[05] Quick Checks, Expanded

A unary mark: one stroke, notch or dot per item. On its own it is the simplest possible number system; grouped, it becomes readable at a glance. See Ledger 02.

People can recognise up to about four items without counting — the effect is called subitizing. A closing fifth stroke turns each group into a single unit the eye reads instantly.

The Lebombo bone from southern Africa, roughly 43,000 years old with 29 notches. The Ishango bone from the DR Congo, about 20,000–25,000 years old, is the best known. Both interpretations are debated. See Ledger 01.

Graded notches recorded a sum, from a palm-width cut for £1,000 down to a scratch for a penny. The stick was split: the stock went to the payer, the foil stayed with the Exchequer. Matching halves settled the account.

For everyday counts, the five-bar gate and 正 are comparable. Dot-and-line packs ten into one cell and saves paper on high counts, at the cost of a learning curve. The desk's scoring is in Ledger 02.

The mechanism is dependable; operators are not. Zero-check before each period, write readings down at fixed intervals and never use one clicker for two categories. See Ledger 03.

Block estimation: count a block of 10, 50 or 100 birds, judge how many blocks fill the flock and multiply. A second observer counting independently gives a measurable error rate.

Yes. UK parliamentary and Canadian federal elections are counted by hand under observation. In Taiwan each ballot is read aloud and tallied with 正 on a public board. See Ledger 04.

Every ball gets a mark: a dot for no run, a numeral for runs, W for a wicket. Six dots in a scoreless over are joined into an M for a maiden. Scorers reconcile batting, bowling and total columns.