![Sfarim](./gen/img/rainbowline.gif)
Fibonacci and Genesis
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The Fibonacci sequence is one of the most famous formulas in mathematics. Also known as the Golden Ratio, its ubiquity and astounding functionality in nature suggests its importance as a fundamental characteristic of the Universe. This fact has intrigued mathematicians, artists, designers and scientists for centuries.
The Fibonacci sequence follows a precise mathematical pattern. Namely, each successive number is the sum of the two preceding numbers.
It starts like this:
1 | 1 | 2 | 3 | 5 | 8 | 13 | 21 | 34 | 55 | 89 | 144 | and so on, endlessly |
=1+0 | =1+1 | =1+2 | =2+3 | =3+5 | =5+8 | =8+13 | =13+21 | =21+34 | =34+55 | =55+89 |
When we make squares with those widths, we get a nice spiral:
![](./gen/img/gm/fibo_square.jpg)
This "Fibonacci spiral" reveals itself all over nature. Its fingerprint appears in flower petals, seed heads, pinecones, tree branches, lightning bolts, shells, body and limb proportions, hurricanes, and even spiral galaxies, to name a few.
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Golden Ratio
The Fibonacci sequence is tightly connected with the "Golden Ratio". For when we take any two successive Fibonacci numbers, their ratio is very close to the "Golden Ratio", also known as "Phi" = 1.618034... and the bigger the pair of Fibonacci Numbers, the closer their ratio converges exactly to the Golden Ratio.
This Golden ratio also appears everywhere in nature. From limb proportions in humans and animals to DNA molecules and quantum resonances in atomic nuclei[1]!
The phenomena is very real. Almost everything in nature has properties of the Golden Ratio, and as many traders have discovered, even the stock market tends to follow this pattern.
The golden ratio is also used by artists, designers, and architects. Why? Because this ratio has been found to be remarkably pleasing to the human eye, it produces what is called a Golden Rectangle. If the short side of the rectangle is 1, the long side will be 1.618..
Interestingly, in Exodus 25:10, G-d commands Moses to build the Ark of the Covenant, in which to hold His covenant with the Jewish people, saying: "they shall make a chest of acacia wood two and a half cubits long, a cubit and a half wide, and a cubit and a half high". The ratio of 2.5/1.5 is 1.666 which is as close to the Golden Ratio (1.618..) as you can come with such simple numbers and is not visibly different to the eye.
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סדרת פיבונאצ'י | = | 913 |
בראשית (Beresheit) | = | 913 |
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Hebrew Alphabet
The Fibonacci series begins with number 1.According to the Midrash, the first letter "Aleph" represents the "Alufo Shel Olam" - the Master of the World, i.e. G-d (Midrash Otiyot d'Rebbi Akiva).
Alef is the first letter and number, the start of everything. Likewise, G-d preceded all existence, and is the Source of everything that exists.
The Hebrew word for G-d is "E-l" which is spelled Aleph-Lamed. This term appears many times in the Torah such as "I am the G-d (E-l)" (Genesis 46:3).
Amazingly, the Milui (letter expansion) of Aleph yields the even Fibonacci sequence as follows:
Fibonacci Sequence | Number of Letters | Letter Expansion of Aleph |
1 | -- | |
1 | 1 | א |
2 | -- | |
3 | 3 | אלף |
5 | -- | |
8 | 8 | אלף למד פא |
13 | -- | |
21 | 21 | (אלף למד פא) (למד מם דלת) (פא אלף) |
34 | -- | |
55 | 55 | אלף למד פא למד מם דלת פא אלף למד מם דלת מם מם דלת למד תאו פא אלף אלף למד פא |
89 | -- | |
144 | 144 | אלף למד פא למד מם דלת פא אלףלמד מם דלת מם מם דלת למד תאופא אלף אלף למד פאלמד מם דלת מם מם דלת למד תאו מם מם מם מם דלת למד.... |
233 | -- | |
377 | 377 | אלף למד פא למד מם דלת פא אלףלמד מם דלת מם מם דלת למד תאופא אלף אלף למד פאלמד מם דלת מם מם דלת למד תאו מם מם מם מם דלת למד.......... |
610 | -- | |
987 | 987 | אלף למד פא למד מם דלת פא אלףלמד מם דלת מם מם דלת למד תאופא אלף אלף למד פאלמד מם דלת מם מם דלת למד תאו מם מם מם מם דלת למד................ |
1597 | -- | |
2584 | 2584 | אלף למד פא למד מם דלת פא אלףלמד מם דלת מם מם דלת למד תאופא אלף אלף למד פאלמד מם דלת מם מם דלת למד תאו מם מם מם מם דלת למד...................... |
4181 | -- | |
6765 | 6765 | אלף למד פא למד מם דלת פא אלףלמד מם דלת מם מם דלת למד תאופא אלף אלף למד פאלמד מם דלת מם מם דלת למד תאו מם מם מם מם דלת למד........................... |
"Aleph" expansion gives perfect match for all even Fibonacci numbers to infinity |
The number of letters in every subsequent Aleph expansion corresponds exactly to the even sequence Fibonacci numbers.
This is quite amazing and it occurs despite that the 3rd row introduced a new letter Dalet, and the 4th row introduced a new letter Tav and the 6th introduced a Vav, etc.
1 | 1 | 2 | 3 | 5 | 8 | 13 | 21 | 34 | 55 | 89 | 144 | etc. |
Fibonacci Sequence | Number of Letters | Letter Expansion of Lamed |
1 | -- | |
1 | 1 | ל |
2 | -- | |
3 | 3 | למד |
5 | -- | |
8 | 8 | למד מם דלת |
13 | -- | |
21 | 21 | (למד מם דלת) (מם מם) (דלת למד תאו) |
34 | -- | |
55 | 55 | למד מם דלת מם מם דלת למד תאו מם מם מם מם דלת למד תאו למד מם דלת תאו אלף ואו |
89 | -- | |
144 | 144 | למד מם דלת מם מם דלת למד תאו מם מם מם מם דלת למד תאו למד מם דלת תאו אלף ואו מם מם מם מם מם מם מם מם.... |
"Lamed" expansion gives perfect match for all even Fibonacci numbers to infinity |
Thus, both Aleph and Lamed match perfectly all the even sequence Fibonacci numbers (no other Hebrew letters act like this).
Aleph Lamed spells the Hebrew word for G-d: א-ל.
(this divine Name represents G-d's attribute of kindness)
Interestingly, the Gematria of א-ל = 31 = the total number of verses in the creation account (Genesis chapter 1).
What about the odd numbers of the Fibonacci numbers?
Here too, another incredible result - it turns out these can be generated by two other letters in the Hebrew alphabet - Peh and Heh, and only these two. These two letters form the word "Peh-Heh"=mouth in Hebrew.
Fibonacci Sequence | Number of Letters | Letter Expansion of Peh |
1 | 1 | פ |
1 | -- | |
2 | 2 | פא |
3 | -- | |
5 | 5 | פא אלף |
8 | -- | |
13 | 13 | (פא אלף) (אלף למד פא) |
21 | -- | |
34 | 34 | פא אלף אלף למד פא אלף למד פא למד מם דלת פא אלף |
55 | -- | |
89 | 89 | פא אלף אלף למד פא אלף למד פא למד מם דלת פא אלף אלף למד פא למד מם דלת פא אלף למד מם דלת מם מם דלת למד.... |
"Peh" expansion gives perfect match for all odd Fibonacci numbers to infinity |
The Peh expansion matches perfectly the odd sequence Fibonacci numbers.
1 | 1 | 2 | 3 | 5 | 8 | 13 | 21 | 34 | 55 | 89 | 144 etc. |
The letter Heh also matches perfectly all the odd sequence Fibonacci numbers.
Fibonacci Sequence | Number of Letters | Letter Expansion of Heh |
1 | 1 | ה |
1 | -- | |
2 | 2 | הא |
3 | -- | |
5 | 5 | הא אלף |
8 | -- | |
13 | 13 | (הא אלף) (אלף למד פא) |
21 | -- | |
34 | 34 | הא אלף אלף למד פא אלף למד פא למד מם דלת פא אלף |
55 | -- | |
89 | 89 | הא אלף אלף למד פא אלף למד פא למד מם דלת פא אלף אלף למד פא למד מם דלת פא אלף למד מם דלת מם מם דלת למד.... |
"Heh" expansion perfect match for all odd Fibonacci numbers to infinity |
Thus "Aleph Lamed" = G-d form the even Fibonacci numbers while "Peh-Heh" = "mouth", form the odd Fibonacci numbers. This hints that the world was created through G-d's speech.
![](./gen/img/gm/fibo_milui.jpg)
The only letter expansion versions that matched the Fibonacci sequence are solely the "Milui Aleph" version for all letters used in the expansions. Of course, it would already have been a wonder if even one Hebrew letter matched the Fibonacci sequence, much less four letters.
But the fact that only the Milui Aleph matches for all four letter makes it an even greater wonder.
This again emphasizes the Aleph which represents the Alufo Shel Olam - Master of the World.
- To Summarize:
- All the Even sequence Fibonacci numbers can be generated by the expansion of Aleph or Lamed
- Aleph-Lamed spells the Hebrew word for "G-d".
- All the Odd sequence Fibonacci numbers can be generated by the expansion of Peh or Heh
- Peh and Heh spells the Hebrew word for "mouth"
- Only the Milui Aleph expansion versions generated the matches.
More connection to Genesis 1:1
The Gematria of Genesis 1:1 = 2701 = 37×73
37 is the Gematria of Hevel (breath). The numeric structure of Genesis 1:1 is largely built around this number as we saw previously.
For the world was created and is sustained through the "breath" of G-d, so to speak. G-d created the world through "speech" - namely, the 10 sayings of creation.
Aleph/Heh Grouping
This is further confirmed by the Gematria Ketanas (small Gematrias) of Aleph, Lamed, Peh, Heh.Gematria Ketana (small Gematria) | |||||||||||||||||||||
א | ב | ג | ד | ה | ו | ז | ח | ט | י | כ | ל | מ | נ | ס | ע | פ | צ | ק | ר | ש | ת |
1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 1 | 2 | 3 | 4 |
אלף(=8,3,1) ה(=5) are all Fibonacci numbers. |
Amazingly, all four letters Aleph,Lamed, Peh, and Heh are Fibonacci numbers. Furthermore, the letters אלף are all from the even sequence Fibonacci numbers while ה is from the odd sequence.
The group of the 3 letters Aleph, Lamed, Peh form the word Aleph which represents G-d while the letter Heh which is by itself represents the Divine Mouth in the Tzelem Elokim (Divine Image, see Etz Chaim, Shaar Af, Ozen, Peh).
ה | ו | ה | י |
mouth | nose | ears | eyes |
אֵ֣לֶּה תֽוֹלְד֧וֹת הַשָּׁמַ֛יִם וְהָאָ֖רֶץ בְּהִ֣בָּֽרְאָ֑ם בְּי֗וֹם עֲשׂ֛וֹת יְ-הֹוָ֥ה אֱ-לֹהִ֖ים אֶ֥רֶץ וְשָׁמָֽיִם
The Heh in בְּהִ֣בָּֽרְאָ֑ם is written "small" in the Torah. Rashi brings the oral tradition that says this is to teach the world was created with the Heh, which refers to this "Divine Mouth" in the Tzelem Elokim (Divine Image).
The pronounciation of Heh is also like the breath itself - Haaah. This is unique to the letter Heh.
This reflects its sublime role in the creation of the world through the Divine mouth (i.e. the Sefirah of Malchut).
Let us strive to use our mouths for holy things, with G-d's help.
See the original video by Oren Evron here (Hebrew) for more.
Binary Digits
Last but not least, converting the gematria values of the first four words in the Torah into BINARY REPRESENTATION reveals a pixillated illustration:Plotting the four binary numbers (1 number per line with 1=Black, 0=white)
![](./gen/img/gm/sefart.jpg)
A picture resembling the letters "Aleph-Lamed" is revealed! (discovered by Sefart, see the works of Adam Woolfe for more). Note that the "Lamed" is missing the top branch but this is the best possible representation within the limits of a four row pixel image. Some prayer books write Lamed with the top cut or bent for lack of space). I tried to look at the rest of the book of Genesis in binary pixels and nothing even remotely appears like Hebrew letters (or any letters for that matter).
(note: the most merciful name of G-d is E-l (א-ל) meaning 31 which are the 2 first numerals of Pi, then Sh-aday (ש.ד.י) has 3 numerals of Pi 314 and these 2 holy Names appear together many times, ex. Gen.43:14)
>> Next: Central Prime
Footnotes
- [1] https://www.sciencedaily.com/releases/2010/01/100107143909.htm
here is a screenshot:return to text
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