Fibonacci and Genesis
based on a Hebrew video by Oren Evron here (with permission)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:
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.
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 follows 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.
Also interesting is that the opening word of the Torah - Beresheit has the same Gematria as "Fibonacci Sequence" in Hebrew.
סדרת פיבונאצ'י | = | 913 |
בראשית (Beresheit) | = | 913 |
Furthermore, the Torah's opening word "Beresheit" starts with a large "Beit", the 2^{nd} letter in the Hebrew alphabet. As before, each successive number in the Fibonacci sequence is constructed by summing the 2 previous numbers. Thus, perhaps the Beit in Beresheit hints to the Fibonacci sequence.
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 Name of G-d in Genesis 1:1 - Elokim begins with Aleph-Lamed.
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.
Interestingly, the Gematria of א-ל = 31 = the total number of verses in the creation account.
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 הא) |
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.
It is interesting to note that there are different versions of letter expansions, corresponding to different Divine Names and attributes.
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 much more.
Additions
(the below is not in the original video)Interestingly, the Gematria of Genesis 1:1 = 2701 = 37*73
55 is the exact midpoint between 37 and 73, the prime factors of 2701.
55 is also the 10th Fibonacci number and also the 10th Triangle number (1+2+3+4+5+6+7+8+9+10=55). This is the only place where Fibonacci numbers and Triangle numbers intersect. Two 55 triangles also combine to make the 73 star of David in the star of stars we saw previously.
Interestingly, the middle word in Genesis 1:1 is את and has Gematria of 401.
Center Word of First Verse | ||||||
בְּרֵאשִׁ֖ית | בָּרָ֣א | אֱ-לֹהִ֑ים | אֵ֥ת | הַשָּׁמַ֖יִם | וְאֵ֥ת | הָאָֽרֶץ |
913 | 203 | 86 | 401 | 395 | 407 | 296 |
The Fibonacci sequence also appears to be connected to the central 401 prime as follows (discovered by Leo Tavares):
The Fibonacci sequence is related to the Golden Ratio - Phi = 1.6180339...
If we index the first 37 digits of Phi according to the Fibonacci sequence we get a sum of 401 (Genesis 1:1 is rooted in the number 37):
For example:
For the 1st digit of phi = 6, the 6th Fibonacci number is 8.
For the 2nd digit of phi = 1, the 1st Fibonacci number is 1.
For the 3rd digit of phi = 8, the 8th Fibonacci number is 21.
Thus for 37 digits of Phi:
=1.618033988749894848204586834365638
Phi | Corresponding Fibonacci # | ||
6 | the 6th Fibonacci number | = | 8 |
1 | the 1st Fibonacci number | = | 1 |
8 | the 8th Fibonacci number | = | 21 |
0 | the 0th Fibonacci number | = | 0 |
3 | the 3rd Fibonacci number | = | 2 |
3 | the 3rd Fibonacci number | = | 2 |
9 | the 9th Fibonacci number | = | 34 |
8 | the 8th Fibonacci number | = | 21 |
8 | the 8th Fibonacci number | = | 21 |
7 | the 7th Fibonacci number | = | 13 |
4 | the 4th Fibonacci number | = | 3 |
9 | the 9th Fibonacci number | = | 34 |
8 | the 8th Fibonacci number | = | 21 |
9 | the 9th Fibonacci number | = | 34 |
4 | the 4th Fibonacci number | = | 3 |
8 | the 8th Fibonacci number | = | 21 |
4 | the 4th Fibonacci number | = | 3 |
8 | the 8th Fibonacci number | = | 21 |
2 | the 2nd Fibonacci number | = | 1 |
0 | the 0th Fibonacci number | = | 0 |
4 | the 4th Fibonacci number | = | 3 |
5 | the 5th Fibonacci number | = | 5 |
8 | the 8th Fibonacci number | = | 21 |
6 | the 6th Fibonacci number | = | 8 |
8 | the 8th Fibonacci number | = | 21 |
3 | the 3rd Fibonacci number | = | 2 |
4 | the 4th Fibonacci number | = | 3 |
3 | the 3rd Fibonacci number | = | 2 |
6 | the 6th Fibonacci number | = | 8 |
5 | the 5th Fibonacci number | = | 5 |
6 | the 6th Fibonacci number | = | 8 |
3 | the 3rd Fibonacci number | = | 2 |
8 | the 8th Fibonacci number | = | 21 |
1 | the 1st Fibonacci number | = | 1 |
1 | the 1st Fibonacci number | = | 1 |
7 | the 7th Fibonacci number | = | 13 |
7 | the 7th Fibonacci number | = | 13 |
Sum=401 |
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)
A picture resemblings the letters "Aleph-Lamed" is revealed! (discovered by Sefart, see this article for more).
>> Next: First and Last
Footnotes