Keys to the Cipher

What numerology is

Numerology gives symbolic meaning to numbers, usually by boiling a large number down to a single digit.

Digit reduction. Add the digits and repeat until one digit is left: 1913 → 1 + 9 + 1 + 3 = 14 → 1 + 4 = 5. Letters can be given digits too (A = 1 … I = 9, J = 1 again), which is often called the Pythagorean chart.

Master numbers. Modern numerology leaves 11, 22 and 33 unreduced and treats them as having a heightened meaning.

Date reduction. The common modern method adds every digit of a date: 12/23/1913 → 1+2+2+3+1+9+1+3 = 22. The book usually keeps two-digit chunks instead: month + day + first two year digits + last two (12 + 23 + 19 + 13 = 67).

Number mysticism goes back to the followers of Pythagoras in the 6th–5th centuries BCE (described by Aristotle, Metaphysics I.5), and later to Renaissance writers such as Agrippa (1533). The letter charts, "life path" numbers and master numbers of today's numerology come mainly from early-20th-century American writers, notably L. Dow Balliett and later Juno Jordan. "Pythagorean" is a modern label.

What gematria is

Gematria gives each letter a number. A word's value is the sum of its letters, and words with equal sums are read as connected.

Hebrew

Example: חי (chai, "life") = 8 + 10 = 18. The book's example is מלכות (Malkhut, "kingdom") = 40 + 30 + 20 + 6 + 400 = 496.

Hebrew letters served as numerals by the 2nd century BCE. Gematria appears in rabbinic interpretation (among the 32 rules attributed to Rabbi Eliezer ben Yose HaGelili) and became central to medieval Kabbalah.

Greek: isopsephy

Greek letters were numerals too (α = 1 … ι = 10 … ρ = 100 … ω = 800). A Pompeii graffito reads "I love the girl whose number is 545," and Revelation 13:18 gives the "number of the beast" as 666.

English ciphers (modern)

• English Ordinal: A = 1 … Z = 26 (Q = 17, used in the book).
• Full Reduction: A–I = 1–9, J–R = 1–9, S–Z = 1–8.
• Reverse Ordinal: Z = 1 … A = 26.
• "Sumerian": Ordinal × 6. The name refers to base-60 counting; there's no historical tie to Sumerian writing.
• Hebrew-style (English): Latin letters given Hebrew place values (A = 1 … K = 10 … T = 100). A modern convention with several versions.

Sources: Encyclopaedia Britannica, "Numerology," "Gematria"; Jewish Encyclopedia (1906), "Gematria"; U. Dudley, Numerology: Or What Pythagoras Wrought (MAA, 1997); W. Burkert, Lore and Science in Ancient Pythagoreanism (1972).

Mirrors and reversals

Some ciphers work by reading things backwards. The calculator below shows each of these for whatever you type.

Atbash. A Hebrew cipher that reverses the alphabet: the first letter (א aleph) swaps with the last (ת tav), the second with the second-to-last, and so on. Jeremiah 25:26 and 51:41 name "Sheshach" (ששך), which is traditionally read as Atbash for Babel (בבל). The same swap works in English (A ↔ Z, B ↔ Y), and an Atbash word's ordinal equals the original's Reverse Ordinal. Sources: Jeremiah 25:26, 51:41; Jewish Encyclopedia, "Atbash"; Wikipedia, "Atbash".

Palindromes. Words, numbers or dates that read the same both ways. The Latin SATOR AREPO TENET OPERA ROTAS square reads the same in every direction; copies scratched at Pompeii date to before the eruption of 79 AD. A date such as 02/02/2020 is palindromic when written 02022020. Sources: Pompeii Archaeological Park, "The Sator Square from the Palestra Grande"; Wikipedia, "Sator Square"; Wikipedia, "Palindromic number".

Reversed writing. Early Greek inscriptions, such as the Gortyn law code on Crete, were written boustrophedon ("as the ox turns"), with alternate lines running in opposite directions. Leonardo da Vinci wrote his notebooks in mirror script; the British Library notes that, as a left-hander, he did this to avoid smudging the ink, not for secrecy. Sources: Wikipedia, "Boustrophedon"; Wikipedia, "Gortyn code"; British Library, Arundel MS 263; British Library on Google Arts & Culture.

The riddle accounts use the same device: @321yugelbaraeb is "bearableguy123" reversed, and Mr Pool posted "the swan does not wait" backwards. Reading these as connected to the old traditions is the book's interpretation, not a documented link.

How the book uses them

Every worked number puzzle in the book is below, in the book's own steps, with a link to its chapter. Added explanations are marked General background.

Recurring keys

• Friday the 13th, 1307. The Templar arrests on "Friday, October 13, 1307" (1307: The Templar Correspondent Grid) seed the number 43. The date really was a Friday. Linking it to the Friday-the-13th superstition is a modern association; the superstition is first clearly documented in the 19th century.
• 1307, 1913, 1971. The Templar arrests, the Federal Reserve (Dec 23, 1913) and the Nixon Shock (Aug 15, 1971) are the book's recurring nodes (From 1307 to 1913).
• 11 and 33. The book calls 11 "the master number" and 33 "the master number of architectural building."
• Saros 126. The book describes the Saros as an "18-year, 11-day" eclipse cycle and names Saros 126 as the riddler's anchor (The Stellar Clockwork of the Ages). A Saros is about 6,585.3 days, or 18 years plus 10–12 days depending on leap years.
• 13:17 and 77. Decoders matched a Q post at 13:17 UTC to a 1:17 PM tweet, used A = 1, B = 2 to weigh phrases, and read two posts that both totalled 77 as a sign (The Modern Manifestation).