TIMEKEEPING—OBJECTIVE, GEOMETRIC, NUMERICAL, FRACTIONAL, DIGITAL

THE SANDS OF TIME ARE ONLY ONE way we describe its passage. The positions of stars and angled points of a sundial are geometric. We have numerals: “three fifty-two.”  Also, fractions: “quarter to” and “half past.” And these days we’re familiar with the seven-segment stick numerals of digital clocks. Here are tidbits gleaned from 3:52 a.m. and other instances. (Daughter Suz says I really need melatonin.)

Origins. Wikipedia says, ”The history of timekeeping devices dates back to when ancient civilizations first observed astronomical bodies as they moved across the sky…. Sundials and water clocks were first used in ancient Egypt c. 1200 BC and later by the Babylonians, the Greeks and the Chinese….”

An ancient Egyptian sundial. Image from the Rijksmuseum van Oudheden via Wikipedia.

Wikipedia continues, “The hourglass, invented in Europe, was one of the few reliable methods of measuring time at sea.”

A marine sandglass. Image by Marie-Lan Nguyen/Wikipedia Commons.

Fractional Time. Halves and quarters are familiar fractions of time, but not without some linguistic confusion: I recall my mother had an ESL friend whose learning the English word “quarter” convinced her there were 25 minutes in a quarter-of-an-hour. Divisions of a clock face were much more abstract. 

Image from U.S. Mint via Wikipedia.

Seven-Segment Digital Representation. We’re all familiar with digital numerals 0 through 9 constructed by turning on or off the seven elements forming stick-figures. Wikipedia notes “Seven-segment representation of figures can be found in patents as early as 1903 (in U.S. patent 1,126,641), when Carl Kinsley invented a method of telegraphically transmitting letters and numbers and having them printed on tape in a segmented format.”

The 16 x 8 grid showing the 128 states of a seven-segment display. Lurking are the numerals 0-9 as well as many reasonably recognizable letters A-Z/a-z. Hint: alphabetical suggestions at Wikipedia.

11:47 P.M. Thoughts. There’s a wealth of numeric tidbits in a digital clock display. 

For instance, which numerals have “their correct” number of segments? What’s the minimum sum of elements ever seen on the time display? And the maximum? Discount the “:” throughout. (Answers at the conclusion.)

What about the numerals themselves: At what time do they make up the smallest sum? At what time is their sum a maximum?

How often are they numerically sequential, either increasing or descending? 

My answers: (Only 4, 5, and 6.) (Six elements at 1:11.) (19 elements at 8:58.) Oops: 8:08 gives 20! (sum 1, at 1:00 and 10:00.) (sum 23, at 9:59.) (Increasing 1:23, 2:34, 3:45, 4:56, 12:34; descending 6:54, 5:43, 4:32, 3:21, 2:10.) Have I forgotten any?

I leave for the reader’s own 3:52 a.m. thoughts: What about European 24-hour notation, i.e, 15:24 for 3:24 p.m. Jus’ askin’…. ds 

© Dennis Simanaitis, SimanaitisSays.com, 2024