The Pythagorean Plinth

One of the most common methods of numerology of traditional Western occulture is that which might be considered combative or comparative techniques, where two names are compared according to their numerological values to decide which of them conquers, overcomes, or wins against the other in some sort of fight, contest, debate, suit, or other endeavor.  The traditional name for this method is “The Pythagorean Plinth”, but it may also be referred to as “The Letter of Pythagoras to Tēlaugēs”, the most common framing text that presents such techniques, or more simply as the Method of Pythmenes, where the πυθμήν or pythmēn of a number is its “base” where it is reduced from any high value to a single value that ranges from 1 to 9.  Once the pythmēn of one name is calculated, it may be compared in a regular manner to the pythmēn of any other name.

The basic method is straightforward:

  1. Calculate the numerological (e.g. isopsephic or gematria) value of a name.  Divide this value by nine and take the remainder; this is the pythmēn of the name.  Alternatively, given the sum of any name calculated from the pythmēn of the individual letters, repeatedly subtract 9 until a number that ranges from 1 to 9 inclusive results.
  2. Calculate the pythmēn of a second name.
  3. Compare the two pythmenes of the names:
    1. If one pythmēn is odd and the other pythmēn is even, the larger number (and thus, the party represented by that number) wins.
    2. If both pythmenes are odd but are different numbers, the smaller number wins.
    3. If both pythmenes are even but are different numbers, the smaller number wins.
    4. If both pythmenes are odd and are the same number, the attacker wins.
    5. If both pythmenes are even and are the same number, the defender wins.

The pythmenes of the individual Greek letters, omitting the obsolete letters Digamma, Qoppa, and Sampi, are as follows:

Letters Number
α, ι, ρ 1
β, κ, σ 2
γ, λ, τ 3
δ, μ, υ 4
ε, ν, φ 5
ξ, χ 6
ζ, ο, ψ 7
η, π, ω 8
θ 9

Many variations on this technique are found in numerological literature, some of which are found in Hippolytus’ Refutation of All Heresies (book IV, chapter 14):

  • Discount repeated letters.
  • Discount a letter that is repeated twice and only twice.
  • Discount letters that repeat a pythmēn value within the same name, e.g. Ω and Η.
  • Divide the end result by 7 instead of 9 to obtain a remainder.
  • Separate the letters out into three groups (vowels, semivowels, and consonants) and apply the comparison to each group of letters in the two names.  Best two of three “rounds” wins overall.

The text that follows is a translation of what Paul Tannery  gives in his Notice sur des fragments d’onomatomancie arithmétique from Notices et extraits des manuscrits de la Bibliothèque nationale et autres bibliothèques (vol. 31, part 2, 1886, pp.231—260).  In that text, Tannery presents a translation of three different texts that use similar methods of the Pythagorean Plinth, all three of which are found in the Bibliothèque national de France:

Rather than translating directly from Greek, I used Tannery’s translation into French and translated it from French into English, along with various edits to content and structure.  Those who are interested in the original Greek or the French translation are encouraged to investigate Tannery’s own article linked above.


Pythagoras to Tēlaugēs, greetings!
After long studies and many tests, I send you this little letter, which contains a very precious table, because the one who has it will be able, thanks to the explanations accompanying it, to know the present, the past, and the future.

This is based on the Table of Ninths, which follows.  Take two names that are given at birth, not nicknames, for two adversaries, such as those in a trial, in a single fight, or in general any dispute over a victory, prize, or a crown.  Calculate separately for each of the two names the sum of the numeric value of the letters in that name, counting as follows:

Letters Number
α, ι, ρ 1
β, κ, σ 2
γ, λ, τ 3
δ, μ, υ 4
ε, ν, φ 5
ξ, χ 6
ζ, ο, ψ 7
η, π, ω 8
θ 9

After figuring the sum of the two names as numbers by their letters, one sum for one name and the other sum for the other name, subtract nine as many times as possible from each number and note what remains of the two numbers, then look for these numbers in the Great Table below, and you will know the one who overcomes and the one who succumbs, as the winning numbers are marked as such.

If the names of both contestants are not the same number, here is how you can know the winner.  If both numbers are odd, the lesser number will win.  If both numbers are even, the lesser number again will win.  If the first number is odd and the second even, or if the first is even and the second odd, the greater of the two will win.

If the names of both contestants result in the same number, here is how you can know the winner.  If what remains is 1 and 1, the one who accuses or provokes will win; if 2 and 2, the one who defends himself; if 3 and 3, the attacker.  Whenever two numbers remain that are the same, if they are both odd, the one who attacks will win, and if they are both even, the accused or the provoked.  The attacker, in this case, refers to whichever party attacks, accuses, is male, is free, or is the older of the two.  The defender, likewise, is whichever party defends, is accused, is female, is enslaved, or is the younger of the two.

For example: consider the name Hector (ΕΚΤΩΡ), which is 5 + 2 + 3 + 8 + 1 = 19.  If you subtract 9 twice, the number 1 remains.  For the name Patroclus (ΠΑΤΡΟΚΛΟΣ), for which the calculation is 8 + 1 + 3 + 2 + 7 + 2 + 3 + 7 + 2 = 34.  Subtracting 9 three times, the number 7 remains.  Both names result in odd numbers, 1 and 7, and so the lesser of the two will win, which is 1.  Looking in the Great Table, you will find that 1 overcomes 7, and so Hector will win over Patroclus.  The calculation will be done in the same way in all cases.

The Great Table
9 and 1
1 wins
9 and 2
9 wins
9 and 3
3 wins
9 and 4
9 wins
9 and 5
5 wins
9 and 6
9 wins
9 and 7
7 wins
9 and 8
9 wins
9 and 9
Attacker wins
8 and 1
8 wins
8 and 2
2 wins
8 and 3
8 wins
8 and 4
4 wins
8 and 5
8 wins
8 and 6
6 wins
8 and 7
8 wins
8 and 8
Defender wins
8 and 9
9 wins
7 and 1
1 wins
7 and 2
7 wins
7 and 3
3 wins
7 and 4
7 wins
7 and 5
5 wins
7 and 6
7 wins
7 and 7
Attacker wins
7 and 8
8 wins
7 and 9
7 wins
6 and 1
6 wins
6 and 2
2 wins
6 and 3
6 wins
6 and 4
4 wins
6 and 5
6 wins
6 and 6
Defender wins
6 and 7
7 wins
6 and 8
6 wins
6 and 9
9 wins
5 and 1
1 wins
5 and 2
5 wins
5 and 3
3 wins
5 and 4
5 wins
5 and 5
Attacker wins
5 and 6
6 wins
5 and 7
5 wins
5 and 8
8 wins
5 and 9
5 wins
4 and 1
4 wins
4 and 2
2 wins
4 and 3
4 wins
4 and 4
Defender wins
4 and 5
5 wins
4 and 6
4 wins
4 and 7
7 wins
4 and 8
4 wins
4 and 9
9 wins
3 and 1
1 wins
3 and 2
3 wins
3 and 3
Attacker wins
3 and 4
4 wins
3 and 5
3 wins
3 and 6
6 wins
3 and 7
3 wins
3 and 8
8 wins
3 and 9
3 wins
2 and 1
2 wins
2 and 2
Defender wins
2 and 3
3 wins
2 and 4
2 wins
2 and 5
5 wins
2 and 6
2 wins
2 and 7
7 wins
2 and 8
2 wins
2 and 9
2 wins
1 and 1
Attacker wins
1 and 2
2 wins
1 and 3
1 wins
1 and 4
4 wins
1 and 5
1 wins
1 and 6
6 wins
1 and 7
1 wins
1 and 8
8 wins
1 and 9
1 wins
Table Against 1 Table Against 2 Table Against  3
9 and 1 1 wins 9 and 2 9 wins 9 and 3 3 wins
8 and 1 8 wins 8 and 2 2 wins 8 and 3 8 wins
7 and 1 1 wins 7 and 2 7 wins 7 and 3 3 wins
6 and 1 6 wins 6 and 2 2 wins 6 and 3 6 wins
5 and 1 1 wins 5 and 2 5 wins 5 and 3 3 wins
4 and 1 4 wins 4 and 2 2 wins 4 and 3 4 wins
3 and 1 1 wins 3 and 2 3 wins 3 and 3 Attacker wins
2 and 1 2 wins 2 and 2 Defender wins
1 and 1 Attacker wins
Table Against 4 Table Against 5 Table Against 6
9 and 4 9 wins 9 and 5 5 wins 9 and 6 9 wins
8 and 4 4 wins 8 and 5 8 wins 8 and 6 6 wins
7 and 4 7 wins 7 and 5 5 wins 7 and 6 7 wins
6 and 4 4 wins 6 and 5 6 wins 6 and 6 Defender wins
5 and 4 5 wins 5 and 5 Attacker wins
4 and 4 Defender wins
Table Against 7 Table Against 8 Table Against 9
9 and 7 7 wins 9 and 8 9 wins 9 and 9 Attacker wins
8 and 7 8 wins 8 and 8 Defender wins
7 and 7 Attacker wins

The letter Υ (Upsilon) signifies in three parts what is the nature of life.  The first line, the lower straight line, represents childhood; the two other lines that diverge above it belong to the two geniuses of life, one to the good genius, the other to the evil genius, all depending on the actions of youth.

In our alphabet, there are 24 letters: seven vowels, eight voiced consonants, and nine unvoiced consonants.  The table below demonstrates their division, with the first line given to the voiced consonants which are given to Youth, because as in Youth one does not yet know what their character will be, whether good or bad, the voiced consonants are between the fully voiced vowels and the wholly mute unvoiced consonants.  Likewise, the vowels are given to the character of the good genius, and the unvoiced consonants to that of the evil genius.

Life Type Letters
Youth Voiced consonants β, γ, δ, ζ, λ, μ, ν, ρ
Good Genius Vowels α, ε, η, ι, ο, υ, ω
Evil Genius Unvoiced consonants θ, κ, ξ, π, σ, τ, φ, χ, ψ

Before, a single sum for each name is calculated, and the matter of who wins is decided based on those two sums.  However, if one is in doubt with two names, instead of counting a single whole sum of each name, three sums each may instead be counted: one for the vowels, one for the voiced consonants, and one for the unvoiced consonants.  With each sum being made for the two names, each sum of each name may be compared, the two sums of the vowels, the two sums of the voiced consonants, and the two sums of the unvoiced consonants.  Using this method, we compare the best two out of three using the same method as the Great Table above.

In accounting and other fields of numbers, many numbers have a value greater than 9, such as ι for 10, κ for 20, ρ for 100, σ for 200, and so forth.  However, for the purposes of the Great Table, you shall use the method of reduction to the number’s base, where you reduce in units by thousands, by hundreds, and by tens; thus for 1000, reduce it to 1; for 100, to 1; for 10, to 1.  Likewise for 2000, to 2; for 3000, to 3; and so on, as in for 200, to 2; for 300, to 3; and so on.  The same goes for the other numbers until a number from 1 to 9 is obtained.

What follows are our methods to determine victory in business and lawsuits and other matters, so that you may learn it and keep it with you in your memory.  Remember: the lesser number prevails over the greater number of the same type, such that the lesser odd numbers prevail over the greater odd numbers and the greater odd numbers succumb to the lesser odd numbers, and the same for even numbers.  However, the opposite is true for two numbers that are not of the same type, such that the greater odd number prevails over the lesser even number and vice versa.  In this way, each number wins four times and loses four times, and the ninth time depends on who attacks and who defends and the type of number.

To that end, here are the general rules of our method.

On theft: Take the names of all the suspected individuals, arrange them in pairs two by two, and calculate the sums according to our method; divide always by 9, as it is said above, and compare the remaining numbers in each pair of names to see which numbers are victorious and which numbers are conquered.  Discard the vanquished numbers and their names, and compare the winners who remain by forming new couples between them.  Continue discarding the vanquished until you find the winner of all the names; it is this winner who is the thief.

On marriage: Take the names of the two people to be married, the man and the woman, according to their the proper names, not their nicknames.  If the man wins, the marriage will be advantageous; if the woman, disadvantaged.

On stolen objects: Take the name of the one who has been stolen from, and that of the one who stole, if the name is known.  If the one who has been stolen from victorious, the stolen object will be returned; if the thief, it will not be returned.

On lost objects: Take the name of the one who has lost an item and the name of the item.  If the one who has lost the object is victorious, the lost object will be found; if the lost object, it will not be found.

For a sick person, whether he will live or if he will die: Calculate the patient’s name and the day they took to bed ill and compare them.  If the patient prevails, he will live; if it is the day of decumbiture that prevails, there will be death.  If both numbers are equal and even, there will be a quick return to health; if equal and odd, a long illness.

On journeys: Calculate the name of the one who wants to travel and that of the city they wish to travel to.  If you find the name of the person who is to travel to be victorious, it is advantageous to travel; if the place name wins, it is disadvantageous.

On which of two will survive longer: Calculate the names of two people and compare them.  He who loses according to the comparison will die first.  If the numbers are equal, the younger of the two will be victorious and live longer; if the names are the same, the older will be victorious and live longer.

Assured calculation for patients and various other questions: Find the precise date when the patient has taken to bed ill, when child is born, when a fugitive has escaped, when a journey has been embarked upon, or for any other event that you desire.  Count how many days have elapsed since the last 18th of May.  From this day, subtract 36 as many times as possible so that what remains is 36 or less.  Find the number that remains in the following table.  If the number that remains is in the uppermost line, then say that the patient will live, the navigator will make a happy journey, the fugitive will be reclaimed, the child will live long, and so on.  If the number is in the second line, the disease will be long but without danger of death, the fugitive will not be found for a long time but will eventually be found, travelers will will weather storms or other dangers but eventually reach their destination, and so forth.  If, however, the number is on the third line, death is marked for the patient, the fugitive will never be found, and for all other questions there will only be misfortunes.

Result Numbers
Good life 1, 4, 7, 10, 13, 16, 19, 22, 25, 27, 31, 34
Tending to the middle 2, 5, 8, 11, 14, 17, 20, 23, 26, 29, 32, 35
Facing death 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36

Calculation of the days of the week to predict life or death: Learn exactly what day of the week the patient took to bed ill, counting 1 as Sunday, 2 as Monday, and so forth to 7 as Saturday, and how many days old the Moon was on that day, counting from the New Moon.  Add the number of the day of the week, the number of the age of the Moon, and the number of the true name of the patient, then add 10.  From this number subtract 30 as many times as possible so that what remains will be 30 or less.  Look to find what remains in the table below.  If the number is Above the Earth, the patient will live; if Below the Earth, the patient will die.  It is, however, important to remember that the first day of the disease, which is called ἀκατάκλισις (akatáklisis, the day of decumbiture, the day on which one takes to bed ill) should not be counted, but only the day after the day of decumbiture.

Position Result Numbers
Above the Earth Life 16, 28, 26, 23, 21, 20, 14, 13, 11, 10, 9, 7, 3, 2, 1
Below the Earth Death 30, 17, 19, 29, 27, 25, 24, 22, 18, 15, 12, 8, 6, 5, 4

Little bird, do not share this with strangers.  Rather, behold that this is something that can serve you; it is short and intended for those philosophers who are or wish to become astronomers.