See the Pen TernaryClock embed by CZ Chrome (@cz-chrome) on CodePen.
This is a balanced ternary clock. It goes around once a day just like a regular digital clock, but it works a little differently: the time it keeps is based on divisions of three. You can watch it tick right here or go to the Apple App store to get the free iOS app that has some nice extra features, like an analog style round clock dial and adjustable display colors. I’ve also made a browser-based installable web app that should work on any device.
This clock divides the day into 27 hours. Each hour is divided into 27 minutes, which are in turn divided into 27 seconds. This means that the ternary hour is a bit shorter than a standard hour (because there are now more hours in the day: 27 instead of 24), while the ternary minute is about twice as long as a standard minute (because there are fewer minutes per hour: only 27 instead of 60).
The ternary second lasts about 4.4 standard seconds. This is quite close to the duration of time we experience as ‘now’, sometimes called the ‘extended present’. So in a sense, this clock really ticks off ‘moments’ one by one.
The digital clock display is made out of ‘trits’, ternary digits that can each have 3 values. The lowest value is ‘\’, the center value is ‘|’ and the highest value is ‘/’. You can think of these as representing 0, 1, and 2, but there are other (and perhaps more fitting) ways of thinking about them as well, such as ‘−1, 0, +1’, ‘down, center, up’ or ‘left, middle, right’.
Each segment of the display (hours, minutes and seconds) is made up out of three individual trits. Together these combine to give 27 (3x3x3) possible values. With 9 trits in total, the day is divided into 19683 equal steps.
Unbalanced number systems, like the standard decimal system or the binary system that computers use, do not have a center value. Their most basic ingredients are 0 and 1, and negative numbers need a special sign. In balanced ternary, this is different. You can think of it like using a compass: North and South are opposite directions, but neither of them is more fundamental than the other. In balanced ternary, you can use a single digit to denote the North Pole, the South Pole or the equator (the balance point).
As you add more digits, you can describe your North–South position with increasing accuracy. This way of counting is very well suited for keeping track of things that rotate, like the passage of the day (which tracks the rotation of the Earth around its axis). At noon, all the digits on this clock are centered at ‘|’. At midnight, the display flips over from its highest value, ‘///·///·///’ to its lowest value ‘\\\·\\\·\\\’ and the next day begins.
Interestingly, the exact opposite of noon is not a ‘tick’ of the clock but rather the moment halfway between the highest and lowest value. Midnight is a boundary that the clock approaches and then passes over but never quite lands on. This is a fundamental property of any balanced number system: there is only one precisely defined center, and on the opposite end of that is ‘infinity’, a value that cannot be expressed precisely as a number.