The Saadia Commentary
on The Sefer Yetzirah

by Saadia ben Joseph al-Fayumi (882-942 AD)

Jewish scholar, b. Egypt. He was known as Saadia Gaon. He was the head of the great Jewish Academy at Sura, Babylonia, which under his leadership became the highest seat of Jewish learning, and a vigorous opponent of the Karaites (A Jewish fundamentalist schismatic sect, reputedly founded (8th cent.) in Persia by Anan ben David and originally known as Ananites, but after the 9th cent. they were called Karaites. The Karaites attacked the Talmudic interpretation of the Bible, rejected the oral law and - in the usual way of fundamentalists everywhere and everywhen, interpreted the Bible literally). Saadia's Book of Language laid the foundation of Hebrew grammar; he also wrote a Hebrew dictionary, the Agron, and made an Arabic translation of the Old Testament that became the standard version for all Arabic-speaking Jews and exerted an important influence upon Muslims as well. He also compiled the first comprehensive siddur (daily prayerbook). His great philosophical work is The Book of Beliefs and Opinions (tr. Samuel Rosenblatt, 1948). Writing in a period of spiritual doubt and confusion, Saadia attempts in this work to defend Jewish religious faith on the basis of rational argument, using the methods of Islamic speculative theology known as kalam. The first defense of Judaism in rational terms, Saadia's work laid the basis for all subsequent Jewish philosophy.


  1. On the Origin of the World According to the Pythagoreans & the Sefer Yetzirah
  2. On the Divine Epithets and the Aristotelian Categories
  3. On the "Closed" Numbers, Mothers, Doubles, & Simples
  4. On the Creation's "Witnesses"
  5. On the Geometrical "Whirlwind" of the Hebrew Letters
  6. On the Rotation of the Letters and the Zodiac
  7. On the Ethereal Realm and its Relation to Prophecy
  8. On the Geometry of Phonetics and the Order of the Alphabet
  9. On the 231 Gates of Letter Permutation
  10. On the Crowning of the Letters

1. On the Origin of the World According to the Pythagoreans & the Sefer Yetzirah

... The seventh system belongs to the theorist who admits a creation of things, but asserts that the first things created were numbers. By means of numbers, substances and particles are differentiated. Geometry and figures are based on number, for all created things necessarily have some kind of form. According to this theory, the figure of the created object precedes the object itself, for it is the object's material. However, if this theorist - may God have mercy upon you! - supposes the potential, and not actual, anteriority of numbers to numbered things, then we must accept this as a just and irrefutable theory. We maintain that the number, in potentiality, has prefigured the numbered object; that the form has preceded the formed thing; the figure, the figured thing; geometry, the geometrical body; and composition, the thing composed - all in potentiality and not in actuality. But if this theory posits the actual anteriority of pure numbers, isolated compositions, and abstract theorems, the supposition is inadmissible for two reasons: (1) the theory implies that the Mover and the moved were joined by a third thing: motion; with the forming agent and the formed object, it names another object: form; and along with the Creator and his creature, it posits a necessary third: creation. This is absurd; (2) it is contradictory to speak of abstract composition and pure theorem, for these are necessarily based upon at least two terms.

The eighth system belongs to the theorist who accepts a creation, but ascribes the origin of things to numbers and letters. This theory belongs to the author of this book. In fact, he ascribes the origin of the Creator's creation to thirty-two things: the ten numbers and twenty-two letters. He does not say, however, that they are abstract and isolated. He only says that God has created the air and has established the thirty-two things in it. The numbers, according to him, traverse the air, which is composed of distinct particles. When the air current follows these direct and inflected lines, it produces figures. After examining this theory, we find these points to be correct, but they need to be completed by the following exposition. The same applies to the letters. When their creator established them in the air, they were cleaved, and figures of diverse appearance and geometrical forms were created according to the faculty of each isolated letter, two letters combined, or one compound of numerous letters.

Our rabbis say something similar with regard to the scene at Mt. Sinai in the Scripture, for it is said: "And all the people saw the thunderings," [Exodus XX, 15]. The rabbis asked how it was possible to see sounds? They explained that the Sage brought a powerful and brilliant fire down upon the mountain, as it is said: "Because the Eternal descended upon it in fire," [Exodus XIX, 18]. Then He surrounded it with a black cloud, "and the mountain burned with fire unto the midst of heaven, with darkness, clouds, and thick darkness," [Deuteronomy IV, 11]. This darkness is the black cloud, as it is said: "He made darkness his secret place; his pavillion round about him were dark waters and thick clouds of the skies," [Psalms XLVIII, 12]. Thus did He create the scintillating voice in the fire; the voice emanated from fire and its form appeared in the cloud according to the impulsion given by the pronunciation's movement in the air. The people saw this form and knew then that the fire's scintillation had projected it into the surrounding black air, as it is said: "And the Eternal spoke unto you out of the midst of the fire,"[Deuteronomy IV, 12], and it is said: "when ye heard the voice out of the midst of the darkness," [Deuteronomy V, 23]. As an example of this, we see that when someone speaks on a cold day, the articulation of the voice cuts the air and produces forms varying in straight or inflected lines according to the current which the sounds follow. Similarly, the author says that numbers and letters are the origins of things; he means with the air, as we have just demonstrated.


2. On the Divine Epithets and the Aristotelian Categories

What do the ten names of God enumerated at the beginning signify and why does the author limit himself to one? The names of God, like the names of all beings, refer to actual or alleged events. In the Ma'aseh bereshit [Work of Creation], God is called Elohim, the name of essence. He is not called Eternal [Adonai, Yod-Vav-Yod] before the creation of the creatures, because to be Lord, He must be the Master of someone. The Sages have said: "He has mentioned a full name for a full world," [Beresit Rabba, XIII]. He is called El Shaddai ["Almighty God," Genesis, XVII, 1] when He orders Abraham's circumcision and says: count on me who helps and saves.

He called Himself "I am that I am," [Ehyeh asher ehyeh, Exodus III, 14] when He produced the miracles and marvels like the phenomena of creation, the ten plagues and the rest. He is the One who realizes but cannot be realized. He called Himself Yah [Yod-He] when He produced the extraordinary miracles on the Red Sea. He called Himself Elohim Hayyim ["Living God "] when He revealed His voice to the people and they heard, and did not die but were given life, as it is said: "For who is there of all flesh that hath heard the voice of the living God," [Deuteronomy, V, 26]. He called Himself Adonai Sabaoth ["Eternal (or Lord) of Hosts"] when the people's pilgrimage and assembly in the sanctuary was recounted, as it is said: "And this man went up out of his city yearly to worship and to sacrifice unto the Eternal of hosts in Shiloh," [I Samuel I, 3]. He is called High and Extolled [Ram v'Nisah] when Isaiah speaks of Uzziah, king of Judah: "In the year that king Uzziah died I saw the Lord sitting upon a throne, high and lifted up," [Isaiah VI, 1]. On account of Uzziyahu, he has said: "But when he was strong his heart was lifted up to his destruction: for he transgressed against the Lord his God," [II Chronicles XXVI, 16]. He called Himself Lord [Adon] when He announced that He would raise the noble among the people, for it is said: "For behold the Lord, the Lord of Hosts doth take way from Jerusalem," Isaiah III, 1]. He is most often called Eternal God [Yod-Vav-Yod Elohim] in the books of Jeremiah and Ezekiel, and not Eternal of Hosts [Yod-Vav-Yod Tsvaot (Sabaoth)] because Israel's legions had been dispersed and His totality had been fragmented. When the Israelites gathered in the second temple, He called Himself Eternal of Hosts, and this appellation is always used in the prophecies of Haggai, Zechariah, and Malachi. Only once is He called Eternal God of Israel. This is in the verse: "Let him send her away saith the Eternal, the God of Israel," [Malachi II, 16]. This name can be understood in a general and a restricted sense. In the restricted sense, the law of divorce can be applied to the Israelite only by another Israelite, and not by the pagans. If the pagans compel the divorce, it is nullified. In the general sense of the word, it refers to the Lord's possession of Israel. Though Israel has been chased and exiled, the Lord has neither abandoned nor forsaken her, but considers her His own. He has been called "changeth the times and the seasons," [Daniel II, 21] when He transforms the era of domination into one of servitude. He has been called "He removeth kings and setteth up kings," [Daniel II, 21] when He dethroned Sedecias and made Nebuchadnezzar king. He has been called: "He giveth wisdom unto the wise," [Daniel II, 21] because He taught wisdom to Daniel. He has been called "He revealeth the deep and secret things" [Daniel II, 22] for He revealed the nature of vision to Daniel. Finally, it is said: "And Esdras blessed the Lord, the Great God," [Nehemiah VIII, 6], for God has said: "The glory of this latter house shall be greater than of the former," [Haggai II, 9].

The names of angels correspond in like manner to events which are the angel's task to realize. When God dispatched angels to Abraham to announce the glad tidings, they resembled and were thus called "men" [anashim, Genesis XVIII, 2]. When God sent the angels to destroy Sodom, they were called "angels" [malachim, Genesis XIX, 1]. When God sent them unto Isaiah to burn him with hot coal because he neglected to warn Israel, they were called "seraphim" as it is said: "Then flew one of the seraphim unto me having a live coal in his hand....and he laid it upon my mouth," [Isaiah VI, 6-7]. When Ezekiel saw them in the form of unreasoning animals, they were called "hayyot" ["creatures," Ezekiel I, 5]. The angels between them, which turned not when they went, were called "ophanim," ["wheels," Ezekiel I, 15]. The most elevated between them have been called "cherubim" [Ezekiel X, 1] because each elevated being among men is called "cherub," as it is said of the king of Tyre: "Thou wast the annointed Cherub that covereth," [Ezekiel XXVIII, 14].

The names of the celestial bodies vary according to their different characteristics. The one with a bright light in the center is called "bright" [or "luminary"] as it is said: "All the bright lights," [Ezekiel XXXII, 8], according to the term for the Sun. The star with lesser brilliance is called "Nogah" ["shining"] after a name for the Moon, as it has been said: "neither for brightness shall the moon give light unto thee," [Isaiah LX, 19]. Nogah is also the Hebrew name for Venus. Stars with a hot nature are called "Kesilim" ["constellations" and "Orion"], as it is said: "For the stars of heaven and the constellations" [Isaiah XIII, 10]. This refers to the name Orion, which is Kesil and its fires. Luminaries with a cold nature are called Mazzaroth ["Pleiades"], as it is said: "Canst thou bring forth Mazzaroth in his seasons?" [Job XXXVIII, 32]. Israel's different names of praise such as Jacob, Israel, and Jeshurun [Deuteronomy XXXII, 15]; and her different names of blame like "M'shuva" ["backsliding," Jeremiah III, 6], "B' gedah" ["treacherous," Jeremiah III, 8], "Oholah" and "Oholibah" [Ezekiel XXIII, 4] correspond to particular events. These names of the angels, luminaries, and the nation are an interpretation of actual characteristics. The names of the Creator, however, are only indications and extractions [abstractions] of his powers - may He be praised and exalted!

The author of our book intends to show us how the existence of beings is realized. When the wise grasped this knowledge, they discovered the ten and only ten categories which reason can use to order all things: substance, quantity, quality, relation, space, time, possession, position, action, and passivity. When the sages precisely established these ten categories, no conception remained unconnected to them except the idea of the Creator, for He is above all intuition and comprehension. Therefore, our author has enumerated these ten categories at the beginning of his book in a style befitting the rest of his exposition. The name Yah refers to substance [essence] for the author translates it as Eternal, and he derives it from the word hayyot [being or creature] and "hayu" ["they have been"]. This name applies to eternity, and God is the Creator of all substances. The name Eternal Sabaoth [Eternal of Hosts] corresponds to the categories of action and passivity. The Eternal is active, as it is said: "I am the Eternal that maketh all things," [Isaiah XLIV, 24]. The passive, which is great in number, is called "legion" [host or armies]. The name Living God [Elohim Hayyim] refers to Elohim as the Creator of quantity, for the measure of life (i.e., age) is a quantitative measure. The name El Shaddai ["Almighty God"] refers to God the Creator of quality, for the name Shaddai [Shin-Dalet-Yod] derives from "dai"[Dalet-Yod, "sufficient"] and "daim" [Dalet-Yod-Mem, "sufficiently"]. The name Elohei Israel, God of Israel, refers to relation. The name Lofty [Ram] refers to God as Creator of the Good, while the name Nisah ["elevated"] refers to the category of position. The name Shokhen Ad ["dwelling in eternity"] indicates the time before and after which He is; and finally, the epithet Qadosh Shmo ["Holy be His Name"] refers to the category of possession and to the noble attributes which allow our intelligence to reach an approximate idea of Him. Therefore, the ten names clearly suit the ten categories, and according to our author, there remains nothing which God has not created.

After a deep examination and detailed analysis, we conclude that the Ten Commandments heard by our fathers before Mt. Sinai correspond to these same ten categories which encompass every precept. The commandment "I am the Eternal" alludes to the category of action, as it is said: "I am the Eternal that maketh all things," [Isaiah XLIV, 24]. The commandment "Thou shalt have no other gods..." refers to substance, for it adds: "that is in heaven above or that is in the earth beneath or that is in the water under the earth." The commandment "Thou shalt not take (the name of the Lord in vain) refers to quality since most oaths only apply to modes of being. The commandment: "Remember the Sabbath day" explicitly relates to the category of time. The commandment: "Honor thy father and thy mother" is the relation itself. The commandment: "Thou shalt not kill" indicates the category of passivity, as it is said: "for in the image of God made He man" [Genesis IX, 6]. The commandment: "Thou shalt not commit adultery" designates the category of position, for this act is a kind of position and contact. The commandment: "Thou shalt not steal" directly corresponds to possession. The commandment: "Thou shalt not bear false witness" refers to quantity since most false witnessing applies to measurement. Finally, the commandment: "Thou shalt not covet" indicates space and everything corresponding to it; thus the Sage adds: "the house of thy neighbor." Therefore, the decalogue clearly comprehends all the notions in the world. By the same token, the 613 precepts must therefore be contained in the decalogue without exception.

By co-ordinating these precepts in accordance with the Ten Commandments, I have discovered that 80 precepts correspond to the first commandment, 60 precepts correspond to the second commandment, 48 correspond to the third, 75 to the fourth, 77 to the fifth, 50 to the sixth, 58 to the seventh, 59 to the eighth, 52 to the ninth, and 54 to the tenth. This amounts to 613. There are 620 letters in the decalogue, of which 613 correspond to the 613 precepts. The remaining seven letters are contained in the two concluding words: "that is your neighbor's," but they are already subsumed in the words immediately before them: "nor anything" [Exodus XX, 17]. Blessed be the Sage who put so many things in so few words!

The words [from Sefer Yetzirah] "He created His world in three sefarim" indicate the three ways of recording all things. The sages counted four aspects: substance, word, writing or thought. For example, we see a man in substance; or we say the word: "man"; or we write the letters: M A N; or we represent an image of the man in thought. Now why does our author only enumerate three aspects of a thing? He calls them "three sefarim" ["three books"] or "three divans," and these are: scripture, number and word. When the category of substance is added to them, they comprise the four aspects. Substance and thought do not vary. Viewed according to these two categories, the object makes the same impression on all men. The other two aspects, scripture and word, do vary, for we see many different languages and scripts. However, the ideas underlying these are not different.


3. On the "Closed" Numbers, Mothers, Doubles, & Simples:

The author then explains the thirty-two paths, and says that these are ten numbers and twenty-two letters. We translate the word "b'limah" as "closed." The proper sense is: 'provided with a brake,' as it is said: "whose mouth must be held in with bit and bridle," [Psalms XXXII, 9]. The author then divides the letters into "three fundamental mothers". The sense of the word [Alef-Vav-Mem, m] is "mother" and this is a term in the Mishna. It is said: "There is one mother for the tradition and one mother for the reading" [Pesahim 6b; Sukkah 6b]. This means that the Law has been interpreted in two ways: according to the principle of the Scripture and according to the principle of oral lecture. The word [m] is called the primitive origin of the body part where leprosy resides, as in the passage: "either the primitive origin of the wound has disappeared or dimished" [Nega'im, I, 5]. Using this metaphor, the author says "three fundamental letters" [yesod gimel otiot].

The proper sense of the words "sheva k'phulot" is "seven doubles," for it is said that there are two kinds of knowledge: "the secrets of wisdom, that they are double to that which is" [Job XI, 6]. This is the knowledge of the Creator and the knowledge of the creature. There are also two kinds of punishments: "for she [Jerusalem] hath received of the Lord's hand double for all her sins" [Isaiah XL, 2]. These are the punishments in person and fortune, of the sacred and the profane, for the king and the multitude, and among the distinguished and the vulgar.

The words "shtem esre ph'shutot" indicate the "twelve simple" letters. With respect to composed objects, isolated and separate things are called "simple" to distinguish them from compounds, as it is said: "a simple year" to distinguish it from the embolismic year. The simple year is of twelve months, the embolismic year has thirteen months. One also says "first born" and "simple". "First born" refers to two parts, and "simple" to one part. In astronomical charts of complex years, this is an approximate measure of a certain star's revolution. The simple years are the average of its progression through each solar year. Since the seven letters are double, the remaining letters are called simple to distinguish them from the compound.


4. On the Creation's "Witnesses":

"By means of these [32 paths], the Eternal, Master of armies, God of Israel, living Elohim, Almighty, Unique, Lofty and Dwelling in Eternity, Holy Be His Name has traced three mothers and their progeny, seven chiefs and their armies, and twelve limits of the angle. Proof of this is given by the trustworthy witnesses: the universe, the year and the person [soul]. To each applies the rule of ten, three, seven and twelve and their correspondents: the sphere, the Dragon and the heart. [Chapter One, 4].

I translate "fathers" [avot] as "mothers", for as I have previously stated, the words: fathers, mothers, principals, materia prima, initial substance, etc. all have the same meaning. I translate the word "kobeshin" as "chiefs" because they conquer countries, as it is said: "And shall consume the earth before the Eternal," [Deuteronomy XXXII, 22]. Elsewhere it is said: "of all the nations which he had subdued," [II Samuel VIII, 11]. I translate the words "g'vulei alakson" as "limit of the angles" because this is the sense of the words frequently found in the Talmud. There it is said: "every cubit forms a cubit and two-fifths in diagonal" [Baba Batra, 101 b]. This means that the diagonal is one and two-fifths cubits in every square with a simple side of one cubit, though this is not quite correct. The exact measure of the diagonal is the square root of two.

Tali [Tav-Lamed-Yod]can be defined as the dragon. I understand this to be the place where two orbits intersect [the orbit of the sun and the orbit of the moon] like the equator and the sun's orbit. Actually, the circle of the sun's orbit is inclined twenty-three degrees and a fraction to the circle of the equator. When we suppose that the two orbits are aligned, they necessarily intersect at two opposite points. One of the two points is called the spring equinox and the other, the autumnal equinox. Just as the solar and lunar orbits intersect one another at two opposite points (each point called "dragon"), one of these points is sometimes called the head, and the other, the tail. This explains the origin of the dragon's name. It is not a constellation resembling a dragon or any other creature. "Dragon" refers to the coils and curves which it forms when one sphere is positioned in the north and the other in the south. The Hebrews have given it a similar name, since it is said: "By his spirit hath he garnished the heavens; His hand hath formed the crooked serpent...."


5. On the Geometrical "Whirlwind" of the Hebrew Letters:

"The ten closed numbers are ten and not nine, nor eleven; understand in wisdom and ponder them in intelligence; know, reflect and believe; situate the thing according to its evidence and establish the Creator according to its quality. The numbers correspond to ten infinities, whose beginning flashes like lightning; but one finds no end to them when searching for their limit; and the decree of the Creator made them like angels who ran and returned; and they pursue his decree like a whirlwind, and it is as if they would prostrate themselves before his throne."[Chapter Two; 1.]

Of the two statements which follow the three propositions, the first is: "His decree is with them, and they ran and returned." The author's meaning is that every time the numbers arrive at ten, they return and begin again eternally and without limit for us, as it is also said of the angels: "And the living creatures ran and returned as the appearance of a flash of lightning" [Ezekiel I, 14]. They return and then depart again, and it is as if they had been stationary, as it is said: "Canst thou send lightnings, that they may go, and say unto thee, here we are?" [Job XXXVIII, 35]. They have faces on all sides, and thus it is said: "And behold, the angel that talked with me went forth, and another angel went out to meet him," [Zechariah II, 3]. It is not said that the angel appeared "behind him" because the angel presents a face every direction it turns. Like the numbers, the letters also always repeat themselves, following and succeeding without an end for us.

The second of the two statements is: "And they pursue his speech like a whirlwind." The author's intention here is to emphasize how the letters and numbers are formed in the air. He says that the whirlwinds describe figures and forms in the air, and though they all differ, they are still all circular. Among their material forms, some are more oblong, others combine circle and square, others combine circle and triangle, some are composed of superimposed spheres, and still others are composed of interpenetrating spheres. All of these are types of whirlwind. This analogy explains how the letters and numbers are formed and have sprung into the air; and this is why it is said: "The Eternal hath his way in the whirlwind and in the storm," [Nahum I, 3]; and also: "For behold, the Eternal will come with fire, and with his chariots like a whirlwind" [Isaiah LXVI,15]. Ezekiel demonstrated this with respect to the ophanim and the hayyot; the circles [or 'wheels'--trans.] interpenetrate like tubes within tubes. The same thing can be said for the junction of whirlwind within whirlwind and tempest within tempest. Thus it is clear that God - be He celebrated and exalted - has revealed the lights of the hayyot and the ophanim which have circular forms. The prophets were also shown winds which have the same circular forms, as it has been said: "Then the Eternal answered Job out of the whirlwind" [Job XXXVIII, 1], and elsewhere: "out of the whirlwind" [Job XL, 6]. If one has properly comprehended the formation of the letters in the air, this will not seem difficult. As for the saying: "They prostrate themselves before His throne," [it only alludes to the numbers and letters obeying him and executing his decrees. The word "prostrate" should not be understood in the literal sense....


6. On the Rotation of the Letters and the Zodiac:

"When we say that it is by means of these media that the Eternal, Master of hosts, God of Israel, Living Elohim, Almighty, Sufficient, Noble and Sublime, Dwelling in Eternity, Holy Be His Name has traced the twenty-two letters according to the construction of the sphere, we refer to the sphere's rotation which displaces to the rear what was positioned to the fore. It is the same with the letters when one inverts them, putting to the rear what had been at the fore. Proof of this is demonstrated when one says 'oneg' ['delight'] which is something desirable, and when one says 'nega' ['plague'] which is something detestable: the letters are the same, only inverted."

This verse is the pivotal point of the book, namely that the Creator - Holy Be His Name - has so disposed some of the letters and numbers to create a kind of body. Later He transposed their positions in order to create a body different from the first. The author gives us two comparisons drawn from the rotation of the sphere and the rotation of the letters. More examples could be adduced, but we will begin with these two. If the three letters : Het, Tsadeh and Resh are combined, their meaning in this order is "courtyard." If we change the position of the Tsadeh and Resh, pronouncing the word harats, its meaning becomes "to cut." If we combine the letters in the order of Resh, Tsadeh and Het, which is pronounced retsah, the meaning is changed to 'murder'. If we combine the letters in the order of Tsadeh, Het, and Resh, this is then pronounced tsohar and means "whiteness". These four words are examples of the same letters used in different order. Sometimes the different ways of combining letters do not have a significance. If the letters Qof, Shin and Resh are combined in this order, they signify qashar, "to bind." If they are recombined in the form of Qof, Resh and Shin, or qeresh, the meaning is "beam." The same letters combined as sharaq means "hiss," and the combination of Resh, Shin and Qof is pronounced reshaq and means "happiness". There is, however, no meaning to the combination of Resh, Qof and Shin in this language. A word with four letters multiplies the number of possible combinations just as a word with five letters multiplies them even more so.

It is especially clear to anyone versed in the science of the sphere's revolution. When the sphere turns the measure of one zodiacal sign, diverse figures result which bring a corresponding influence into play, according to the data of this science. Let us examine the represented image of the sphere for this present day, which is Tuesday, the twelfth of Sivan in the year 1242; the Sun was at the 7 of Gemini, the Moon at the 2 of Scorpio, Saturn at the 14 of Capricorn, Jupiter at 25 of Pisces, Mars at 40 of Pisces, Venus at 25 of Cancer, and Mercury at 20 of Taurus. If we begin our work in the first and second hours of the day, the most powerful luminaries in the celestial sphere are the Sun at the horizon and Jupiter and Mars since they are both in the middle of the sky. The four other planets are hidden since Venus is in the 2, the Moon in the 6, Saturn in the 8 and Mercury in the 12. Everything under the influence of the first three is strongly effected because their light falls on the horizon. The influence from the four other planets is weak because the horizon does not receive their light. If we do our work during the third and fourth hours of the day, the celestial sphere has already turned one sign. Cancer is on the horizon, the Moon is at the 5, Saturn in the 7, Jupiter and Mars at 9, Mercury at 11s. The influence of each of them depends upon its force from its position. If we do our work during the fifth and sixth hours of the day, two signs have turned and Leo is on the horizon. The powerful luminaries in the sphere are the Sun because it is in the 11, Mercury at 10, and the Moon at 4. As for Venus, Saturn, Jupiter and Mars, they are all hidden, and those under their influence will feel their effect. If we conduct our work during the seventh and eighth hours of the day, a quarter of the sphere will have turned, Virgo will be at the horizon and none of the planets will be hidden. The Moon will be at 3, Saturn at 5, Jupiter and Mars at 6, Mercury at 9, Venus at 11. In this case, all the influences compliment one another. If we are working in the ninth and tenth hours of the day, one animal of the sphere will have turned. Scorpio will appear along with the Moon, and the sphere will take another form according to its revolution. The influence of the rays, the horoscope and other astronomical conditions are subsequently transformed as the sphere revolves. Fixed stars, changing stars, and stars which have two bodies likewise demonstrate this transformation during each quarter of the day (which begin anew each six hours). I have drawn out these examples only because the author has stressed them by saying: "the sphere turns forwards and backwards."


7. On the Ethereal Realm and its Relation to Prophecy:

The Holy Scriptures call the second, more tenuous air Kavod ["glory"], as it is said: "the whole earth is full of His glory" [Isaiah VI, 3]; and God Himself has declared: "But as truly as I live, all the earth shall be filled with the glory of the Eternal" [Numbers XIV, 21]. The people call him Shekhinah ["dwelling" or "abode"] as it is said: "And the glory of the Eternal abode" [Exodus XXIV, 16], and elsewhere: "that glory may dwell in our land" [Psalms LXXXV, 9]. The author of our book has called Him "breath of the Living God" as it is said: "And my spirit will remain in the midst of thee, that thou fearest not," [Haggai II, 5]. Via this second, tenuous air, the word of prophecy was delivered, as it is said: "The Spirit of the Eternal God is upon me" [Isaiah LXI, 1]. It is also via this second, tenuous air that all the visible miracles appeared to the prophets, as it is said: "in a vision by the Spirit of God" [Ezekiel XI, 24]. This is evidently a created thing, for everything outside the Creator - may His Name be exalted! - is a created thing, as it is said: "there is none other beside Him" [Deuteronomy IV, 35]. By way of this second, tenuous, but created air, which is in the world as life is in man, the created word heard by Moses in the visible air has been produced along with the decalogue heard by our fathers. This has been called: "voice of the living God" [Deuteronomy V, 26]. Through the voice of the living God, the seven qualifications of the voice of the Eternal were spoken. From this second air comes the knowledge of wisdom, which God bequeaths to distinguished men, as it is said: "And the spirit of the Eternal shall rest upon him, the spirit of wisdom and understanding, the spirit of council..." [Isaiah XI, 2]. From this knowledge come the faculties of courage and bravery, which God grants to whomsoever He will, as it is said: "Then the Spirit of the Eternal came upon Jephthah" [Judges XI, 29] and: "But the Spirit of the Eternal came upon Gideon" [Judges VI, 34]. For this reason, the author of our book has given "life of the worlds" as the first name.

As for the sense of the words: "whose throne is fortified from the beginning," this means that the second, tenuous air is for God - may He be celebrated and exalted! - just as the throne, by comparison, is for the king. Thus it is said: "The Eternal hath prepared His throne in the heavens; and His kingdom ruleth over all," [Psalms CIII, 19]. This is the reason why the Tabernacle has been called His throne, according to the verse: "they shall call Jerusalem the throne of the Eternal" [Jeremiah III, 17].

As for the meaning of the words: "blessed and whose name is blessed" this is a general appellation for the light which enters the visible air of the entire world below, as it is said: "And blessed be His glorious name for ever: and let the whole earth be filled with his glory" [Psalms LXXII, 19]. This object is also what the Wise have called "Ruach Ha-Qodesh" ["Holy Spirit"]. Actually, after the prophecy had disappeared, a light appeared to them as if it were reflected by a mirror, and they heard a voice like an echo, that is to say that the desert reverberated it to them, and this has been called "Bath Qol" ["daughter of the voice"], which means child by the voice. With regard to this, Scripture has said: "And thine ears shall hear a word behind thee, saying. . . ." [Isaiah XXX, 21]. Scripture has not said: ["before thee"].

The author of our book says that this concept was the first created thing, and it is the most tenuous thing in existence, but also the strongest. This is followed by the visible air where the Creator has formed the ten numbers and the twenty-two letters.


8. On the Geometry of Phonetics and the Order of the Alphabet:

The twenty-two letters are three principals, seven doubles, and twelve simples, which are cleaved in the air, traced by the voice and situated in five places in the mouth. They have divided themselves into five sections: (1) Alef, He, Het, Ayin are pronounced at the extremity of the tongue with the uvula; (2) Bet, Vav, Mem , Peh are pronounced with the lips touching and with the tip of the tongue; (3) Gimel, Yod, Kaf, Qof are articulated with the side of the tongue; (4) Dalet, Tet, Lamed, Nun, Tav with the middle of the tongue; (5) Zayin, Shin, Samekh, Resh, and Tsadeh are pronounced between the teeth with a quiet tongue [Chapter Four, 3].

According to the different locations in the mouth necessary to articulate them, there is also a difference between the letters as they are traced into the air. Thus the author has said "cleaved in the air," "traced by the voice". The voice traces the letters, dispatches them through the air, cleaves and orders them. The group Alef, He, Het and Ayin [ahacha] is the more delicate and produces a straight line in the air. This is followed by Gimel, Yod, Kaf and Qof [gikhaq], which produce either unequal or equilateral triangular figures in the air according to their motion. This group is followed by Dalet, Tet, Lamed, Nun, Tav [datlanat] which produce square figures, either simple or complex according to their movement. Then follows Zayin, Shin, Samech, Resh, and Tsadeh [zshosrots] which produce oblique figures, some right angled, others acute or obtuse according to their movement in the air. Finally the letters Bet, Vav , Mem and Peh [bumaph] produce spherical forms in the air according to the force of their pronunciation, some being simple and others more complex. The author has enumerated the group [bumaph] after [ahacha] because Bet is the second letter of the alphabet. He who first established the alphabetical sequence, situated Bet towards the beginning to separate these five different letter groups, and to prevent their combination, as well as to eliminate any difficulties for students and children in pronouncing the letters. Actually, the composition of words with these twenty-two letters usually combines only the letters corresponding to the different vocal organs. Two letters which belong to the same letter grouping are very rarely combined with one another. Thus Zayin and Shin never appear next to each other in the Hebraic tongue; nor do Samech and Shin; nor Kaf and Gimel; nor are Dalet and Tet coupled in the same word. I have already explained this in the first of the grammatical books. ...


9. On the 231 Gates of Letter Permutation:

When He traced, cut, multiplied, weighed and inverted the twenty-two letters, He created everything which has been created, and everything which will be created in the future. How did He multiply them? Aleph [] with each of the letters and each with Alef, Bet with each one and each one with Bet, and the same for Gimel. He turned and inverted them all, and formed the totality of 231 words. All the creatures and all the words cannot exist without another being above them. [Chapter Four, 4].

I have translated the words "hozerot halilah" as "they turn in a circle and invert themselves" because every hollow thing is so called in the Hebrew language. The words "n'vuv luhot" ["hollow with boards," Exodus XXVII, 8] are written as "halil luhin" in the Targum. Concerning the orifices of the body, it is said that: "God has created in it many holes and cavities" [Berakhot 60 b]. In paraphrase, the Targum has likewise said of the king of Tyre: "But you have not considered your body which has been made with cavities and holes which are indispensible" [paraphrase of Ezekiel XXVIII, 13]. Similarly, the totality of air in the world is called "hollow of the world" because it always revolves [circulates].

This passage is sometimes misunderstood to say: "They are found to exit through two hundred twenty-one gates," and this is incorrect. Though we have learned that calculation demands that this number total two hundred thirty-one, the only number that I have seen written is "two hundred twenty-one." I have no doubt that this is an error. A similar mistake can be found in the Four Gates: "every Tishri of an embolismic year which begins before 695 parts of the twelfth hour." Now, in all the texts I have found "the 11th hour" written instead of the twelfth, but this is an error. If you add the surplus of two years, one of which is an embolismic year, the new moon will be at exactly five o'clock on the Sabbath, but it must be at exactly six o'clock. It will not be at six, however, unless the twelfth hour is set as the starting point. Analogously, in response to our author's question, "How did he multiply them," it is correct to give the number two hundred thirty-one as the answer. I will explain this in accordance with the principle which the author himself applies: "Alef with all the letters and all with Alef, Bet with all and all with Bet," etc. This kind of multiplication can be found in the cities of Palestine and Egypt. The children write this in order to learn how to spell, and these are the twenty-two series which are called rows [files]. The first row is Alef-Alef, Alef-Bet, Alef-Gimel, Alef-Dalet, Alef-He, Alef-Vav, Alef-Zayin, up to Alef-Tav. The second row is Bet-Alef, Bet-Bet, Bet-Gimel, Bet-Dalet, Bet-He, Bet-Vav, Bet-Zayin up to Bet-Tav. The third row is Gimel-Alef, Gimel-Bet, Gimel-Gimel, Gimel-Dalet, Gimel-He, Gimel-Vav, Gimel-Zayin up to Gimel-Tav. It is the same for Dalet-Alef, He-Alef, up to Tav-Alef, Tav-Bet, Tav-Gimel etc., up to Tav-Tav. In all, this amounts to twenty-two multiplied by twenty-two or four hundred eighty-four. Of this total, twenty-two words must be subtracted which are not products [of one letter with another], namely Alef-Alef of the first row, Bet-Bet of the second row, Gimel-Gimel of the third row, Dalet-Dalet of the fourth row, and so on up to Tav-Tav of the twenty-second row. The reason for this subtraction is as follows: if Dalet is combined with Dalet, for example, it simply produces the same figure in the air and a single word in the verse, and they remain in their original state when they are inverted. Once we have subtracted these twenty-two [duplicates], we are left with four hundred sixty-two. Of these four hundred sixty-two, however, only a half are actually different sets of pairs. The pair Alef-Bet in the first row is like the pair Bet-Alef in the second row; Alef-Gimel in the first row is like Gimel-Alef in the third; Alef-Dalet in the first is like Dalet-Alef in the fourth, and so on for each of the series. One therefore discovers that one half of the letters simply reproduces the other half, and thus it is said: "And they all turn in a circle" because they turn into their reverse. When one subtracts half of the four hundred sixty-two, the remainder is two hundred thirty-one. Thus we have said: "The letters are found to exit through two hundred thirty-one gates". A person can make visible sense of this simply by calculating with coins or by writing rows of letters and counting them.

I have heard that a commentator on our book has kept the mistake of two hundred twenty-one gates. He has attempted to justify this error by saying that the total of Alef-Alef, Alef-Bet, Alef-Gimel, Alef-Dalet and so on is only twenty-one since Alef-Alef is not multiplied [combined] and Alef revolves only around itself. This commentator then multiplies these twenty-one by ten, i.e., the ten numbers, and this amounts to two hundred ten. Then he adds the ten numbers and Alef, which is the first unity, and this amounts to two hundred twenty-one. But - may God have mercy upon thee - this is a concatenation of a tissue of errors, all due to the fact that the commentator does not know how to multiply. We can cite five reasons why his explanation is in error: (1) he has multiplied Alef with all the letters but not all the letters with Alef. Later on he repeats this mistake by failing to multiply Bet with all or all with Bet, and the same with the other letters. He has only multiplied Alef with all; (2) he has multiplied the sum of Alef with all (i.e., twenty-one) by ten, but there is no reason to multiply by ten. The author of our book has not given this direction. He has only directed the inquirer to multiply the letters, and he says "Alef with all" and "Bet with all". He has not mentioned the ten numbers in this section. The commentator has thus neglected this direction and has done what was not directed at all; (3) he has separately added the ten numbers to his product, but this is the chapter on multiplication and not abstraction. Were this the chapter on abstraction, one would add the twenty-two isolated letters, and this would then amount to two hundred forty-three; (4) the commentator has omitted the double Alef without multiplying it by ten, and therefore must add the isolated Alef, but there is no reason for this procedure; (5) this commentator's book also contains the phrase: "and they all turn in a circle." Now if the letters are multiplied one by another, they do turn in a circle, but they do not turn in a circle if they are merely multiplied by ten. With that said, I should like to know what remains of this commentator's argument to be defended.

Our author's purpose in this chapter on multiplication is to demonstrate that the Creator - may He be exalted! - by composing these twenty-two letters through the five procedures of tracing, carving, multiplying, weighing and transposing has created all that has been and will create all that will exist in the future. Actually, when He traced straight lines through the circumferences, triangles in the squares, and drew oblique lines in these circumferences, triangles and squares, the results were surfaces and volumes folding in upon one another according to these marvelous methods which create all forms. This is by the penetration of the Bet in the Gimel, the Dalet in the He, etc. For this reason, the pairs Alef-Alef, Bet-Bet,Gimel-Gimel, Dalet-Dalet up to Tav-Tav do not enter into such multiplication. If you say Alef one hundred times, it only results in a single form in the air, namely a straight line. And if you speak Bet a hundred times, you will only trace a single circular form repeatedly. This explains the creation of the letter forms in the air. However, we can only establish this form in our spirit. We will not be able to realize this form because it belongs to the Master of the worlds - may He be praised and exalted! The wise, therefore, first teach their students mathematics and geometry, for these are the origin of knowledge.


10. On the Crowning of the Letters:

The reference to each letter, "and He attached a crown to it" conforms to an ancient principle - of happy memory! One tradition of the letters is that they have been revealed with ornaments and crowns, as it is said: "Seven letters necessitate three adornments: Shin, Ayin, Tet, Nun, Zayin, Gimel and Tsadeh" [Menahot 29 b]. It is the same for each letter. For some letters, these adornments augment and for others they restrain the deductions drawn from them, as The Book of Crowns has explained. The ancients also had the tradition that when the crowns are not carefully written in the Torah, it is forbidden to pronounce benedictions upon it, and it is not permitted to read it in public. For this reason, they say that one who hastily rushes through it will not live long. The ancient amulet makers say that the letters are worthless if they have not been written with their crowns. Similarly, our author says that it is not possible to form the triangular, square, folded, chain-formed, or convex figures (which the letters were meant to form) without a crown. He says, therefore, that "He attached a crown to it".