And God created man in His own image, in the image of God created He him; male and female created He them. And God blessed them; and God said unto them: “Be fruitful, and multiply, and replenish the earth, and subdue it . . . . Genesis 1:28
God created man, male and female, and commanded them to be fruitful and multiply, fill the earth, and subdue or conquer it. While the literal meaning of this verse is apparent—fill the earth with your progeny by procreating—it begs a question. Specifically, the phrase “fill the earth” seems superfluous—wasn’t it enough to say “Be fruitful and multiply”? Indeed, the Hebrew word milupim (“to multiply”) is etymologically related to the word mil’u (“to fill”). If humans were to multiply, as commanded by God, they would naturally fill the earth. It seems that the phrase “fill the earth” carries an additional meaning. And what is meant by subduing the earth?
The word mil’u (“to fill”) has a fractal (as in fractal geometry) connotation. We can use the procedure called Otiyot beMilui (“filled letters”) to expand the word by replacing each letter in that word with a word for that letter. Let us take, for example, the word av (“father”). It is spelled alef-bet. The numerical value of this word is 3. The first iteration of milui (filling out the word) replaces each letter with its name. So, the letter alef (spelled alef-lamed-peh) is replaced with three letters: alef, lamed, and peh; and the letter bet (spelled bet-yud-tav) is replaced with three letters: bet, yud, and tav. Putting all these letters together, we have a new five-letter word spelled alef-lamed-peh-bet-yud-tav, with a numerical value of 523. For the next iteration of milui, we need to replace each letter in this new word with the spelling of that letter. So, the letter alef becomes alef-lamed-peh; the letter lamed becomes lamed-mem-dalet; the letter peh becomes peh-heh; the letter bet becomes bet-yud-tav; and the letter tav becomes tav-vav. Putting it all together, we have a new word spelled alef-lamed-peh-lamed-mem-dalet-peh-heh-bet-yud-tav-tav-vav, which has a numerical value of 1088. And so on. The fractal nature of this procedure is evident in the fact that we apply the same algorithm for each iteration.
Similarly, in fractal geometry, we create curves or figures by iteratively applying the same algorithm. For example, to produce a Koch snowflake, an example of a fractal curve, we start with an equilateral triangle. We divide each side into three parts, remove the middle part, and double it by pushing the bend outward. This procedure is repeated with each step, creating a smaller equilateral triangle. The result is a snowflake:
Dr. Alexander Poltorak is Chairman and CEO of General Patent Corporation. He is also an Adjunct Professor of Physics at The City College of New York. In the past, he served as Assistant Professor of Physics at Touro College, Assistant Professor of Biomathematics at Cornell University Medical College, and Adjunct Professor of Law at the Globe Institute for Technology. He holds a Ph.D. in theoretical physics.