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Date: Mon, 11 Aug 1997 16:14:23 -0500 (EST)
From: "Edward Pothier, Physics Dept." <POTHIER@neu.edu>
Subject: Re: CIPHER NUMBERS IN GREEK MANUSCRIPTS
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"Brian E. Wilson" <brian@twonh.demon.co.uk> wrote:
>
> In English we can write the number "two" either as a word - TWO - or as
> a cipher - 2. In many Greek papyri of parts of the New Testament, very
> roughly half of the numbers are written as words, and the other half as
> ciphers. Thus a lone Alpha with a superscript line is the cipher for
> the number one, and a lone Beta with superscript line is the cipher for
> the number two, used in roughly half of the instances of the numbers
> one and two, whereas elsewhere the numbers are written as the words
> EIJ and DUO, and so on.
>
> I am interested in finding out whether this is a characteristic of
> Christian writing in Greek. Does anyone know, please, whether
> manuscripts of Classical Greek literature use ciphers for numbers? Where
> can I read about this (apart from ploughing through facsimiles of
> manuscripts!)?
>
> Also, does anyone know how the Greek ciphers for larger numbers are
> worked out?! Maybe mathematics and B-Greek have something in common
> after all?!
---------------------- end quoted material
I was engaged in a recent discussion of the representation of the
number in Rev 13:18. Since many summers ago I wrote a lengthy paper on
that subject, I am including a edited version of PART of it. Even when
Greek NT manuscripts use a numerical rather than verbal representation,
they use three different symbols for the digits (chi=600, xi=60, and
stigma=6 [Stigma or digamma being an obsolete letter]).
From: SIX HUNDRED SIXTY-SIX BUT NOT 666 (Part III of original)
Edward L. Pothier (July 1991)
III. Greek Alphabetic Numbers at the Time of the New Testament
Since the Book of Revelation, like the other twenty six
books of the New Testament, was written in Koine Greek in the
first or early second century AD, we must study how numbers were
represented at that time in Greek.[5]
One early Greek numeral system, known as Attic numerals,
started at Athens and used symbols for the key numbers 1, 5, 10,
50, 100, etc. The individual symbols of each type were repeated
as often as needed (up to four times) to make up a number's
representation. This can be called a REPETITIVE 1-5 system.
This system was similar to the later (but more familiar to us)
system of Roman numerals except that it was always additive
(repetitive) unlike the Roman numeral system which has also
subtractive forms.[6]
Another system also existed (not surprisingly considering
the independence and non-cooperation of Greek city states). This
system, known as the Ionian or Milesian (from Miletus in Asia
Minor)[7], may have started in the 6th century BC. The Attic
system was fading out of use, disappearing almost entirely in the
time of the Roman Empire. The Milesian alphabetic numeral system
was officially adopted in Athens in the first century BC.[8]
By the time of the New Testament we need only consider the
Greek alphabetic numeral system. Although the Greeks had ways of
representing numbers in the thousands and also those above
ten-thousand (myriads), we will only consider how they
represented numbers up to nine hundred ninety nine.
These Greeks, like us, used a decimal system but, unlike us,
they did not use a zero number[9]. Thus, although it was a
decimal system, it was not a place-value system. Therefore more
symbols were needed than just the nine (plus zero) which we use.
To represent the numbers up to our 999, they needed 27 different
symbols: nine for the units 1, 2, ..., 9; nine for the tens 10,
20, ..., 90; and still another nine for the hundreds 100, 200,
..., 900.
For symbols they used the letters of the Greek alphabet.
However, an immediate problem arose since the Greek alphabet
contained only 24 letters. To fill in the missing three, they
used old obsolete letters from previous alphabets and, somewhat
confusingly, these were interspersed with the regular letters.
The following table show the assignments[10].
TABLE OF NUMERICAL VALUES OF GREEK LETTERS
1 alpha 10 iota 100 rho
2 beta 20 kappa 200 sigma
3 gamma 30 lambda 300 tau
4 delta 40 mu 400 upsilon
5 epsilon 50 nu 500 phi
6 [digamma] 60 xi 600 chi
7 zeta 70 omicron 700 psi
8 eta 80 pi 800 omega
9 theta 90 [koppa] 900 [sampi]
Note the obsolete letters in brackets in the table: digamma
for 6, koppa for 90, and sampi for 900. The koppa and sampi will
not affect us further except that the presence of koppa for 90
pushes letters such as rho, sigma, etc., one position down.
The digamma at 6, however, will be directly relevant for the
representation of six hundred sixty-six. This letter also became
known as stigma (note the "t") because the form of writing it
looked like the ligature (writing together) of the two Greek
letters sigma and tau, roughly corresponding to our s and t. [If
not done carefully, it can even look like just a sigma, which
would be an error.] For most of the rest of this study this
obsolete letter pushed into service to represent the numeral for
6 will be referred to as stigma.
Now to represent a number in alphabetic symbols in the first
century AD[11] Greek writers could just use the individual
symbols concatenated together similarly to how we do it. Because
there was no zero, more possible symbols were needed (the 27
listed above). However, to represent a number which has a zero
in our representation, they would need less characters. Our
number 123 would be represented the three letter symbols
(rho)(kappa)(gamma). Our number 209 could be represented by only
two letters (sigma)(theta) and 300 by only one letter (tau).
To distinguish letters used as numbers from normal letters a
horizontal line was usually written above the letter-numbers or
sometimes just a tick mark[12]. It should be noted that the
order of the letters needed to represent a number is not
important, since this system is not a place-value system. Most
often, however, the highest valued letter would be put first.
Thus to represent our number of interest, six hundred
sixty-six, rather than using three identical characters (666) as
we do in our decimal PLACE-VALUE system, a first century Greek
writer (if not spelling out the words just as we also can) would
use three distinct characters (chi)(xi)(stigma)!
-- NOTES --
[3]. For a detailed description of the evolution of our
current number system and how it gradually made its way to the
West see such works as:
Graham Flegg (ed), NUMBERS THROUGH THE AGES (London:
Macmillian Education, 1989) 88-130.
Georges Ifrah, FROM ONE TO ZERO: A UNIVERSAL HISTORY OF
NUMBERS (New York: Viking, 1985) 428-497.
Karl Menninger, NUMBER WORDS AND NUMBER SYMBOLS: A CULTURAL
HISTORY OF NUMBERS (Cambridge: MIT Press, 1969) 389-445.
[4]. Incidently, some modern apocalyptic fanatics (or
"prophecy" students) who are most alarmed at the number 666 and
worry about large computer-based control systems that the Beast
will use should perhaps worry about a hexadecimal based system
(base 16) rather than the decimal based 666 number. In the
modern computer hexadecimal number system a number is represented
using 16 possible "numeral" symbols: our usual 0-9, then 6
additional "numerals": A=10, B=11, C=12, D=13, E=14, F=15. In
hexadecimal notation instead of having units, tens, hundreds
places one has units, sixteens, two hundred fifty-sixs places.
Thus six hundred sixty-six is represented as 29A (hexadecimal)
since decimally 666= 2x256 + 9x16 + 10x1.
[5]. The relevant sections in the works in [3] are:
Flegg, NUMBERS THROUGH THE AGES, 88-101.
Ifrah, FROM ONE TO ZERO, 261-274.
Menninger, NUMBER WORDS AND NUMBER SYMBOLS, 268-274.
Also see O.A.W. Dilke, MATHEMATICS AND MEASUREMENT (London:
British Museum Publications, 1987) 13-16.
[6]. A subtractive form means that sometimes a number such
as 9 is represented as IX, with the smaller unit (I) preceding
the larger (X) meaning one less than 10, rather than additively
as VIIII meaning four more than five.
Interestingly, the Roman numeral system, which uses the
symbols I, V, X, etc., for 1, 5, 10, etc., gives a peculiar
representation for our number of interest: six hundred sixty
six. Since 666 = 500+100+50+10+5+1, in Roman numerals it is
represented as DCLXVI, using every symbol through D (=500) once
and only once.
[7]. Miletus is mentioned in the NT (but with no numerical
connection) in Acts 20:15,17 and 2 Tim 4:20.
[8]. Menninger, NUMBER WORDS AND NUMBER SYMBOLS, 268.
Dilke, MATHEMATICS AND MEASUREMENT, 14.
[9]. Later, the Alexandrian Greek astronomer Ptolemy (2nd
century AD) used a symbol similar to zero in some astronomical
tables, but it never seemed to be developed by the Greeks.
[10]. Bruce M. Metzger, MANUSCRIPTS OF THE GREEK BIBLE: AN
INTRODUCTION TO GREEK PALAEOGRAPHY (New York: Oxford University
Press, 1981) 7-9.
[11]. These alphabetic numerals have mainly fallen out of
modern Greek which uses the regular decimal Arabic place-value
numbers. They are still used, perhaps similarly to how we use
Roman numerals, to annotate items in a list. An example of
useful non-library research was the discovery on the wall of a
local Greek pizza/submarine sandwich shop of a 1987 map of
Greece. Around the edge was a table of the land areas of various
political regions of Greece. Although the numbers for the areas
were written in Arabic numerals, the labels beside the names of
the regions used Greek letters: alpha, beta, etc.
Interestingly, at the sixth location the two greek letters
(sigma) and (tau) were used, obviously from the old stigma. The
list then continued with single letters up through the tenth
entry (iota), then double letters up to the fourteenth and last
element, represented by (iota)(delta).
[12]. Metzger, MANUSCRIPTS OF THE GREEK BIBLE, 9.
=============================================================================
= Edward L. Pothier pothier@nuhub.dac.neu.edu =
= Physics Department BUT PREFERRED EMAIL:pothier@hex.neu.edu =
= Northeastern University / Boston, MA 02115 =
=============================================================================