The Shape of Every Idea

An early sketch — thinking out loud about an idea for an essay, and a visual toy to go with it.

The idea

We name a small number of very large ideas — democracy, capitalism, evolution, entropy — and each one feels like it contains a library. But try to define one in the fewest, simplest words you can, and something strange happens: the library collapses to a single sentence, and the sentence has a shape.

Democracy — the many overrule the one. Evolution — what makes more, stays. Entropy — all order drifts to disorder, and never back. Emergence — many small things make one big thing that no one planned.

The game is compression: what is the shortest true thing you can say about a concept using only ordinary words? And the surprise is that when you play it across politics, physics, biology, and mind, the answers don’t sprawl. They fall into three families.

The three shapes

A loop — the end feeds the start. Evolution, capital, life, feedback. Something comes out the far end and is pushed back in the front, and the whole thing runs on itself.

An arrow — one direction, no return. Entropy, time, gravity, power. A quantity that only ever moves one way; you can’t run the film backwards.

A jump — many become one. Democracy, markets, emergence, consciousness. A crowd of small things, none of them in charge, producing a single big thing nobody designed.

That’s the whole claim, and it’s the thing worth arguing about: almost every profound concept, compressed, is a loop, an arrow, or a jump. Below, filter a first batch by shape — hover any card for its one-line gloss.

Can we build the machine?

The seductive next step: if concepts are short sentences in simple words, could we enumerate them — grind through the combinations and find ideas nobody has named yet? Here’s where the honesty has to come in, because the naive version doesn’t work, and the reasons it fails are the interesting part.

How many words per sentence? The good glosses above sit at three to six words. Cap it at six: below three you can’t state a relation, above six you’re writing compounds and the space fills with noise.

Which words? Don’t hand-wave “simple English” — fix a real lexicon, because everything scales off its size. There are pre-built options: Anna Wierzbicka’s Natural Semantic Metalanguage (~65 universal “semantic primes” — I, you, do, happen, good, big, people, because — found in every human language), the constructed language Toki Pona (~120 words, and it comes with a grammar), or Ogden’s Basic English (850 words). For this game the ~65 primes are the honest floor: the actual atoms of meaning.

How big is the space? It’s just words-to-the-power-of-length. With 65 words and up to 6 slots that’s 65⁶ ≈ 75 billion ordered strings. With Toki Pona’s 120 it’s ~3 trillion; with Basic English’s 850, ~4 × 10¹⁷. Almost all of it is gibberish. That is the whole point — the space is enormous and very nearly empty.

How many are real sentences? Two ways to count. Analytically: tag each word with a part of speech (say ~25 nouns, ~15 verbs, ~10 modifiers, ~15 function words), then a grammatical sentence is a template filled from the right buckets and you just multiply. noun–verb–noun gives 25 × 15 × 25 ≈ 9,000; allow a modifier and a second clause and you climb to tens of millions. Against 75 billion raw strings, the grammatical fraction is well under a tenth of a percent — a thin skin of sense on a huge dead volume. Empirically: sample random strings, judge each, and multiply the pass-rate by the total. The judge is the new ingredient — a language model can now rate a string for grammatical → coherent → names a real pattern — so you can actually run the sieve and watch what survives.

The catch, and the reason this is art and not a discovery engine: grammatical ≠ meaningful ≠ true ≠ good. Enumeration hands you Borges’ Library of Babel — every truth, every falsehood, and an ocean of well-formed nonsense, with no way to tell them apart from inside the list. The filter that picks out the real concepts is not a step in the algorithm. It’s the whole of human judgment.

So what makes a concept good?

Here’s the idea that ties the knot: a good concept is itself a compression. Entropy folds billions of observations into one arrow; evolution folds all of biology into one loop. A concept earns its place if naming it makes the world shorter to describe than not naming it. The junk the machine spits out will be grammatical but compress nothing — it shortens no description, so it’s empty. “Good,” in other words, is the same minimum-words game played one level up.

And there’s a clean line between the two kinds of good concept — discovery versus invention — with a single test: re-run history. Does it come back?

A discovery is a pattern already running in the world; any observer would eventually hit it. Gravity, entropy, evolution, π. Re-run the tape and you get them again — and, tellingly, these are mostly the arrows and loops, the ones that were turning before anyone looked. An invention is a configuration that works but wasn’t inevitable; other choices would also have worked. Democracy, money, chess, capitalism. Re-run the tape and you’d get something adjacent, not identical — and these are mostly the jumps, the things we assembled.

So the two axes cross. Shape (loop / arrow / jump) tells you how an idea moves; origin (discovered / invented) tells you whether the universe handed it to us or we built it. Every concept lands somewhere on that grid — and that grid, not a flat list of definitions, is the real spine of the piece.

Where this goes next

Three things worth building from here. Fix the 65-word lexicon with part-of-speech tags and actually run the sieve — enumerate the grammatical sentences, score them with a model, and see what evocative near-concepts fall out (most will be nonsense; a few will read like koans). Plot the concept grid properly — shape against origin, with the compression “weight” of each idea as a third dimension. And chase the honest floor: how few words really define everything? Wierzbicka’s answer is ~65. The art is in the descent toward it — because every time you refuse to cheat, a word you leaned on cracks open into smaller words, and you spiral down toward the irreducible core.

That descent is the whole show. Loops, arrows, jumps — and a very small bag of words underneath it all.