Math and RealityOne of the greatest enigmas of all time is the bewildering relationship between mathematics and reality.
This mystery has baffled scientists and philosophers for millenia. The advent of modern science has only deepened the mystery. For all physical laws ever discovered are nothing but mathematical statements.
This is a wonder! Why should the world of physical reality obey laws that belong in the world of mathematical forms? Aren't mathematical forms just mental thought constructs?
To quote Nobel prize physicist Richard Feynman:
"What turns out to be true, is that the more we investigate, the more laws we find, and the deeper we penetrate nature, the more this disease persists. Every one of our laws is a purely mathematical statement in rather complex and abstruse mathematics. Newton's statement of the law of gravity is relatively simple mathematics. It gets more and more abstruse and more and more difficult as we go on. Why? I have not the slightest idea... It is impossible to explain honestly the beauties of the laws of nature in a way people can feel without their having some deep understanding of mathematics... Mathematics is not just a language. It is a tool for reasoning... It is in fact the results of some person's careful thought and reasoning (emphasis mine). By mathematics it is possible to connect one statement to another... - The Character of Physical Law, Feynman pg.42What is the answer to this enigma?
The opening word of the Torah is "Beresheit" (in the beginning). This word is rendered "with wisdom" (Targum Yerushalmi). For the world was created with divine, boundless wisdom.
This is the answer to the riddle! The world was created "with wisdom", i.e. truth (Baal HaTurim Gen.1:1). In our physical realm, this manifests as the wisdom of mathematics.
According to the Midrash, the Torah was used as the blueprint of the world (Gen.Rabba 1:1). No surprise then that at its lowest level, the Torah also contains underlying mathematical wisdom and symmetries of incredible proportions.
More Teachings on Gen.1:1 by the Vilna Gaon"In the Beginning G-d created the Heavens and the Earth".
According to the Vilna Gaon (Aderet Eliyahu) there are 28 letters = 4×7 corresponding to the four worlds.
28 letters = 4×7|
Four Mysterical Worlds
|בְּרֵאשִׁ֖ית בָּרָ֣א||אֱ-לֹהִ֑ים||אֵ֥ת הַשָּׁמַ֖יִם||וְאֵ֥ת הָאָֽרֶץ|
7 letters corresponding to the 7 Heavens.
These are split into 2/5 letters corresponding to how they are above
7 letters corresponding to the 7 Lands (continents?) and the 7 levels of Gehinom.
These levels are also split into 2/5.
"Beresheit" - the letters spell "Yira Boshet" corresponding to the two types of fear; fear of G-d's greatness and fear of punishment. These are called "Yira Shamayim" and "Yira Aretz" (fear of Heaven and fear of Earth). "Beresheit", because of these two fears, G-d created Heaven and Earth.
The verse also alludes to the 10 Sefirot used to create the world
(see Vilna Gaon's book Aderet Eliyahu for much more).
Based on all the intricate mathematical structures we have seen already, it is a wonder the words have any meaning.
In his kabalistic commentary on Sifra d'Tzniuta (ch.5), the Vilna Gaon writes:
"The general principle - everything that was is and will be forever, everything is included in the Torah from Bereisheit to "the eyes of Israel" (last verse); and not just the general matters only, but even the details of every species and every individual human being, everything that happened to him from the day he was born until his end, and all the gilgulim (reincarnations). And likewise for every animal species and every living creature, and every plant and inanimate object. All their details and details of details of every species and every individual of every species and what will happen to them and their root.."And in the Likutim there he writes:
"And everything is written generally there in the first chapter (Genesis ch.1), and it is written more generally in the first verse in the 7 words (Genesis 1:1) corresponding to the 7000 years.. The first 6 days were a Klal (general overview) of the 6000 years (of the Jewish calendar). Therefore, one who knows these verses to their full depth, then he can know what will happen every second of the (6000) years".
>> Next: Sturdy Foundation
-  see the interesting article "Is G-d a Mathematician" https://www.washingtonpost.com/wp-srv/style/longterm/books/chap1/godmath.htm for more on this return to text