SAPIR 861 · Research · Chumash and the AI code
Equal sums are not equal meanings: testing gematria with word vectors across the whole Tanakh
Word meaning computed the way language models compute it — from contexts, over 201,175 words of the Tanakh. Words with equal letter-sums are, on average, no closer in meaning than random pairs. Where they are closer, they share a root, which is visible without any numbers.
What was tested
The old claim of gematria: if two words have the same letter-sum, they are linked in meaning. We took this literally and tested it with the instrument used to measure meaning in computational linguistics and inside language models: a word is the vector of its contexts. Two words are close in meaning if they occur in similar surroundings. No semantics assumed in advance — only the text.
Data and method
Text: Open Scriptures Hebrew Bible (Leningrad Codex with morphology, CC BY 4.0), all 39 books, 23,213 verses. Only content morphemes were used — nouns, verbs, adjectives: 201,175 tokens, 8,550 lexemes by Strong's number. 1,312 lexemes with 20 or more occurrences entered the computation. Window ±4 words within a verse, PPMI matrix, singular value decomposition to 150 dimensions — the standard recipe of distributional semantics. The letter-sum is taken from the lexeme's dictionary form in the open Strong's lexicon (CC BY 4.0). All rules were fixed before the result; code and tables are open.
The raw result — and what is behind it
There are 2,139 lexeme pairs with equal sums. Their mean similarity is 0.046 against 0.032 for random pairs; in 2,000 permutations of the sums across words this never happens (z ≈ 8). The claim looks confirmed. But the top pairs of the list are נדר and נדר (the verb “to vow” and the noun “vow”, similarity 0.84), טמא and טמא, זבח and זבח, קבר and קבר, and the anagrams כפרת and פרכת, שמעיה and מעשיה. These are not coincidences of sums — they are the same set of letters: one root, or a permutation of it. Such pairs are 570 of the 2,139, and the whole effect sits in them.
The controlled result
Remove the pairs with identical letter sets and permute sums only among words of the same length. 1,569 pairs remain: similarity 0.0352 against 0.0325 for random, z = 1.5, p = 0.06. In five other settings (frequency threshold, window, number of dimensions) z ranges from 0.7 to 2.8, and the difference itself is about 0.003 cosine. For scale: a same-root pair scores 0.5–0.8. Second test: among the ten nearest words by meaning, an equal sum occurs in 0.20 % of cases against 0.25 % expected — less often than chance. The “im ha-kolel” allowance (±1): z = 1.3, p = 0.09. The letter-sum does not predict meaning — neither exactly nor with the allowance.
And the pairs from the classical books?
From our base of 8,629 attestations, 103 pairs that authors of the 12th–20th centuries actually called equal could be tied to corpus lexemes. Their mean similarity is 0.031 against 0.022 for random pairs with the same sum; p = 0.16. There is a difference, but of the size chance produces. In other words, the commentators did not, and could not, systematically pick “meaningful” equalities: the meaning was added by them, through interpretation — and that is the honest nature of the genre.
What this changes for the site
Nothing in the computations and everything in the words. We still show the Torah word with the number of your name, the chapter and the verse — that is a fact about the text and it can be checked. But we do not say that this word “reveals” the name: the measurement showed that the letter-sum tells nothing about meaning. The word with your number is an address in the text, a point from which to start reading. What to do with that point is yours to decide. We give the number, the address, and the code it was computed with.
The data of this study
The lexeme table with its sums and vectors, the list of semantic neighbours for equal sums, and the code that recomputes everything are collected in a separate package and are being prepared for deposit in the archive. Once it has a permanent number, it will appear here as a link.
Coincidence is cheap · Exact and ±1 · Our data and code in the archive (DOI) · Code and full reproduction (GitHub)
The structure of 354 pages of 861 letters follows the edition Binyamin Pichkhadze, “Chumash 354” (חומש 354), Bnei Brak, 2002. The calculation was reproduced independently from the Westminster Leningrad Codex (CC BY 4.0); 31 of 31 control pages match the edition.