The Other Conquest

The years 5727-5734 brought Jewish sovereignty over the Land of Israel. In the same period, another decisive conquest took place, in Science.

In the beginning of 5728, the staunch Jewish atheist Steven Weinberg proposed a theory that describes two forces of Nature, Electromagnetism and the Weak Interaction, in a unified way. At first, Weinberg's theory seemed artificial and replete with technical problems, until four years later Martinus Veltman and his student Gerard 't Hooft proved a cosmic result: Weinberg's theory is "renormalizable."

The background of the discovery is that the mathematical framework of high-energy physics (quantum field theory) shows a general tension between fundamental physical constraints such as causality, and the computability of the theory's predictions. Between Weinberg and Veltman, it was established that there is a mathematical framework, involving "gauge" symmetries, that "allows" a world like ours to exist. The philosophical corollary is that the physical world can only exist because of hidden mathematical symmetries.

The Weinberg-Veltman-'t Hooft theory was confirmed by experiment, and established definitively the centrality of the notion of gauge symmetry, and that of symmetry breaking. The revolution led to another. From understanding how a world like ours can exist, we came to understand much better how our world came into existence, some 13 billion years ago.

עז

The Jewish Square

Torah scholars bring peace to the world. How? Don't they fight all the time? A Torah scholar brings peace to the world to the degree that he leaves place for his opponents. This not only brings peace. This is essential to attaining Truth. The Torah was given to sixty myriads of Jews, and is encompassed only by all of Israel. Who does not leave place to his opponent will loose sight of the truth the opponent does have. His end will be heresy.

This is the message of the passage of the heretics Simcha and Sasson in Talmud Bavli, Succah 48b. Simcha and Sasson differ, but the Talmud does not explicitly mention the subject matter of their dispute. That is apparently quite irrelevant. We must understand the heresy of Simcha and Sasson in the light of the discussion the Talmud is reporting. It is a status discussion. I am greater than you, says Sasson to Simcha. No, I am greater than you, says Simcha to Sasson.

In Torah, the greatest is he who learns from everybody. We must consider the other greater, even when disagreeing fiercely. If we don't, we will all be heretics. Who sees his truth rejected, will naturally reject the truth of his rejecter in return. The result is division, leading to heresy, leading to more division, and more heresy. Apply this to the truths of the divided Jewish square: Halacha, Kabbala, Eretz Yisrael, Chochmot HaOlam.

The Truth is One. The truth of Sasson is essential to Simcha, and the truth of Simcha is essential to Sasson. Being unable to submit to a joint understanding, Simcha and Sasson push each other into heresy. As long as division reigns in Israel, not a single corner of the Jewish square is free of heresy. Only in Unity we will find the Truth, together with Peace.

The Torah tells us how to achieve Unity. We must sit together in a Sanhedrin. Then Sasson will say to Simcha: You are greater, as you have truth that I do not have, and Sasson will attain Simcha's truth. Then Simcha will say to Sasson: You are greater, as you have your truth and you have mine.

עו

Revelation of the Name

The two identities for 8! and 9! can be written as

8! + 9^2 = (67*3)^2
9! + 27^2 = (67*9)^2

and correspond to the Tikkunim of years מ and ס.

The number 67 hints at Ateret haYesod. The powers of three, 3, 9, 27, hint at a staged revelation of the Name of 26 during the three years ס , נ, מ. The 9 refers to nine months of trouble, largely in the year נ, which lead to the revelation of the Name in year ס.

How will be able to survive year נ, and reach from מ to ס? By holding on to the great principle that appears between the Nun's in BaMidbar 10:35-36:


ויהי בנסע הארן ויאמר משה קומה ה' ויפצו איביך וינסו משנאיך מפניך
ובנחה יאמר שובה ה' רבבות אלפי ישראל


"When the Ark would journey, Moshe said: "Arise, HaShem, and let Your foes be scattered, let those who hate You flee from before You. And when it rested, he would say, "Reside tranquilly, O, HaShem, among the myriad thousands of Israel."


מלכותך מלכות כל עולמים ומשלתך בכל דור ודור
סומך ה' לכל הנופלים וזוקף לכל הכפופים

(תהלים קמ"ה)


עה

The Holy Arrow

The two identities

6! + 3^2 = 27^2
7! + 1^2 = 71^2

which correspond to the Tikkunim of years ה and ו of the current Machzor Gadol, relate the numbers 7, 6, 3, 1 at the left-hand sides to the numbers 27 and 71 at the right hand sides.

Translating the numbers 7, 6, 3, 1 into letters, one gets זוג א, a hint at the first Zivug between Zeir Anpin and Malchut. The result is represented by the numbers 27 and 71, which together have the gematria of חץ, the Holy Arrow that protects Israel. The number 27 hints at the revealed Name of 26, whereas number 71 hints at the hidden Name of 72. The Holy Arrow that results from the first Zivug protects in revealed and hidden ways. One result must be the restoration of Sanhedrin.

"Oy, to the nation that will stand in the way in the hour that the Almighty will bring redemption to his sons, and to he who will throw his cover between two lions in the hour that they come together to mate." (Sanhedrin 106)


קם אחד בקירטא ודא שכינתא תתאה וחד בקשתא דא ברית צדיק עליה אתמר שופ"ר הול"ך פז"ר גדו"ל גירין דילה אינון צדיקים דישראל דקבילו ברית דבזכותיה נפקין מגלותא ורזא דלה הא לכם זרע דאינון טפין דא זרק"א קמו תנאין ואמוראין דלעילא ובריכו ליה ואמרו מטרה תהא אגינת עלך מחצים בגלותא עלך אתמר לא תירא מפחד לילה מחץ יעוף יומם וקשתא וחצא דסטרא דקדושה יגן עלך ותחת כנפיו תחסה צנה וסחרה אמתו

(תיקוני זוהר תקון כא)


עד

Sanhedrin of Keter

In addition to the 12 identitities of the intermezzo, there are two elementary identities that relate factorials to squares:

0! + 0^2 = 1^2
1! + 0^2 = 1^2

Altogether, therefore, there are 14 such identities, for 14 numbers n for which (ceiling(sqrt(n!)))^2 - n! is square. They correspond to the 14 Tikkunim of Zeir Anpin and Malchut. The small squares represent the Tikkunim that raise the imperfect factorials to perfect squares.

More specifically, 0! corresponds to the first Samech. The next three identities, for 1!, 4! and 5!, belong to the triple Sephirot not associated to Machzor HaGadol - Yesod, Gevura, and Chesed. From 6! onwards, the identities follow the Tikkunim of Machzor HaGadol. Therefore, the identity for 6! belongs to ה, and 7! + 1^2 = 71^2 is for ו. The 71 at the right-hand side hints at Sanhedrin, in line with the meaning of the Tikkun at ו.

Towards the end, the awesome series of identities for 13! through 16! corresponds to the three Tikkunim of the Sofit letters ץ, ם, Aleph Sofit, and the final Samech.

The identity for 11! corresponds to ת, the start of the count of Arich Anpin. It can be written as (12-1)! + (19-1)^2 = (89*71-1)^2. This hints at the following. From 7! + 1^2 = 71^2 we can learn that size 71 of Beit Din HaGadol derives from the left, from the number 7, the length of the cycle of Din. Conversely, 89 is related to the right, to the cycles of 12 and 19, of Chesed and Yesod.

If one will say that also 71 appears in the identity for (12-1)!, the answer is that the left is included in the right. We will reach a new spiritual level. The emphasis of Sanhedrin will change from Law to Truth. The latter includes, must include, the former. Who thinks we can do without Law, is up to destroy the world. Who would propose that Law can contain the Truth, would also destroy the world.


אורייתא איהי חילא דימינא כמה דאת אמר (דברים לג) מימינו אש דת למו ושמאלא אתכליל בימינא. מאן דעביד ימינא שמאלא ושמאלא ימינא הא איהו כאילו חריב עלמא

(זוהר במדבר פרשת קרח דף קעו עמוד א)

At the start of the count of Arich Anpin, the size of Sanhedrin is appropriately increased with one quarter, to 89, in order to encompass five Partzufim rather than four.


עג

Intermezzo

For all integer numbers n bigger than one, the factorial n!, defined to be the result of the multiple product n*(n-1)*(n-2)*...*2*1, cannot be a square number, as was most neatly proven by Erdős. However, the difference between n! and the first square number k^2 that is bigger than n!, is amazingly often a square number:

4! + 1^2 = 5^2
5! + 1^2 = 11^2
6! + 3^2 = 27^2
7! + 1^2 = 71^2
8! + 9^2 = 201^2
9! + 27^2 = 603^2
10! + 15^2 = 1905^2
11! + 18^2 = 6318^2
[ (12-1)! + (19-1)^2 = (89*71-1)^2 ]
13! + 288^2 = 78912^2
14! + 420^2 = 295260^2
15! + 464^2 = 1143536^2
16! + 1856^2 = 4574144^2

I postulate that there are no more such identities. In other words, I postulate that

(ceiling(sqrt(n!)))^2 - n!

cannot be a square number if n is greater than 16.

P.S. It was brought to my attention that the above observation is known and that I am not the first to state the postulate. I was not aware of this.


עב