י"ט - הטבלה המחזורית - Periodic Table of Elements
On the board
The topic that we are going to discuss today and tomorrow is the periodic table of the elements.
In the Torah we find the thought of the ancient peoples that there are four elements in the natural world which are referred to as air water and earth.
In Chinese philosophy there are five as earth is divided into wood and metal. There is also a strong foundation for this in the Torah.
But nowadays science has discovered many more elements in nature. There are 92 natural elements. There are others that can be synthesized artificially in the laboratory—they do not exist in nature. What interests us is those elements that exist in God’s nature.
What we are going to discuss is the source of the number alluding to this number, 92, in the torah. Everything in the natural world has to have some source in the Torah. It is said by the sages that God looked in the Torah and created the world.
Though we might not find an explicit reference in our Talmudic sources to the number 92, nonetheless a truth which science has found must be found implicitly somewhere. It is a mitzvah to look in the Torah and find references to this. If we find true sources then each, the torah and science, will enrich the other.
For instance, now in Quantum Physics we find wonderous parables for understanding deep concepts in the Torah. By inter-relating science and the Torah, we can even point science in the right direction.
This is called the unification of the higher and lower waters. The higher and lower waters are divided by a firmament. But the purpose of the firmament is not to completely divide, but there are windows in the firmament that are meant to allow the unification between the higher waters, the wisdom of the Torah, Divine wisdom and the lower waters, scientific knowledge.
Many scientists today acknowledge that science begins with numbers. And in mathematics, number theory is described as the queen of mathematics. Understanding phenomena that relate to the natural numbers is the most sophisticated in mathematics. Even the deepest things in mathematics relate back to the integers like 1, 2, 3, 4, etc.
Therefore, for us also, taking a number that is accepted (like 92) and contemplating on it is a foundation for our understanding of that number.
The first thing is to find the factors of a number:
92 = 2 x 2 x 23
The greatest prime factor of this number is 23. That it is a multiple of 4 (2x2) relates back to the idea that the ancients had 4 elements. Obviously not every number divides by 4 (only 1 in every 4 numbers does).
So, if we were to posit that each of the elements of the ancients contains 23 elements then we would
In Kabbalah, there are two numbers that appear again and again in the story of creation: they are 23 and 37. They usually appear as a pair.
If we start counting the primes from 1 we find that 23 is the 10th prime number (note that mathematicians differ on whether
Of 10, the Torah says that “the tenth will be holy to God.” A prime number in general represents an essential state of being (עצם), which does not divide. An essential state of being, by definition, does not divide.
There is no formula to foretell what the primes are. This is one of the most important mysteries of number theory.
37 is the 13th prime number. 13 also has very special significance in the Torah.
The second pair of most important numbers in the Torah is 7 and 13. Indeed, 13 is the 7th prime number. 7 is also the midpoint of 13.
To have a sense of numbers is called a “holy game” in the Torah (שעשוע). There are two general levels of studying Torah. The first is learning Torah as normative, as teaching us what to do. The second is learning the Torah for the sake of partaking in God’s own delight, His own delight in the Torah.
One special mitzvah that we do that relates to natural numbers is sefirat omer. In fact, when you count from 1 to 49, you have actually counted 1225 which is both the triangle of 49 and the square of 35.
This phenomenon repeats itself in relation to lighting the Chanukah candles. Tri 8 = square of 6.
This is a wonderful thing that there are two mitzvoth in the Torah that reflect this.
When we count the omer we don’t say today is the first day, the second day, etc. We say “today is one day,” “today is thirty four days,” etc. So it is very clear from the mitzvah that it is an additive process.
Where is the first indication in the Torah, the first allusion to the fact that God created the world with 92? This is in the first verse of the Torah:
בראשית ... הארץ
The first and last letters of each verse is known as its “sign” (its siman). There is a minhag to say after the amidah a verse that begins and ends with the first and last letter of your name. this is like what the sages say that הכל הולך אחר הפתיחה, הכל הולך אחר החיתום.
The siman of the first verse is thus בץ = 92.
The entire first verse adds up to 37 x 73. There are amazingly many 37s in this verse. The division into 2 and 90 reminds us of the configuration of the periodic table where there are two elements in the first row, hydrogen and helium, and the rest of the elements beneath them.
The next thing that alludes to 92 in creation is that there are 469 words in the description of creation, but only 92 are different, meaning that they come from different roots. In the entire Five Books of Moses there are 1820 roots altogether. A root is an indivisible essence. It can repeat itself many times, but the root itself is the essence.
Now, if we divide the 92 roots into 2 and 90, then the 2 would be the first two roots which are the roots of the two words בראשית ברא: they are: ראש ברא, which mean “head” and “create.”
It is clear that the first element is like the head. What this means is that there must be some creative power in helium.
What today is in common to these two elements is that they are both very explosive in both fusion and fission. They are like lights of chaos, they incorporate in themselves explosive energy. The other that is associated with bombs is uranium, which is number 92. We see then that the beginning is enwedged in the end.
Now the third thing that we would like to do is look for a Torah portion that has 92 verses. At the end of every portion of the Torah, the Ba’alei Hamesorah wrote a sign, a word whose numerical value equals the number of verses in the portion. There is only one such portion (according to the zohar there are 53 portions, today we count 54, so really two must be combined), pekudei, which is the 23rd portion in the Torah. The root of the parsha’s name is פקד = 184 = 2 x 92.
The parshah of pekudei is especially connected to the counting of the elements, because it includes an enumeration of the elements of the tabernacle which is itself a microcosm of creation.
As we mentioned the masoretic transmitters give a sign for each parshah, except for one parashah. If you look in older editions of the Torah you will find that pekudei is the only parashah to which they did not give a sign. The Lubavitcher Rebbe gave a whole sichah to explain this phenomenon and he came up with an ingenious idea that the sign that was written was בלי כל סימן. The printer misinterpreted this to mean that there was no sign, but really בלי כל = 92.
Amram Lida, one of our students in Eretz Yisrael noticed that the בעלי המסורה usually tried to bring their sign from something that relates to the last verse of the parashah. The last four words of the parashah are: לעיני כל בית ישראל. The word כל appears explicitly, and the initials of the other three words is בלי.
Now the value of the entire four words: לעיני כל בית ישראל = 1173 = 23 x 51. Again, pekudei is the 23rd Torah portion. If we take out the sign itself we get 47 x 23 = 1081 = תפארת, which is an important word in the Torah and the name of the middle sefirah.
1081 = tri 46 or tri (1/2 x 92). It’s like the half life of 92…
To calculate a triangular number quickly you calculate: n x (n + 1)/2, so in this case we calculate it as 47 x 23.
If you divide 92 into 2, then the first element of the first half is H, and the first element of the second half is Ag, silver.
If we are already mentioning silver then let us say something about gold. Gold is 79.
Let us take another example of this is that during Hoshanot we take the first and the 37th of the 72 three letter names of God, the first of the first half and the first of the second of the second half: אני והו. In the Talmud we learn that there are 36 tzadikim. But Kabbalah teaches that there are 36 revealed and 36 concealed. By taking the first of each half, we are combining the head of the revealed (אני, this is consciousness) with the first of the concealed (והו, this is the concealed like הוא).
The same holds true for the entire alphabet, where the first of the halves spells אל, the name of Hashem.
Now getting back to the allusion of בלי כל, we may say that it means that the 92 elements do not yet manifest the כל = 50, which alludes to the fiftieth gate of the Torah. More simply, כל alludes to the creator who is called כל יכול. Meaning that the 92 elements are an invitation to bring the consciousness of the Almighty into the natural world.
כל יכול = 116.
If we indeed add these two we get 208 = יצחק = 2 x גם אני!
Now let us explain this. Until some time ago there was a thought that there are two elements that could not be found naturally, they were numbers 43 and 61. Only recently, small traces of these elements have been found in nature. So today we would say that these are the most elusive of the elements. They were discovered in the crust of the earth.
Esav said “me too.” He said it twice to his father יצחק and as we mentioned יצחק = 2 x גם אני. Altogether this phrase appears 28 times in the Bible.
So in general this mentality is an Esav mentality, a non-Jewish mentality. But there are a few times that this phrase has a positive context. One of them appears in Psalms 71: גם אני אודך, which means that I too will praise you God. Actually, there are three phrases in this Psalms that begin with the word “also….” When you add up the three verses, you get 3120 = 104 x 30.
Indeed if we look at this pair of numbers, we find that:
Tri 43 = midpoint of tri 61.
This phenomena is few and far between. When is the first time that this phenomena appears? The first is discussed explicitly by Abraham Abulafia, one of the most important early Kabbalists: tri 7 = mid tri 10.
28 = mid(55).
Indeed from the pair 7,10 to 43 and 61 there is no other pair.
253 358 are the next pair. 358 = משיח and 253 = אבנר, the minister of war of king Saul, who the sages say if he would have joined David (before being killed) would have made David into the Mashiach.
Now would any chemist in the world explain that these two elements go together in this mathematical way. This is an example of taking the delight of the Torah, especially as it comes from pure number theory and applying it to science.
Let us make another observation: these two elements are unstable. This is the reason that they are so rare in nature. They are much more unstable than uranium. Uranium is radioactive but it is not considered to be unstable. How many unstable elements are there amongst the 92? There are 8, which are: 84, 85, 86, 87, 88, 89. You might expect that the lower the atomic number, the less unstable they would be, but 43 and 61 are the most unstable of all the unstable elements. Like we said, instability is a world of Chaos property, which relates to Esav who feels that “he deserves”: “I too deserve so and so.” This is the cause of the shattering of the vessels.
The sum of the values of all the unstable elements is 623 = 7 x 89, which is the upper limit of the unstable elements. Meaning, that thanks to 43 and 61, 89 becomes there upper limit.
There is another very basic thing in number theory called Fibonacci numbers:
1 1 2 3 5 8 13 21 34 55 89
So of these, 89 is the most important number of the Fibonacci series.
The atomic number of gold is 79. When you have a finite set from 1 to n, then you have a phenomenon of reflected light. If you have an infinite set, you do not have a reflected aspect to it. This is one of the things that finiteness has more than infiniteness. What this means in simple numbers is that it is important and legitimate to count from the beginning and to count from the end.
For example if gold is 79 is the first from the beginning, then it is the 14th from the end. Indeed, in Hebrew זהב = 14.
There is a beautiful thing in the Torah in relation to this. The Torah says that the three basic metals from which the tabernacle was built is that copper is the 29th word from beginning of the parashah (Cu = 29).
Silver is the 47th element. It is therefore the 46th from the end. (to compute this you add one to the last number and subtract: 93 + 1 – 47 = 46).
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