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Plato · 5,040
420
Plato, Laws 5.737e: 5,040 households. 5,040 ÷ 12 = 420 per tribe. Timaeus 55c: a dodecahedral cosmos of twelve faces. Arithmetic and a textual neighbor, not one proof that Plato encoded 420 as a keyword.
Plato imagined a city of 5,040 households, split among twelve tribes. 5,040 divided by 12 is 420. He prized 5,040 because it divides many ways. He did not write the word 420. The arithmetic is later.
What it supports
Hard text, hard arithmetic. Laws 5.737e, late-classical Athens, a civic thought-experiment. 7! = 5,040. Twelve tribes give 420 households each. Timaeus 55c, next door, gives the cosmos twelve faces. Neighbor, not identity. Symposium remains the love walk. This is the civic clock.
What it does not
Plato does not write 420 as a keyword. Timaeus does not prove the city. Neighbor is not identity. Same 420, different operation.
Calculation
5,040 ÷ 12 = 420
Division of Plato’s civic 5,040 by a twelve-fold order. 7! = 5,040.
ExactnessDerived mathematics
Form420
Unithouseholds
Strengthhard