środa, 11 kwietnia 2012

The Number of the Beast: A Numerological Primer

The Number of the Beast: A Numerological Primer

by Michael Gilleland

Revelation 13:18
The Identity of the Beast
The Validity of Numerology
Links
Java Applet
Java Source Code
Appendix 1: Isopsephia
Appendix 2: Significant Numbers in Literary Works

Revelation 13:18

Our starting point is the last verse of the 13th chapter of the last book of the Bible (Revelation 13:18). In the King James Version, this verse reads:
Here is wisdom. Let him that hath understanding count the number of the beast; for it is the number of a man, and his number is six hundred, three score and six.
Scholars of every persuasion are almost unanimous in interpreting the beast in this passage to be the Antichrist. For practically every verse in the Bible, manuscripts offer variant readings, and this verse is no exception. One of the variants in this verse is the actual number of the beast. While most manuscripts read 666, some read 616 instead. We'll look at one possible explanation of this discrepancy below.

The Identity of the Beast

Before the discovery and widespread use of what we call Arabic numerals (0123456789), letters of the alphabet did double duty as numbers. It is this twofold function (letters serving as numbers, as well as letters) that lies behind the pseudo-science of numerology, known also as gematria (in Hebrew), isopsephia (in Greek), and abjad (in Arabic).
In the following sections, we'll examine the claims of several candidates to be the Beast:
The list could easily be expanded. Perhaps, after learning some tricks of the numerological trade, you could add your favorite villain to the list.

Nero

The Roman emperor Nero (lived 37-68 AD, ruled 54-68 AD) persecuted the first Christians. He accused them of starting a fire which destroyed half of the city of Rome in 64 AD (Tacitus, Annals 15.44).
Like all Roman emperors, Nero took the name Caesar. In Greek, Nero Caesar becomes Neron Kaisar. If we transliterate Neron Kaisar into Hebrew, we get NRWN QSR (vowels were omitted in written Hebrew). The spelling NRWN QSR actually appears in one of the Wadi Murrabba'at documents (18.1, dated 55/56 AD): see D.R. Hillers, "Rev. 13, 18 and a scroll from Murabba'at", Bulletin of the American Schools of Oriental Research 170 (1963) 65.
The following table of Hebrew letters and their corresponding numerical values is adapted from R.K. Harrison, Biblical Hebrew, 11th impression (Hodder and Stoughton, 1986), p. 11:
Name Transliteration Numerical
Value
Aleph (smooth breathing) 1
Beth BH, B 2
Gimel GH, G 3
Daleth DH, D 4
He H 5
Waw W 6
Zayin Z 7
Heth H 8
Teth T 9
Yodh Y 10
Kaph KH, K 20
     
Name Transliteration Numerical
Value
Lamedh L 30
Mem M 40
Nun N 50
Samekh S 60
Ayin (rough breathing) 70
Pe PH, P 80
Cadhe C 90
Qoph Q 100
Resh R 200
Sin SH 300
Taw TH, T 400
Let's look at the letters of NRWN QSR:
N R W N     Q S R
50 200 6 50 100 60 200
If we add the numbers in the second row, their total is 666, the Number of the Beast. Note that if we used a Latin form of Nero's name (Nero Caesar) instead of a Greek form (Neron Kaisar), the value of the Hebrew equivalent (NRW QSR) would be 616 instead of 666. This is a plausible explanation of the variant 616 which appears instead of 666 in some New Testament manuscripts.
Early Christian tradition identified the emperor Nero with the Antichrist. Here are a couple of examples:
  • According to F.F. Bruce, 1&2 Thessalonians (Waco: Word Books, 1982), p. 182:
    The Ascension of Isaiah, an early Christian document, incorporates a Testament of Hezekiah, in which the ultimate Antichrist appears as an incarnation of Beliar (the Greek spelling of Belial, as in 2 Cor 6:15), the spirit of evil in the world. This expected incarnation of Beliar, moreover, is identified with the returning Nero, described by King Hezekiah as "a lawless king, the slayer of his mother" (Asc Isa 4:2) -- a reference to Nero's widely suspected responsibility for the slaying of the younger Agrippina.
  • St. Augustine (City of God 20.19, translated by Marcus Dods), commenting on 2 Thessalonians 2:7, wrote:
    He [St. Paul] alluded to Nero, whose deeds already seemed to be as the deeds of Antichrist. And hence some suppose that he shall rise again and be Antichrist. Others, again, suppose that he is not even now dead, but that he was concealed that he might be supposed to have been killed, and that he now lives in concealment in the vigour of that same age which he had reached when he was believed to have perished, and will live until he is revealed in his own time and restored to his kingdom.
It is interesting that the emperor Nero figures in another well-known numerological calculation. In his Life of Nero (39.2), the biographer Suetonius quotes a Greek lampoon about Nero's murder of his mother Agrippina (in 59 AD), which may be transliterated as follows:
NEOPSEPHON. NERON IDIAN METERA APEKTEINE.
J.C. Rolfe cleverly translates this as:
A calculation new. Nero his mother slew.
In order to appreciate the calculation, we must know the numerical values associated with the letters of the Greek alphabet. I've adapted the following table from William Watson Goodwin, Greek Grammar, revised by Charles Burton Gulick (Boston: Ginn, 1930), pp. 93-94:
Name Transliteration Numerical
Value
Alpha A 1
Beta B 2
Gamma G 3
Delta D 4
Epsilon E (short) 5
Vau W 6
Zeta Z 7
Eta E (long) 8
Theta TH 9
Iota I 10
Kappa K 20
Lamda L 30
Mu M 40
Nu N 50
      
Name Transliteration Numerical
Value
Xi X 60
Omicron O (short) 70
Pi P 80
Koppa Q 90
Rho R 100
Sigma S 200
Tau T 300
Upsilon Y 400
Phi PH 500
Chi CH (hard) 600
Psi PS 700
Omega O (long) 800
Sampi SP 900
The letters vau, koppa, and sampi were used only as numbers (not as letters) in classical Greek.
We now have the key to interpret the lampoon quoted by Suetonius:
N E R O N
50 5 100 800 50 1005


I D I A N     M E T E R A     A P E K T E I N E
10 4 10 1 50 40 8 300 5 100 1 1 80 5 20 300 5 10 50 5 1005
The numerical value of "Nero" (NERON = 1005) is equal to the numerical value of "killed his own mother" (IDIAN METERA APEKTEINE = 1005) -- this is the "new calculation" of the lampoon.

The Pope

One of the titles of the Pope is "Vicar of Christ". The word vicar is rare nowadays outside of theological discourse. It means one who acts as the representative of someone else.
Since Jesus Christ is the son of God, we can replace "Christ" in the Pope's title with "Son of God". If we do this, we get "Vicar of the Son of God", which in Latin (the language of the Church) is "Vicarius Filii Dei". Latin inscriptions are often capitalized, and capital U is written as V, which yields "VICARIVS FILII DEI". Let's extract those letters of "VICARIVS FILII DEI" which do double duty as Roman numerals, and see what happens:
V I C A R I V S    F I L I I    D E I
5 1 100 1 5 1 50 1 1 500 1
If we add all of the figures in the second row of this table, we arrive at 666, the Number of the Beast.
Attempts have been made to identify particular Popes (rather than the Pope in general) with the Beast. Michael Stifel (1487-1567, better known for introducing modern symbols for addition, subtraction, and square root) proved that Pope Leo X (lived 1475-1521, Pope 1513-1521) was the Beast by means of the following calculation, as described by Howard Eves, An Introduction to the History of Mathematics (NY: Rinehart, 1953), p. 217:
From LEO DECIMVS he retained the letters LDCIMV. He then added X, for Leo X, and omitted the M, because it stood for mystery. A rearrangement of the letters gave DCLXVI, 666, or the "number of the beast".

Martin Luther

Faced with the embarrassing identification of the Pope with the Beast, Catholic scholars responded in true ecumenical spirit with their own preferred candidate: the Protestant reformer Martin Luther (1483-1546).
Petrus Bungus, in Numerorum Mysteria (Bergamo, 1599; reprint Hildesheim: Olds, 1983), used the following letter/number combinations:
A B C D E F G H I/J K L M N O P Q R S T U/V W X Y Z
1 2 3 4 5 6 7 8 9 10 20 30 40 50 60 70 80 90 100 200 300 400 500 600
By slightly contorting Martin Luther's name (to MARTIN LUTHERA) and regarding the I as equivalent to 1 rather than 9 (it's a Roman numeral, after all), Bungus succeeded in identifying his archenemy with the Beast:
M A R T I N L U T H E R A
30 1 80 100 1 40    20 200 100 8 5 80 1 666
Some authorities (e.g. Howard Eves, loc. cit.) give Bungus' name as Bongus.

Napoleon Bonaparte

In Leo Tolstoy's novel War and Peace, Book 9, Chapter 19, Pierre, the son of Count Cyril Bezuhkov, convinced himself that Napoleon was the Beast, by the following reasoning (translation by Louise and Aylmer Maude):
The French alphabet, written out with the same numerical values as the Hebrew, in which the first nine letters denote units and the others tens, will have the following significance:

A B C D E F G H I/J K L M N O P Q R S T U V W X Y Z
1 2 3 4 5 6 7 8 9 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160

Writing the words L'Empereur Napoleon in numbers, it appears that the sum of them is 666, and that Napoleon was therefore the beast foretold in the Apocalypse.
L'Empereur Napoleon, of course, is French for The Emperor Napoleon. The identification with Napoleon only succeeds if the e in Le, dropped by elision in L'Empereur, is restored:
L E E M P E R E U R N A P O L E O N
20 5    5 30 60 5 80 5 110 80    40 1 60 50 20 5 50 40 666

Ellen Gould White

Some members of the Seventh-Day Adventist Church, hostile towards Roman Catholics, like to identify the Beast with the Pope. Books by Adventist authors which accept this identification include:
  • Roy Allen Anderson, Unfolding the Revelation (Mountain View: Pacific Press, 1974)
  • Carlyle Boynton Haynes, Our Times and Their Meaning (Nashville: Southern Publishing Association, 1929)
  • Uriah Smith, Daniel and the Revelation (Battle Creek: Review and Herald Publishing Company, 1897)
But turnabout is fair play. Martin Gardner, The Magic Numbers of Dr. Matrix (Buffalo: Prometheus Books, 1985), pp. 14-15 (with footnote), reports that an anonymous religious pamphlet of the 1930s (published by the People's Christian Bulletin) identified the Beast with one of the founders of the Seventh-Day Adventist Church, Ellen Gould White (1827-1915). The scheme is similar to that used for the Pope, with U representing Roman numeral V and W (double U) standing for V + V, or 10:
E L L E N G O U L D W H I T E
50 50    5 50 500    10 1 666

Adolf Hitler

Another mapping of letters to numbers used by numerologists is shown in the following table:
A B C D E F G H I J K L M N O P Q R S T U V W X Y Z
100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125
By this table, it is evident that the Beast is Adolf Hitler, since the numbers corresponding to the letters in his name add up to 666:
H I T L E R
107 108 119 111 104 117 666

Ronald Reagan

Numerologist Gary D. Blevins, author of 666: The Final Warning (Kingston, TN: Visions of the End Ministries, 1990), identifies Ronald Wilson Reagan as the most likely candidate for the Beast of Revelation 13:18. Note that each of Reagan's three names has six letters, and that the entire name has six syllables.
Blevins uses the following scheme, which he calls the Bible's Secret Code:
A B C D E F G H I J K L M N O P Q R S T U V W X Y Z
6 12 18 24 30 36 42 48 54 60 66 72 78 84 90 96 102 108 114 120 126 132 138 144 150 156
Unfortunately, plain old RONALD REAGAN only adds up to 660, so Blevins is compelled to pad the name to A RONALD REAGAN in order to reach 666:
A R O N A L D R E A G A N
6    108 90 84 6 72 24    108 30 6 42 6 84 666
Blevins' ingenuity doesn't stop there, though. He shows that dozens of phrases containing the name Reagan also add up to 666, including:
  • Brain of Reagan
  • Faith of Reagan
  • Ranch of Reagan
I have not seen Blevins' book. My knowledge of it comes from Martin Gardner's review in Did Adam and Eve Have Navels? (NY: W.W. Norton, 2000), pp. 291-293, 296. Gardner points out that Minnesota governor Jesse Ventura could be the Beast according to Blevin's code, since the letters in J. Ventura add up to 666. I lived in Minnesota for four years under Ventura's administration, so I'm inclined to favor this interpretation (even though Ventura's real name is James George Janos). For more "evidence" that Reagan was the beast of Revelation, see Ronald Wilson Reagan = 666.

Bill Gates

The American Standard Code for Information Interchange (ASCII) is a system for representing symbols numerically. Here are the ASCII numerical values that represent capital letters:
A B C D E F G H I J K L M N O P Q R S T U V W X Y Z
65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90
Microsoft founder Bill Gates' full name is William Henry Gates III. The total of the ASCII values of the characters in BILL GATES plus 3 = 666:
B I L L G A T E S III
66 73 76 76    71 65 71 69 83    3 666

The Validity of Numerology

If it's not already apparent, I consider numerology as hokum and a fraud, along with astrology, crystals, pyramid power, and other such New Age flimflam. Martin Gardner (a national treasure) has labored mightily to debunk modern manifestations of numerology. How anyone can take numerology seriously after reading the following writings by Gardner is beyond my comprehension:
  • "Farrakhan, Cabala, Baha'i, and 19", in Did Adam and Eve Have Navels? (NY: W.W. Norton, 2000), pp. 247-256
  • "The Numerology of Dr. Fliess", in Mathematical Carnival (NY: Knopf, 1977), pp. 150-160, reprinted as "Fliess, Freud and Biorhythm", in Science: Good, Bad and Bogus (Buffalo: Prometheus Books, 1981), pp. 131-139
  • "The Numerology of Dr. Khalifa", in Did Adam and Eve Have Navels? (NY: W.W. Norton, 2000), pp. 257-263
  • "The Second Coming", in Did Adam and Eve Have Navels? (NY: W.W. Norton, 2000), pp. 288-296
The combination of numerology with anti-Catholic bigotry is an especially poisonous and vicious brew, which shows no signs of abating, if one can judge by the popularity of such recent books as Canyon Adams' 666: The Beast Revealed (Epiphany Press, 1999). Adams and his ilk, when tempted to make a serious identification of someone or something with the Beast, would do well to take the advice of F.F. Bruce (op. cit., p. 187) and ask the question: Master, is it I? (Matthew 26:25).

Links

An asterisk by the following links indicates that the author takes numerology seriously. Nevertheless, good historical information can sometimes be found even on those pages, if you sift carefully through the nonsense.

Java Applet

The following Java applet allows to enter the name of your favorite villain and get the number corresponding to the name. You can choose from one of four numerological schemes: Blevins' secret Bible code, Roman numerals (with J equivalent to I, U to V, and W to V + V), ASCII, and the units/tens/hundreds scheme.

Java Source Code

Here is source code for the Numerology.java class used in the applet: 
//----------------------------------
// A numerology class (just for fun)
//----------------------------------

import java.util.Vector;

public class Numerology {
  private Vector asciiScheme;
  private Vector blevinsScheme;
  private Vector romanNumeralScheme;
  private Vector unitsTensHundredsScheme;
  private Vector schemes;

  private static final int AVALUE = 65;
  public static final String ASCII_SCHEME = "ASCII";
  public static final String BLEVINS_SCHEME = "Blevins";
  public static final String ROMAN_NUMERAL_SCHEME = "Roman Numeral";
  public static final String UNITS_TENS_HUNDREDS_SCHEME = "Units, Tens, Hundreds";

  //------------
  // Constructor
  //------------

  public Numerology () {

    // ASCII scheme

    int val = AVALUE;
    asciiScheme = new Vector ();
    for (int i = 0; i < 26; i++) {
      asciiScheme.addElement (new Integer (val++));
    }

    // Blevins' scheme

    val = 6;
    blevinsScheme = new Vector ();
    for (int i = 0; i < 26; i++) {
      blevinsScheme.addElement (new Integer (val));
      val += 6;
    }

    // Roman numeral scheme

    romanNumeralScheme = new Vector ();
    Integer intObj;
    char ch;
    for (int i = 0; i < 26; i++) {
      ch = fromASCII (i + AVALUE);
      switch (ch) {
        case 'I':
          intObj = new Integer (1);
          break;
        case 'J': // alternate for I
          intObj = new Integer (1);
          break;
        case 'V':
          intObj = new Integer (5);
          break;
        case 'U': // alternate for V
          intObj = new Integer (5);
          break;
        case 'W': // double U, i.e. double V
          intObj = new Integer (10);
          break;
        case 'X':
          intObj = new Integer (10);
          break;
        case 'L':
          intObj = new Integer (50);
          break;
        case 'C':
          intObj = new Integer (100);
          break;
        case 'D':
          intObj = new Integer (500);
          break;
        case 'M':
          intObj = new Integer (1000);
          break;
        default:
          intObj = new Integer (0);
          break;
      }
      romanNumeralScheme.addElement (intObj);
    }

    // Units, tens, hundreds scheme

    val = 1;
    int multiplier = 1;
    unitsTensHundredsScheme = new Vector ();
    for (int i = 0; i < 26; i++) {
      intObj = new Integer (val * multiplier);
      unitsTensHundredsScheme.addElement (intObj);
      if (++val == 10) {
        val = 1;
        multiplier *= 10;
      }
    }

    // Scheme names

    schemes = new Vector ();
    schemes.addElement (BLEVINS_SCHEME);
    schemes.addElement (UNITS_TENS_HUNDREDS_SCHEME);
    schemes.addElement (ASCII_SCHEME);
    schemes.addElement (ROMAN_NUMERAL_SCHEME);

  }

  //---------------------------------
  // Convert ASCII value to character
  //---------------------------------

  private static char fromASCII (int val) {
    byte[] b = new byte[1];
    b[0] = (byte) val;
    String s = new String (b);
    return s.charAt (0);
  }

  //---------------------------------
  // Convert ASCII value to character
  //---------------------------------

  private static int toASCII (char ch) {
    Character charObj = new Character (ch);
    String s = charObj.toString ();
    byte[] b = s.getBytes ();
    int asc = (int) b[0];
    return asc;
  }

  //-------------------------------------------------
  // Get index into Vector corresponding to character
  //-------------------------------------------------

  private static int getIndex (char ch) {
    int asc = toASCII (ch);
    int idx = asc - AVALUE;
    if (idx < 0 || idx >= 26) {
      idx = -1;
    }
    return idx;
  }

  //------------
  // Get schemes
  //------------

  public Vector getSchemes () {
    return schemes;
  }

  //-----------
  // Get scheme
  //-----------

  private Vector getScheme (String name) {
    Vector v = null;
    if (name.equals (ASCII_SCHEME)) {
      v = asciiScheme;
    }
    else if (name.equals (BLEVINS_SCHEME)) {
      v = blevinsScheme;
    }
    else if (name.equals (ROMAN_NUMERAL_SCHEME)) {
      v = romanNumeralScheme;
    }
    else if (name.equals (UNITS_TENS_HUNDREDS_SCHEME)) {
      v = unitsTensHundredsScheme;
    }
    return v;
  }

  //-----------------------------------------------------------
  // Get number corresponding to string, using specified scheme
  //-----------------------------------------------------------

  public int getNumber (String schemeName, String s) {

    // Find the scheme corresponding to the name

    Vector scheme = getScheme (schemeName);
    if (scheme == null) {
      return 0;
    }

    // Find the number corresponding to the string

    int n = 0;
    String caps = s.toUpperCase ();
    Integer intObj;
    int idx;
    char ch;
    for (int i = 0; i < caps.length (); i++) {
      ch = caps.charAt (i);
      idx = getIndex (ch);
      if (idx >= 0 && idx < 26) {
        intObj = (Integer) scheme.elementAt (idx);
        n += intObj.intValue ();
      }
    }
    return n;
  }

}

Appendix 1: Isopsephia

The Greek word isopsephia is derived from isos (equal) and psephos (pebble). Since pebbles of different colors were used in voting, isopsephia originally had a meaning similar to "one man, one vote".
But pebbles were also used in simple counting (calculus is the Latin word for pebble), and the term isopsephia later referred to verses where the numeric values of the letters were identical. Aulus Gellius, Attic Nights 14.5.4, mentions a book which asked the question "qui sint apud Homerum uersus isopsephi" (what lines in Homer are isopsephic). In the Iliad, the pair 7.264-5 are nearly isopsephic, as are 19.306-7.
The Greek astrologer and poet Leonidas of Alexandria, who lived in the first century AD, intentionally wrote isopsephic verses. A few specimens survive in the Greek Anthology (6.321-322 and 323-329). Two (321, 328) are addressed to Caesar. Which Caesar is uncertain, although it may well be Nero.
Also from Alexandria, a bit earlier than Leonidas, was the grammarian Apion. An anecdote in Seneca's Letters to Lucilius (88.40) attributes a curious bit of numerological lore to Apion:
He used to say that Homer, after completing both of his works (the Iliad and Odyssey), added opening verses to the work in which he described the Trojan War [i.e. the Iliad]. As proof he adduced the fact that Homer intentionally placed in the first line two letters which contained the number of his books.
There are 24 books in the Iliad, and 24 in the Odyssey (48 total). The first word of the Iliad in Greek is menin (wrath), whose first two letters (mu and eta) also represent the numbers 40 and 8 (total 48). In Apion's completely bogus view, this "proved" that the first lines of the Iliad must have been composed after both the Iliad and Odyssey were otherwise complete. It is in the Oneirocritica (Interpretation of Dreams) by the Greek writer Artemidorus (late 2nd century AD), however, that we find numerological speculation (isopsephia) in its full glory. Sections 2.70, 3.34, and 4.24 of the Oneirocritica deal with numbers in dream interpretation. In 4.24, Artemidorus says that if a sick man sees an old woman in a dream, it means he will die, because the numerical value of "old woman" and "funeral" are both 704. He conveniently omits the definite article with "old woman", while including it with "funeral":
G R A U S
3 100 1 400 200 704


H E E K PH O R A
8    5 20 500 70 100 1 704
An anonymous epigram from the Greek Anthology (10.43, translated by W.R. Paton) recommends a six-hour work day (those wise, sensible Greeks!):
Six hours are most suitable for labour, and the four that follow, when set forth in letters, say to men "Live."
The four numbers following 6 are 7, 8, 9, 10. The letters corresponding to these numbers are zeta, eta, theta, iota, which spell the Greek imperative meaning "live" (zethi). Another anonymous epigram from the same collection (10.335, also translated by W.R. Paton) has a numerological basis:
Someone, hearing that "Damagoras" and "pestilence" were numerical equivalents [isophephon], weighed the character of both from the beam of the balance. But the scale, when raised, was pulled down on Damagoras' side, and he found pestilence lighter.
In other words, even though Damagoras and pestilence (loimos) are numerically equivalent, Damagoras is worse than pestilence. They both add up to 420:
D A M A G O R A S
4 1 40 1 3 70 100 1 200 420


L O I M O S
30 70 10 40 70 200 420
A naughty epigram from the Greek Anthology (12.6) by Strato notes the numerical equivalence of fundament (proktos) and gold (chrysos). They both add up to 1570:
P R O K T O S
80 100 800 20 300 70 200 1570


CH R Y S O S
600 100 400 200 70 200 1570

Appendix 2: Significant Numbers in Literary Works

Only tangentially related to numerology, but still interesting, is the phenomenon of significant numbers of lines, verses, chapters, etc., in literary works.
Richard J. Clifford, Proverbs: A Commentary (Louisville: Westminster John Knox Press, 1996), p. 108, points out that Proverbs 10:1 - 22:16 bears the title "The Proverbs of Solomon." The Hebrew consonants of Solomon add up to 375.
SH L M H
300 30 40 5 375
375 is also the number of two-line verses in this section of Proverbs.
Corpus Inscriptionum Latinarum 8.212-213 is a two-part Latin verse epitaph from a mausoleum in Kasserine, Tunisia, dated at the middle of the 2nd century A.D. The number of lines in the two parts combined is 110. The deceased, Titus Flavius Secundus, lived 110 years, according to the accompanying prose inscription (CIL 8.211): "uix(it) an. cx". This was apparently first noticed by F. Bücheler. A recent commentator, E. Courtney, in Musa Lapidaria: A Selection of Latin Verse Inscriptions (Atlanta: Scholars Press, 1995), p. 400, says that the coincidence "is hardly accidental."
On this subject, I've never been convinced by the fantasies of George Duckworth, Structural Patterns and Proportions in Vergil's Aeneid (Ann Arbor: University of Michigan Press, 1962) , who finds everywhere in the Aeneid that the ratio M/(M + m), where M is the line count of major passages and m is the line count of minor passages, is 1.618 (the Golden Ratio).
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