What “Close in Meaning” Actually Measures — and How to Guess Well in Proximity

When Proximity tells you that tea is the third-closest word to today's answer, it is making a claim about meaning that sounds almost mystical. It is not. The number comes from a measurement that can be written down in a paragraph, and understanding it changes how you play. This article explains the measurement, why the game shows you a rank rather than the raw number, why the colour scale is logarithmic, and what all of that implies for actually finding the word.

You shall know a word by the company it keeps

The linguist J. R. Firth wrote that line in 1957, and it is the whole theory in one sentence. Words that mean similar things tend to appear in similar contexts. Tea and coffee both show up after “a cup of,” before “with milk,” near morning and kettle and mug. Bicycle shows up near ride and wheel and lane. If you count, for every word, which other words it tends to appear beside, you get a description of that word that has nothing to do with its spelling and quite a lot to do with what it means.

A word-embedding model is a compressed version of those counts. Instead of a row of millions of co-occurrence tallies per word, it keeps a few hundred numbers per word, chosen so that words with similar contexts get similar lists. The list is called a vector, and the whole table of vectors is what the previous article calls the map.

The number

Two vectors can be compared by the angle between them. Vectors pointing the same way have a similarity of 1; vectors at right angles score 0; vectors pointing opposite ways score minus 1. This is cosine similarity, and it is what the game computes between your guess and the secret word. In practice the numbers for real word pairs cluster in a narrow band — strong synonyms might score 0.7, loosely related words 0.3, unrelated words somewhere around 0.1 — which is the first reason the game does not show you the raw number.

The second reason is that a raw similarity is meaningless without knowing what the rest of the vocabulary looks like. Is 0.42 good? It depends entirely on how many words score higher. A rank answers that directly: “this is the 40th-closest word out of everything the game knows.” Rank is what the game shows because rank is what you can act on.

Why the scale is logarithmic

If you sort the whole vocabulary by similarity to one secret word and plot the numbers, the curve is not a straight line. A handful of words score high, a few dozen score moderately, and then thousands of words trail off in a long, flat tail where the differences between them are essentially noise. The 400th-closest word and the 900th-closest word are both, for practical purposes, unrelated to the answer. The 8th and the 20th are meaningfully different.

The colour scale in Proximity follows the shape of that curve. Red covers the long tail, where movement means little. Yellow begins where the ranks start to carry information. Green is the small region where you are genuinely close. Mapping colour to rank linearly would paint the first twenty guesses as steady progress when most of them are random wandering, and would compress the final approach into one indistinguishable green. The logarithm puts the resolution where the information is.

Why the opposite of the answer scores well

This is the single most common complaint about semantic guessing games, and it follows directly from the theory. Hot and cold appear in nearly identical contexts — the water was hot, the water was cold; a hot day, a cold day — so their vectors are close. The model does not know they are opposites, because opposites keep the same company. Guess the antonym of the answer and you will usually land in the yellow.

This is not a flaw that can be patched without changing the kind of model. It is also, once you know it, a strategy: if warm scores well and hot scores better, do not neglect to try cold, because the answer might be on that side of the axis.

What the model does not know

• Definitions. The map records usage. Coffee and morning can outrank coffee and beverage, because people say “morning coffee” far more than they say “coffee beverage.”
• Which sense you mean. Every spelling has one vector. Bank sits between rivers and money and behaves oddly in both directions.
• Anything about letters. Teal shares four letters with tea and is nowhere near it. Word-length games and letter games are a different genre entirely.

A strategy that follows from all this

Because the score is about neighbourhoods rather than spelling, the efficient way to play is to search the map, not the dictionary.

1. Start with categories, not candidates. Animal, place, feeling, tool, food. A category word sits in the middle of a region, so its rank tells you whether the answer is in that region at all. Five category guesses partition the map far better than five specific nouns.
2. Move toward the best rank, but read the second-best too. If animal scores 60 and food scores 90, the answer is probably an animal that is also food, or something that lives near both — fish, chicken, farm. Two moderate ranks in different directions locate the answer better than one good rank alone.
3. Once you are in the yellow, think in associations. Stop asking “what is a synonym” and start asking “what appears in the same sentence.” If kettle scores 15, try steam, boil, mug, morning — the company the word keeps.
4. Try the opposite. See above. It costs one guess and frequently jumps the rank.
5. Save the hint for a stall. The hint returns a word roughly halfway between your best rank and the answer. Used at rank 400 it hands you a word at rank 200, which is still red. Used at rank 30 it hands you rank 15 and often the answer with it.

Played this way, most daily words fall in ten to twenty guesses. Some take sixty. The days it takes sixty are the days the answer is a word whose neighbourhood you would never have guessed, and those are usually the ones people remember.