From epothier@lynx.dac.neu.edu Wed Jul 14 21:08:17 1993 Received: from rodan.UU.NET by aramis.rutgers.edu (5.59/SMI4.0/RU1.5/3.08) id AA03489; Wed, 14 Jul 93 21:08:17 EDT Received: from relay1.UU.NET by rodan.UU.NET with SMTP (5.61/UUNET-mail-drop) id AA16285; Wed, 14 Jul 93 21:08:16 -0400 Received: from lynx.dac.neu.edu by relay1.UU.NET with SMTP (5.61/UUNET-internet-primary) id AA15648; Wed, 14 Jul 93 21:08:00 -0400 Received: by lynx.dac.neu.edu (5.65/DEC-Ultrix/4.3) id AA12165; Wed, 14 Jul 1993 21:06:59 -0400 Newsgroups: soc.religion.christian Path: epothier From: epothier@lynx.dac.neu.edu (Edward Pothier) Subject: Six Hundred Sixty-six but not 666 was Re: 66.6 Message-Id: <1993Jul15.010654.12102@lynx.dac.northeastern.edu> Summary: Representation of Greek numbers Organization: Division of Academic Computing, Northeastern University, Boston, MA. 02115 USA References: Date: Thu, 15 Jul 1993 01:06:54 GMT Apparently-To: soc-religion-christian@uunet.uu.net In article , nichael@bbn.com (Nichael Cramer) writes: > > Minor point: It is correct that in most modern editions of the Greek > NT the number is spelled out as "six hundred sixty-six" (in Greek, of > course), however in the various manuscripts this appears in a variety > of forms: "six hundred sixty-six", "666", "six six six", etc. > > Also, as pointed out elsewhere, in a handful of manuscipts this number > appears as "616"; in one manuscript it is given as "646". > There has been some recent discussion of the representation of the number in Rev 13:18. Since two 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]). SIX HUNDRED SIXTY-SIX BUT NOT 666 (Parts II-III) Edward L. Pothier (July 1991) II. Our Modern Decimal Place-Value Numbers To represent numbers we use a decimal (base-10), place-value system. Using just the ten Arabic (or more properly Hindu-Arabic or Indian) numerals (1, 2, 3, 4, 5, 6, 7, 8, 9, and 0) we can represent an arbitrarily large number. The use of the zero is especially important in that it enables us (in a decimal system) to need only the other nine numerals. The same numeral can be used to represent a number of units, tens, hundreds, thousands, etc. Its position or place in the composite number determines its actual value. Because each place in the number represents how many of a "power-of-ten" is contained in the composite number (including none in some cases), we have a PLACE-VALUE system. For example, we interpret the number 123 as 1x100 + 2x10 + 3x1. Similarly, our designated number 666 is 6x100 + 6x10 + 6x1. Without a zero as a place holder, however, we would not be able to represent a number like two hundred nine. But since we do have a zero, two hundred nine can be represented as 209 = 2x100 + 0x10 + 9x1. This all seems trivial. We learned all this in elementary school. However, this relatively modern representation of numbers, like many inventions, is the endpoint of much evolution and even revolution. At the time of the New Testament's writing such numbers were far in the future. In the West we received our numeral system from the Arabs (hence the usual name, Arabic numerals) through Spain. The Arabs in turn had obtained them from India. The earliest introduction of these numerals into Spain seems to be at the end of the first millennium AD, but it was well into the second millennium before they took control[3]. Until then, i.e. well into the Middle Ages, Roman numerals were the standard method until eventually displaced by our current decimal, place-value system.[4] 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 epothier@lynx.dac.neu.edu = = Physics Department PREFERRED EMAIL: pothier@neuhep.hex.neu.edu = = Northeastern University / Boston, MA 02115 = From epothier@lynx.dac.neu.edu Wed Jul 14 21:14:22 1993 Received: from rodan.UU.NET by aramis.rutgers.edu (5.59/SMI4.0/RU1.5/3.08) id AA03549; Wed, 14 Jul 93 21:14:22 EDT Received: from relay2.UU.NET by rodan.UU.NET with SMTP (5.61/UUNET-mail-drop) id AA16719; Wed, 14 Jul 93 21:14:21 -0400 Received: from lynx.dac.neu.edu by relay2.UU.NET with SMTP (5.61/UUNET-internet-primary) id AA19677; Wed, 14 Jul 93 21:14:25 -0400 Received: by lynx.dac.neu.edu (5.65/DEC-Ultrix/4.3) id AA12664; Wed, 14 Jul 1993 21:13:03 -0400 Newsgroups: soc.religion.christian Path: epothier From: epothier@lynx.dac.neu.edu (Edward Pothier) Subject: More on representation of Six hundred sixty-six (Rev 13:18) Message-Id: <1993Jul15.011257.12607@lynx.dac.northeastern.edu> Keywords: Greek Organization: Division of Academic Computing, Northeastern University, Boston, MA. 02115 USA Date: Thu, 15 Jul 1993 01:12:57 GMT Apparently-To: soc-religion-christian@uunet.uu.net Since there has been some discussion of representation of the number in Rev 13:18, I am including more of a paper I wrote 2 summers ago. SIX HUNDRED SIXTY-SIX BUT NOT 666 (Parts V-VI) Edward L. Pothier (July 1991) V. Greek NT Readings of Rev 13:18 Having described above the Greek alphabetic number system, it is now possible to look at how Rev 13:18 is represented in the Greek New Testament. Until the Greek NT was first printed in the early 16th century, each copy of each book in the NT was written by hand. Variations were introduced, either accidently or deliberately. Since we no longer have the absolute original autograph copies as they came from the hands of the authors, a process of textual criticism must take place.[17] Textual criticism is both the art and science of taking all the evidence as found in all the various existing copies and attempting to reconstruct, as well as possible, what the original text was. There are two major modern critical editions of the Greek New Testament which serve as a DE FACTO "standard text." They are the Nestle-Aland twenty sixth edition (NA26) and the United Bible Societies Greek New Testament third edition (UBSGNT3)[18]. These are not independent critical editions since they share common editors and agree on the text readings included in the text itself. They differ in punctuation and typographical features as well as in the documentation of textual variants of different manuscripts. In the "standard" modern critical edition the verse we are considering is given (using a transliteration scheme which enables the reproduction of Greek text in Roman letters) as: "ho:de he: sophia estin. ho echo:n noun pse:phisato: ton arithmon tou the:riou, arithmos gar anthro:pou estin, kai ho arithmos autou hexakosioi hexe:konta hex." (Rev 13:18, NA26) In this verse one sees several times the Greek word for number (arithmos), from which we get our English word arithmetic. What is most important for our consideration is the last three words which are the Greek words representing six hundred, sixty, and six. As can be seen from the transliteration, they all begin with "hex", which is the Greek prefix which comes into English in such words as hexagon and hexameter. So when the number words are written out in the Greek text, i.e. not in just the alphabetic numerical symbols, a Greek reader sees a identical start to each of the words ("hex"), just as an English reader sees a "six" in the English words. In addition to the scholarly reconstruction of the "best", i.e. as close to original as possible, text (obviously to some degree a matter of opinion based on the evidence and scholarly presuppositions), a critical edition also shows how the various manuscript readings differ. The NA26 edition does this through a set of symbols in the text itself (omitted in the above transliteration) and a compact set of "footnotes" which detail each variant, listing the variant readings and telling which manuscripts (using a standard notation for the names of the manuscripts) contain which reading(s). The variants and the manuscripts which contain them are listed for the number words at the end of Rev 13:18. A text for the three words exactly matching that of the critical text is contained in the fifth century manuscript Codex Alexandrinus. A very slight variant involving only some insignificant grammatical endings is recorded for some more manuscripts, including the fourth century Codex Sinaiticus. (Another important fourth century manuscript Vaticanus is now incomplete, missing all of the Book of Revelation and some other books at the end of the NT). A major different reading (from the reading of the critical edition text) is recorded for another fifth century manuscript, Codex Ephraemi Syri Rescriptus, which contains the number six hundred sixteen instead of six hundred sixty-six. There is also another single late manuscript which contains a reading of six hundred sixty five![19] Of particular interest to us are a set of manuscripts which are recorded as affirming the reading for the number included in the critical text. These are the manuscripts which, instead of writing out the words for the number, use the Greek alphabetic notation, i.e. the three Greek letters (chi)(xi)(stigma). The manuscripts so listed are P47 (a papyrus manuscript, hence the P in the name, from the third century, known as Chester Beatty III), a tenth century manuscript known as 051, and the "Majority-text" symbol (which indicates many late Byzantine manuscripts). P47 is from the third century and is the oldest manuscript of the Book of Revelation. It contains parts of chapters 9-17. We will consider its readings for numbers in Rev 13:18 and neighboring verses in the next section. Because, as listed above, the majority of the manuscripts (mostly late Byzantine miniscule manuscripts) include the representation of the number six hundred sixty-six by the three letters (chi)(xi)(stigma), the text presented in another modern (but non-standard) edition called not surprisingly THE GREEK NEW TESTAMENT ACCORDING TO THE MAJORITY TEXT, does so also.[20] Note that there is a major disagreement in presuppositions about the value of various manuscripts and manuscript groups between the editors of this edition and those of the standard editions.[21] The so-called Textus Receptus which acted as the standard from the 16th century (the actual term first being used in the 17th) until well into the 19th century when modern critical editions started to displace it, was an evolution of early printed editions of the Greek NT. Its printed text also used the (chi)(xi)(stigma) notation. The main textual basis of this edition was only a handful of fairly late manuscripts, a subset of the majority text. VI. Papyrus P47 in Detail on the Numbers of Rev 13:18 As mentioned above, P47 is the oldest extant manuscript which contains part of the Book of Revelation. However, its method of representing the number six hundred sixty-six (using Greek alphabetic numerals) is not the one selected by the "standard" critical text (which spells out the number words). The textual apparatus of NA26 shows other variations of P47 from the usual text, even in other places in Rev 13:18. Although the use of a modern printed critical edition of the Greek New Testament is within the ability of anyone who can read the Koine Greek, the potential of looking at actual copies (reproductions) of individual manuscripts is slight. Even many theological libraries would not have the printed (published) editions which would contain photographs of the desired manuscript. In this case we are lucky because Kurt and Barbara Aland in their widely available textbook (pun-intended) THE TEXT OF THE NEW TESTAMENT (in both the first and second English editions of 1987 and 1989) include a Plate 23 on page 90 which shows Rev 13:16-14:4 of P47. (Note that the caption of this plate is incorrect in that it attributes P47 to the the second century whereas in other places in the book they give the usual third century date). As mentioned in the description of the Greek alphabetic number system above, the usual way to signal that letters are being used as numerals is by a horizontal line above the letter-numbers. (A horizontal line can also mean something else.) On the ninth line down from the top of this fragment (all line counts will exclude what might be counted as the first line which seems to include only one character at the very top of the plate) we can see the first horizontal line overscore. This is indeed over the three letters (chi)(xi)(stigma) which represents the six hundred sixty-six of Rev 13:18. Verse 14:1 starts immediately afterward (no gaps or separations in such manuscripts), a clear reminder that the chapter and verse divisions which we find so essential in locating and referring texts are late additions, many centuries after the books of the NT were written. Two lines further down the overscore is above the letters (rho)(mu)(delta). This is for the alphabetic numeral representation of the one hundred forty four thousand. In this P47 manuscript, at least, the number (one hundred forty four) is written out in the Greek alphabetic mode. The word for "thousands" is written following these "digits". The same (rho)(mu)(delta) again with overscore also occurs four lines from the bottom of the fragment picture. As an example that the horizontal line above letters does not always indicate a Greek alphabetic number representation, note the three letters (pi)(rho)(sigma) on line 12 that also have the horizontal line above them. This, however, is not a number. The order is reversed from the usual descending order (which is still possible) and two of the letters would stand for different hundreds (100 and 200). This horizontal line above letters serves to signal that this is a NOMINA SACRA, a form of abbreviation used in some Christian Greek scriptures for certain COMMON "theological" words[22]. This is the abbreviation for patros the Greek word for father (in genitive case), as in "the name of his father" (Rev 14:1). -- NOTES -- [17]. Two of the standard introductions to the textual criticism of the Greek New Testament written by editors of the main critical editions of the NT are: Bruce M. Metzger, THE TEXT OF THE NEW TESTAMENT: ITS TRANSMISSION, CORRUPTION AND RESTORATION 2nd ed. (New York: Oxford University Press, 1968). Kurt Aland and Barbara Aland, THE TEXT OF THE NEW TESTAMENT (Grand Rapids: William D. Eerdmans, 1987 based on German edition of 1982). [18]. Standard modern critical editions: NA26: Kurt Aland, Matthew Black, Carlo M. Martini, Bruce M. Metzger, and Allen Wikgren (eds), NOVUM TESTAMENTUM GRAECE 26th edition (Stuttgart: Deutsche Bibelgesellschaft, 1979). UBSGNT3: Kurt Aland, Matthew Black, Carlo M. Martini, Bruce M. Metzger, and Allen Wikgren (eds), THE GREEK NEW TESTAMENT 3rd edition (New York: United Bible Societies, 1979). [19]. All descriptions and dates of manuscripts in this summary are from tables in NA26 or in Aland and Aland, THE TEXT OF THE NEW TESTAMENT. [20]. Zane Hodges and Arthur L. Farstad (eds), THE GREEK NEW TESTAMENT ACCORDING TO THE MAJORITY Text 2nd ed (Nashville: Thomas Nelson Publishers, 1985). [21]. D.A. Carson, THE KING JAMES VERSION DEBATE: A PLEA FOR REALISM (Grand Rapids: Baker Book House, 1979) contains a sane discussion on the subject. The title indicates that the topic of the book is broader than just the majority text vs. other critical editions. The King James Version was translated from a Textus Receptus type text which has similarities to, but is not identical to, the Majority text as compiled today. [22]. Metzger, MANUSCRIPTS OF THE GREEK BIBLE, 36-37. -- ============================================================================= = Edward L. Pothier epothier@lynx.dac.neu.edu = = Physics Department PREFERRED EMAIL: pothier@neuhep.hex.neu.edu = = Northeastern University / Boston, MA 02115 =