By dkl9, written 2025-260, revised 2025-260 (0 revisions)
Plenty of calculators are called "four-function" sith they can do exactly four things between numbers:
When the inputs are natural numbers, addition and multiplication tend to increase them, while subtraction and division tend to decrease them. Multiplication and division are (in basic forms) iterated from addition and subtraction, respectively. Thus the four basic actions of arithmetic can be classified in two orthogonal pairings.
Likewise, when you can measure time, there are four basic functions you can implement:
Those are just common names with more specific meanings:
All those functions take in when the user asked for them. A clock and a stopwatch each give a number, while an alarm and a timer each take a number and respond at another time. The clock and the alarm work just like the stopwatch and the timer, except for the different form of the numbers and an implied starting point. Thus the four basic actions of time-keeping can be classified in two orthogonal pairings.
You can make any basic arithmetic operation ultimately out of addition. a - b solves x + b = a. Multiplication is repeated addition, and division inverts (and so is defined from) multiplication. But such indirect methods are inconvenient.
Likewise, a timepiece can provide any of its four functions from just acting as a clock. For an alarm, check the time occasionally until the target is passed. For a stopwatch, check the time at the start and end, and subtract. For a timer, check the time at the start, add the duration, and check occasionally until the calculated end. But such indirect methods are inconvenient.
A basic watch only acts like a clock, as defined here. The next step is for it to natively offer the other three functions. A smartwatch might act like a clock by default, but offer the other modes deep in bespoke menus. An analog watch might more elegantly offer all four functions by respect to the dichotomies exposed above.
Each function either gives or takes a time-number. Any watch should can move its hands, and the crown typically lets the user move the hands of the watch. Thus the position of the hands serves as both output and input. The buttons for clock and stopwatch would tell the hands to swivel to show a time. The buttons for alarm and timer would tell the internals to note the time marked by the hands.
Such button-oriented workings go against the norm that a watch shows the current time sans touch. To restore that norm, tweak the design and compromise its symmetry.