Osnat Youssin
Hebrew magic: The Priest, the Scribe, (the prophet) and the woman. As seen in the Hebrew Scriptures through mathematical number theory.1 Abstract: Perfect numbers appear in Scriptures either plainly or encrypted as gematria – numerical value of the word/sentence. Why this symbolism? How could be that the gematria
1
Oil painting on cover is reproduction of “New Moon Prayer “ by O.Youssin
appears before Hellenism – as usually accepted time for this method? The sequence of perfect numbers can be used as decoding sequence in Scriptures, which brings us somewhere – to the curse of Eva, to the lost and found Torah book. Greek-Jewish antagonism. We argue that perfect numbers in early traditions – had double meaning of perfection and curse, especially related to women, and that that tradition was overcome and ceased to exist – and the curse no longer was attributed to women – in later times. Subject matter: Judaism, Hebrew, mathematical linguistics Keywords: Hellenism, gematria2, perfect numbers, bible, encryption Other important words: life, death, perfection, beauty, temple, Sabbath, sanctity Hellenism, gematria, sofrim3, perfect numbers.
2
Gematria – from Greek, is the numeric value of the
world, calculated as sum of numeric values of Hebrew letters, see Liberman “Hellenism” on use of gematria and “Tikkun sofrim” – corrections of the scribes. According to Wikipedia - (http://en.wikipedia.org/wiki/Gematria )”The first attested use of gematria occurs in an inscription of Assyrian ruler Sargon II (727–707 BCE) stating that the king built the wall of Khorsabad 16,283 cubits long to correspond with the numerical value of his name.”
3
Scribes, who wrote (and still write) Torah scrolls on permanent
– without vowels or musical – liturgical signs. First it was written in
Let’s begin by introducing a notion of perfect numbers, a special numbers, which play important role in mathematical Number theory. The perfect number is a number, that the sum of its dividers is equal to it. The first perfect number is 6=1+2+3, the second 28=1+2+4+7+14, and the third 496. The question whether there are odd perfect number remains an open problem to this day, there are also several other open questions concerning those numbers.4
antique “Ashurit” script, which was changed later to the Hebrew script (see tractate Sofrim), the same script is used in Israeli modern press. See also 4
In fact, the writer of this article does not know of any other
perfect numbers except in the form p-1
2
p
*(2 -1) p
Where p is a prime number and 2 -1 is also prime, which is to say -does not have any dividers with exception of 1 and itself. For an introduction to elementary number theory see any introductory course. According to the theorem of Euclid, any number can be shown as multiplication of powers of some prime numbers in unique way, for 3
4
2
1
3
2
example 24=2 * 3, 360=2 * 3 * 5 , 1960=2 * 7 * 5 q1
q2
and in general X=P1 * P2 * P3
q3
1
qn
* …* Pn
Where P1, P2... Pn are prime numbers and q1,q2...qn –natural numbers. There is a Euclid’s Algorithm for such a form, which is called factorization. It takes long to find all prime dividers of very big integers. It is why some forms of cryptography use factorization as an encryption method. It is why it will be not so unusual for the sages and sofrim(sofer actually means “scribe”, but literally – somebody who counts, as sofer Torah was usually counting words, letters, verses and, perhaps also gematria, out of habit seeing letters also as numbers.
Number Letter 1
א
2
ב
3
ג
4
ד
5
ה
6
ו
A few years ago there was a (mathematics) internet site, promising 100K $ for finding a next perfect number (from some mathematical fond), which would be really very big, millions of signs, by using combined calculative power of computer networks and sophisticated algorithms. So, perhaps, fascination with perfect numbers is not so unusual for modern times also, though it is difficult for me to understand immediate use of those numbers, rather – of algorithms to find them, which, as is easy to see, are algorithms of quick factorization, which, as I said, is used today in cryptography, but perhaps will be not used in future if quantum computer will replace the common one. Here is analytic version of generalization of perfect numbers. Theorem Let’s define σ(n)=Σd(d divides n, including 1 and n itself). Let’s study function f(n)= σ(n)/n, Obviously f(n) = 2 for perfect n. 1.prove, that f(n) is not limited when n→∞ 2. prove, that f(n) is dense everywhere 3. What values f (n) takes and does not take?
ז
7
ח
8
ט
9
י
10
כ
20
ל
30
מ
40
נ
50
ס
60
ע
70
פ
80
צ
90
ק
100
ר
200
ש
300
ת
400
ת"ק
500
ת"ר
600
ת"ש
700
ת"ת
800
900 תת"ק
Gematria (from Greek) is sum of numerical values of Hebrew letters, which correspond to an order of
1000 תת"ר
alphabet. Tanaim were interpreting words according to their common gematria usually as means of
entertainment or for better remembering of things. Gematria was known at least from time of Tanaim 70-200 CE: Mishnah in Pirkei Avot 3:235 Rabbi Eleazar Chisma said: the laws of mixed bird offerings and the key to the calculations of menstruation days—these, those are the body of the “halakhah”6 . The calculation of the equinoxes and gematria are the desserts of wisdom. .
. תקופות וגמטריאות פרפראות לחכמה. קנין ופתחי נדה הן הן גופי הלכות,רבי אלעזר בן חסמא אומר 6
Jewish religious Law
5
Perfect numbers in Jewish tradition Perfect numbers were known, for example, to Philo from Alexandria, the Jewish-Hellenistic philosopher from 2nd century. In his allegorical commentary to the book of Genesis he writes, that the 6 days of creation were not necessarily 6 days, but is just allegory for perfection, as the number 6 is perfect, which means - the creation is perfect. God had celebrated the perfection by sanctifying the seventh (Kiddush Sabbath) – plus than perfect day, as do we in His steps. Let's first assume that Philo is right and let's see if there is any significance to next perfect numbers... The next holiday (which occurs more often than others) and the first commandment given to Israel as the newly emerging nation, in the book of Exodus is Rosh-Hodesh, the New Moon holiday, which happens about every 29.5 days,
the exact phase calculated already in tractate RoshHashanah. The New Moon is sanctified by the people of Israel (Kiddush levana) from ancient times (Exodus). Actually, it is considered to be the first “mitzvah” commandment – given to Israel (not counting 1-2 commandments in the book of Genesis) to observe the moon and sanctify it (at the beginning of its phase). The holiday was celebrated in ancient times in much more festive way, with additional Temple services, one or two days, leaving exactly 28 days of the rest of the month, which is a perfect number. The other cosmic event related to number 28 is “blessing of the sun” (“Birkat haHama”), which is first mentioned in Baraita brought in Babylonian Talmud. Sabbath does not depend on whether Israel keeps or sanctifies it. In contrast, It is rather Israel who sanctifies the “astronomical” events and objects. The sanctification is final; it does not matter whether the accounts were precise or wrong. So many consider the blessing of the sun be a rather symbolic event, which gives an opportunity to bless it. As in IQ test, we can try to find the allegory of perfect number as we understand it in Modern Judaism (some people could try it in Christianity). Is there any holiday associated with number 496 (next perfect number) or 497? As Jewish holidays are based on lunar-sun cycles and 365.25 (number of days in the year) is
far from 496, it seems, there was no such holiday. 7 So, let's see, when else there is sanctifying (K D SH)? In modern Judaism the next best guess is – marriage, to be precise – a woman is “sanctified” (meKuDeShet). The New Moon prayer, which is recited by men alone, resembles – in some aspects, of course - the sanctifying of woman, as the Moon is obviously feminine, her period is exactly this as woman’s and the men promise to avoid touching it and sanctify her exactly as if it was a woman. There is no “sanctifying” in the blessing of the sun; “haHama” obviously is associated with the masculine. Marring a woman involves the act of sanctifying also, but it is not usually associated with any perfect number. Sabbath could also be considered feminine, the ‘bride’, though this association appears much later with the kabalistic nuances. 496 As the next perfect number 496 is not easily found in Bible, we can try Jewish numerical methods to find uses of it. For example – gematria 8
7
There is in fact 497=“HaSUKOT” and “SUKOTA” (first
station of Israel in the desert after exodus from Egypt), in full spelling, but it does not appear in (menukad) vocalized text, instead it appears in full text in Exodus 12:37: And children of Israel moved from Raamses to Sukkoth, about 6 hundred thousand legs of men, not counting children. מאות אלף רגלי- כשש, סוכותה,ישראל מרעמסס-ויסעו בני לבד מטף,הגברים. 8
If you by accident have Bar-Ilan University’ “”שו"תים
The first time the gematria of a word equals 496=24 * ( 25 1) -first big enough perfect number encoded as gematria, is the word “VeYaFT” in the phrase “ אלוהים ליפת וישכן9ויפת “ ”"באוהלי שםGod enlarge Japheth, and he shall dwell in the tents of Shem ““ (Genesis 9,27). 10,2 The sons of Japheth: Gomer, and Magog, and Madai, and Javan…(Greece) This verse is usually understood as saying that the Greek Sciences are used – can find their place - in the religion of Jews. So it would be perhaps no wonder, if the Bible was using perfect numbers, or number theory, known to already to a Greek Euclid about 600 B.C.E. The verse can also serve as a reminder, that gematria appeared as Hellenism in Hellenistic period. If the gematria was not meant when the Torah was written, the words with gematria 496, if any, would be random – would have random meaning. In the theme of Abraham's trial in sacrifice of Isaac in Genesis , we see that המאכלת- “HaMAKeLeT”- the knife for sacrifice, used here as testing instrument of innocence of Isaac (according to modern Hasidic interpretation) in the life-death justice, have gematria of 496. Genesis 22:6-11
9
Actually the word translates as ‘and (he, she, you, I, we, they)
(worked, made, did) beautifully’ which could be understand as a Torah encouraging answer to a researcher – “you do nice”, because the word was find with the aid of the software, which hence could be seen as an Artificial Intelligence program, communicating with the researcher personally.
6 And Abraham took the wood of the burnt-offering, and laid it upon Isaac his son; and he took in his hand the fire and the knife; and they went both of them together. 7 And Isaac spoke unto Abraham his father, and said: 'My father.' And he said: 'Here am I, my son.' And he said: 'Behold the fire and the wood; but where is the lamb for a burntoffering?' 8 And Abraham said: 'God will provide Himself the lamb for a burnt-offering, my son.' So they went both of them together. 9 And they came to the place which God had told him of; and Abraham built the altar there, and laid the wood in order, and bound Isaac his son, and laid him on the altar, upon the wood. 10 And Abraham stretched forth his hand, and took the knife to slay his son. 11 And the angel of the LORD called unto him out of heaven, and said: 'Abraham, Abraham.' And he said: 'Here am I.' 12 And he said: 'Lay not thy hand upon the lad, neither do thou any thing unto him; for now I know that thou art a God-fearing man, seeing thou hast not withheld thy son, thine only son, from Me.' , ויקח בידו,יצחק בנו- וישם על,עצי העלה-ו ויקח אברהם את,כב ז ויאמר יצחק, כב. יחדו,המאכלת; וילכו שניהם-האש ואת-את הנה האש, הנני בני; ויאמר, ויאמר, ויאמר אבי,אברהם אביו-אל לו- אלהים יראה, אברהם,ח ויאמר, כב. לעלה, ואיה השה,והעצים המקום- אל,ט ויבאו, כב. יחדו, בני; וילכו שניהם,השה לעלה - ויערך את,המזבח- ויבן שם אברהם את,לו האלהים-אשר אמר ממעל,המזבח- וישם אתו על,יצחק בנו- את,העצים; ויעקד , לשחט,המאכלת- ויקח את,ידו-י וישלח אברהם את, כב.לעצים , ויאמר,השמים- מן,יא ויקרא אליו מלאך יהוה, כב.בנו-את ,הַ מַעַ ר-תִּ שְׁ לַח י ָדְׁ ָך אֶ ל- ַאל,יב ו ַי ֹאמֶ ר. הנני,אברהם אברהם; ויאמר ו ְֹׁלא,י ְֵׁרא אֱ ֹלהִּ ים אַ תָ ה- כִּי, כִּי עַ תָ ה י ָדַ עְׁ תִּ י: מְׁ אּומָ ה,תַ עַ ׂש לֹו-ו ְַׁאל . מִּ םֶ מִּי,י ְׁחִּ ידְׁ ָך- ִּבנְָׁך אֶ ת-חָ ׂשַ כְׁתָ אֶ ת And those are “TUMIM” and “HaMeARRIM”.
“TUMIM” first appears in relation to Rivka, who was caring twins, but have other meaning – as in “URIM” and “TUMIM” - the oracle used in first the Temple. “HaMeARRIM” bringing curse – describes the “bitter water” given in the Temple to the adulterous wife. Though different, both words have common meaning of a just judgment - a curse to the guilty and the blessing to the just. Both devices were attributes of Cohen and used in the first Temple. So, the similarity can hardly be random. Twins, tricking, adultery. Rivka and Tamar. 25,21 And Isaac entreated the LORD for his wife, because she was barren; and the LORD let Himself be entreated of him, and Rebekah his wife conceived. 25,22 And the children struggled together within her; and she said: 'If it be so, wherefore do I live?' And she went to inquire of the LORD. 10 25,23 And the LORD said unto her: Two nations are in thy womb, and two peoples shall be separated from thy bowels; and the one people shall be stronger than the other people; and the elder shall serve the younger.25,24 And when her days to be delivered were fulfilled, behold, there were twins in her womb. "( "וימלאו ימיה ללדת והנה תומים בבטנהGenesis).
10
Tumim”
The expression means usually asking God through “Urim and
Here “twins” is written in deficient form, so that its gematria is equal to 496, the word itself being the same as in “Urim and Tumim”. Perhaps the word “( ”תמיםwith aleph and vav omitted) alludes also to Jacob, who is called TaMIM – either perfect or timid. Rashi following Midrash says that Rivka went to the BeitMidrash (house of study) of Shem to ask. Possibly in Midrash Tumim number 496 is regarded not as perfect, but as kind of curse, that the gematria of 496 (of “TUMIM” as of “HaMeARRIM”-bitter OR cursed) is alluding to the curse, as a curse after the transgression of Eva (and curse of Adam as a result, too) in the sixth (and perfect) day of creation. There indeed was a sort of curse in twins of Rivka – it is why she went to house of study of Shem, which helps us seek explanation in ancient tradition coming from Shem=Malkizedek, the king of “Salem”, and he *is] Priest to the God Most High. Midrash seeks similar points in Rivka and Tamar, which can explain why both gave birth to twins. So it says, the scarf “ZʼIF” - of Rivka and Tamar signifies their double- faced behavior – tricking. The (possibly unconscious) line of thought, which links TUMIM with HaMeARRIM (both 496), continues to ask – how come Torah uses the cursed number with relation to her? Of course she was adulteress – she uses the scarf! Let’s examine the Torah passage in the book of Numbers (5) about a sota, a pervert woman, to whom the whole tractate is dedicated.
Sota – adulterous woman, the water and the Cohen11
ה,יא וידבר יהוה ,אל-משה לאמור .ה,יב דבר אל-בני ישראל ,ואמרת אליהם :איש איש כי-תשטה אשתו ,ומעלה בו מעל .ה,יג ושכב איש אותה ,שכבת-זרע ,ונעלם מעיני אישה ,ונסתרה והיא נטמאה; ועד אין בה ,והיא לא נתפשה .ה,יד ועבר עליו רוח-קנאה וקינא את-אשתו ,והיא נטמאה; או-עבר עליו רוח-קנאה וקינא את-אשתו ,והיא לא נטמאה .ה,טו והביא האיש את-אשתו ,אל-הכוהן ,והביא את-קרבנה עליה ,עשירית האיפה קמח שעורים; לא-ייצוק עליו שמן ,ולא-ייתן עליו לבונה--כי-מנחת קנאות הוא ,מנחת זיכרון מזכרת עוון .ה,טז והקריב אותה ,הכוהן;
והעמידה ,לפני יהוה .ה,יז ולקח הכוהן מים קדושים ,בכלי-חרש; ומן-העפר ,אשר יהיה בקרקע המשכן ,ייקח הכוהן ,ונתן אל- המים .ה,יח והעמיד הכוהן את-האישה ,לפני יהוה ,ופרע את- ראש האישה ,ונתן על-כפיה את מנחת הזיכרון מנחת קנאות היא; וביד הכוהן יהיו ,מי המרים המאררים .ה,יט והשביע אותה הכוהן ,ואמר אל-האישה אם-לא שכב איש אותך ,ואם-לא שטית טומאה ,תחת אישך--הינקי ,ממי המרים המאררים האלה .ה,כ ואת ,כי שטית תחת אישך--וכי נטמאת; וייתן איש בך את-שכובתו, מבלעדי אישך .ה,כא והשביע הכוהן את-האישה ,בשבועת האלה, ואמר הכוהן לאישה ,ייתן יהוה אותך לאלה ולשבועה בתוך עמך--
11
Oil painting reproduction “Sephardi woman” by O.Youssin
כב ובאו המים, ה.בטנך צבה- ואת,ירכך נופלת-בתת יהוה את ולנפיל ירך; ואמרה, לצבות בטן, במעייך,המאררים האלה ;בספר-- הכוהן,האלות האלה-כג וכתב את, ה. אמן אמן,האישה ,מי המרים- את,האישה- את,כד והשקה, ה.מי המרים- אל,ומחה כה ולקח הכוהן, ה. למרים,המאררים; ובאו בה המים המאררים ,המנחה לפני יהוה- את מנחת הקנאות; והניף את,מיד האישה -המנחה את-כו וקמץ הכוהן מן, ה.המזבח-והקריב אותה אל - את,האישה- והקטיר המזבחה; ואחר ישקה את,אזכרתה נטמאה ותמעול מעל- והייתה אם,המים-כז והשקה את, ה.המים וצבתה בטנה ונפלה,ובאו בה המים המאררים למרים--באישה לא נטמאה-כח ואם, ה. בקרב עמה,ירכה; והייתה האישה לאלה ,כט זאת תורת, ה. ונזרעה זרע,וניקתה-- וטהורה היא,האישה ,ל או איש, ה. ונטמאה, אשר תשטה אישה תחת אישה,הקנאות -אשתו; והעמיד את-וקינא את--אשר תעבור עליו רוח קנאה לא, ה.התורה הזאת- את כל, ועשה לה הכוהן, לפני יהוה,האישה } {פ.עוונה- תישא את, מעוון; והאישה ההיא,וניקה האיש 5,17 And the priest shall take holy water in an earthen vessel; and of the dust that is on the floor of the tabernacle the priest shall take, and put it into the water. 5,18 And the priest shall set the woman before the LORD, and let the hair of the woman's head go loose, and put the meal-offering of memorial in her hands, which is the meal-offering of jealousy; and the priest shall have in his hand the *1 water of bitterness that causeth the curse. 5,19 And the priest shall cause her to swear, and shall say unto the woman: 'If no man have lain with thee, and if thou hast not gone aside to uncleanness, being under thy husband, be thou free from this *2 water of bitterness that causeth the curse; 5,20 but if thou hast gone aside, being under thy husband, and if thou be defiled, and some man have lain with thee besides thy husband-- 5,21 then the priest shall cause the woman to swear with the oath of cursing, and the priest shall say unto
the woman--the LORD make thee a curse and an oath among thy people, when the LORD doth make thy thigh to fall away, and thy belly to swell; 5,22 and this *3 water that causeth the curse shall go into thy bowels, and make thy belly to swell, and thy thigh to fall away'; and the woman shall say: 'Amen, Amen.' 5,23 And the priest shall write these curses in a scroll, and he shall blot them out into the 5,24 And he shall make the woman drink the *4 water of bitterness that causeth the curse; and the *5water that causeth the curse shall enter into her and become bitter. 5,25 And the priest shall take the meal-offering of jealousy out of the woman's hand, and shall wave the meal-offering before the LORD, and bring it unto the altar. 5,26 And the priest shall take a handful of the meal-offering, as the memorial-part thereof, and make it smoke upon the altar, and afterward shall make the woman drink the water. 5,27 And when he hath made her drink the water, then it shall come to pass, if she be defiled, and have acted unfaithfully against her husband, that the *6water that causeth the curse shall enter into her and become bitter, and her belly shall swell, and her thigh shall fall away; and the woman shall be a curse among her people. 5,28 And if the woman be not defiled, but be clean; then she shall be cleared, and shall conceive seed. 5,29 This is the law of jealousy, when a wife, being under her husband, goeth aside, and is defiled; 5,30 or when the spirit of jealousy cometh upon a man, and he be jealous over his wife; then shall he set the woman before the LORD, and the priest shall execute upon her all this law. 5,31 And the man shall be clear from iniquity, and that woman shall bear her iniquity. {P} The water is called ‘sacred ‘first time, then 6 more times (perfect number) it is called HaMeAReRIM, which is 496 in
gematria. At first glance, it can be hardly an accident. But according to some linguistic researches (though mostly of English language) there is a certain predictability of word forms.12 However, that predictability, is in our opinion de facto, which is to say that without further research, we can postulate, that occurrence of certain words with gematria 496 will be 6 exactly in different Hebrew Bible books.
12
See for example. “Using probability distributions to account for recognition of cano nical and reduced word forms” Meghan Clayards, Centre for Research on Language Mind and Brai n, McGill University, Montreal, Quebec Canada, “Speech production and the predictability of words in context “,Frieda Goldman-eisler, The Quarterly Journal of Experimental Psychology, Volume 10, Issue 2 May 1958 , pages 96 – 106
Sarah . Sarah’s age at death, which is 127=27 -1 is basis of perfect number (because 27 -1 =127 is prime), which is
(27 -1) *26=8128
Rashi following Midrash says that Sarah was as beautiful as a seven year old. Which always presented some problem, and we left that as it was. But if beautiful as seven years old means just the same as 497 years old, at least we do not have difficulty in suspecting Rashi in nymphomania. Gematria of “XaIeI” (life of somebody) חייis 28, which is perfect, moreover, this word we met exactly 6 times in the Genesis -2 times in relation to death of Sarah (23:1), once in relation to death of Abraham(25:7) and Ishmael (25:17) and twice in relation to death of Jacob in Egypt (47:9). 13
13
In Exodus – three times in relation to death of Levi (6:16),
Kehat (6:18), Amram (6:20):
. מאה שנה ועשרים שנה ושבע שנים—שני,א ויהיו חיי שרה,כג חיי שרה חָ י-חַ יֵּי ַאב ְָׁרהָ ם—אֲ שֶ ר- י ְׁמֵ י שְׁ נֵי,ז ו ְׁאֵ לֶה,כה ו ְׁשֶ בַע,מְׁ ַאת שָ נָה ּושְׁ ֹלשִּ ים שָ נָה-- שְׁ נ ֵי חַ יֵּי י ִּשְׁ מָ עֵ אל,יז ו ְׁאֵ לֶה,כה עַ םָ יו- וַיֵָאסֶ ף אֶ ל,שָ נִּים; וַיִּ ְׁגו ַע וַיָמָ ת. ַ ְׁ י ְׁמֵ י שְׁ נֵי מ,פַ ְׁרע ֹה- אֶ ל,ט ו ַי ֹאמֶ ר י ַעֲ ק ֹב,מז שְׁ ֹלשִּ ים ּומְׁ ַאת,גּורי י ְׁמֵ י שְׁ נֵי חַ יֵּי- ו ְֹׁלא הִּ שִּ יגּו אֶת, הָ יּו י ְׁמֵ י שְׁ נ ֵי חַ יַי, מְׁ עַ ט ו ְָׁרעִּ ים:שָ נָה ֵ ְׁ בִּימֵ י מ,אֲ ב ֹתַ י. גּוריהֶ ם If we take into account complex relations of our forefathers with Egypt – Abraham and Sara's stay in Egypt in times of the famine, Sara' staying at Pharaoh, birth of Ishmael from Hagar- the Egyptian slave, Joseph's selling to Egypt and Jacob's ascending there, we can probably suggest that those occurrences are in fact Egyptian-isms. Isaac went never to Egypt. According to Jewish tradition, the Hebrew alphabet was given at revelation and Torah. How they were writing numbers prior to Sinai?
ּוקְׁ הָ ת ּומְׁ ָר ִּרי; ּושְׁ נֵי,ג ְֵׁרשֹון-- לְׁתֹלְׁד ָֹתם, ֵלו ִּי-טז ו ְׁאֵ לֶה שְׁ מֹות ְׁבנֵי,ו שֶ בַע ּושְׁ ֹלשִּ ים ּומְׁ ַאת שָ נָה,חַ ֵּיֵּי ֵלו ִּי. , ו ְׁחֶ בְׁרֹון ו ְׁעֺ זִּיאֵ ל; ּושְׁ נֵי חַ ֵּיֵּי קְׁ הָ ת,עַ מְׁ ָרם וְׁיִּצְׁהָ ר--יח ּו ְׁבנֵי קְׁ הָ ת,ו שָ ֹלש ּושְׁ ֹלשִּ ים ּומְׁ ַאת שָ נָה. ַאהֲ רֹן- אֶ ת, ו ֵַתלֶד לֹו, לֹו לְׁאִּ שָ ה,יֹו ֶכבֶד ד ֹדָ תֹו-כ וַיִּקַ ח עַ מְׁ ָרם אֶ ת,ו שֶ בַע ּושְׁ ֹלשִּ ים ּומְׁ ַאת שָ נָה,מ ֹשֶ ה; ּושְׁ נֵי חַ יֵּי עַ מְׁ ָרם-ו ְׁאֶ ת. It does not appear in other Torah books.
The fourth perfect number 8128. Kingdom Though this research is focused mainly on 5 Torah scrolls, as we need to check whether the use of perfect numbers was kind of Egyptian-isms, we decided to see in the whole of Hebrew Bible for bigger perfect numbers. The gematria of Kingdom ( )מלכותis 496 – important, but does not appear in this form in 5 books of Moshe.14 For searching occurrences of the perfect number 8128 we used the Bar-Ilan computer program15, to find a sentence or part of it with sum of gematria of consecutive words 8128. (The next perfect number after 8128 is too big to be part of a sentence.) There were two occurrences in the Bible, both – in relative proximity, we read also what is between - in the book of Kings: מלכים ב פרק יח פסוק ד.1 אֶ ת הַ םַ צֵב ֹת וְׁכ ַָרת אֶ ת הָ אֲ שֵ ָרה וְׁכִּתַ ת נְׁחַ ש הַ מְׁח ֹשֶ ת אֲ שֶ ר עָ ׂשָ ה מ ֹשֶ ה כִּי עַ ד הַ יָמִּ ים הָ הֵ םָ ה הָ יּו ְׁבנֵי י ִּׂשְׁ ָראֵ ל מְׁ קַ טְׁ ִּרים לֹו וַיִּקְׁ ָרא לֹו נְׁחֺ שְׁ תָ ן Kings 2: 18:4 He (Hezekiah the son of Ahaz king of Judah) removed the high places, and broke the pillars, and cut down the Asherah; and he broke in pieces the brazen serpent that ;Moses had made
14
" "מלכותin this form appears, for example 6 times in the Chronicles. 15
Bar-Ilan University SHUTIM project, version 14
for unto those days the children of Israel did offer to it; and .it was called Nehushtan The verse is about how the righteous King Hezekiah – who could be a Messiah, - deals with the magic brazen serpent which remained from the times of Moshe. (See Numbers 2116) So our modern concept of Messiah – the revolutionary, as in the poem “12” by Russian poet from the time of communist revolution Alexander Block, is right: the Messiah-the revolutionary destroys the idols of predecessor (though sometimes also the art and the culture) This verse brings to a definite end theory of the primordial sin of Eva as a cause for all human suffering as it no longer imply woman but the Serpent as a source of sin and evil. It is also clear, as a parable of God’s creation of serpent, evil, “big Leviathan”, Crocodile, Dragon etc., that an evil was
16
4.”And they journeyed from mount Hor by the way to the Red
Sea, to compass the land of Edom; and the soul of the people became impatient because of the way. 5 And the people spoke against God, and against Moses: 'Wherefore have ye brought us up out of Egypt to die in the wilderness? for there is no bread, and there is no water; and our soul loatheth this light bread.' 6 And the LORD sent fiery serpents among the people, and they bit the people; and much people of Israel died. 7 And the people came to Moses, and said: 'We have sinned, because we have spoken against the LORD, and against thee; pray unto the LORD, that He take away the serpents from us.' And Moses prayed for the people. 8 And the LORD said unto Moses: 'Make thee a fiery serpent, and set it upon a pole; and it shall come to pass, that every one that is bitten, when he seeth it, shall live.' 9 And Moses made a serpent of brass, and set it upon the pole; and it came to pass, that if a serpent had bitten any man, when he looked unto the serpent of brass, he lived”
made or created– and not co-existent with God from primordial times – for some good purposes, but can be controlled. Notice, that in Sukkot prayer we ask to sit in the future in Jerusalem in Sukkah made from the leather of Leviathan. ( = לויתן496) מלכים ב פרק כג פסוק ג.2 הַ ב ְִּׁרית לִּפְׁ נֵי י ְׁקֹו ָק ָל ֶלכֶת ַאחַ ר י ְׁקֹו ָק וְׁלִּשְׁ מ ֹר מִּ צְֹׁותָ יו ו ְׁאֶ ת עֵ דְׁ ֹותָ יו ו ְׁאֶ ת חֺ ק ֹתָ יו ְׁבכָל לֵב ּו ְׁבכָל נֶפֶ ש לְׁהָ קִּ ים אֶ ת דִּ ב ְֵׁרי הַ ב ְִּׁרית הַ ז ֹאת הַ כְׁתֺ בִּים עַ ל הַ ןֵ פֶ ר הַ זֶה וַיַעֲ מ ֹד כָל הָ עָם
Kings 2: 23:3 And the king (in the eighteenth year of King Josiah) stood on the platform, and made a covenant before the LORD, to walk after the LORD, and to keep His commandments, and His testimonies, and His statutes, with all his heart, and all his soul, to confirm the words of this covenant that were written in this book; and all the people stood to the covenant. ---------------------------------------
This second verse is about sort of a covenant made by the King Josiah, after discovering the book of Torah in the Temple by High Priest at the time of repairing-maintenance of the Temple. (Apparently it was lost or destroyed by previous idolatrous king – see Kings 2 chapters 18-23). By the way, the scribe and the High Priest, the most important heroes in the current paper, make the discovery.
It was impossible to find those verses without software, but possible to encode, whoever did it – the prophet Jeremy wrote the book. In fact, why should those verses be important – possibly because the Torah was once lost and could be lost again. The names of small animals of three of main personages are a little puzzling – we have the rabbit the scribe, the rat the prophetess and the mouse the secretary, as if their names taking all of importance of their position, the council of the mice. So research about the chain of perfect numbers, proving in a way authenticity of the Hebrew Bible, comes to end, the full an analysis of the story of how the High Pries Hilkiah and the scribe Shaphan have found or rewritten the book is beyond the scope of this paper. Conclusions 496= testing by perfectness Philo was obviously a Hellenist. The sixth day would be perfect – but ...The sixth day in Jewish tradition is associated also with Adam and Eva, Eva's speaking to the snake and eating from the forbidden fruit, expulsion from the Eden, Curse of Eva in childbirth and being ruled over by the man, and curse of man in his labor of the Earth. The mentioned perfect numbers were associated with the curse of Eva in early traditions... Here are a few hypotheses. -The problem : according to Liberman, Gematria was a Hellenistic innovation (Liberman. Hellenism) ~323 BC, but
as, according to oral tradition, the alphabet in its order was already known or given at the Sinai with Torah,17 the Scribesi could use the gematria long before that. If so, the linguists, working on proving that the possible proto-language is some ancient form of Hebrew18, which has a divine origin, would gain the numbers, arithmetic or even some kind of number theory, which the people of Israel received in the same package. -Or is it possible that some of early traditions from the Flood time, where Shem and Japheth had the same alphabet, were included in Torah (“Torah was given scroll after scroll”).with gematria, forgotten but reintroduced in times of Hellenism? Not according to Wikipedia. -The other possibility is, it could be that any meaning which appears here was really not there. Information theory does not prohibit "noise" from appearing to be sometimes meaningful. Some unusual patterns can randomly appear. We needed to define statistical test in advance in order to determine if those results exhibit patterns that overcome the level of noise .
17
Changes in Torah made by scribes, who copied the Torah
scrolls. According to Liberman in “Hellenism”, following early sources, there are two different opinions regarding the “Tikkun sofrim” – corrections of scribes. One is that the scribes corrected a few specific places in Torah so as to eliminate „dirty‟ language in relation to the high. The other – that the scribes wrote the Torah in this way originally (corrected in place).
18
References to origin of language
-Other attempt to explain it is, that those “Hellenisms” were introduced as a reminder of the beauty of the Jewish woman and danger in such beauty, instead of Goddess Aphrodite (statues of Aphrodite were present in ancient Israel – and mentioned in Mishnah), and later the same instrument of gematria by factorization of a word and combining from dividers other words as “signs”, was used in creation of Jewish halacha as well.
In traditional Judaism the myth of Eva's transgression as a source of evil is replaced with more philosophical and nonmagic view. The “feminine” is demystified and becomes more of a companion. The serpent is demystified and evil becomes small and easy to overrule. TUMIM and bitter water will not be in the Second Temple. The gematria and factorization of words as method for remembering things and deriving additional clues where there were none and where it does not matter (it does not matter, for example strictly speaking how many forbidden works in Sabbath there were, as long as there is some sort of system and limits) In the piutim for Shabbat, Israel is called “the nation which sanctifies the seventh”, which could mean not only seventh day – Shabbat, but any seventh. The seventh year – “SMIiTa”, when the fruits have a “kdushat shviit| - “seventh sanctity”, numerous examples of sanctifying or purifying from various impurities, involving Cohen, frequents in Leviticus and Numbers.
So, there probably are some more-than-perfect numbers, too. We lack the 496+1. Let's seek it. Sabbath and Melacha – some calculations of words/laws using gematria. In Tractate "Shabbat" we learn that there are 39 "mel'achot" - kinds of work, which is forbidden to perform on Shabbat, for example building, coloring etc. Why this number - because there are 40 occurrences of the world "Mel'acha" - work, in the Torah (in some specific wordforms), or maybe 41 according to other saying.19
19
תלמוד בבלי מסכת שבת דף מט עמוד ב הדור יתבי וקמיבעיא להו :הא דתנן אבות מלאכות ארבעים חסר אחת כנגד מי? אמר להו רבי חנינא בר חמא :כנגד עבודות המשכן. אמר להו רבי יונתן ברבי אלעזר כך אמר רבי שמעון ברבי יוסי בן לקוניא: כנגד מלאכה מלאכתו ומלאכת שבתורה -ארבעים חסר אחת .בעי רב יוסף+ :בראשית לט +ויבא הביתה לעשות מלאכתו ממנינא הוא ,או לא? אמר ליה אביי :וליתי ספר תורה ולימני! מי לא אמר רבה בר בר חנהאמר רבי יוחנן :לא זזו משם ,עד שהביאו ספר תורה ומנאום .אמר ליה: כי קא מספקא לי -משום דכתיב +שמות לו +והמלאכה היתה דים ממנינא הוא ,והא -כמאן דאמר לעשות צרכיו נכנס ,או דילמא :ויבא הביתה לעשות מלאכתו ממנינא הוא ,והאי והמלאכה היתה דים -הכי קאמר :דשלים ליה עבידתא? תיקו .תניא כמאן דאמר כנגד עבודות המשכן ,דתניא :אין חייבין אלא על מלאכה שכיוצא בה היתה במשכן ,הם זרעו -ואתם לא תזרעו ,הם קצרו -ואתם לא תקצרו ,הם העלו את הקרשים מקרקע לעגלה -ואתם לא תכניסו מרשות הרבים לרשות היחיד .הם הורידו את הקרשים מעגלה לקרקע -ואתם לא תוציאו מרשות היחיד לרשות הרבים ,הם הוציאו מעגלה לעגלה -ואתם לא תוציאו מרשות היחיד לרשות היחיד .מרשות היחיד לרשות היחיד ,מאי קא עביד? -אביי ורבא דאמרי תרוויהו ,ואיתימא רב אדא בר אהבה: .מרשות היחיד לרשות היחיד דרך רשות הרבים
The passage decides, that phrase about the God, who rests from his work ("Mel'achto") on the 7-th day, and the phrase about Joseph, who, after "sexual harassment" of the wife of Potiphar, returned to do his work ("Mel'achto") do not count because those occurrences have other meanings. In continuation of discussion the sages abundantly use gematria. (Perhaps, the number of works-mel’acha – was already predefined)20
20
gematria of Shabbat is 702=18*39
= שבת300+2+400 ֵּ( חיalive, living being in Hebrew – important thing in Judaism, gematria of the word is 18)
( חטאsin, transgression; the word “hataat” – sacrificial offering in case of unintentional transgression – has the same root) has gematria of 18 too. Is 300+2+400=702=18*39, where 18 is gematria of HI, ‘live’ in Hebrew; and one of most important principles of observing Shabbat is to violate its laws in order to save life, as it is written “and you should live in them” (the commandments). Additionally, 18 is the gematria of “Het” – transgression, and from here we can deduce also the rule that the number of forbidden works (just for classification, many other prohibitions considered to derive from those main 39 root laws) was fixed to be 39 because gematria of Shabbat is 702=18*39. We find theproof of our argument in the following sentenceses: Anyone, who knows about Shabbat, its interdictions and performing many transgressions, is guilty of every one of them – must bring sacrificial offering in times of Temple (for each one ). (Mishnah Shabbat) But usually gematria in modern days is regarded as joke, like the one I heard from rabbi Haiim Meir Kahane, a Viznitz Hassid, a Cohen, who was imprisoned in Siberian Soviet camps for years.
The whole passage seems to put some additional and mutual meaning in "Mel'achto" of God and of Joseph. In both cases the word does not mean real human work. In case of Joseph it is just a reference to his affair with the wife of Potiphar, meaning his – spared at the end - sexual act with her. The sexual act is one way of sanctifying a woman. In case of God it is obviously not human work, but perhaps, in light of a cabbala, or “breaking of the vessels” conception, is also some kind of divine sacred act, sanctifying of the reality by performing kind of intercourse with it. The gematria of “Mel’achto” is 497=496+1. The next after the perfect number. The God sanctified Shabbat after performing his "Mel'achto". The Scribes. Letter –arithmetics. Edward Belaga and (independently) some people in Bar – Ilan University (see for example “ ערכים מדוייקים של פאי ”) במקורות היהדות
21
wrote articles about a π number
encoded in the book of Kings, when the ration of “Kri” to “Ktiv” gives a most outstanding approximation for the
Rabbi Kahane treated me as Shabbat guest to kugel: “you know why you should eat kugel? Because it equals Shabbat in gematria.” “Not at all! Its gematria is much less than Shabbat!” “Then take some more kugel” Though not gematria, but the perimeter or the surface area or the volume of kugel (which is a round cake ) is a .transcendent number, perhaps as transcendent as a Shabbat 21
http://u.cs.biu.ac.il/~tsaban/Pdf/exactpi.pdf
irrational (and transcendent22 ) number π– the perimeter of a circle with radius 1. Again this “Kri” and “Ktiv” – the read (written as a comment) and “Ktiv” – the written words are found in the verses related to the building of the Temple. This fact brings us to the suggestion, that those fully and not fully vocalized words were encoded for some purpose perhaps by scribes. (Tikkun Sofrim23?) The play with full or omitted vowels permits a multi-dimensional meaning when using gematria. It is not to say that scribes introduced some mathematical calculation while changing Torah text, but just that many Jewish religious laws and thoughts are incorporated in those plain-missing vocalization, transliteration, and gematria. That however, was not explicitly written elsewhere, specifically not - complex, perhaps factorizations of significant numbers.24 But this analysis proves that such a work was going on. If perfect numbers were known, than in addition to “addition” method, used in cabala, which combines gematria of few words so that the sum will be equivalent to
22
Irrational number is a number which cannot be presented as a fraction, as for example √2, while transcendent is a number, which is not algebraic – is not root of any algebraic equation, as is number π 23
Liberman See 4
24
There is no use for “gematria” of words as factorization (for example. SBT(702)=TL(39)*HI(18)) in late Jewish sources, only use of gematria for purposes of decomposition word as sum of other words, with exception of passage in Sefer Yezira, where it is mentioned that some word “beats” the other, in sense, its gematria is divisible by gematria of the other word.
the gematria of some other word, as means of commentary, we have a multiplicative letter arithmetic. It is quite possible that some known laws and ideas were incorporated by that way in Mishnah, if we had such oral tradition – and some of Jews perhaps have it, we could try to unveil the whole Mishnah or Midrash with use of this instrument. Let’s demonstrate how a gematria conveys an additional or even opposite meaning. “( ”חסדי ה' כי לא תמנוPsalms) “The mercy of God, though we did not were perfect “. After calculating TaMNU=496 which is perfect number we see that perhaps we were perfect, at least in God’ eyes. TMIMA=495=496-1. Gematria conveys us a contrary meaning that Torah misses one to be perfect, or that Torah is perfect while missing one, which is a meaning of Midrash “Better that Torah will lose one letter, than the name of God be desecrated publicly”, which in turn means that in the danger of desecration of God’s name it may be sometimes permitted to cancel one of the laws. (Libermann) Conclusion: Canonization of Hebrew Scriptures So, either way it seems, that there was a”numeric magic” in Torah of Moshe (perhaps – against numeric magic of Egypt), which was abolished and maybe called “Hellenism” by modern scholars. Otherwise we have to decide that (final?) canonization of Hebrew Scriptures took place somewhere in time of Hellenism; and perfect numbers (among other, possible complex Masoretic traditions ) were points of “signing” of the Bible, so that there would be some easy checks of the authenticity of the final version. ii
Appendix: table of numerical values of letters in gematria
1 א 2
ב
3
ג
4
ד
5
ה
6
ו
7
ז
8
ח
9
ט
10
י
20
כ
30
ל
40
מ
50
נ
60
ס
70
ע
80
פ
90
צ
ק
100
ר
200
ש
300
ת
400
ת"ק
500
ת"ר
600
ת"ש 700
800 ת"ת Appendix 1.
900 תת"ק
The numeric puzzle
1000 תת"ר
The most famous song for woman (long accepted here as an allegory to Wisdom, Shechina, Torah) which is recited on Sabbath eve is “Eshet Hail” (“The woman of glory”, end of “Parables” of King Solomon). The Hebrew Alpabet does not appear anywhere in Bible before Psalms25, some of which are structured in form of Alphabetical verses.26 Let’s assume that we do not have a
25
The 176 verses of Psalm 119 are in Alphabethical order, while
each letter is repeated 8 times. The verses of Psalm 145 – just one time. 26
and it is the reason why the piut „Akdamot“, which has all its
verses in alphabethical order, is recited in Synagogues on Shavuot - the festival of Torah revelation, “ after Kohen has been called to the Torah, but before he recites his blessing...Composed by rabbi Meir ben Itzhak (11 century, Worms, Germany) ...written in a difficult Arameic ... its first 44 verses form a double acrostic of the Aleph-Bet...Each verse is concluded with suffix תא, the last and first letters of Hebrew Aleph-Beth.“ (The complete Artscroll Siddur). Here we have perhaps another mathematical idea, appropriate for the time. If we arrange letters around the circle, a.
the letters can be regarded as vectors
b.
the letters can be regarded as complex numbers
c.
the sum of all letters is equial to 0
specific Alphabet order, neither gematria yet. We want to create a “magic” effect, where some important objects have a “perfect number” value. The Hebrew Oral Tradition, though, asserts, it came at times of Moisey revelation on mount Sinai.
*see about hebrew Aleph-Beth in Jewish sources and in Wikipedia
If the order of hebrew 22 letters was fixed at some time, the gematria could be also easily fixed, by assigning to first 9 letters numbers 1-9, than 10-90, and finally 100-400 to the rest. Whoever did it, some sage or priest, if it was not fixed at the time of receiving Torah, could have either special guidance or some possibly secret intentions, why assign 1 to Aleph and 2 to Beth.
( while it does not matter which letter is first or second..). If we take into account that important philosophic idea of a time, that the world was created „ex-nihilo“, and another cabbalistic idea about creation with letters, and combine those ideas, we can almost visualize that creation of things arranged in some order, like some mathematical unknots – trivial knots, f.e famous „ סולם “יעקב, a tricky knot, which becomes just circle, when dragged someplace.
Gematria is used to say something like „word A is the same as word B in gematria“, employing these words are related and are various presentation of the same number. While researching perfect gematria in Torah, and have found that gematria of some important words (cleary visible or repeated, but rare) was 496. Assuming, that somebody, who assigned the order of letters and defined gematria, had in mind to show or encrypt some special words, -and some other words could have the same values by accident, we find that
694=המאררים=תומים=מלכות The first two are attributes of Kohen (High priest) in two and only almost magical rituals27, which involve priests, the third – the king. The mathematical rebus, which perhaps Somebody thus cleverly resolved, is a simple ancient linguistic puzzle, but as the resulting value is a perfect number, and perfect number 6 and probably 28 play some significant role in priestly rituals. The Torah, however, in this Alpabethical order begins with the second letter, the fact to which numerous Midrashim had to seek an explanation. The word „my life“ appears six times in Genesis, so perhaps its value was 28 82=חיי
Appendix 2 Urim and Tumim – multiple choice statistical game? God maybe does not play dice28 (as Einstein put it), but Jews do! Prof.Eli Merzbach (probabilities& statistics) had answered question about it in newspaper. He basically said that from statistics point of view it is highly improbable to receive a "TRUE" answer by it (he actually had calculated that probability, which was like probability to win a lottery). Perhaps, he thought, that by that he was affirming that it was a miracle. So he brought us to think about Urim and Tumim as a divine instrument, which miraculously prescribed the right course of action. And, if so, perhaps the precious stones, from which if was made, were doing the task, as the alchemists would think. But there is another look at it as a probabilistic game, when the player receives a blessing to go in the particular way that he got in a game. Perhaps, it is a many centuries dispute. According to the Babylonian Talmud 29 , Urim and Tumim where used just to make a decision very much like court decision whether to act in some way or the other, the results of the action were not automatically guaranteed, so 28
Einstein did not accept probabilistic or non-deterministic
description of God governing the Universe. See, for example correspondence between Einstein-Bohr. 29
See, for example Babylonian Talmud, Adin Steinsaltz’s
commentary for Ioma
the Cohen used his Holy spirit to interpret the reading. So, in fact, it could be that the Urim and Tumim was a machine for making a choice in multiple choice game, where different options could have different weights. The king through Cohen was playing a fortune game, while assigning various probabilities to different outcomes - reasonable probabilities to win while choosing various ways of action, and it was probably a Cohen who was manipulating the Holy instrument and assigning realistic probabilities.30
תלמוד בבלי מסכת יומא דף עג עמוד ב
30
שלא כסדר ,והחזירו לו כסדר .וכיון שידע ששאל שלא כסדר -חזר ושאל כסדר ,שנאמר +שמואל א' כג +היסגרו בעלי קעילה אתי ואת אנשי ביד שאול ויאמר ה' יסגירו .ואם הוצרך הדבר לשנים -מחזירין לו שנים ,שנאמר +שמואל א' ל +וישאל דוד בה' לאמר ארדף אחרי הגדוד הזה האשיגנו ויאמר (ה') לו רדף כי השג תשיג והצל תציל ,ואף על פי שגזירת נביא חוזרת, גזירת אורים ותומים -אינה חוזרת ,שנאמר +במדבר כז +במשפט האורים .למה נקרא שמן אורים ותומים? אורים -שמאירין את דבריהן ,תומים -שמשלימין את דבריהן .ואם תאמר :בגבעת בנימין מפני מה לא השלימו? -הם שלא ביחנו אם לנצח אם להנצח ובאחרונה שביחנו -הסכימו ,שנאמר +שופטים כ +ופינחס בן אלעזר בן אהרן עמד לפניו בימים ההם לאמר האוסף עוד לצאת למלחמה עם בני בנימן אחי אם אחדל ויאמר ה' עלו כי מחר אתננו בידך .כיצד נעשית? רבי יוחנן אומר :בולטות ,ריש לקיש אומר: מצטרפות - .והא לא כתיב בהו צד"י! -אמר רב שמואל בר יצחק: אברהם יצחק ויעקב כתיב שם - .והא לא כתיב טי"ת! -אמר רב אחא בר יעקב :שבטי ישורון כתיב שם .מיתיבי :כל כהן שאינו מדבר ברוח הקודש ושכינה שורה עליו -אין שואלין בו ,שהרי שאל צדוק ועלתה לו ,אביתר ולא עלתה לו ,שנאמר +שמואל ב' טו+ ויעל אביתר עד תם כל העם וגו' - .סיועי הוה מסייע בהדייהו .ואין שואלין אלא למלך .מנא הני מילי? אמר רבי אבהו :דאמר קרא +במדבר כז +ולפני אלעזר הכהן יעמד ושאל לו במשפט האורים וגו' הוא -זה מלך ,וכל [בני] ישראל אתו -זה משוח מלחמה ,וכל העדה -זו סנהדרין .הדרן עלך בא לו כהן גדול.
i
ii
See http://en.wikipedia.org/wiki/Masoretic_Text See http://en.wikipedia.org/wiki/Development_of_the_Jewish_canon
Appendix 3. Can Elisha use the axiom of choice?31
31
The axiom of choice is the axiom in mathematical Set
theory, not accepted by all mathematicians, basically it assumes, that if you have a multitude of non-empty sets, you can choose an element from each one of them. The proof of Banach-Tarsky theorem is based on the axiom of choice.
Here is one of the most important miracles in Judaism at Hellenistic period that can be of interest to mathematicians – Hanukkah’s miracle of oil in the Temple. Are all miracles mathematically justified?32
32
Mathematics being a priory, remains unchanged in any
possible world
It seems, the Hanukkah’s miracle is. Indeed according to the Banach-Tarsky paradoxical theorem, it is possible, believe it or not, to cut an orange33 into finite number of pieces that can be rearranged to produce two oranges, the same size and volume as the first. One can easily obtain from here the other miracles of a kind. (Seeing any quantity of oil as many spherical drops). (The theorem uses “Axiom of choice”, not universally accepted.) It is different with two-dimensional surfaces: it is impossible to cut a circle, for example, and 34combine two circles the same size from its parts It being the case, it is clear, why one cannot, even theoretically, multiply paper money, 35except by coping it ! Apart from paper money we can imagine the textile roll unrolling and cut to million pieces of material, for this we certainly need another theorem, and the process seems definitely Arab, perhaps they have some corresponding mathematical proposition .
33
Actually, the theorem is about identical spheres.
34
This impossibility results from the fact, that you can always
define a measure on any two-dimensional set; and obviously the area of a circle is less than the combined area of two such circles, which is not the case with three dimension objects: there you can cut (theoretically) an object in immeasurable parts 35
Our own intuitive reason for it being impossible is that by
multiplying money you actually do not create goods (possibly all goods must be 3-dimensional in this world, which the money said to represent, so it is not a miracle, it is a fraud!
The first oil (or maybe second, if we count the similar food miracle of the prophet Elijah in Kings 1, 17: 8-16 ) miracle in the Bible occurs in Kings 2, 4:1-7. One important probably point is that both miracles (Elisha' and Hanukkah’s) were performed with oil – which usually serves for sacred purposes, as for lighting Menorah in the Temple or lighting Sabbath or Festival candles at home. The other important point is – that the oil was multiplied (in case of Elisha) or maybe made longer-lasting (in Hanukkah’s case) from an existing amount of oil.
Bibliography
[1]Saul Liberman “Greek and Hellenism in Jewish Palestine” [2] Sid Shnayer Z. Leiman “The Canonization of Hebrew Scripture: The Talmudic and Midrashic Evidence “
[3] Babylonian Talmud [4] The Hebrew Bible [5] Canon and Masorah of the Hebrew Bible, An Introductory Reader
[Library of Biblical Studies series *6+ Lee Martin McDonald, James A.Sanders “The Canon Debate” [7] Michael A. B. Deakin and Hans Lausch "The Bible and Pi" The Mathematical Gazette July 1998 Volume 82 Number 494 [8] ""מקור ראשון *9+ Osnat Youssin “Morphi – the universal morphological analyzer, software”, Blue&White, 1999, Jerusalem – Max Plank, Leipzig *10+ Yael Shemesh “Elisha and The Miraculous Jug of Oil” The Journal of Hebrew Scriptures,
Appendix 4 Introduction We have heard about TC (=Torah Codes) more than 20 years ago, while participating in some Torah Seminar. About 8 years ago we planned to write software dialing with TC, but soon after that such a tool already appeared in the market, with a booklet, in which it was promised prediction of future events with its aid. This article analyzes the claims and explains results of research in TC on 3 levels:
Mathematical (probability, statistics)
Linguistic (meaning, mathematical methods in linguistics)
Jewish – Philosophic – Halacha
Basically, TC is reading Torah with some step, for example every 5-th letter beginning from 123-th letter. (See for example Wikipedia article on Torah Codes) The history of this idea is not completely known, but recently - in previous century - some mathematicians took interest in this. Some wrote scientific articles (for example Eliahu Rips). Few claims, based on experiments, about such reading were made.
There appeared many related words and phrases in near proximity with
corresponding Torah passages (such as ‘ahava’ – love, in the story of Adam and Eve)
One can find any important event, people, and so on, while reading with
an appropriate step.
It is possible to predict a future by such means (this claim does not
however appear in writings and is completely rejected by founders of TC and is only supported and propagated by the software vendors)
The question is: how to prove or reject those axioms appeared important to supporters of TC (there were some mathematicians among them) and to the opponents. There were some experiments that produced interesting results, such as “Great Rabbis” experiment and others. Some saw in this a proof to the “divinity” of Torah, which some people tried to show statistically. However their approach and methods were rightly criticized, as a research was sometimes inaccurate, besides allegedly similar results were obtained in analyzing of other books such as the “War and Peace” by Tolstoy. The “Great Mathematicians” experiment (GM) The GM experiment took place before 1990. The group of mathematicians, supporters or opponents of TC theory, approached prof. N, authority in the field of probability and statistics, asking him to define scientific experiment that will prove correctness (Heavenly origin of Torah) of TC or prove the contrary. Prof.N had suggested the following experiment: he listed twenty names of famous mathematicians, asking to find in Torah (with the aid of TC, and I believe the computer program calculating Torah Codes with different steps and differences was needed for this end) the names of at least 18 from the list with addition of words: “great mathematician” (‘X’ is a great mathematician, ’Y’ is a great mathematician’ etc., in Hebrew: )‟מתמטיקאי גדול ‘שם. After searching the Torah with all possible steps, there were found 17 names from the list and the 18-th was found in the form: ‘Z’ is a genial mathematician! (In Hebrew:)‟מתמטיקאי גאון ‘שם Everybody becomes merry and begins to laugh upon hearing this. Some, perhaps, were happy because the experiment obviously succeeded, and also showed, as if intentionally, by choosing other words for the 18th mathematician, that it is as a living intelligent challenger. Obviously, the
Torah is divine and also is laughing at those who made an experiment. I laughed too, but perhaps had other reasons. I myself was discouraged from seeking Torah Codes for long. But why it really seems, that Torah is joking? The experiment succeeded. But it had, additionally, an unexpected end. It seems that the experimenters should have thought about such linguistics nuance, as finding instead of a “great mathematician” a synonym. But it was not explicitly said, as I remember it, though perhaps was meant. It is perhaps even question of “halacha”, the topic of the tractate “Nazir”36 about the use of language, in this case, whether we should consider every expression with the same meaning acceptable. Otherwise, from the point of view of statistics, it seems that the experiment failed. Furthermore, what if we will find not exactly synonyms, or even antonyms of what we look for? How we should interpret the results? Why should Torah comply with our definition and give us the result? Perhaps, we could discover that Torah does not consider some mathematicians exactly genial. Of course, we assume that the mentioned statistical test took the size of the text and other its qualities into consideration. So, I suppose, the output proves the divinity of Torah for the examiners. But perhaps not for all, as some would design the test otherwise. There are few points, which generally can constitute a problem:
36
In the begining of tractate „Nazir“ there is a discussion about linguistic expression in which a person accepts a vow to be a „nazir“. In many cases not explicit expression still .constitutes a vow
1. Were we not looking for exact phrase we would probably find a lot of related material in any sufficiently long text researched. According to the law of great numbers, if we will wait very long, we will find any given sentence with probability 1 (almost sure) when reading text typed par hazard by a monkey. Is it our will for confirming the uniqueness and possibly not-human origin of Torah that gives us inspiration to interpret the result or are those results really encoded? 2. If we are speaking of meaning then the purpose of the research also defines it. Here, for example, we were not looking to find great mathematicians of the times, our aim was to prove or disprove something about Torah itself. 3. Such statistical methods are clearly not applicable to text, where almost anything has meaning: in Hebrew almost half of combinations of any two letter is a word, almost any root has no more than 3 letters, as vowels are omitted and we are free to interpret the rest. The general problem in applying mathematical methods to text is however the right way of using it. 4. Originally, the meaningful discoveries by applying steps and arithmetic progressions were made manually. The full research is impossible, obviously in this way. However, using a computer program instead of the manual method of searching for meaning makes TC not exactly codes in Torah, but more of an Artificial intelligence program, which is Torah-based. Perhaps it is impossible then to prove heavenly origin of Torah, based on TC, nor to disprove it. Perhaps it is self-referencing in a way, so logically problematic. It reminds us some paradoxes of Set theory and ambiguity language. Here we will give two examples of such paradoxes, which the reader can find in internet. (Wikipedia.)
Grelling Paradox: Grelling-Nelson paradox37 iii
Conclusions - methodological:
We must formulate more appropriate methods for dealing with natural
languages, perhaps to translate the problem and the proof to formal languages of logic.
As to allege similar results in research of “War and Peace” – so what?
Great works of human mind such as of Tolstoy or Bach or Escher can be also heavenly inspired.
Why not be satisfied with just observing the Torah Codes? (not try to
prove anything and not to come to conclusion and predictions) Divinity – what it employs? Assuming, we have a mathematical prove of Torah’ divinity, we may ask ourselves: what does it employ? Some people will try to find explanation and (additional, not directly written) treatment of things in Torah Codes, some will try to predict the future, or ask for a sign before taking important decisions. While anybody with appropriate software can do Torah Codes, is it legitimate or appropriate to use it in such a way? Does it not remind us of some kind of witchcraft and sorcery? Firstly, in ancient times, people were using this kind of method, when a man was turning to a passing by child (usually – student in Beit-Midrash – religious school) and asking him “ –”פסוק לי פסוקיךsay a verse from the Scriptures for me!
37
Then the man was interpreting the verse from Scriptures the child picked for him (from head) as answering to his question. 38 We can examine Talmudic sources concerning the “asking for a sign.” The passage in Talmud ) תלמוד,” ("ארבע שאלוstates “Four has asked in inappropriate way, three of those were answered in appropriate way, and one was answered in inappropriate way”. One of them was Eliezer, servant of Abraham, when he was asking for a sign for right choice of the bride for Isaac,39 who has asked in inappropriate way, because the girl could be an old,
38
“From the times the Temple was destroyed, the prophecy passed to imbeciles and the children” 39
(Genesis) 24,10 And the servant took ten camels, of the camels of his master, and departed; having all goodly things of his master's in his hand; and he arose, and went to Aram-naharaim, unto the city of Nahor. 24,11 And he made the camels to kneel down without the city by the well of water at the time of evening, the time that women go out to draw water. 24,12 And he said: 'O LORD, the God of my master Abraham, send me, I pray Thee, good speed this day, and show kindness unto my master Abraham. 24,13 Behold, I stand by the fountain of water; and the daughters of the men of the city come out to draw water. 24,14 So let it come to pass, that the damsel to whom I shall say: Let down thy pitcher, I pray thee, that I may drink; and she shall say: Drink, and I will give thy camels drink also; let the same be she that Thou hast appointed for Thy servant, even for Isaac; and thereby shall I know that Thou hast shown kindness unto my master.' 24,15 And it came to pass, before he had done speaking, that, behold, Rebekah came out, who was born to Bethuel the son of Milcah, the wife of Nahor, Abraham's brother, with her pitcher upon her shoulder. 24,16 And the damsel was very fair to look upon, a virgin, neither had any man known her; and she went down to the fountain, and filled her pitcher, and came up. 24,17 And the servant ran to meet her, and said: 'Give me to drink, I pray thee, a little water of thy pitcher.' 24,18 And she said: 'Drink, my lord'; and she hastened, and let down her pitcher upon her hand, and gave him drink. 24,19 And when she had done giving him drink, she said: 'I will draw for thy camels also, until they have done drinking.' 24,20 And she hastened, and emptied her pitcher into the trough, and ran again unto the well to draw, and drew for all his camels. 24,21 And the man looked stedfastly on her; holding his peace, to know whether the LORD had made his journey prosperous or not. 24,22 And it came to pass, as the camels had done drinking, that the man took a golden ring of half a shekel weight, and two bracelets for her hands of ten shekels weight of gold; 24,23 and said: 'Whose daughter art thou? tell me, I pray thee. Is there room in thy father's house for us to lodge in?' 24,24 And she said unto him: 'I am the daughter of Bethuel the son of Milcah, whom she bore unto Nahor.' 24,25 She said moreover unto him: 'We have both straw and provender enough, and room to lodge in.' 24,26 And the man bowed his head, and prostrated himself before the LORD. 24,27 And he said: 'Blessed be the LORD, the God of my master Abraham, who hath not forsaken His
ugly or otherwise inappropriate wife for Isaac. But God had answered (his prayer) in appropriate way. From other hand Jephtah40 has asked in inappropriate way – (Talmud: the living being who came to meet him could be inappropriate for sacrificing, like any unclean animal –dog, horse, etc.) – and was answered accordingly. So, just perhaps pay attention to your wording!
mercy and His truth toward my master; as for me, the LORD hath led me in the way to the house of my master's brethren.' 40
Judges : 11,30 And Jephthah vowed a vow unto the LORD, and said: 'If Thou wilt indeed deliver the children of Ammon into my hand, 11,31 then it shall be, that whatsoever cometh forth of the doors of my house to meet me, when I return in peace from the children of Ammon, it shall be the LORD'S, and I will offer it up for a burnt-offering.' {P} 11,32 So Jephthah passed over unto the children of Ammon to fight against them; and the LORD delivered them into his hand. 11,33 And he smote them from Aroer until thou come to Minnith, even twenty cities, and unto Abel-cheramim, with a very great slaughter. So the children of Ammon were subdued before the children of Israel. {P} 11,34 And Jephthah came to Mizpah unto his house, and, behold, his daughter came out to meet him with timbrels and with dances; and she was his only child; beside her he had neither son nor daughter. 11,35 And it came to pass, when he saw her, that he rent his clothes, and said: 'Alas, my daughter! thou hast brought me very low, and thou art become my troubler; for I have opened my mouth unto the LORD, and I cannot go back.' 11,36 And she said unto him: 'My father, thou hast opened thy mouth unto the LORD; do unto me according to that which hath proceeded out of thy mouth; forasmuch as the LORD hath taken vengeance for thee of thine enemies, even of the children of Ammon.' 11,37 And she said unto her father: 'Let this thing be done for me: let me alone two months, that I may depart and go down upon the mountains, and bewail my virginity, I and my companions.' 11,38 And he said: 'Go.' And he sent her away for two months; and she departed, she and her companions, and bewailed her virginity upon the mountains. 11,39 And it came to pass at the end of two months, that she returned unto her father, who did with her according to his vow which he had vowed; and she had not known man. And it was a custom in Israel, 11,40 that the daughters of Israel went yearly to lament the daughter of Jephthah the Gileadite four days in a year. {P}
Predictability From here we arrive to the problem of predictability. Are there certain predictable events? It seems that it would contradict the free choice. Consider situation, date of your death or other important event for you, is written in Torah, so not only you know it, but also others! From other side, banks, meteorological services, and almost every other service rely on it and spend lots of money while researching the future. So the difficulty lies only in finding the predictable future in the Torah itself, which is divine and absolute, especially when our sages, specifically Maimonides, taught strongly against that. Though there is infinitely many events (we percept the future in this way, though, of course, according to modern physics, there will be end to the Earth in normal sense), there are not infinitely many letter-combinations with specific length in Torah: though there will be many different phrases (say, of maximum 30 letters) if we allow “equal-length jumping”, there still will be finite. iv
Linguistic difficulty It is an old thing that everybody heard about, that there is some encoding in Torah, that all the Torah is names of the God. However, it is difficult to accept that Torah is encoded this way. In next parts I propose a much more likely encryption method of Torah. Perhaps it will bring us some results. Bibliography for the TC appendix [1] Feller “Probability theory” [2] Statement by 55 mathematicians http://math.caltech.edu/code/petition.html http://www.math.washington.edu/~greenber/BibleCode.html
Appendix 2: Linguistics-mathematical paradoxes
Grelling Paradox: Grelling-Nelson paradox (see Wikipedia) The Grelling-Nelson paradox can be taken as a demonstration that natural language does not necessarily partition all objects of thought into welldefined categories that will stand up to arbitrary logical scrutiny. And a word is not itself the same as what it refers to.
The second paradox can be formulated as follows: The number of all natural numbers is infinite. The set of all English sentences consisting of no more than 20 words is finite. (If a dictionary consists of 100000 words, set of phrases of no more than 20 words has 100000 power 20 members, which is large, but finite). Let’s try to correspond each natural number to a sentence from this set, so numbers will be defined by corresponding English sentence of no more than 20 words. As the number of all natural numbers is infinite, there will be some numbers without corresponding sentence. Let’s take the first such number – the smallest one which has not corresponding English sentence. But the sentence: “the smallest natural number which cannot be defined by English sentence with no more than 20 words” has only 17 words, is English and completely defines that number! This is a contradiction.
Blue&White publishing 2010 Copyright© Osnat Belaga – Youssin
iii
iv
Let’s X be number of letters in Torah (or just Genesis) and N – length of phrase.
So, even if we allow to continue from the beginning of Torah, (when we did not yet count N letters in specific jump, but already arrived to the end) There will be maximum X*X different phrases.
