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THE ORIGIN ,
OF LETTERS AND NUMERALS
ACCORDING TO THE SEFER YETZIRAH
BY
PHINEAS MORDELL
PHILADELPHIA -
PH IN E A S M O R D E L L
1914 *
Printed by H. Fle is ch mann
Breslau (Germany)
$1215 or-73; oes
(£ ºg dø/.2%&
24-7-727
DEDICATED
TO T H E M E M O R Y O F M Y S IST ER
SARAH MORDELL
t * * '; ſ * w
The present thesis appeared in the JEWISH QUATERLY REVIEW
new series for April 1912 vol. 11, and for April 1913 vol. 111. Published
by the Dropsie College Philadelphia Pa.
3. } rº
Mathematics
2–2-
, Nº. 8
CHAP. I
THE ORIGIN OF LETTERS AND, NUMERALS ACCORDING
TO THE SEFER YETZIRAH
BY PHINEAS MORDELL
THERE is hardly another book in Jewish literature, the
Bible and the Talmud excepted, that has been so much
commented upon as the Sefer Yetzirah. It has been the subject
of deep study, not only to the mystic, who regarded it as the
source of esoteric lore, but also to the philosopher and the
Talmudist. And yet, despite all the efforts of a large number
of scholars of repute for more than, 2, thousand years, the Sefer
Yetzirah remains a sealed book. The various commentaries
upon it are more apt to bewilder the student than to enlighten
him. Indeed, it would seem that every commentator endeavored
to read his own views and theories into this little book, with
hardly any concern whether they agreed with the text or not.
There is no book in Jewish literature that is so difficult
to understand as the Sefer Yetzirah. For it was originally
written in an obscure half-mystical style. To make matters
worse, the commentators of the eighth or of the ninth cen-
tury blended the original “Sefer Yetzirah" with an early
commentary, which may be referred to as “Sefer Yetzirah II. “
It thus happened that all the commentaries written on the
“Sefer Yetzirah" since the beginning of the tenth century
6 THE ORIGIN OF LETTERS AND NUMERALS.
are chiefly based on this commentary and not on the original
Sefer Yetzirah. Although the Sefer Yetzirah is exceedingly
hard to understand, the solution of its many difficulties is
not impossible. The reason why they have remained so long
an unsolved problem is partly due to a lack of knowledge of
Hebrew orthography, on which the Sefer Yetzirah is based.
In spite of the numerous works written on Hebrew orthography
since the beginning of the tenth century, there is not one
which may be considered as really based on the Hebrew. For
the Hebrew orthography which has been and is still taught,
is not Hebrew but Arabic. The Hebrew grammarians under
Arabic influence came to believe that those rules of Ortho-
graphy which the Arab grammarians invented for the language
of the Koran hold good also for the language of the Old
Testament. When the Honorable Mayer Sulzberger heard rae
-expressing my views on Hebrew Orthography, he advised me
to make a study of the Sefer Yetzirah which in his opinion
constitutes the earliest Hebrew grammar extant. Finding that
my views on Hebrew orthography harmonized with those of
the Sefer Yetzirah, I made an exhaustive study of it. After
many years of study, I reached the conclusion that the Sefer
Yetzirah, as the earliest Hebrew grammar, contains not only
the fundamental rules of Hebrew orthography, but also an
account of the origin of letters and numerals. This account
it is my present purpose to Seth forth').
1) I wish to express here my thanks to J. Broyde, Miss Henrietta
Szold, Prof. Henry Malter, and Dr. Isaac Husik for many courtesies
extended to me in this work, both in the arrangement of the material
and in style. - - $.
THE ORIGIN OF LETTERS AND NUMERALs. ... 7
The first Mishnah reads as follows: many ºnw bºwºw
-ep met eips msn's mº m ppm nisºe. ."
“Thirty-two mysterious ways has the Lord, the Lord of
hosts, ordained through Scribe, Script and Scroll."
The thirty-two mysterious ways are the twenty-two letters
of the Hebrew alphabet, which represent thirty-two sounds.”)
In accordance with the belief of the ancients that the
letters are of divine origin, the Sefer Yetzirah explains that
the thirty-two ways of wisdom were ordained by God through:
(1) "pip (Scribe), the man whom God inspired to invent
the alphabet; , ;
(2) met (Script), the letters;
(3) net (Scroll), the material On which the letters were
displayed. t
In order to show how the twenty-two letters of the alphabet
constitute the thirty-two ways of wisdom, the author proceeds
to the division of the letters in the second and following Mishnahs.
He divides them into simple and double sounds, and also into
vowels and consonants. The simple letters he called mºve, and
the double, nºes; the vowels, mos (=mas), and the consonants,
nºn. Altogether they form thirty-two sounds: the twenty
sounds of the ten") double letters, and the twelve of the twelve
simple letters. -
*) All the commentators explain that the thirty-two ways of wisdom
are the twenty-two letters and the ten Sefirot. Below will be found the
reasons why the present writer cannot accept this interpretation.
*) Below will be explained that, according to the Sefer Yetzirah,
there are ten double letters and not only seven, as is believed by all
commentators since Saadya. . .
8 THE ORIGIN OF LETTERS AND NUMERALs.
The Sefer Yetzirah*) emphasizes that the number of the
double letters is no less and no more than ten, and the number
of the simple letters no less and no more than twelve. The
Sefer Yetzirah urges us to investigate and examine the letters,
that we may have a clear insight into the subject. This proves
that, at the time when the book was written, the nature of the
letters, or of some of them, was misunderstood. We know,
indeed, that at the time when the Greek translation of the
Bible was made, it was believed that the y, for example, could
be transliterated by e, a, or g, and the translators accordingly
rendered it variously by one of these three sounds. &
Arguments have repeatedly been advanced in favor of the
view that the Hebrew y had not only the sound of the Arabic 2,
but also of the é. But according to the Sefer Yetzirah, the
y is a simple letter. If it has the sound of a it is impossible
that it should also have the sound of £, Moreover, if the y
was originally a vowel only and had no sound of g, as main-
tained by Jerome, it can have only one vowel sound. If we
ascribe to it the sound of A, it is impossible that it should
have also the sound of E or O, etc. Furthermore, according
to the Sefer Yetzirah, the letters n, b, s are also simple letters,
and each must have had only one sound and not two as in Arabic.
The author of the Sefer Yetzirah apparently cautioned against
the very errors and mistakes into which all writers on Hebrew
grammar have fallen. By dividing the twenty-two Hebrew
letters into ten double and twelve simple, representing thirty-
two sounds, the author desired to make clear how different the
*) See text, § 3.
THE ORIGIN OF LETTERS AND NUMERALs. 9
Hebrew alphabet is from the alphabet which is known as Arabic
and which the Arabs themselves used to call suri. By siri
was apparently meant Assyrian. The so-called Arabic alphabet
consisted, originally of only seventen letters. It was apparently
originally invented to represent the Assyrian-Babylonian
language, which consisted of seventeen or eighteen sounds.
Hence the name “suri.” When the Arabs, whose original
alphabet was the Himyarite, consisting of twenty-eight letters,
adopted the “suri” alphabeth, they gave to some “suri” letters
two or even three sounds, and such letters are each counted
now as two or three letters, -
As according to the Sefer Yetzirah the Hebrew alphabet
consists of ten double letters and twelve simple, therefore to
each double letter must be ascribed two sounds and to each
simple letter only one sound without any regard to their value
in Arabic. -
The best transliteration of the double letters is as follows:
s = e, s = 0, E = b, E = v, i = g, i = as English j (?)
T = d., T = th in “the,” i = u, = w, D = k, D = German
ch or Arabic h, p = p, e = f, or ph, n = 1, T = r or Ara-
bic g, w = sh, w = French j (?), n = t, n = thin “think.”
The best transliteration of the simple letters is as follows:
T = h, j = English 2, n = h (Arabic h, to = t, = German
i, * = \, e = m, = n, E = s. v = a, s = t2, P = }
After giving this division of the letters, the Sefer Yetzirah
shows how, from these twenty-two letters, all the words that
have ever existed or ever will exist can be formed.")
*) See text, §§ 5, 6 and 7.
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THE ORIGIN of LETTERS AND NUMERALs. 11
The purpose of the author was to e.phasize the superiority
of alphabetic writing over the non-alphabetic writing (ideographic
and syllabic) used by all the nations of antiquity, and even
now by a great portion of mankind. If we arrange alphabeti-
cally all biliteral combinations, as the Sefer Yetzirah directs,
joining x with all letters, 5 with all letters, etc., there must
result a list of 484 combinations (22°= 484). (See preceding page.)
Furthermore, by the expression pºp) Tins, Dº ºn inn
yi. Herº py" isy Hºyº y intº the Sefer Yetzirah indi-
cates that the biliteral combinations can be made the basis of
all triliteral combinations. If we desire to arrange all the
triliteral combinations that can be formed from the 22 letters,
their number will be 22° or 10,648. For this it would be
necessary to draw up twenty-two tables with the biliteral com-
binations, leaving sufficient space between every two combinations
for the addition of a letter. On one table an s would have to
be added at the beginning of each biliteral combination, and
the result would be a complete table of 484 triliteral combina-
tions beginning with an 8; on another a n would be added in
the same way, making a complete table of 484 triliteral com-
binations with the letter - at the beginning. Proceeding thus
with the remaining letters, we should get all possible triliteral
combinations that can be made out of the twenty-two letters.
In this way two-thirds of the labor otherwise necessary is saved,
for adding the third letter is only one third of the labor required.
to produce all the triliteral combinations. Should we desire to
write all the quadriliteral combinations that can be made out
of the 22 letters, we have only to make twenty-two copies of
12 THE ORIGIN OF LETTERS AND NUMERALs.
all the triliteral combinations, leaving sufficient space between
two successive combinations for the addition of a new letter;
then by adding an s at the beginning of each triliteral com-
bination, we shall attain 10,648 quadriliterals beginning with
an 8. Proceeding in the same way with 5, we shall obtain
10,648 quadriliterals beginning with 5, and so forth with the
remaining letters, which would give a total of 22*, or 234,256.
The number of quinqueliteral combinations would amount to
22*, or 5,153,632.
- ... The powers of twenty-two up to 12 are as follows:
- 484 = 22?
10,648 = 22%
234,256 = 224
5,153,632 = 225
113,379,904 = 22%
2,494,357,888 = 227
54,875,873,536 = 22°
1,207,269,217,792 = 229
- 26,559,922,791,424 = 221"
% - - 584,318,301.411,328 = 22”
- 12,855,002,631,049,216 = 22.1%
Thus it is evident that the twenty-two letters will admit
-
of an infinity of combinations and arrangements, sufficient to
& represent, not only all conſeptions of the mind, but all words
in all languages whatever.
The same results would be obtained, according to the
Sefer Yetzirah, by adding a letter at the end of each combination.
When a letter is added at the beginning, the process is called
THE ORIGIN OF LETTERS AND NUMERALs. 13
Bºe ºn Tim, the table “turns” in front of each letter, as
JJ “turning” in front of the y becomes ly, and when a letter
is added at the end, it is called mns ºn mm, the table
“turns” behind each letter, as JJ turning behind the y becomes
yl). Thus, as either y or y), can be formed from the com-
bination 15 by adding an y, so all the triliteral combinations can
be made out of the biliteral combinations, by adding an addi-
tional letter, either at the beginning or at the end of the
biliteral combinations, and the quadriliterals from the triliterals.
etc., without the necessity of writing the letters anew, when
new combinations are desired.
How infinite numbers of words are formed out of the
twenty-two letters, the Sefer Yetzirah demonstrates by permu-
tations in which letters never repeat themselves but only change
their places. Out of two letters") two biliteral words are formed
as: EN, 85. Out of three letters six triliteral words are formed
as: 358, Bls, JNR, 835, 58), NE. Out of four letters 24 quadri-
literal words are formed as: Tlºs, XTEN, TEN, ETN, lin. TN, EXTN,
TINE, ATN-7, TN35, RTI-, INTs, Nºrth, 7583, in TNN, TNinj, NThä, ENT),
Nin"), in NT, DYNT, Nin", NXET, in NXT, NEXT. Out of five letters
120 quinqueliteral words are formed, out of six letters 720 six-
letter words are formed and out of seven letters 5,040 seven-letter
words are formed. The Sefer Yetzirah gives the factorials up
to that of seven and concludes the Mishnah by saying: “Go
and count further, what the mouth is unable to pronounce, and
the ear is unable to hear.”
*) See text, § 8.
14 THE ORIGIN OF LETTERS AND NUMERALS,
The factorials up to that of 12 are as follows:
1 = (1
2 = (2
6 = (3
24 = (4
120 = (5
720 = (6
5,040 = (7
40,320 = (8
362,880 = (9
3,628,800 = (10
39,916,800 = (11
479,001,600 = (12
The factorials up to 36 are given in Rees’ Encyclopedia,
art. Cipher. The Mishnah treating of permutation was well
explained by all commentators, especially by S. Donnolo.
W. Stanley Jevons on the subject of permutation says"):
*Thus the letters A, B, C, will make different permutations
according as A stands first, second or third; having decided
the place of A, there are two places between which we may
choose for B; and then remains but one place for C. Accor-
dingly, the permutation of these letters will be altogether 3 x
2 x 1 or 6 in number. With four things or letters A, B, C,
and D, we shall have four choices of places for the first letter,
three for the second, two for the third, and one for the fourth, so
that there will be altogether 4 x 3 x 2 x 1, or 24 permutations.
The same simple rule applies to all cases; beginning with the
7) The Principles of Science, London 1887, 178, 179.
THE ORIGIN OF LETTERS AND NUMERALS. - 15
whole number of things, we multiply at each step by a number
decreased by a unit. . . . . . . . 22
He further says: “Many writers have from time to time
remarked upon the extraordinary magnitude of the numbers with
which we deal in this subject. Taquet calculated that the
twenty-four letters of the alphabet may be arranged in more
than 620 thousand trillions of orders; and Schott estimated that
if a thousand million of men were employed for the same number
of years in writing out these arrangements, and each man filled,
each day, forty pages with forty arrangements in each, they
would not have accomplished the task, as they would have
written only 584 thousand trillions instead of 620 thousand
trillions.”
CHAP. II
THE TETRAGRAMMATON AND THE WOWELS
All words arising from the combination of the letters are
combined and permuted with the Tetragrammaton, called by
the Sefer Yetzirah “One Name” NTNT", from which emanated the
whole of creation and all languages”). According to the Sefer
Yetzirah, the alphabet did not consist of consonants only, as
is held by many Semitic scholars, but had vowels also, the
letters of the Tetragrammaton themselves being vowels. Indeed,
the ancients transcribed Tin" by the vowels i-e-u-o, and i-a-0-u-e°).
*) See text, § 9.
9) Comp. Renan, History of the People of Israel, Boston 1888, I, 69.
16 THE ORIGIN OF LETTERS AND NUMERALS.
To understand how the letters of the Tetragammaton can
be vowels, it is necessary to know what the Hebrew vowels
are. Here the view of various writers, differ widely. Dunash
Ibn Tamim”), whose opinion was shared by many Hebrew
writers, maintained that the three letters "N are the Original
vowels of the Hebrew alphabet; Roger Bacon”), Masklef, and
others held that the six letters yºmins were originally vowels;
and Jerome and many others asserted that the five letters y”"N
were the original vowels. In my opinion the original vowels
are the four letters ºys, which are still used as vowels in tran-
scribing other languages in Hebrew characters. The Sefardic
Jews, when writing Spanish with Hebrew letters, transcribe a
by 8; i and e by "; and u and o by The Ashkenazic Jews,
when writing German with Hebrew letters, transcribe a and 0
by 8, e by y, u by l, and i or j by ". An investigation into
the relation of the letters to the vowel points according to the
Ashkenazic pronunciation led me to the conclusion that y has
the sound of a, 8 of e, and o, of i, and of u, besides its
sounds of w.
If this opinion with regard to the original letters be cor-
rect, not only an N is hidden under a T of the Tetragramma-
ton TT, as believed by Dunash Ibn Tamim,”) Judah ha-Levi,.
and Abraham Ibn Ezra, but also an y. In order to understand
the secret of the Tetragrammaton, the nature of the T must be
better defined. We have seen that many authors since Jerome
*) Sefer Yetzirah, London 1902, 20, 45, 48.
**) See JOR., XV, 336. ---
**) Sefer Yetzirah, London 1902, 45.
THE ORIGIN OF LETTERS AND NUMERALS. 17
believed T to be a vowel. This is not the opinion of the Sefer
Yetzirah. It counts " among the simple letters, and, conse-
quently, no sound in addition to that of h can be attached to
it. On the other hand, the T occurs at the end of words as
silent, indicating that it occupies the place of a vowel letter.
We must therefore assume that the Sefer Yetzirah considers
T to play the same part among the vowel letters as zero does
among numerals. As Zero is not a digit itself, but only
Occupies the place of a digit, so the silent T is not a vowel
itself, but merely occupies the place of a vowel. In the Tetra-
grammaton, both the T after the and the T after the occupy
the place of a vowel letter. The original letters of the Tetra-
grammaton were shy" instead of TT.
Now, what is the “great secret," which the three mother
letters (vowels) wros contain according to the Sefer Yetzirah?
Dunash Ibn Tamim declared it to be the three vowel letters
“s, which he identified with the Tetragrammaton Rin the
“secret name.“ In my opinion, wbs stands for lys, and nos
which occurred in the Rashi text of the Sefer Yetzirah (Rashi,
commentary on Job 28, 27; S. Sachs, TJTT, p. 94) stands for
*ys. According to the original Sefer Yetzirah there are four
mother letters, nºbs, cryptograms which should be deciphered
by the letters mys: the s by s, the to by the y, the w by
the and the n by the ". From these four letters emanated,
according to the Sefer Yetzirah, the four elements, air, water,
fire, and earth.
The Sefer Yetzirah apparently used nwos as secret
characters representing ºys, because the Hebrew alphabet is
t 2
* -
18 t
THE ORIGIN OF LETTERS AND NUMERALS.
arranged with the 8 at the beginning, the b in the middle,
and the w and the n at the end ; while the Arabic alphabet
was originally arranged with the 8 at the beginning, the y in
the middle, and the and , at the end. The Arabic alphabet
consisted originally of the following seventeen letters: **)
s : * c : * * – a + o- C - 9 z -
H > t > S > y tº s v - " i = N
- The fact that the Arabic alphabet has the 8 at the be-
ginning, the y in the middle, and the and the at the
*) As "hys were originally vowels and as H has an aspirate
sound, which originally may not have been counted as a censonant,
therefore there are only twelve consonant letters in this alphabet. Hugo
Winckler (Die Babylonische Kultur, Leipzig 1902 (P. 47) Says: Es wurden
ursprünglich Zwölf mach dem Tierkreiszeichen benannte , Komsonanten"
unterschieden, welche durch drei Vokale regiert werder, wie der Tierkreis
durch die drei Regenten. The Hebrew letters according to the Arabic

order would be as follows ºn ºp? Tºp Feye psy pi *-in. nasc,
If this were also the original order of the Hebrew alphabet, the N
must have been at the beginning, the y in the middle and the and
the at the end, instead of N at the beginning, b in the middle, and ty
and n at the end. -
Although the N has been placed at the beginning of the alphabet
its two sounds e and 0, however, harmonize between a and u the sounds
of y and , respectively. Fººs, np-my ( =) "w nob- (y –) p"p
Dºnjºn y^*Do (Text $ 10). This would indicate that the author knºw
also of an order of the vowel letters, as YNy == Yºssy = i, u, o, e, a.
G. H. von Meyer (The organs of Speech, New York 1884 p. 225)
says: “Czermack first showed that the elevation of the soft palate diſfered
with the utterance of each vowel, the greatest elevation occurring with
the vowel i (ee in see) and that the elevation gradually diminished when
the vowels were uttered in the following order: i, u, o, e, a.” The Sefer
Yetzira seems to be of the same opinion.
THE ORIGIN of LETTERS AND NUMERALs. 19
end, leads to the conclusion that the arrangement of the Arabic
alphabet is older than that of the Hebrew, although the con-
trary is generally believed to be the case. -
The alphabet was anciently believed to symbolize the
whole universe. The vowels which were the original letters
of the Tetragrammaton, were placed at the beginning, in the
middle, and at the end of the alphabet, to signify that TT is
the God of the whole universe, that He is the beginning, the
middle, and the end.
According to their sounds, we may count, in the Hebrew
alphabet, thirty--two letters, divided into five vowels (y = a,
N = e, N = 0, j = u, * = ?) and twenty-seven consonants. Each
vowel, according to the Sefer Yetzirah (see text, S 12), stands
by itself, but the consonants are dependent on the vowels. The
vowels and consonants were made in the form of a “state and
arranged like an army in battle array.” Isaac Taylor *) says:
“Like soldiers on parade the characters in the alphabetic line
have been dressed.” + -
CHAP. III.
SEFIROT.
The origin of the alphabet was, and still is, a burning
question to scholars. Did it spring from the Egyptian hiero-
glyphics, or from the cuneiform systems of the Assyrians, or
from the hieroglyphics of the Hittites, or from the Syllabary
*) The Alphabet, London 1883, I, 125.
20 - THE ORIGIN OF LETTERS AND NUMERALS.
of Cyprus? The Sefer Yetzirah answers: “From the Sefirot” ”).
But what does it mean by Sefirot? On this point endless dis-
cussions arose; and it has even been disputed whether they are
designed to express theological, philosophical, or physical
mysteries. Most of the writers, bent on explaining the Sefer
Yetzirah in a philosophical way, maintain that by nin'ED Tºy
Hoºn, the Sefer Yetzirah meant the so-called Arabic numerals,
1, 2, 3, 4, 5, 6, 7, 8, 9, and 0. This view is shared by
Dunash Ibn Tamim *), who, however, admits that some people
object to it, and maintain that if the Sefer Yetzirah had meant
the Arabic numerals, it would have said ninet yºn (nine Sefi-
rot): for as the cipher is not a digit, there are only nine signi-
ficant numbers. A much weightier reason for opposing the
identification of the Sefirot with the Arabic numerals is the fact
that the Sefer Yetzirah gives ten as the total number resulting
from the addition of the numerals 1, 2, 3 and 4, and the
total of the 9 Arabic numerals added together is 45.
However, there can be no doubt that the Sefirot philo-
sophy of the Sefer Yetzirah rested on some system of numeral
notation. I have studied various systems of antiquity and I
have found that it harmonizes with a numeral system con-
sisting of a series of strokes from one to four, amounting in
all to ten | || ||| ||||, and the zero 0. Indeed, the numbers
1, 2, 3, and 4 were originally indicated by such a series of
strokes, as is well known to all familiar with the old Roman,
Greek, and South-Arabian systems of notation. The numeral
**) See text, Ś 14. -
**) See Sefer Yesirah, London 1902, 24, 25.
THE ORIGIN OF LETTERS AND, NUMERALS. 21
***-a-ai-º-º-º:
indicated the numbers 5, 6, 7, 8 and 9 by the first four groups
of strokes, as TTTITF5, IITTTFG, TIII ||= 7, II ||
||| = 8, and || || || = 9. There can be no doubt, there-
fore, that by ninet ºwy the Sefer Yetzirah meant 1, 2, 3, and
A written in strokes, their number amounting, when added together,
systems of the Phoenicians, Egyptians, Babylonians etc., even
. *ºr: ***…

to ten"), and by Moºn, it meant zero, which, being a symbol
for nothing, is the equivalent of Toºn, “nothing” in Hebrew.
My belief is that originally the text must have had ninet ºwy
Tº = ten digits and zero. --
As, according to the Sefer Yetzirah, it is possible to ex-
press all numbers by the ten Sefirot"), we must demonstrate
how all numbers, even those higher than nine, may be indi-
cated by the ten strokes. The strokes to indicate numbers
were anciently written vertically and horizontally as —===
*mºs ºs ººms e
* * *ms
By means of the strokes and the Zero, all numbers may be expressed,
as they are expressed by the Arabic numerals. The numbers
10, 20, 30, 40, 50.... 500... 5000.... 50000 may be expressed
as — 0, 0, ± 0, E 0, E 0, ...... = 00, E000, E 0000.
0
=
=
1907 for instance would be represented thus: _
19).
**) Dr. H. Malter calls my attention to the following passage of
Abraham Abulafia in Jellinek's Hºsph Toºn Yiji, Leipzig 1853, p. 20:
mºssn nºmy sº yºns- pºss Env nºt ºwy "elp pººn by imp
Eºs Tº ens: ºss) is two mºss, mºssh -vs 1": -'s 7-1-
ni ºnns Tī). This passage proves that the true meaning of the Sefirot
had been known to some Hehrew writers.
18) See text, § 16.
*) Some Pythagoreans used the strokes with the principle of posi-
tion without a zero in the columns of an abacus (Dr. M. Cantor's Mathe-
ºnatische Beiträge, page 202).
22 THE ORIGIN OF LETTERS AND NUMER ALS.
Such a system of notation is practically the abacus on paper
and apparently was the source of the scientific system of no-
tation of the Chinese, and may have been the source of the
Arabic numerals, the origin of which is admittedly doubtful.
To avoid writing too many strokes, the Chinese made one stroke
to represent five units. The numerals 1, 2, 3, 4, 5, 6, 7, 8,
mºsºms tº tº
9, 0, were written, I, II, III, IIII, IIII, T, TI, III, IIT, 0.
1405536 for instage was written | = 0 = ||||| =T(see M.
Cantor’s Mathematische Beiträge, Halle 1863, 46 and 47; first
table figures 15, 16). t
The East-Arabian figures ), *, *, s (1, 2, 3, and 4) origina-
ted from the primitive numerals || || || || ||. They are only
a combination of two, three, and four strokes, to indicate the
respective numbers. The figure • for 5 originated from the
circle, which in the primitive system of numeral notation was
the fifth symbol representing a zero, and in the South-Arabian
system of numeral notation was a symbol representing ten units.
The East-Arabian figures, , , , (6, 7, and 8) are each a
combination of two strokes. The figure originated apparently
from a circle and a stroke, and a dot indicated a zero. -
Many writers maintain that only at a later period the
principle of position and the Zero was discovered. We are,
however, now certain that in Babylon, many centuries before
* ******--------. s. -
- *** rºs º-as-e-
- *--------->
*rº- ~~~~TT gº - . . . " `--~~~ : --- `-- ~. ---
the Christian Era, a sexagesimal position was known. In my
20pinion, the sexagesimal position originated from the decimal
positions—and not the reverse; for the earliest abacus, which
**********-es---
* –7----------------- . . . . . . .” -- ~Tri-Tº-
was doubtless based on a decimal position, is older than the
THE ORIGIN OF LETTERS AND NUMERALS. 23
Sexagesimal system. F. Cajori says:”) “The principle of
position in its general and systematic application required a
symbol for zero. We ask, Did the Babylonians possess one?
Had they already taken the gigantic step of representing by a
symbol the absence of units?” ... I am inclined to believe that
the zero is as old as the principle of positions. The fil
perfection of the so-called Arabic system of notation consisted,
not in the discovery of the principle of position and the zero,
but rather in pointing out how the primitive principle of posi-
tion and the Zero can be conveniently used with nine figures,
such as 1, 2, 3, 4, 5, 6, 7, 8, and 9.
Although the Sexagesimal position was anciently known in
Babylonia, yet it was used only, in higher mathematics, as in
20) A History of Mathematics, New York 1894, p. 7.
2) In the American Mathematical Monthly, 1909, p 177, G. A. Miller
calls attention to the recent change of view in reference to several im-
portant questions in the history of elementary mathematics. On page
576 of Cantor's Worlesungen über Geschichte der Mathematik (second
edition, vol. I), the following words are found: “According to our opinion
the discovery of zero is due to the Hind00s.” The corresponding state-
ment in the third edition, page 616, reads as follows: “According to
our opinion the discovery is due to the Babylonians, the deepening of
the concept is due to the Hindoos.” G. A. Miller further says: “The
discovery of zero, as used above, implies its use in positional arithmetic.
It is certain that the Greeks employed zero in the second century B. C.
to denote the absence of degrees, minutes, or seconds in their sexagesi-
mal notation. The earliest known use of this symbol in Babylonian in-
scriptions belongs to the third century B. C., but it is supposed that it
was in use at a much earlier date. At the Internati
Congress held in Paris in 1900, §aſitºr suggested that Zărºwāş-prº
|bably-in-use among the Babyloni as—es 0 B. C. Even if
such an early date cannot be established, it appears likely that scholars
will hereafter attribute the discovery of positional arithmetic to the
Babylonians instead of the Hindoos.” ----------------~~~~



24 • THE ORIGIN OF LETTERS AND NUMERALS.
*
astronomy, etc.; for Ordinary purposes there was a decimal
system of notation, without the principle of position. When
we find that in Egypt and Phoenicia only a decimal system of
notation was used, without the principle of position, it may
not be taken as proof that the decimal position and zero were
unknown. A decimal system of notation without the principle
of position was in ancient times considered more convenient
than a decimal system of notation based upon the principle of
position. -
When it was, that the primitive numerals, |, || || ||||,
o, were changed into the figures used by the East-Arabs, to
indicate the numbers 1, 2, 3, 4, 5, 6, 7, 8, and 9. I shall
not venture to conjecture. But it is proper to assume, that
they may have been known to a few learned men long before
they began to be widely used. They may have even been
known to the author of the Sefer Yetzirah”). Yet by ºwy
*) As an early Arabian mathematician Mohamuled ben Musa Alkhowa-
rezmi said that the Indians practiced the so-called Arabian system of
notation (M. Cantor's Mathematische Beiträge, Halle 1863, page 269),
arguments have been advanced that the Indians invented this system, or
at least taught it to the Arabs. But it is very doubtful what Mohammed
ben Musa meant by Indians. By Indians he might have meant Ethio-
pians, or any other nation under the torrid zone which the ancients
used to denominate as Indians (T. Astle, The Origin and Progress of
Writing, London 1784, p. 41; nºwn, IX, 354, 439). Or he could have
meant Jewish astronomers like Mashallah, who was called by Abraham
ibn Ezra an Indian sage (TNT DOT) (see M. Steinschneider, Arab. Lite-
ratur der Juden, Frankf, a.M. 1902, p. 15). As the Arabic numeral system
of notation apparently originated from the Sefirot philosophy of the
Sefer Yetzirah, it is proper to share the view of those who claim the
Hebrews as its inventors (E. Brooks, the Philosophy of Arithmetic, Phila-
delphia 1876, p. 24). -
THE ORIGIN OF LETTERS AND NUMERALS, 25
neº- men the author meant, not the Arabic numerals, but
the primitive numerals, , || || ||||, 0, from which the Arabic
numerals originated.
As, according to the Sefer Yetzirah, the alphabet origina-
ted from the ten Sefirot, which are, as was demonstrated, the
first four groups of strokes amounting to ten, we must assume
that the first alphabet must have been constructed out of these
strokes. This peculiarity harmonizes best with the Libyan-
Berberic alphabet, in which we actually find each of the first
four groups of strokes: _ = =#| = |, || || || and the
circle O or G) is each a letter. Moreover, the other letters of
the same alphabet have such forms as point, without a doubt,
to their origin in the first four groups of strokes, || |||||||.
Two, three, or four strokes are so combined as to indicate the
various letters as: F- -], I-I T.
etc. *). I T, L, C T || || DEF
Similar to these characters are the linear letters, which
have been found on the Egyptian pottery. On this subject,
Mr. W. J. Harding King *) says: “Mr. Evans and Professor
Flinders Petrie have shown that certain linear characters which
have been found 9n the Egyptian pottery . . . . . . form a sig-
nary in which a large number of the characters are identical
with the Libyan and Tifinagh. The linear characters in Egypt
are earlier than the hieroglyphics, though a few of the forms
may ultimately have been fused with the latter. Evolved at a
*) K. Faulmann, Geschichte der Schrift, Wien 1880, p. 257. Bickell,
Hebrew Grammar, Leipzig 1877. Table of Semitic characters by Julius
Euting, No. 52, 53.
*) A Search for the Masked Tawareks, London 1903, p. 322.
26 THE ORIGIN OF LETTERS AND NUMERALS.
date when hieroglyphic writing was unknown, they persisted
with a strange vitality, and were never absorbed or ousted.”
It is proper to note that, in some Berberic alphabets”), one,
two, three, or four dots are placed in various positions, to
indicate different letters. The four groups of dots
., which may be arranged in triangular form . . . . . . . . as
the Pythagoreans arranged them, were originally also symbols
representing the first four numbers 1, 2, 3, and 4*). As al-
ready demonstrated, the first alphabet invented was similar to
that still used by the Berbers, whence the inference, that there
may have been a time when the Hebrews also used such an
alphabet. May not Hsiaº Enº ") originally have meant Libyan
writing?
According to J. Halévy's decipherment of the Libyan
alphabet or – is 8, or = is , || or = is V, III is m.
According to the Sefer Yetzirah (§§ 10, 11, 18, 19, 20, 21)
or — is 8, or = is 9, or = is , || or = is . Hence,
the vowel-letters Tys were originally indicated by the four
groups amounting to ten strokes, , || || || Or –===
If these vowel sounds were originally the numeral words for
one, two, three, and four, we may assume that the vowel sym-
bols were invented at the same time as the numerals. The
invention of such an alphabet as the Libyan must have con-
sisted, chiefly of symbols for consonants, because vowel sym-
*) K. Faulman, p. 257–8.
28) Cyrus Thomas in the 19th Annual Report of the Bureau of
American Ethnology, Smithsonian Institution, 1897–98, p. 860, -
**) Sanhedrin 21b. -
THE ORIGIN OF LETTERS AND NUMERALS, 27
bols were already in existence from the time the numerals
were invented.
In this way we can understand why the vowels (the Tetra-
gammaton) were originally identical with the ten digits Tºy
minºr, || || ||||. This is also in harmony with the follo-
wing quotations from the commentary 'm Tsis”): “In His great
name which is Jehovah, Tºm sin ºn town, for He comprises
the Ten Sefirot,” nºt " *-* ºn sin º. “When it men-
tions the ‘mothers' (vowels) it means the Seifirot themselves.”
ninepr rºsy- n-Tº nips nºmy: “It was explained in the se-
cond chapter that, wherever it says ‘mothers,’ it alludes to the
Sefirot themselves.” non nºs "psy pipe ºn 2 - "es 'wº n->
n-ºpen ºsy”.
The four elements, air, water, fire, and earth, from which
it was anciently believed everything was created, emanated,
according to the Sefer Yetzirah, from the vowels sys; air
emanated from the S, water from the y, fire from the , and
earth from the ". As the vowels were originally identical with
the ten Sefirot, it is from the Sefirot that the whole universe
emanated”). The Sefirot cosmogony is given by the Sefer
Yetzirah as follows: *
, With ‘one, the living God of the Universe graved and
hewed out voice, air, and speech, and this is the Holy Spirit.
With ‘two' God graved and hewed out void and chaos. Void
is a green line that surrounds the whole universe, and chaos
refers to viscous stones, sunk in the abyss, whence water comes
forth.” * - "... " -
*) Sefer Yetzirah, Warsaw 1884, p. 69, 74, 90.
*) See text, § 17.
28 THE ORIGIN OF LETTERS AND NUMERALS,
..With ‘three’ God graved and hewed out mud and clay.
He arranged them like a garden bed. He set them up like a
wall. He covered them like a pavement, and poured upon
them snow, and the earth was formed.” -
“With ‘four’ God graved and hewed out the Throne of
Glory, the ophanim, the seraphim, the holy animals, and the
ministering angels”).
Chaos signified in the ancient cosmogonies the vacant, in-
finite space-out of which sprang. all things that exist. Later
cosmogonists, such as Ovid, represent it as the confused,
shapless mass, out of which the universe was formed into a
cosmos, or harmonious order. W. Enfield**) says: “By Chaos
some writers understood water, and make this the first material
principle”. He further says: *) “The theogonists certainly do
not suppose God to have been prior in the order of time to
matter: they speak of Chaos as eternal, and seem to have been
wholly unacquainted with the doctrine of creation from nothing”.
This is at variance with the Sefer Yetzirah, which emphasizes
the doctrine of creation from nothing by the statement: “He
(God) formed existence out of void, something out of nothing”
(Mishnah 22). It holds that chaos was not even the first thing
created, but was preceded by voice, air, and speech”).
*) See text, §§ 18–21.
**) History of Philosophy, London 1819, 1, 180.
**) Ibid., 131.
**) The number philosophy of Pythagoras has been explained (W.
Enfield, History of Philosophy London, 1819 vol. 1. p. 383) as follows:
,Intelligible numbers are those which subsisted in the divine mind be-
fore all things, from which everything has received its form, and which
always remain immutably the same. It is the model, or archetype, after
THE ORIGIN OF LETTERS AND NUMERALS, 29
The numeral system of the Sefer Yetzirah, as I have ex-
plained, may be considered to consist of five symbols, , ||,
|||, ||||, 0, the cipher being the fifth symbol. From this sym-
bol originated the numeral 0 (5) in the East-Arabian notation.
It is identical in form with the letter s (n) of the Arabic alpha-
bet. As the T indicates the absence of a vowel letter, and is
similar in its nature to the zero, which indicates the absence
of a digit, it is possible that the T originated from the zero.
The first primitive numerals || ||, || ||||, 0, were thus pri-
marily identical, with the five vowel-letters Tºys which were
originally the letters of the Tetragrammaton TT. The five
primitive symbols are the five elements with which God created
which the world, in all its parts, is framed. Numbers are the cause of
essence to beings . . . The Monad, or unity, is that quantity which,
being deprived of all number, remains fixed; whence called Monad. It
is the fountain of all numbers. The Duad is imperfect and passive, and
the cause of increase and division. The Triad, composed of the Monad
and Duad, partakes of the nature of both. The Tetrad, Tetractys, quater-
nian number, is the most perfect. The Decad, which is the sum of the
four former, comprehends all arithmetical and musical proportions. Accor-
ding to some writers, the Monal denotes the active principle of nature,
or God; the Duad, the passive principle or mother; the Trial, the world
(in the Sefer Yetzira, the earth) formed by the union of the two former:
and the Tetl actys, the perfection of nature. Some have understood by
this mysterious number the four elements; others, the four faculties of
the human mind; others, the four cardinal virtues; and others have been
so absurd as to suppose Pythagoras made use of this number to express
the mame of God, in reference te the word Him', by which that name is
expressed in the Hebrew language. But every attempt to unfold this
mystery has hitherto been unsuccessful“.
The reader will find below my view on the origin of the Pythago-
rean philosophy. I will only say here that there is no absurdity in
idéntifying the Tetractys with the Tetragrammaton; and moreover the
identity is established by the Sefer Yetzirah,
30 THE ORIGIN OF LETTERS AND NUMERALS.
the universe, the T or the zero being the fifth element, as the
Sefer Yetzirah says: *) Bºrs -sm lºw lys Hwy, web ºne nº
Tns nim jºb ºnw ºnwy intº jºb wen; lysw Yºse nºis.
“He formed existence out of void, something out of nothing,
andº. He hewed large stones out of intangible air, thus, twenty-
two in number, one in spirit.”
The word inn (void) has the same meaning as Toº it
is also equivalent to zero, which symbolizes the creation of so-
mething out of nothing. This is in accordance with the tea-
ching of the Pythagoreans who counted the void surrounding
the universe as a fifth element (Wilhelm Bauer, Der ſiltere
Pythagoreismus, Berne 1897, pp. 83, 84, 88, 89).
We must conclude that the so-called Arabic numerals and
the alphabet originated from the ten digits and the zero, or
rather from two symbols, 1 0, the stroke and the circle. L. D.
Nelme *), in his essay on the origin of letters, shows that all
**) See text, § 22.
**) Comp. “An Essay towards an Investigation of the Origin and
Elements of Language and Letters” by L. D. Nelme, London 1762. On ,
page 16 we read as follows: “All his (Gods) creation, and every minutest
part thereof, participates of two most essential forms; , the line 1 the
symbol of the altitude, and the circle 0 the symbol of the horizon.
These symbols contain in them the first elements, the forms of all crea-
ted nature. There doth not exist in the whole creation any being, or
thing, that doth not partake of the first principles; nor can the human
mind conceive of any exis' ence, without ideas that include these first
elements; which are not only forms essential to all matter but also to
every idea of matter that arises in the human mind: they contain in
them the elements of every art, and of every science known to man;
and they are the radix of letters also, which we have already considered
as symbols expressive of ideas.” . . . . . . .
THE ORIGIN OF LETTERS AND NUMEir ALS. 31
elementary characters, or letters, derive their forms from the
line and the circle. As I understand the Sefer Yetzirah, it
also holds that all written characters Originated from a line
and a circle, but from a line that was originally a symbol for
unity, and a circle that was originally the symbol for zero.
Similarly, all cuneiform characters originated from two symbols
Y K those for one and ten.
L. L. Conant*) says: “Two centuries ago the distinguish-
ed philosopher and mathematician Leibnitz proposed a binary
system of numeration, the only symbols needed in such a
system would be 0 and . . . . Leibnitz found in the represen-
tation of all numbers by means of two digits 0 and a fitting
symbolization of the Creation out of chaos or nothing, of the
Universe by the power of the Deity.” We have seen that not
only a binary system of numeration, but even the decimal
system may be expressed by a stroke and a zero. Moreover,
it has been pointed out that the alphabet and the so-called
Arabic numerals originated from these two symbols. There-

r
fore, the author-ef the Sefer—Y-etăţah—#. Q.N.9-#9łłłłłzº-ſº
, with which God created void and—ehra(JS, a digit and a
zero; for as the ten digitSTmay be expressed by nine digits
and a zere. So may two digits be represented by a digit and
5: s; Sefer—Yetzirah—hay—have—believed two di-
gits, o and |, a fitting symbolization of the creation, out of
chaos or nothing, of the universe, by the power of the Deity.
Because the zero in the number ten occupies the space of
a digit, only nine strokes, not ten, are used; and, therefore, we
*) The Number Concept, New York 1896, p. 102.
/t
4/L2.
32 THE ORIGIN of LETTERS AND NUMERALs.
may say that the numeral system of the Sefer Yetzirah, con-
sists of nine digits and the zero. For |||||||||| 0 = ||||||||| 0,
and the symbol + expresses the whole numeral system. The
latter figure was anciently known in South Arabia, and it re-
presented, according to Halévy, an y”). The Sefer Yetzirah
calls the letters “stones” (Rºss), because they originated from
the numerals (Sefirot), which were originally indicated by stones.
It is possible, therefore, that the # is the philosopher's stone,
from which the Arabic numerals, the alphabet, and all civiliz-
ation originated.
Moreover, since in + are united the ten Sefirot, the vowels
and the Tetragrammaton, it apparently symbolized the angel
containing the name mº, referred to in Exodus 23, 20, 21.
This angel is chiefly known in kabbalistic literature by the
name D'JET "w intetop “Metatron, Prince of the Face” and is
identified with the prophet Elijah ºy. He is the T'sºn Tw
“Prince of Creation,” or the , Logos,” with which God created
the universe. Upon the crown of the head of this angel “The
Holy one – Blessed be He” wrote letters with which were crea-
ted heaven, earth, seas, rivers, etc., and all the elements of
creation”). To this angel God intrusted all the secrets of the
Law, and of wisdom; and all the mysteries of creation are
known to him as they are known to the Creator Himself").
As the A+abic numeral system of notation, the vowels, and the
*") Comp D. H. Müller, Epigraphische Denkmäler aus Arabien, Vienna
1889, p. 19. -
*) Inish ºp”, Lemberg 1860, p. 47b.
**) Ibid., 52b.
40) Ibid, 48b.
THE ORIGIN OF LETTERS AND NUMERALS. 33
Tetragrammaton were originally identical, they all contain the
same “great secret the revelation of which is forbidden by the
author of the Sefer Yetzirah (text, §§ 10, 11, 14). This secret
apparently is the angel -
- pºem "w ºnebº = sºn inºs
symbolized by the letter y, which was anciently written also
as #.
The most mysterious character in Jewish history is the
prophet Elijah. It was he who demonstrated that TT is the
true God and no other. He is called the angel of the Cove-
nant, nºn-Fi Tsºp. He is believed to be present at the cir-
cumcision. It is also believed that he is bound to come and
decide all knotty points in the law, and to appear before the
true Messiah arrives.
In kabbalistic literature, not only the vowel letter y, but
all the letters are considered images of angels. In Sefer Raziel :
(ed. Amsterdam, p. 126) occurs the following:
Hºpm ºn: Hym inely nºsºon Enis mbi º nºns ppmw 5-iss
Yºn ty, Fºst ºne- ns ppm ºwn ºne own pºem.
“Like Adam who engraved letters out of the likeness of
those angels who had been driven away, whom the Holy One,
Blessed be He, rebuked and cast down from the high heavens.
He then graved their likeness from Aleph to Taw.”
The vowel letters, however, the letters of the Tetra-
grammaton, are images and pictures of superior angels. Since
the cipher T is also a letter of the Tetragrammaton, it is also
a picture and image of a Superior angel. The angel which
the cipher T symbolizes, is apparently Satan jºy, who appears
before God to prosecute all mortal beings as he prosecuted
34 THE ORIGIN OF LETTERS AND NUMERALs.
Job and Joshua Son of Jehozadak (Job 1, 6–12; 2, 1–7;
Zechar. 3, 1). Like the cipher T so the zero in the Arabic
system of notation, and in the system from which the latter
Originated, was anciently believed to symbolize the evil deity,
or Satan **), in contrast to the numeral one 1, which was
thought to symbolize the good God, from whom all good
emanated. The numeral one 1 and the zero 0 are a fitting
symbolization of the two opposing principles concerning which
the Sefer Yetzirah (§ 23) says as follows:
“Also God set the one over against the other, good against
evil, and evil against good; good out of good; and evil out of
evil; good testing evil, and evil testing g00d; good is stored
away for the good, and evil is stored away for the evil.”
The account of the origin of letters and numerals the
author of the Sefer Yetzirah concludes as follows:
“When Abraham our father arose, he looked and saw and
investigated and observed and engraved and hewed and combin-
ed and formed and calculated, and his creation was successful.
Then the Master of all revealed himself to him, and made a
**) “It was not very easy to comprehend at first the precise force
of the cipher, which, insignificant by itself, only serves to determine the
rank and value of the other digits. A sort of mystery, which has im-
printed its trace on language, seemed to hang over the practice of
numeration, for we still speak of deciphering, and of writing in cipher,
in allusion to some dark or concealed art” (The Philosophy of Arith-
metic, by John Leslie, Edinburgh 1817, p. 114). “Indeed, in the early
history of arithmetic in Europe . . . . the system was regarded as be-
longing to black art and the devil ; and it was, no doubt, this popular
prejudice that delayed its general introduction into Christian Europe"
(E. Brooks, The Philosophy of Arithmetic, Philadelphia 1901, p. 107).
THE ORIGIN OF LETTERS AND NUMERALS. 35
covenant with him and with his seed forever. He made a
covenant with him on the ten fingers of his hands, and this is
the covenant of the tongue; and on the ten toes of his feet,
and this is the covenant of circumcision; and tied the twenty-
two letters of the “Torah” to his tongue and revealed to him
their secret. . .”
The name of Abraham which is mentioned in the closing
Mishnah suggested to many commentators that Abraham him-
self wrote the Sefer Yetzirah. As such a view is entirely re-
pugnant to the modern critical mind, some writers regard this
closing Mishnah as a later interpolation. In my opinion there
is no doubt that this Mishnah belongs to the original Sefer
Yetzirah, for it is in perfect harmony with all the original
material. The mention of the name of Abraham does not
indicate that the Patriarch wrote the Sefer Yetzirah, but that
he was the inventor of the alphabet, the scribe ("Pip) mention-
ed in the opening Mishnah as the person whom God inspired
with it. *
It is worthy of note that Philo attributes the first inven-
tion of letters to Abraham (Rees, Cyclopedia; art. Letter; comp.
also Suidas in Abraham and Isidor Hispal, Origg, 1, 3).
CHAP. IV.
THE TEXT.
No Hebrew book has been so tampered with as the Sefer
Yetzirah. As early as the tenth century there existed several
versions of it, varying in length and in arrangement. There
3”
36 THE ORIGIN OF LETTERS AND NUMERALs.
were the short and the long version, which were edited in
Mantua in 1562, and Saadia’s text, edited by M. Lambert, in
Paris, in 1891. Each of these three texts is different from the
others. Although Saadia’s version is almost of the same length
as Mantua II, it differs materially therefrom in the arrange-
ment of the chapters and the paragraphs, and it thus happens that
the matter contained in one chapter in Mantua II may be found
scattered through several chapters in Saadia’s text ; while entire
paragraphs in Saadia’s text are cut up and distributed among
three different chapters in Mantua II. Both Mantua texts agree
in a general way with each other in their arrangement, but
Mantua II contains twice as much material as Mantua I, the
former numbering about 2400 words, the latter only 1200
words. -
A critical study leads to the conclusion that these ver-
sions contain only obouth 600 words of the original Sefer
Yetzirah. The remaining 600 words in Mantua I or the 1800
words in Mantua II are all interpolations nnd not of the original
Sefer Yetzirah. All the matter belonging to the original Sefer
Yetzirah, I arranged as a separate treatise, which may be reffe-
red to as Sefer Yetzirah I. All the interpolations I arranged
also as a separate treatise, which may be referred to as Sefer
Yetzirah II. Having already explained the Sefer Yetzirah I, it
now remains to explain the Sefer Yetzirah Iſ.
Of the Sefer Yetzirah II little need be said ; it abounds
in trifles, contradictions and repetitions. Although it was inten-
ded as a commentary on Sefer Yetzirah I, its author had no con-
ception whatever of what the original Sefer Yetzirah was. He
THE ORIGIN OF LETTERS AND NUMERALs. 37
saw in it only a cosmogony based upon the letters of the al-
phabet and the Sefiroſh. According to him God created the
universe with thirty-two wonderful ways of wisdom. These ways
are the ten Sefiroth and the twenty-two letters. The ten Se-
firoth are : The Spirit of God, Air, Water, Fire, Height, Depth,
East, West, North, and South. From the first emanated the
second; from the second the third, from the third the fourth,
and the remaining six sefiroth emanated from the six permuta-
tions of the letters ºn. With the second Sefirah (Air) God
created the twenty-two letters, and divided them into threw
parts, or books (ºner Tºw); three mothers wes; seven double
letters nºne: Tºn, and twelve simple letters: Psy blº ºn mn. -
With these three classes, or groups, of letters were created
the various parts of the world (Bºy), of the year (ºw) and
of the soul. (2/23). -
The author of the Sefer Yetzirah II contradicts himself ;
he explains that by the three mother letters, wox, which the
original Sefer Yetzirah declares to be a “great secret” (ºti TE)
are meant the letters ºn of the great name "Tº the mothers
thus not being a separate class at all but part of the simple
letters. - -
As a matter of fact, he himself abandons the division of
the letters into three parts, and rearranges them in a twofold.
division, one of ten and one of twelve letters. For, finally, he
counts the letters tºps with the seven double letters nTED T35,
as one class. The whole theory of the world, of the year,
and of the soul, is expressed by tens and twelves. Indeed he
says”) as follows:
“) Mantua II chap VI Sepher-yeairal-in-cimpºv.
38 THE ORIGIN OF LETTERS AND NUMERALS.
. Twy pºw; nºwys nºt cºny
. Twy ºwn nºwys Hnºep Hºw
, -wy ºwn nºwys Hnºt we
The world is countet by ten and twelve .
The year is counted by ten and twelve
The soul is counted by ten and twelve
It therefore follows that, according to the author of the
Sefer Yetzirah II, the twenty-two letters are divided into ten
double nies The wes and twelve simple letters Psy pyº ºn nr.
According to the author of the Sefer Yetzirah II, however, each
double letter represents only one way of wisdom, as each simple
letter does. The twenty - two letters, therefore, are, according
to him, only twenty - two ways of wisdom. The remai-
ning ten ways of wisdom are the ten Sefiroth, which he
explained to be the Spirit of God, air, water, fire, height, depth,
east, west, north, and south. The author of the Sefer Yetzirah II
understood the numeral words. . yams ...wºw . . .5°ng . . .nns
occurring in the original Sefer Yetzirah, to mean first, second,
third and fourth. He imagined that the author of the origi-
nal Sefer Yetzirah had counted only four Sefiroth, and had for-
gotten to count the remaining six Sefiroth, and after explain-
ing that the four Sefiroth are the Spirit of God, air, wat-
er, and fire, he counted height, depth, east, west, north, and
south as six Sefiroth to complete the number of the ten Se-
firoth. The truth is that the numerals . . . . Bºnº' . ... nns
. . . vans . . . . wºw mean, not first, second, third and fourth,
but one, two, three and four, and these numbers themselves
are the ten Sefiroth from which all letters of the alphabet (par-
THE ORIGIN OF LETTERS AND NUMERALS. 39
ticularly the vowel letters) originatad. The Sefiroth, therefore,
cannot be counted as ten separate ways of wisdom. The latter
view requires that the twenty-two letters shall be taken to be
all the thirty-two ways of wisdom, not only twenty-two ways of
wisdom as explained by the Sefer Yetzirah II which is followed
by all commentators.
CHAP. W.
Saadia, who was the first to divide the letters into five
groups ynns, Apia, Poº, niºbi, Pºwel, believed all the letters
to be consonants. He interpolated this division in the Sefer
Yetzirah without knowing that by nibs the original Sefer Yetzirah
meant vowels. The first to perceive that nibs means vowels
was Dunash Ibn Tamim *), who explained that by the three
mother letters ºbs the Sefer Yezirah meant the three vowel
letters ºx. He failed, however, to see that by way of contrast
mtºn must necessarily mean consonants. Now, he knew that
his version of the Sefer Yetzirah contained many mistakes, that
ignorant people had blended the original and an early commen-
tary”), and consequently the original text did not exist. Yet
he did not perceive the absurdity of the division of the letters
into three classes named: three mother letters ºbs, seven
double letters nº T- and twelve simple letters blº ºn mm
Psy. The category mothers' (mos) is not in any sense coordinate
**) ,Sefer Yetzirah", London, 1902, p. 45.
*) Ibid., p. 65.
40 THE ORIGIN OF LETTERS AND NUMERALS,
^ -h 1 × 7. n pſ
jo a 9 º'
3)
with that of “double letters” and “simple letters”, which con-
trast admirably with each other. Moreover, he failed to
perceive that according to the Sefer Yetzirah, there are ten
double letters and not only seven. He is also at variance with
all the known versions of the text, which give twelve simple
letters, while he, in counting the total number of sounds 29,
of which 14 are contained in the seven double letters ºnes tº
makes the simple letters number 15. Besides, it is very hard
to understand how Dumash could have counted the letters. *N
as simple letters having one sound, and declare at the same
time that originally they were vowels and consequently must
have had several sounds: namely the sounds of i and e : of
w, u and 0; 8 of a and other vowel sounds.
Long before I ever saw the Sefer Yetzirah, I had concluded
that the Hebrew alphabet consisted of ten letters with double
sounds and twelve ſetters with simple sounds; thus represen-
ting thirty-two sounds. I came to this conclusion in investig-
ating the pronunciation of the vowels, which the reader will
find in my isºpm TP-n mpnº (will appear shortly), in which
I have discussed it at length. The iſºn double letters are:
in ſº in P 5 , T G = |s
and the twelve simple letters are:
.P s y P G p * * * in In
I base this division on the assumption that the letters
ºys are the original vowels of the Hebrew alphabet, and that
the true sounds of these letters were as follows: y = a, s = e,
X = 0, = i, j = u, i = y. Hence, the letters is are also double
letters, so that these together with the six letters nº 715, the
THE ORIGIN OF LETTERS AND NUMERALS. 41
letter T and the letter tº were known to be double letters:
hence, ten letters with double sounds. After reaching this con-
clusion, I found that the division of the letters of the Sefer Yetzirah
bore a decided similarity to it. In fact, the Sefer Yetzirah gives
the same number and the same classification of the single
letters; the only difference is that it counts the i among the
simple letters, while I considered the as a double letter, and
gave instead the b. Nevertheless, I do not believe from a
grammatical point of view, that the author of the original Sefer
Yetzirah could have counted the letter as a simple letter instead
of the letter b, and could have counted only seven double
letters without including at least the letter w which is still
pronounced as a double letter by a great majority of the Jewish
people. Further investigation proved that anciently there
were counted ten double letters. * -
As is well-known, some old grammarians, among whom
was the author of the “Dikduke ha-Teamim” counted the final
letters as separate letters, thus making the total number of
the letters of the alphabet twenty-seven. This calculation har-
monizes with the statement of the Talmud and Midrash that
the letters nºs form respectively the beginning, the middle,
and the end of the alphabet “), which can be true only if we
count the finals as separate letters and thus make the total
number twenty-seven, for otherwise the p can not be in the
middle of the alphabet. Some grammarians, though they do not con-
sider the finals as separate letters, yet count the letters twenty-
**) According to Rashi, Job XXVIII, 27 the word nº N occurred in
the Sefer Yetzirah; comp. above p. 17. .
42 THE ORIGIN OF LETTERS AND NUMERALS.
* n_2 >/ 7
• Yp?
nine, figuring the double letters Re: T- and the - or the was
fourteen letters. Convinced that there are ten double letters and
twelve simple letters, I concluded that there must have been
a time when the Hebrew alphabet was reckoned thirty-two letters
without the final letters, and thirty-seven or thirty-nine with
the final letters, as follows:
n n w w - - P - sº F = eye p = p + 17: - ; ºn n- + x; 3 = s.s
In such an arrangement of the letters, not the b but the
letter k is in the middle of the alphabet.
On reaching this conclusion, I sought to find some author-
ity in the ancient literature for placing the * in the middle
of the alphabet. This fact, if established, would prove the
correctness of my views on the Hebrew vowel points and their
relation to the vowel letters yºs as explained in #23H-fi
=s*PH and it would also prove that the original Sefer Yetzirah
gave the number of double sound letters as ten, and not seven.
To my great delight, I found, in the sapy -- nyms the
following: “Why is the letter higher than the other letters?
Because it is in the middle of the letters”. I also found in
the Midrash Tadshe "), that the letter is in the middle of the
letters. These passages make it clear that the ancients
counted ten double letters, and in their arrangement of the al-
phabet, they sometimes counted them as twenty “").
*) Epstein, cºmmºn nºjo-pro, Wien 1887 p. XVIII.
**) The philosopher and Grammarian Profiat Duran “Ma’ase Efod”
p. 34) also says that the ancients divided the twenty-two letters of the
Hebrew alphabet into ten and twelve, according to the ten spheres
(pººl) and the twelve signs of the zodiac (nºrs). …
THE ORIGIN or LETTERS AND NUMERALs. * , 43
This seemed to justify my reading of the ten double letters
n wº P = - 1 = 8 mºne: Twy in the Sefer Yetzirah, and not seven,
and my contention that by the thirty-two mysterious ways
are meant the thirty-two sounds of the Hebrew alphabet, con-
sisting of ten double letters and twelve simple letters.
CHAP. WI
AUTHORSHIP.
Thus far, it has been impossible to determine the age and
authorship of the Sefer Yetzirah. Jewish tradition claims divine
origin for it: it was intrusted by the Lord to Adam and after-
wards to Abraham *). A very interesting passage concerning
Abraham and his relation to the Sefer Yetzirah is quoted by
Judah Barfeloni, in his commentary on the Sefer Yetzirah
(p. 268), from an ancient text.
:*INT ºx"|" Nºnº-, jº
ºw ºn- nººn jeº n-wn ºsºp ºnes jºss ºn-ex Tºwn)
H"-n -os tº sº ºpp ims neºn Bºy: Tº º sins cºy
Ennisº Tsw; six n- + -ps, nºn- Tºp; Ernese is nose-
-et- Hºn Tºp: To my sº ºxy Rºw −y sº º H-ps jºins
his ºn sº is jºyo; Tin -v ºn ºn--sº into 5 -es, Hºs
mºnº wºrp Hns tº º Hips, ºp ni Hssw -y ºr is ºn:
pinº ºn sº insi - ºn-pm Hºs, -et ºns--, -ins is ºs psy
Ennis ºn tº a ºn 5-ºw = eam ºn Tosyº ~~P ºn is
j's wo; Ty, pºlyn ns -is: yº mean Bºw ºf Yoy ºwn ºn- ow:
imºvº Bºw 'i -y mys, sº sººn jº sºs ºn is lºw p-sº
- *) Peter Beer, Geschichte religiöser Sekten der Juden, Zweiter
Band, Brünn 1823, p. 10, 12. 21.
44 THE ORIGIN OF LETTERS AND NUMERALs.
;
*Ein Ennis is ºnvoy pen ſº prºv Høj Bººne º mwy' by
- - .nº Hºn- 25 Toº Hºn. Hoon
We find in an ancient reading as follows:
“When Abraham, our father was born, the angels of ministry
said to the Holy One, Blessed be He; ‘o Lord of the World !
Thou hast a beloved one in the world, wilt thou conceal anything
from him º' Directly, the Holy On, blessed be He said, ‘Shall
I conceal from Abraham?' and consulted the Torah. He said to
her, ‘My daughter, come and we will marry thee to Abraham
My beloved.” She said to him, ‘No, not until the meek one com-
es and takes meekness.” God then consulted the Sefer Yetzirah,
which said, 'Yes'. God then handed it over to Abraham, who
sat by himself studying it, without being able to understand
anything, until a heavenly voice came forth and said, ‘Dost
thou seek to compare thyself with Me? I am One I created the
Sefer Yetzirah, and studied it. But thou canst not understand
it alone. Get thee an associate, and look into it together, you
will then understand.’ At once, Abraham went to his teacher
Shem, and stayed wit him three years. They looked into it
and they knew how to form the world. From that time to
this, there is no man who can understand it alone, there must
be two wise men, and they cannot understand it before three
years. But when they do understand it, they can do anything
their hearts desire. When Abraham understood it, his wisdom
increased greatly, and he taught the whole law.”
The world which Abraham and his teacher Shem were
able to form after three years of study of the Sefer Yetzirah
may be understood to mean the world of letters. Indeed, the
Tili; ORiGIN OF LiTTERS AND NUMERALS, 45
.*
invention of letters was anciently spoken of as the creation of
the universe.
The names of Moses, Ezra”), and Rabbi Akiba have also
been advanced as the authors of the Sefer Yetzirah. The attri-
bution of the work to Rabbi Akiba undoubtedly rests on a con-
fusion of titles. The Sefer Yetzirah was called by ancient
writers jºs ETRs ºw mºnis, and was confounded with the Mi-
drash sapy -- ºw nºns, which is called by some authors
Sefer Yetzirah. Thus Gedaliah Ibn Yahya, in his ,Shalshelet
ha-Kabbalah, says : -
--ny Hºg net ºn Hºpi by Hºs, -ee, nºn-et-ºn sm
why sººn ºil wºe ºn Yºo-H -ws Ennis. # *
“He composed the Sefer Mechiltin, and the Sefer Yetzirah on
Kabbalah. There is a Sefer Yetzirah composed by Abraham,
to which Nachmanides made a great and wonderful com-
mentary.”
This passage was apparently misunderstood by some later
Writers, who imagined that Rabbi Akiba was the author of the
Sefer Yetzirah attributed to Abraham. Hence Isaac de Lates;
criticism in the introduction to the Zohar :
Hning. Howe Hºsºp, Hºs, -et ºns; sºpy --, -ni º Ty.
pºin-sp Hºpi pºe: Hºw. -
“Besides, who permitted Rabbi Akiba to write the Sefer
Yetzirah They called it Mishnah, and it was handed down to
them by Oral tradition from Abraham.”
* Peter Beer, Geschichte religiöser Sekten der Juden, zweiter
Band, Brünn 1828, p. 12, 21.
46 THE ORiGIN OF LETTERS AND NUMERALS.
Moses Gordover0°) flatly denies Rabbi Akiba's authorship
of the Sefer Yetzirah. In the Pardes Rimmonim he says :
ºr wº phºwn Yºy lºss ºn--sº nyºn nºg' -ep ºns Hym
.npopº His sºpy --> Inis
“We have a Sefer Yetzira attributed to Abraham. Some
ascribe it to Rabbi Akiba, but there is no general agree-
ment.”
Modern writers are also divided in their opinions concer-
ning the age of the Sefer Yetzirah. Some of them believe it
to be a production of the first or the second century B. C. ;
others place it in the Geonic period, ranging from the seventh
to the ninth centuries of the Christian Era. My personal in-
clination is to accept the late date (about 750–931) for that
portion of the book which has been referred to as Sefer Yetzirah II,
in the discussion of the text ; but I have no doubt that the
part containing the account of the origin of letters, which was
explained above is pre-Talmudic, and is reffered to in the Tal-
mud in the following passages :
by nºris Fyns Hºw H^s. Yet T by "wn) snai sn- sº-
nine sp ºn sº ºne ynwo sp wn sº ºn- Hºpk nºw (sº
ºn in Hywis sº sºn -- ºney? --in ns sººn p 2's nº
enº ºs snºr sºw nº ºne nºw nee: Pey snºw •ºyº º
H-s: nºn- pey ºn snºw ºyº -> sywis -m sºn --->
..(ºriº ºx! Nºnºn sºy nº ºn-ºp
59) Quoted from pºp" pºle by L. Gold sch mid t, Sefer Yetzirah
Frankf., 1905. *
**) Sanhedrin, 65b.
***) Ibid, 67 b.
THE ORIGIN of LETTERS AND NUMERALS, 47
Raba created a man (Rashi says, through the Sefer Yetzirah),
and sent him to Rabbi Zera who spoke to him, but received
no answer. He then said to him, “you are a creature of the
learned, return to your dust.”
Rabbi Hanina and Rabbi Oshaiah sat the entire eve of the
Sabbath studying the Sefer Yetzirah and created a three-year old
calf, and ate it. . . . “Like the case of Rabbi Hanina and Rabbi
Oshaiah who studied the Hilchot Yetzirah every Friday, and
a three-year-old calf was created for them, which they ate”.
The Sefer Yetzirah and the Hiichot Yetzirah, mentioned in
these passages are undoubtedly our original Sefer Yetzirah,
from which was borrowed the Baraitha beginning with the words
of the Sefer Yetzirah:
(* ºr pºlyn ºr rs ºppy prº p ºn inn
, Void is a green line that surrounds the whole universe. “
This passage must have been a part of the original Sefer
Yetzirah and not a later interpolation, for it tallies with the
paragraphs before and after it, that its omission leaves a gap
that no other can fill so satisfactorily -
From a passage of a commentary on the Sefer Yetzirah of
the thirteenth century, which is still extant in manuscript.
(Bodleian Library, Codex 1947), we can see that the commen-
tator believed that the Sefer Yetzirah was written by Joseph ben
Uziel, for he says: . t
... wipH mn ºn mn-, m- ºp Hºpi ex ºsmy in new wº in
- illery ºy nº sºn)
**) Hagigah, 12 a.
48 THE ORIGIN OF LETTERS AND NUMERALS,
“These are the words of Joseph ben Uziel, who received
them from Jeremiah : “Voice, air, speech’, this is the holy spirit
... and restore the creator to his abode.”
As the commentator declares words in the Sefer Yetzirah
to be the language of Joseph ben Uziel, he evidently believed
that he wrote it.
In another passage the commentator says.
. . . . ;--> TE nº sºn men ºn ºsmy in Few 1:
...So Joseph ben Uziel received from Jeremiah the Prophet.
The secret was revealed in Babylonia.”
By Tib is apparently meant the Sefer Yetzirah *); which
he believed to have been revealed and transmitted to Joseph
ben Uziel by the prophet Jeremiah. From the ending of this
commentary we gather that the commentator had before him an
ancient text of the Sefer Yetzirah, which had at the end Pºp
*R*y in For nowo Ennis nowº, “Here ends the Mishnah of
Abraham and the Mishnah of Joseph ben Uziel.” Recanafi and
other writers took this colophon to mean that Joseph ben Uziel
was the author of the commentary. This misunderstanding
caused the bibliopraphers to catalogue it under the title sn"Tº
*Nºmy in Foºt or Hºs, -et.
In the Leipzig Codex (No. XXX, fol. 12) there is another
treatise called ºsmy - Fºrt snºn-, which A. Epstein") con-
siders a work by the same author as the commentary. The
quoted title was given to the treatise apparently because of the
following passage occurring therein:
byush sºs nº ps, sºn Hºon tº nºw ºsmy in App ºn
TYetzirah-
*) pinn, Krakau-Wien 1898–95, II, p. 41.
& * 2 i
THE ORIGIN OF LETTERS AND NUMERALS, 49
“Joseph ben Uziel taught it. It was revealed to him by
Jeremiah the prophet, and it must not be revealed to anyone
except the pious” (the modest?). In this passage the author
doubtless refers again to the Sefer Yetzirah, which was revealed
or handed down by the prophet Jeremiah to Joseph ben Uziel.
J. J. L. Barges”) quotes, from the Paris Cod, 762 the
following passage, which occurs also in the Brit. Mus. Cod.
15299 :
Fppº in ºsmy; Rºb in nºw on 15 m pinep 'n ºn ºn
"Ps -na 'nan snpºpe Heb pºp" net [ºn] ºn Hep Hnºs" -er is:
in ºn- niss P-2 m = myow - pne ºp-e 'n l- whº--- let
ent - yns in p-e ºwn Hwye pºp sºpy - nºn's phe
$5 nºvs, mººn ºne may nic myº ºne mºmpe lip Eby -->
Hºw sin ºr H-ps w-pn m- Pissº ºne six ºr wyn Hºsn p'yºn
* -ps ºn in nº is ºbs, [Rºb El w”usy ºpy cºis »sº ºnne
'n l-nS, E-5-in lºs [Nºt 15) w”usy Ep anº. Few ºw. Tºp Toº
. . . . 'Iº T's, Tep ºns: ºne-
“These are the five Sefarim (books) and the five Sedarim
(orders) which Ben Sira revealed to his son Uziel, and his
grandson Joseph, Sefer Yetzirah, Sefer Tagin, Sefer Dikduk, Sefer
Pesikta Rabbati in two forms, Sefer Zerubbabel, which contains
five chapters: Simeon ben Yohai, Aboth di Rabbi Nathan, Otiot
di Rabbi Akiba, Maase Mishkan, Derek Eretz. The five Se-
darim are : Seder Olam, Seder Pekudoth, Seder Shaot, Seder
Ibbur, Seder Halakoth. When he revealed all these secrets, all
the host of heaven shook, and the holy spirit came out and
said: ‘Who is it that revealed my secrets to mankind P w”bsy
[Ben Siraj arose and said: ‘I Buzi son of Buzi’. The holy
*) ºn Hep, Paris 1866, p. X.
50 THE ORIGIN OF LETTERS AND NUMERALS.
spirit said to him: ‘Enough’. Immediately Joseph sat down
and wrote down these words at the dictation of w”0sy [Ben
Siraj, and he wrote them in five books on the earth : Sefer
Yetzirah, etc. “
Although the greater part of this passage is obviously spu-
rious, attributing, as it does, to Joseph ben Uziel works of other
authors, it may be authentic with regard to the Sefer Yetzirah,
which heads the list. It is not unlikely that originally only the
Sefer Yetzirah had been ascribed to Joseph ben Uziel, but as
there were several other Works in the same volume, some careless
copyist attributed them all to him. The original passage may
have read as follows:
Hºws. Tº ºppº, is ºsmyl; Rºb is nºw Hºs: -et sin m
Hºw Hi sin ºr H-ps wipm nº Hsº pºp six ºf wyn Hin inn
+c Tw- nº ºps ſºns - ºne is nps w”bsy ºpy nºis jºb ºne
.nn's "PE w”usy ep snº FD) aw:
“This is the Sefer Yetzirah, which Ben Sira revealed to
his son Uziel, and his grandson Joseph. When he had revealed
this secret, all the hosts of heaven trembled, and the holy spirit
came out and said: Who is it that has revealed my secret, to
mankind? (2)"Togy arose and said: ‘I Buzi son of Buzi’. Then
the holy spirit said to him: ‘Enough". Immediately Joseph sat
down and wrote down the sefer Yetzirah at the dictation of
ty” togy.” -
This passage also indicates that Joseph ben Uziel wrote
the Sefer Yetzirah. According to this passage, however, not
Jeremiah but Ben Sira revealed the philosophy of the Sefer
Yetzirah to his grandson Joseph ben Uziel. In the Alphabet
of Ben Sira Josef ben Uziel is also mentioned as a grandson
THE ORIGIN OF LETTERS AND NUMERALS. 51
of Ben Sira and Ben Sira’s mother was a daughter") of Jere-
miah. There are also legends that Jeremiah and his grandson
Ben Sira studied together the Sefer Yetzirah.
The “Inish ºp” 20a, Lemberg 1860, quotes from a
cabalistic work Tsºe, as follows:
Hip Hnos" ºp na Hss, Hng Hep- ppyº ºnnn non-
Fibº . . . . ºwn nºs, Tepi, ppyn, in shºp ºss ºn han 1%
Hºm nos inspi ºn H'm Tris nºis Enº Rºj Toson ºn wyry
"sm so in-p-' 9"s nos by 's ms pmb ºn snain ms tº pop
my to nº ºne Hoº Hyn Hºng ins' 1"nch ºwe Tº ºwes º's
inney Ty ºr noRºos Rºl injps: ºne Dix Hºn sº nº-ºp Hoo
"Josh yºvo, nosh Tºy ºn ly-ºw Ty Injo's mp pip” pºts ºn ºn
pºsin ºvyi) nºn- whew Ty ºn-Tº intºp” tºnnn innon mp)
Twº-nº pºwe in pºwly ºn Hyº-Ti, nyly ºn Riny no n\pi,
pºp prºs cº- pºsºm joism nºw T-5 nºn --is is ºn-
./º-y ºrity jºin psyn Drin oppy Ens
“Jeremiah began to study Sefer Yetzira, when a heavenly voice
came forth and said: “Get thee an associate’. He accordingly
went to his son Sira, and they studied the Sefer Yetzira to-
gether. Finally . . . a man was created by them, upon whose
forehead was written “Emet' (nos = truth). The person created
had a knife in his hand, and was erasing the letter Aleph of
the word Emet. Jeremiah said to him, ‘Why do you that ?’.
He answered, 'I will tell you a parable’. This case is similar
to that of a man who built many houses, countries, and towers,
and no one appreciated his art or his work, until two men
induced him to teach them the secret of his art, so that they
knew it all thoroughly. When they learned the art, and the
**) See “Alphabet of Ben Sira", ed. Steinschneider Berlin 1858. 16b.
4%
52 THE ORIGIN OF LETTERS AND NUMER ALS.
man’s secret and method, they began to irritate him with their
words, and finally left him, taking his science with them and
became builders like him. What he did for a denarius, they
did for three peshufim. When people learned of their existence,
they all left the original artisan and went to them, honoring .
them, and negotiating with them in their building enterprises *
This passage, which may also be considered as having
been prefixed originally to a copy of the Sefer Yetzira, not only
indicates that Jeremiah and Ben Sira studied the philosophy of
the Sefer Yetzira (or the invention of the alphabet), but also
gives a reason why this study should be kept secret.
In his work Sefer ha-Gematria, Rabbi Judah he-Hasid
says”):
ºn sº ºnes, ºp ni Hss, Hºg' -ee- ppy; nº sn't in
nºw 'i Rupº in ppy. . . . was nº- ºgs tº ºn T1-5 inwy
ºps mysºn RTs nspi pº nos inspi ºns. Tris E-1s Enº sºn,
Twsºn 5-is ns n'on. Hs-w: . . . H'-ph . . . shºw inst Enº
isnin sº, p nºwy' Misin isy × 25 no sºon nose nis Hmp
Yººn sn-in nºis priº ºps .wºs --> pºlyn in yo sºw p-is in:
:-Pyº nwy, Tºp ºnspiv nosp 's pno, ynecº minish Fºns
“Iben Sira wanted to study the Sefer Yetzira, when a heav-
enly Voice came out and said: ‘Thou canst not do it alone’.
So he went to his father Jeremiah . . . and they studied it.
At the end of three years a man was created by them, on whose
foreliead was written Emet (nbX = truth), as on the forehead
of Adam. Then the one whom they had created said to them:
'God created Adam, and when He wanted to put him to death,
he erased a letter from the word Emet and it became Met
*) Quoted by Epstein in Bºnn nºbipp, Wien 1887, p. 122.
THE ORIGIN OF LETTERS AND NUMERALS, 53
(no = dead). So much the more reason is there why I should
want to do the same, so that you may not again create a man and
the world go astray through him like the generation of
Enosh . . .” Then the man who had been created said to
them: ‘Transpose the order of the letters, and erase the Aleph
from the word Emet (nos) in my forehead. Immediately he
turned into dust.” łº
A work like the Sefer Yetzirah could not have been the
product of the person, who actually put it into writing. Its
contents must have been known, to at least a few persons,
long before it was written down. It is, therefore, not at all
impossible that the prophet Jeremiah and his grandson Ben
Sira studied its philosophy.
From the foregoing it is evident that so far we have no
historic document by which to prove either the authorship or
the exact age of the Sefer Yetzirah. According to the above
quoted legendary passages, however, the Sefer Yetzirah was
written by a Joseph ben Uziel, a grandson of Ben Sira. If
this Ben Sira was the author of Ecclesiasticus, which apparently
was written in the third century B. C. E., his grandson Joseph
ben Uziel could have written the Sefer Yetzirah in the second
century B. C. E. If, however, this Ben Sira was identical
with the high-priest Joshua son of Jehozadak, his grandson
Joseph ben Uziel could not have written the Sefer Yetzirah
later than at the end of the fifth century B. C. E. The authors
of the above quoted passages and the author of the Alphabet
of Ben Sira doubtless believed Ben Sira to be identical with
the high-priest Joshua son of Jehozadak, to whom the wisdom
—t taugh, in Ecclesiasticus was attributed.
54 THE ORIGIN OF LETTERS AND NUMERALS.
Isidore of Sevile in his remote day (620), identified Jesus,
the son of Sira, with Joshua ben Jehozadak, and in the Latin
Mss. of Ecclesiasticus, it is stated that Ben Sira was a son 01
Jehozadak”). Like Ecclesiasticus, the Pseudo-Ben Sira’s “Alpha-
bet of ben Sira” was also attributed to Joshua ben Jehozadak.
Hence its title in the Hebrew-German edition (Offenbach, 1728).
Already Abraham Abulafia perceived that the Pythagorean
number philosophy is identical with the Sefiroth philosophy of
the Sefer Yetzirah. The relation they bear to each other is
variously explained. A. F. Thimus"), shares the view that
the Pythagorean philosophy is an adaptation from the Sefer
Yetzirah. Others hold that the author of the Sefer Yetzirah
borrowed his philosophy from Pythagoras and Plato.
I do not pretend to be able to solve this difficult question.
But I wish to call attention to a few points which may suggest
a solution or at least guide further investigation,
The person of Pythagoras") is as much an unknown
quantity as that of Ben Sira. Philolaus, the first one to publish
**) See Nestle in Hasting's Bible Dictionary, vol IV, p. 542.
**) Die Harmonikale Symbolik, Köln 1876, II, pp. WI, 2, 183, 241.
**) Dr. A. Hirsh (JOR., vol. XX, p. 61) doubts whether there ever
was a Pythagoras, although he has no doubt there existed a Pythagorean
school of philosophers. It is admitted (J. Burnet, Early Greek Philosophy,
page 99) that “all that has come down to us under the names of various
disciples of Pythagoras is pure forgery, of the most worthless kind. The
whole early history of Pythagoreanism is therefore conjectural, and all
we really know of the school is what we are told by Aristotle”. Accor-
ding to some writers Pythagoras was a Greek, according to others, he
was either a Phoenician or a Syriam. There have been also some writers
THE ORIGIN OF LETTERS AND NUMERALS. 55
the Pythagorean philosophy, corresponds curiously to Joseph
ben Uziel who wrote down the Sefer Yetzirah. Would it be
to bold to conclude that the Sefer Yetzirah represents the genuine
fragments of Philolaus?
H-lºgº ->>
(§ P-E)
'N TYºyº
nsºr nºn: pºny, nºwºw
-ep, ºpen nisix mm R. PPn
:-ep
.* 'il Flyto
nºns ºnwy Dwºw in lºsſ
Hºwy ºnwi nº nwy nisºe
nºn's pºny, nºnwy inw mºve
: Hºn ºw
/* Tjºto
;" |} - is nºes nºn's ºwy
ywn sº ºwy ºn 2 - P - )
Hºwy bºny nºwy nns sº ºwy
p : , ſº in , ," nºwe mºnix
nns Rºy Hºwy pºny ſp;x ſyſt ı
Hºwy wºw sº nºwy pºny Hºwy
SEFER YETZIRAH
Chap. I
§ 1
Thirty-two mysterious ways
has the Lord, Lord of hosts,
ordained through Scribe, Script,
and Scroll.
§ 2
These are the thirty - two
mysterious ways, ten double
and twelve simple, which are the
twenty-two letters, of the Torah.
.* § 3
The ten double letters are
in ſº T. E. 5 , ;" |} in 18 ten
and not nine, ten and not
eleven. The twelve simple
letters are , p * * * in T
,P is ſyſt twelve and not eleven ;
who believe that he was a Jew. (Rathgeber, Grossgriechenland und Pytha-
goras, Gotha 1866, pp. 325, 461, 466). He has even been identified with
the prophet Ezekiel. (Ibid., 534). If Pythagoras was a Hebrew he should
rather be identified with the high-priest Joshua son of Jehozadak.
56 THE ORIGIN OF LETTERS AND NUMERALS.
Nº.
by --- Teym -- hipm na n-
:yºr ºy nº ºwn ºn
/* Hyºyº
nippn mºns ºnw ºnwy
He- nylºp mn-, m-iºn ºp-
:nippo Hwon-
'n Hyºyº
lºn ppm nºns ºnw ºnwy
$5 ns no nº lens nºm ºpw
:-ins: Tºnyn º ns) ºn
') ºnjºy
by Fºs ºn-on ºpw Eng Tºº
lºs by nº Fºx by ºn by:
mºnn tº by lºop,n’s pyºs)
nºwn ºn ºn 55 sucy Hººn
: To Rs.`
twelve and not thirteen. In-
vestigate them, examine them,
establish the matter clearly,
and restore the Creator to His
abode.
§ 4
Twenty-two letters are en-
graved by the voice, hewn out
in the air, and fixed in the
mouth in five places.
§ 5
Twenty-two letters He en-
graved, hewed out, weighed,
changed, combined, and formed
Out of them all existing forms,
and all forms that may in the
future be called into existence.
§ 6
How did He combine them,
weigh them, and change them?
8 with all of them and all
of them with 8; 5, with all of
them and all of them with 5;
and so all of them with all of
them turning around in order;
thus all words and all existing
forms are derived from them.
THE ORIGIN OF LETTERS AND NUMERALS. 57
* Hyºyº
nylºp mºns ºnw ºnwy
Hyn-R cºpy, mspyins: ºn
Tinx) cºje ºn ºn pºlyw
py, y Hºyº y ---, ºp.
: yº neph
'n Hyºyº
wºw, ºn- ºxy nºn- pºss ºnw
yonx cºn- nºw nº cºns
nºn- Hynix) cºnwy nºn- cºns
pºwy) nº nylº D'Jax won
n\xo yew n)})= c^jºx ww nºn-
nº D'Jix yew ſoºn- onwy,
}sºn ºn- py--is peºs nwon
:Hen psy no ºwn Rs nº
,ynowº nº msn p's ---' by
(-, P-E)
'º -ijºº
nºn ºn nx nwy, ºpe, Fºx
ºn Rup) inx ow: -)--in ºn nx)
: Ins own xx} +)--in ºp) ºn
§ 7
Twenty - two
fixed
divisions, and the circle turns
forward and backward; thus
in ly [delight], the y is at
the beginning; in 92) plague],
the y is at the end.
§ 8
Out of two stones two houses
letters are
in a circle, with 484
are built, out of three stones
six houses are built, out of
four stones twenty-four houses
are built, out of five stones
one hundred and twenty houses
are built, out of six stones
seven hundred and twenty
houses are built, out of seven
stones five thousand and forty
houses are built. Go and count
further, what the mouth is
unable to pronounce, and the
ear is unable to hear.
Chap. II
§ 9
He combines and changes
and makes all
all speech with
forms and
the One
- 58 THE ORIGIN OF LETTERS AND NUMERALs.
* Fijºyº
Rºep ºil Tºp wes nox why
,ws pºp m- pºssy now Hºp)
yº-op nºn ntory” pºp. Hºyo” w8
nobi p'º -a+ pºp, pºny-
: bºnya yº->e Fºx nºw ºw
N” nyº
Rºp ºil Tip n'es nibs wºw
ſhey pºp mn pºssi. Ho, Hoºp
nvon Hw nºwps nips yº-is
Hyaw, pinwy tº now nºns
:nºn
-** Hywº
Tony --> -nx 25 nºx Hwon
pºp-is pºp m-bin Hyaw) ºnwy
p-y, Hy-To pro swy nins-
The ºs Tr" mis, Honºr ºp-
Ty wip myop ºn ºwn ps:
: Ty Ty
Name; thus all forms and all
speech are derived from the
One Name.
§ 10
Three vowels ºb?' constitute
a great secret, marvellous and
hidden.
air, water, and fire. Fire above
From them go forth
and water below, and airholding
the balance between them; thus
b is mute, tº is hissing, , and
8 holds the balance between
them,
§ 11
Three vowels n'ps constitute
a great secret, marvellous and
hidden. From them go forth
air, water, and earth. Four
vowels n'ºps, which are five
vowels, that gave birth to
twenty-seven consonants.
§ 12
The five vowels stand each
one by itself, but the twenty-
seven consonants are all de-
pendent on the vowels. He
made them in the form of a
state, and arranged them like
THE ORIGIN OF LETTERS AND NUMERALS. 59
}^ Fly?
Hyny) onwy) nºns Hºyton
nºn's pºny, pºwy ºx n-ºn
nºeb hºvo nix-y Hin Hº Toºw
:Hoºpº
(: P-E)
T^ Hyºyº
Tº prº- Hobº ninet ºwy
15% ºn Es) ºn-nº T-by---he
nº m --- by 5 pipes ºw
: nºn-
*"tº nyºyº
jºb yºv, noºn ninet ºwy
nanºws ºp: nºnn nºnna
Eºm Ho-na in nºn- nºwp
•jeº, ºw tº ps. The misw Hy->
: "Elp Finx To Tnx.
an army in battle array. The
God, the
faithful King, rules over them
only One Master,
from His holy abode forever
and ever.
§ 13
The five vowels and twenty-
Seven consonants, these are
contained in the twenty-two
letters which the Lord, Lord
of hosts, established out of the
ten digits and zero.
Chap. III
§ 14
The ten digits and zero —
close thy mouth from speaking
and thy heart from thinking,
and if thy heart should leap,
let it come back to its place; for
concerning this has the coven-
ant been made.
§ 15
The ten digits and zero,
their end is joined with their
beginning, and their beginning
With their end, as the flame
is attached to the coal. Under-
stand wisdom and be wise in
60 THE ORIGIN OF LETTERS AND NUMERALS.
l'º Niyºyº
nºes Hobº ninet nwy
Yp nº ºx innºn) plan HRno-
|'s |
inexpº ºwn sign: Inn ---
In sps ºn ETº Helps
: n\nnº
1"> Hyºyº
Hobº ninet -wyn in nºs
prºbyn ºn ºs bºy ns ppm new
:Yew Tºp Tin-
n^ Hyºyº
mn ºp na -sm ppm nns
:w-prº mn ºn mon
to’s Hyºjº)
Ann inn in- -sm ppm ºnw
$5 ns ºppy pin, p m inn
npºets pºss ºx n-1,\º pºlyn
:nºp pºssy inpu pinna nypwon
understanding, that there is
but one Master, and there is
no second to Him, and before
One, what countest thou?
§ 16
The ten digits and
their appearance is like light-
Zero,
ning; to their aim there is no
limit. They go and come at
His word, and at His command
they pursue like the whirlwind,
and kneel before His throne.
§ 17
These are the ten digits and
zero, with which the Eternally
Living God, blessed be His
name, Ordained His world.
§ 18
One—He graved and hewed
out of it voice, air and speech,
and this is the Holy Spirit.
§ 19
Two—He graved and hewed
out of them void and chaos.
Void is a green line that sur-
rounds the whole universe, and
chaos refers to viscous stones,
THE ORIGIN OF LETTERS AND NUMERALS, 61
'P Tyto
tº wºn H= -sm ppm wºw
Hon Pos =ºn Hainy ºps swy
*w bºy ps" Hºye prºs pop
:Yey nwyll
X^ Tyto
Then sp2 inn asm ppm ynns
ºsºp, wipm nºm cº-w, pºems,
: n-y-
-'5 Hyºyº
Jºy, J'N nwy, worx inno -s;
y’sy nºsp nºt nºns ism
ºny ºnwy ---> \bºt) wen:
:-ins mm lººp
}/> n)???.S
pºsh Hwy m nomy” nins 5.
,-\º nply? yº) ºwn nomyº ºt
ºnary ºn , yºp yº) ºr nº
,-\ton ns "nap y-in ſynn ns
g00d out of g00d,
sunk in the abyss, whence
water comes forth.
§ 20
Three–He graved and hewed
out of them mud and clay.
He arranged them like a garden
bed.
wall.
He set them up like a
He covered them like a
pavement, and poured upon
them snow, and the earth was
formed.
§ 21
Four—He graved and hewed
out of them the throne of
glory, the ophanim, the Seraph-
im, the holy animals, and the
ministering angels.
§ 22
He formed existence out of
void, and made something out of
nothing, and hewed large stones
out of intangible air, thus twenty-
two in number one in spirit.
§ 23
Also God set the one over
against the other, good against
evil, and evil against good;
and evil
62 THE ORIGIN OF LETTERS AND NUMERALS.
Hºpw Hy-m pantº n-mow Hilto
: Dºy--
Tºº Hyº
tº-m lynx Drinns Toyw Yº
Finº ºn ppm pam pm Hsm
is nºn-n +5 nnºy) ºwn ns)
* nºn- nº ºn his bºy nº
ps nºna is nº pºly Ty yniº
mwºn nºn- Rim T. myass nwy
myºss nwy a nº-- Yº nº
ºnwy ºwp. Hºon nºn- sim wºn
nº mwº n-nnn nºns pºny)
wsa pºt pºp- pºp Tip ns tº
mºes nwy; pnm nine wyn
: nºwe nºwy pºny)
out of evil; good testing evil,
and evil testing good; good is
stored away for the good, and
evil is stored away for the evil.
§ 24
When Abraham our father
arose, he looked and saw and
investigated and observed and
engraved and hewed and com-
bined and formed and calcu-
lated, and his creation was
successful. Then the Master
of all revealed Himself to him,
and made a covenant with him
and with his seed forever. He
made a covenant with him on
the ten fingers of his hands,
and this is the covenant of the
tongue; and on the ten toes
of his feet, and this is the
covenant of circumcision; and
tied the twenty-two letters of
the Torah to his tongue and
revealed to him their secret.
He drew them through water;
stormed them through air, kind-
led them in fire, and melted
them into ten double and twelve
simple letters.
CORRECTIONS,
6 l. 16 For heard me expressing my viewrs read: heard my viewrs
12 l. 25 For coneeptions read conceptions
16 l. l J. For o’ read o,
25 1. 16 For T. —l read T. +
31 1. 8 For Y K read Y K
37 l. 11 For thre read three
40 l. 17 For tetters read letters
40 l. 21 For then read ten -
43 1. 14 For Barseloni read Barceloni
44 8 For on read one
. 44 l. 20 For wit read with
The variants to the Sefer Yetzirah 1, the text of Sefer Yetzirah l i,
texts Mantua 1 and Mantua 11 will be found in the Hebrew edition of
this work which will appear shortly.
I have to acknowledge my indebtedness to Dr. H. Malter for reading
ithe proof-sheets; and also to Dr. Israel Davidson for suggesting a few
improvements. -
Printed by H. Fleischmann Treslau Reuschestr. 57
A SOLUTION OF THE
PYTHIAGOREAN NUMBER PHILOSOPHY
SUPPLEMENT TO
“THE ORIGIN OF LETTERS AND NUMERALS"
BY PEIINEAS MORDELL.
copyright iona by phineas Mordell.
The real reason why the Pythagoreans considered numbers
to be the elements and origin of everything was that they believed
numeral symbols to have preceded all other forms of writing."
This is what they really meant when they said: “Numbers by
nature are the first and prior to all things.” (Aristotle's Meta-
physics, Book 1, Chapter 5). The letters of the earliest alphabet
having been numeral symbols, all words were originally made
up of numeral symbols or numbers.
In the Hebrew language which also resembles the Phoenician
language, (and it was anciently believed, that Pythagoras himself
was a Phoenician) both “words” and “things” are designated by
the term Dºº". Since “words” is the equivalent of “things”
the Pythagoreans said that all things (i.e. words) had their origin
and composition in numbers.
Now according to both the Sefer Yetzira and the Pytha-
goreans, the four elements, fire, air, water, earth, emanated from
the first four numbers, I, 11, 111, 1111.
For Iamblichus (Life of Pythagoras, transl. by Th. Taylor,
London, 1815, p. 332) says: “The fourth tetractys is of the
simple bodies, fire, air, water and earth, which have an analogy
according to numbers. For what the monad was in the first
tetractys, that fire is in this. But the duad is air, the triad is
* “The invention of Signs to represent numbers is doubtless much older
than any form of writing” (Chambers Encyclopaedia, 1893, Vol. VII, p. 548).
“Numeral characters, were first invented because they were first necessary
to mankind.” (Th. Astle—The Origin and Progress of Writing, London 1784).
* 65
66 THE ORIGIN OF LETTERS AND NUMERALS
water and the tetrad is earth.” In the Sefer Yetzira however,
air is associated with the number one, water with the number
two, earth with the number three and fire with the number
four.” The real four elements of the Pythagoreans were also a
series of strokes 1, 11, 111, 1111, amounting to ten which were
originally numbers and letters.
The key to the complete identification of the philosophy of
Pythagoras with that of the Sefer Yetzira as interpreted in this
thesis is the Zero. According to the Sefer Yetzira as explained
above Toºn means Zero. Was the Zero a secret known to
the Pythagoreans? A solution to this question will be found in
the Pythagorean dualism.
The “one” in the Pythagorean dualism is the Symbol, I.
Contrary to the prevailing opinion, I believe that the Pythag-
oreans regarded the Zero, 0, as the second element which was
called the infinite, indeterminate duality, infinite binary, etc.
In a binary system of notation the Zero is the second Symbol.
We know now that even the decimal system of notation originated
from the two symbols the one, I, and the Zero, 0. This is in per-
fect harmony with the Pythagorean formula that all numbers
originated from two elements, the limited (the one, 1,) and the
unlimited (the Zero, 0). Therefore, all things according to the
Pythagoreans originated from two elements One, 1, and the
* “Die Pythagoreer fuehrten daher alles auf die Zahl und nicht auf die
mathematischen Figuren zurueck” (S. A. Byk. Die Worsokratische Philosophie
1. Leipzig 1876, p. 116).
* It is the “central fire” (fiery angels the throne of glory) that is associated
in the Sefer Yetzira (above p. 61 para. 21) with the number four or ten which
the principle of place value makes a harmonious one (see below about har-
mony). The harmonious one (zusammengefuegtes Eins) was confounded
with the plain one and thus fire came to be regarded as the Pythagorean
first material element..
THE ORIGIN OF LETTERS AND NUMERALS 67
Zero, 0." Since One, 1 is the finite, the Zero, 0 is the true infinite
of the Pythagoreans. The One, 1 was considered the Good, for
it represents that which exists, but the Zero, 0 was called the
evil, for it represents non-existence.
The Pythagoreans could not have meant by infinite duality
the number two, as many writers believe, for as the one is finite,
so the number two and every other number must also be finite.
Moreover, in a binary system of notation the symbol one, 1 itself
becomes two just as in a decimal system of notation the symbol
one, 1 itself, becomes ten.
Boeckh (Philolaos, pp. 53, 140, 148) made it clear that the
Pythagorean infinity which is identical with infinite duality is
not a number at all. See also A. Heinze, Metaphyische Grundleh-
ren, Leipzig, p. 26.”
As Leibnitz has represented God's Creation of the Universe
out of chaos or nothing, by means of two digits as symbols, so
some Pythagoreans also interpreted the one as God and the
second element the infinite binary (the Zero, 0) as the visible
world. (Plutarch’s Morals translated by W. W. Goodwin, vol.
III, p. 109. Boston 1870).
“The Deity, it is thought by some, was distinguished by the
Pythagoreans as absolute unity, from unity conceived.” (A
4 The Chinese Philosophers even actually said that the circle 0 and the
line are the first elements from which all writing and everything
originated. (Thimus Harmonikale Symbolik Koeln 1876, vol. 1, pp. 79–83).
By the “bounded line” and “unbounded line” from which according
to the Pythagoreans everything originated (Diels H. Die Fragmente der Wor-
sokratiker p. 250) they surely meant the line and the circle the symbols for
one and zero.
* After having written this supplement I found that Mr. S. Klyce (Uni-
verse 1921 para. 43 f) advances the view that zero and infinity are logically
identical.
68 THE ORIGIN OF LETTERS AND NUMERALS
History of Greek Philosophy, Dr. E. Zeller, translated by S. F.
Alleyne, London 1881, vol. 1. p. 398.)
Such a view was apparently that of the Sefer Yetzira (above
p. 59 para. 15) “Understand wisdom and be wise in understanding,
that there is but one Master, and there is no second to him.”
So in "Tº ºpin it is said jºins sº in sºn his Thou art
one which is different from the one that is counted. So Solomon
Ibn Gebirol in nºn hino says: "Ipm wipH-ins: Rºl ins: Fins:
Thou art one and not as the one that is created and counted.
George Boole in The Laws of Thought, London 1854, p. 48,
also says: “The respective interpretations of the symbols 0 and 1
in the system of Logic are Nothing and Universe.”
In ancient times various interpretations were given to the
two symbols 1 and 0, as the Platonic antithesis of “being” and
“non-being.” (Boole, ibid, p. 414,) and Leucippus's “Plenum”
and “vacuum,” into which all existence was resolved (Boole,
ibid, p. 413). The Philosophy and religion of Dualism apparently
arose from an interpretation of the symbols one, 1 and zero, 0.
Various views prevailed about the origin of these two sym-
bols. Some believed that the Zero, 0 preceded the One, 1. Per-
haps the Chinese cosmogony is based on this view." The author
of the Sefer Yetzira and the Pythagoreans believed that the one
preceded the zero. Therefore, the zero was second.
The view held by some Kabbalists that the nine Sefiroth or
numerals (1-9) have emanated from infinity-FD 's implies
that the Zero 0, has preceded the One, 1. But according to the
author of the Sefer Yetzira and the Pythagoreans even infinity
“There was first of all a period when Nothing existed . . . Grad-
ually Nothing took upon itself the form and limitation of Unity, represented
by a point at the centre of a circle” (H. A. Giles, A History of Chinese Lit-
erature, New York, 1901, p. 3).
THE ORIGIN OF LETTERS AND NUMERALS 69
-ºp 's emanated from the One, 1.
- After the invention of the symbols 11, 111, 1111, when the
binary system of notation developed into a decimal, the zero was
regarded as the fifth symbol and hence the fifth element. The
five symbols or elements 1, 11, 111, 1111, 0, were supposed to
symbolize the whole cosmos which was believed to be in harmony
with a decimal system of notation expressible by these symbols.”
*Die Weltkugel besteht aus fuenf Koerpern: dies sind
innerhalb der Kugel Feuer, Wasser, Erde, Luft und ausserdem
fuenftens das Gehaeuse der Kugel selbst.” (Nestle, Die Wor-
sokratiker. Jena 1908, p. 162).
The four elements, air, water, earth and fire
were also symbolized by ten dots . . . . . . . . . . .
arranged in a triangular form and the sphere of void I
encompassing them was symbolized by a circle.
Hence the void and the universe were symbolized by
and apparently was simplified in a |
to Boethius, the Neo-Pythagoreans used as a symbol for zero.
The void and the universe may also be symbol- in:
ized by a circle containing the nine numeral figures
1–9. The nine numerals may be designated by
Kabbalistic names as 1— moºn, 2—niºn, 3—ny",
4—Tom, 5—nnsºn, 6—nnini, 7–ns), 8—Tin, 9–Tip"
and the zero circle embracing them may be des- -
ignated by Hip 's or nºbo ºne. nºr
(About the Hebrew Kabbalistic origin of our numerals see A. J. H.
Vincent in Journal de Mathematiques Par Joseph Liouville Paris 1839
pp. 261-280 and in Revue Archaelogique 1845-1846 pp. 601-621.)
According to the Sefer Yetzira the Hebrew alphabet con-
sisting of ten double letters and twelve simple leters, representing
the vigesimal and duodecimal systems of notation, still more
fully symbolizes the universe.


70 THE ORIGIN OF LETTERS AND NUMERALs
If we consider every stroke as a separate symbol the zero is the
eleventh as 1,1,1,1,1,1,1,1,1,1,0, or the tenth as 1,1,1,1,1,1,1,1,1,0
From a Pythagorean point of view the fifth element “aether”
like infinity is only another name for vacuum.” Therefore, aether
also is logically identical with zero (Com. above p. 30). Now
“modern physics following Einstein asserts that . . . since
the ‘aether' as a substance obstinately evades all our attempts
at observing it, and all phenomena occur as if it did not exist,
the word ‘aether' lacks physical meaning, and therefore aether
does not exist” (M. Schlick, Space and Time, p. 12). “Since we
are free to use words at pleasure there is no objection to using the
word ‘aether’ in the future to represent the vacuum . . . we
must be very cautious, however, not to picture it as matter”
(ibid p. 20). -
In the above explained system of notation from which our
system of notation originated, the principle of position (place
value) plays an important role. It is this principle that makes it
possible to express all numbers, by only two symbols the One, 1
and the Zero, 0. The principle of position is the “miracle” that
makes one, many and many, one. In the Sefer Yetzira (above
p. 59 para. 15) the principle of position is indicated by the words
“The ten digits and zero their end is joined with their beginning,
“*Das fuenfte Element ist also nicht aus der fuenften mathematischen
Figur geworden, da dasselbe als. Urgrund ganz formlos ist. Deswegen
spricht auch Stobaeus von blos vier Elementen, . . . weil das
fuenfte Element als reiner Urgrund noch keine Zahl und daher im Kosmos
nicht voshanden ist.” (S. A. Byk, Die Worsokratische Philosophie 1. Leipzig
1876, p. 94).
“Infinity is not the affirmation of space but its disappearance” (H.
Waldon Carr, The General Principles of Relativity 1920, p. 152).
Perhaps it is more correct to read (above p. 60 para. 16) Flip "Nº ºn"ºn)
“and their termination is infinity” instead of Flb Inh |'s !nººn, “to their
aim there is no limit.” -
THE ORIGIN OF LETTERS AND NUMERALS 71
as a flame is attached to the coal.” Now if the Pythagorean num-
ber philosophy was based on such a system of notation as that
on which the philosophy of the Sefer Yetzira is based, the principle
of position, (place value) must have been known to the Pytha-
goreans and must have played an important role in their phil-
osophy. But how did they express it? Did their “harmony”
mean the principle of position?"
The Pythagorean philosophy is the greatest enigma of all
philosophical systems of antiquity. Various sources such as
Egyptian, Indian, Greek, Phoenician, Hebrew, etc., have been
advanced as the origin of the Pythagorean philosophy. Many
years of study have convinced me that the Pythagorean philosophy
is identical with the philosophy of the Sefer Yetzira and both are
of Hebrew origin. The philosophy of the Sefer Yetzira apparently
emanated from the Hebrew prophetic guild or school as conjec-
tured by Joseph Molitor. That which really was the philosophy
of the Sefer Yetzira, the Greeks designated as Pythagorean
philosophy and transmitted this to posterity in such a mutilated
form that in spite of everything that has been written on the
Pythagorean philosophy since Aristotle, it has never yet been
really understood. The entire Greek account of Pythagoras and
his philosophy is unreliable and most likely is a forgery. However,
that may be, I hope I have at least succeeded in removing some
obstacles to a better understanding of the Sefer Yetzira and the
Pythagorean philosophy and their relation to each other.
* “Das absolute Princip dieser Harmonie sahen die Pythagoraeer in der
Monas, sie ist ihnen die nur im Gedanken vorhandene mit sich selbst noch
unentzweite Einheit, die das viele zu ihrem Gegensatze hat. In diesem Stad-
ium ist sie nur Monas. Zur Harmonie wird sie erst, wenn sie aus sich selbst
zum Wielen wird.” (S. A. Byk, ibid, p. 108).
Supplement Printed by M. Magil, 1311 N. 52nd St., Philadelphia, Pa.
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