quincunx

Name

quincunx — five points — four corners and a center; pour enough through it and chance sets into a curve

Synopsis

quincunx [--beans N] [--rows R] [--fair|--loaded] [--aim BIN] [--seed N]
P(bin k) = C(n,k) / 2^n

Description

quincunx accepts a stream of independent beans and returns a distribution. At each of R rows of pegs a bean takes exactly one bit of input — left or right, on a fair coin — and its final bin is the running sum. Individually the output is noise. In aggregate it is not: the histogram converges on the binomial, and there is no flag to stop it.

The device has no target register. It does not know where the middle is, and neither does any bean in flight. The center bin fills first only because there are more paths that arrive there — one edge requires the same flip R times in a row, the middle tolerates any half-and-half muddle. Order is not imposed at the top of the board. It is counted at the bottom.

Below quorum the pile declines to have an opinion. Feed it enough and the opinion is always the same shape.

Options

--aim BIN

Steer beans toward BIN. Read once at launch, honored at zero pegs. The bean cannot hear you and would not comply.

--nudge

Tilt the whole board toward a preferred outcome. Returns a bell, shifted. Still a bell.

--fair | --loaded

Set the per-peg coin. --loaded relocates the peak; it does not abolish it. Convergence is not optional.

--rows R

Number of peg rows. More rows yield a smoother curve and the identical verdict, slower.

--seed N

Fix the randomness. Reproduces the exact heap you still did not aim.

--patience

Wait for the law to arrive. Has no effect on arrival time. The law was never late.

Exit Status

0

the bell arrived on schedule

0

the bell arrived before you finished watching; you were not consulted

75

too few beans; the law lacks a quorum, retry with more

1

you passed --aim; the board reviewed your request and declined

History

From Latin quinque ("five") and uncia ("a twelfth"): a quincunx was five-twelfths of the Roman as, a coin struck with five pellets in the four-and-one arrangement. Romans reused the layout to plant orchards on the diagonal, and Sir Thomas Browne cataloged it obsessively in 1658. In 1877 Francis Galton built a pegged board he named the quincunx to show the normal distribution as a physical object; the same five-point face survives on dice, dominoes, and every Plinko wall.

Bugs

--aim, --nudge, and --loaded all return a bell. Users report this as three separate defects. Closed as one.

Setting --rows to 0 produces a single bin containing every bean, described in the ticket as 'unusually accurate aiming'. Not a feature.

The center bin is over-represented in every run. Working as designed since 1877; escalations forwarded to the Central Limit Theorem.

See Also

stigmergy(1), hysteresis(3), thrashing(1). The living exhibit demonstrates the word in motion:

▸ operate quincunx

Author

Maintained by The Board, which aims at nothing, lands everything, and issues one fair coin per peg. It has no opinion until it has a quorum, and then only one.