I do not understand "quantum algebra." It posits that the outcome of equations differs according to the order in which they are performed. By way of an oversimplified example, 3x8 is not the same as 8x3. The order of the computation changes the outcome. For the counterintuitive details, consult In Search of Schroedinger's Cat, by John Gribbin.
I bring this up to show that order is a subject of great importance in many disciplines.
A few weeks ago, on the first day of Rosh Hashanah, Rabbi Yaakov Meyer of Denver made a small comment that raises a big question: Does order make a difference in the Torah (Bible), too? For example, in lists of constellations in the zodiac, is there any significance to which comes first? In the command to "honor thy father and thy mother," the father is listed first is this an accident? Did Jacob really cheat Esau out of his birthright, or will an examination of word order reveal a different transaction?
Rabbi Meyer observed that the order of praises of G-d is changed on Rosh Hashanah, with significant implications. A preface to one segment of the morning prayer, "Yishtabach," contains four praises of G-d.
Each of the four praises contains three words.
Picture this as a cross word puzzle.
Spell out each three-world praise of G-d horizontally. Then line up each three-world praise one on top of the other.
The first word in the first praise of G-d occupies the square directly above the first word of the second praise, in the square below. Doing this with all four praises, we get 12 squares three squares across, in four rows.
Just as in a cross word puzzle, we can make new words reading from top down.
On the Sabbath, reading from top down, the first letter of the second word of each three-word praise spells "Isaac" (in Hebrew).
On Rosh Hashanah, Rabbi Meyer observed, the third word in each praise is rearranged so that reading from top down, it now spells "Rebeccah" (in Hebrew).
Isaac's wife's name appears highlighted alongside his own.
This is the point, said Rabbi Meyer: In this week's Torah portion, both Isaac and Rebeccah prayed from deep distress. They were childless. Isaac prayed abundantly that his barren wife conceive; so did Rebeccah (Gen. 25:21, Rashi).
Both were answered.
On Rosh Hashanah, the order of the praises of G-d is rearranged to highlight the power of prayer on the holy day.
This message about prayer and Rosh Hashanah is delivered strictly by the order of the words, through a crossword puzzle effect. Order is a subtle, elegant way of making a difference.
The constellations in the Zodiac are instruments of G-d's will. The use to which G-d puts two constellations, Pleiades and Orion, is revealed by the order in which they are mentioned in Biblical verses.
Pleiades is the source of cold in the world; Orion is source of heat in the world. In Amos 5:8, Pleiades (kimah) is mentioned before Orion. In Job 9:9, Orion (kesil) is mentioned before Pleiades. The Talmud (Berachos 58b) says that this means that G-d uses each constellation to balance the other. Pleiades keeps Orion from boiling the world to death; Orion keeps Pleiades from freezing the world to death.
Exodus 6:26 reads: "This was Aaron and Moses to whom G-d said: 'Take the children of Israel out of the land of Egypt according to their legions.'" Note: Aaron, the future High Priest and Moses' older brother, is mentioned before Moses. In other verses, Moses, the leader of the Children of Israel, is mentioned before Aaron. Rashi, the foremost commentator, comments:
"There are verses in which Aaron is mentioned before Moses and there are verses in which Moses is mentioned before Aaron. This tells you that their importance is equal."
Two verses that record the duty to honor and revere one's parents reverse the order of the parents. The fifth commandment: "Honor your father and your mother" (Exod. 20:12). Elsewhere, however; "Every person, you shall revere your mother and father" (Lev. 19:3).
The duty to "honor" one's parents places the father first. The duty to "revere" one's parents places the mother first. Why?
The Talmud (Kiddushin 30b) says: Honoring one's parents is to feed them, to dress them; generally, to take care of their physical needs. Revering one's parents is not to sit where they sit, not to contradict what they say; generally, not to detract from their stature.
In the command to honor one's parents, the father is listed first. This is because the natural instinct is to honor one's mother more than one's father; therefore, the verse lists the father first, to teach that honor is due to one's father just as much as to one's mother.
In the command to revere one's parents, the mother is listed first. This is because the natural instinct is to revere one's father more than one's mother; therefore, the verse lists the mother first, to teach that reverence is due to one's mother just as much as to one's father. Order in the verses teaches major lessons.
A big thorn in the side of ethicists who root their teachings in the Torah is this question: In this week's Torah portion, how could Jacob withhold food from Esau as he comes back from the field famished? Esau says he will die of hunger, so he sells his birthright to Jacob. Where is the ethics in Jacob's wresting the birthright by holding over Esau the threat of hunger?
The biblical text seem to make it perfectly clear that this is just what Jacob does. First, Esau asks for food (Gen. 25:30). Then Jacob asks for Esau's birthright (25:31). Then Esau sells the birthright to Jacob (25:33). Only then does the Torah record: "And Jacob gave Esau bread and lentil stew" (25:33).
As Avigdor Bonchek points out, translations err when they write, "And Jacob gave Esau bread . . ." It's easy enough to make the mistake. The Hebrew seems to read, And Jacob gave bread; subject, verb, object. However, Biblical Hebrew has no way of expressing the past participle other than word order. "He had given" cannot be said in Hebrew, only "he gave." How, then, does Hebrew indicate, "He had given"? By a subtle change in word order. When the Hebrew wants to indicate the past tense, it writes the verb before the subject, literally "And gave Jacob" (va-yiten Ya'akov). But when it wants to indicate the past participle, its word order is, literally "And Jacob gave" (ve-Ya'akov nasan), meaning, "And Jacob had given."
Meaning, in our context: "And Jacob had already given Esau bread and lentil stew" when they were negotiating over the birthright. Jacob was not holding food over Esau's head, coercing him to surrender his birthright. Esau did so of his own free will. This explains the concluding phrase of their exchange, "And Esau had despised the birthright" (25:34).
The same distinction in word order is found elsewhere in Genesis. "Now Rachel had taken the terafim idols" (subject, verb, ve-Rachel lakchah, Gen. 31:34); "And Adam had known his wife Eve" (subject, verb, ve-ha-adam yada, Gen. 4:1), reflecting the past participle; and "And Isaac entreated G-d" (verb, subject, va-ye'tar Yitzhak), reflecting the past tense.
In the Torah, word order makes a big difference indeed.