Every word in the Bible becomes an arrow. Words used alike point alike — and the angle between two arrows is a number a machine can use.
drawing…
drag either arrow tip · or click a word on the map
–Two arrows, one angle.
What a vector is
A list of numbers read as an arrow: how far along each axis. These arrows are the Bible’s own words — each word’s 32 numbers were learned from which words keep it company, then drawn in the plane that holds the two you chose, so their angle is exact.
What the angle buys you
Similarity without a dictionary. The cosine of the angle between two arrows is 1 when they point the same way and 0 when they are unrelated. Gold and silver: –. Gold and wicked: –. Adding arrows tip to tail is how a model combines meanings.
Evidence. Word vectors: skip-gram embeddings trained on the 66-book World English Bible by biblical_models.represent.train_skipgram (Mikolov et al. 2013), post-processed with all-but-the-top (Mu & Viswanath 2018) and unit-normalised. The picture is the plane through the two chosen 32-dimensional arrows (Gram–Schmidt), so the angle you see between A and B is their true angle and their cosine is exact; the other words are the shadows of their arrows on that plane, which is why they fall inside the circle. Numbers in foundations/data/vectors.json, produced by foundations/compute_data.py.
Nine seconds elsewhere
The foundations in learning order, then the series they lead to. Each lands in about nine seconds.