Babylonian New Year feast started. The guards were so assured that they were drinking wine even while guarding the walls. Cyrus or a high-ranked officer of his ordered a small but elite group of soldiers to invade Babylon through the openings and to go directly to the palace and kill the king. Because the group was small, they had to avoid clashes in their way. Due to the drunkenness of the majority of the soldiers, they reached the palace almost unnoticed. The coup was so effective that there were citizens of Babylon, who came to know that they have a new king many days later.
Now I would like to make a brief estimation of the odds. Roy Reinhold estimated the odds for the matrix in my previous study to be 1 in about 1.6 billion. But he didn’t take into account the contribution of the symmetry of the word salvation (ע ש י ), which is about 1 in 2,700. (This means that the calculated odds must be divided by 2,700.) Yet there is also a contribution of the same word in its central occurrences, which lowers further the chance by a new factor of 300.
I haven’t attempted to estimate chances in the current study. At any rate, the odds are very low indeed. Usually, people hardly get the right idea of the meaning of the values of very low or very high figures. This is a characteristic of the human mind – we are accustomed to linear dependencies in our daily experience and lose the sense of reality when we have to extrapolate to distant scales. What is the significance of, say, the number 10 raised to the power of 18, or 10^18? Well, this number is greater than the age of the Universe expressed in seconds! And I dare say that for the overall chance for the cumulative matrix obtained in both studies, if all parameters are taken into account, there is a considerable likelihood to be below 1 divided by this number, or less than 10^-18.
Finally, we can ask what the general result of our discourse is. The book of Daniel has been considered fabricated in the post-Alexandrian era, which is after 300 BC. Even some Jewish scholars are inclined to assign it to Greek influence. Some researchers date it as late as the first century BC. I believe that our study is the irrefutable evidence of its authenticity.
December 31st 2004
Sofia, Bulgaria
References
[1] Lyuben Piperov, A Strange Code about AD 2006 Discovered in the Torah. Online at:
http://exodus2006.com/2006piperov.htm
http://www.carelinks.net/books/lp/2006a.htm
http://www.ad2004.com/Biblecodes/Hebrewmatrix/2006a.pdf
[2] Lyuben Piperov, Protocol of a Statistical Evaluation of Some Items in the AD 2006 Matrix. Online at:
http://exodus2006.com/Protocol.htm
http://www.carelinks.net/books/lp/protocol2006.htm
http://www.ad2004.com/Biblecodes/Hebrewmatrix/Protocol2006.pdf
[3] Michael Lahanas: http://www.mlahanas.de/Greeks/LaertiosPythagoras.htm
[4] Matheus da Rocha Grasselli, Aspects of Abstraction in the Mesopotamian Mathematics (1996). From http://www.math.mcmaster.ca/grasselli/babylon.pdf
See also John Harris: http://www.spirasolaris.ca/sbb1sup1.html
[5] Michael Lahanas: http://www.mlahanas.de/Greeks/PythagorasStar.htm
[6] Mario Livio, The Golden Ratio: The Story of Phi, the Extra Ordinary Number of Nature, Art and Beauty, Review, London, 2002.
Contact Lyuben Piperov at: l_piperov@yahoo.co.uk
