Imagining a 400° world

Editor’s note: Recently (Issue 103 Jan/Feb 2000) we ran a letter from a reader who had found an old French compass. The card was divided into 400°; apparently the French briefly used 400° as an extension of the metric system (reportedly used mostly on land). This author imagines a fictional world limned by a wholly metric-style system of measure.

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To the editor: ?

Almost 4,000 years ago, in an ancient land, there occurred a congregation of all the Learned People in the known world of the time. The purpose of this meeting was to kick around ideas and numbers, and establish a scientific/mathematical order of things terrestrial and celestial. They got right down to business.

Well, to make a long story not too long, the Learned People soon settled upon an integrated system and named it (in English) Pure Decimal Quadragenary – PDQ for short – and the three basic tenets of PDQ were laid out thus:

1. The circle azimuth shall be 400 evenly spaced degrees; 100, 200, 300 and 400 degrees representing East, South, West and North respectively. Each degree of arc shall be divided into 100 minutes, each minute subdivided into 100 seconds and each second may be further subdivided into as many decimal places as you wish. The minute and second terminology shall be optional, it being determined that the simple decimal divisions of each degree serve so nicely.

2. The basic unit of linear measure shall be the meter – a long step. All of the Learned People shall take long steps, which shall be duly recorded, measured and averaged to arrive at the official meter length. One thousand meters shall equal one kilometer, and the meter, also, may be divided into its decimal parts by adding digits to halfway down the block if such accuracy is required. More on the meter later.

3. Each day shall commence at noon and be divided into four hours of time; each hour shall be divided into 100 minutes; each minute shall be subdivided into 100 seconds and, like the second of arc, each second may be divided into any number of decimal places down to the nano second, the pico second and beyond. Also, as with the arc, the minute and second terminology shall be optional, all digits after the decimal point being merely decimal divisions of the hour.

And that was about it, at least for the time being. The people loved it, especially the 400° circle. Why, just add or subtract 200° to obtain a reciprocal. Add or subtract 100° for a right angle. Multiply or divide by merely shifting the decimal point. Easy to do – very easy, in fact.

In time, as the world went from flat to round, and as this ancient land declined in relative importance as all ancient (and modern) lands eventually must, other Learned People from Other Places would amend PDQ tenet No. 2 with the important addition of a decimal metric latitude/longitude configuration upon the earth. This would consist of 200 evenly spaced parallels of latitude with the south pole designated 0°, the easy-to-remember 100° parallel lying on the equator and 200° being the north pole.

Crossing these, the amendment would specify, shall be 400 meridians of longitude with the 0° meridian passing smack dab through the middle of Milan – one of the great learning centers of the time – then numbered only in westward progression all the way to 400°. In keeping with the decimal metric layout, the 200° of latitude produces 20,000 kilometers pole to pole distance, and the 400° of longitude produces, at the equator, a distance of 40,000 kilometers or 40 million meters. (Although the original meter fit the pistol okay at that time, in later centuries, as the true size and shape of the earth became better known, the meter would be adjusted accordingly to fit the lumpy, somewhat misshapen planet as perfectly as possible.)

As the people were quick to discover, the decimal metric lat/longs made it very easy not only to locate places on the globe, but also to nail down a position with great accuracy, seven digits after the decimal point pinpointing the coordinates on the earth’s surface to a centimeter or less. (In later years, the 400° decimal metric lat/long configuration would prove to be the perfect layout for GPS – the crowning achievement of navigation systems in the late 20th century of our Common Era.)

Now, picture the sun crossing the 0° Milan meridian, the time: noon, 0.0000 hours. As the sun moves to the west it crosses meridians of longitude in remarkably close synchronization with the universal PDQ standard time all the way around to 400° in 400 minutes – at the equator, 40,000 kilometers in 40,000 seconds.

“Wow!” the people exclaim. “The ramifications of all this are awesome.” Yes, indeed. Even children had a seemingly uncanny navigational sense – anywhere they happened to be. Just a glance or two at the sun or a shadow, and given only the exact time they could tell you pretty close where they were, the little buggers. Or, they could tell you the time if they knew their position. Amazing perhaps, but there was really nothing magical about it; they just practiced a lot, using the little computers between their ears and assisted by the simple logic of PDQ.

As time passed, other metric-based calibrations including weight and liquid measure were added to complete the system, and the people, worldwide, continued to marvel. “Incredible, almost childlike simplicity,” were words heard to describe PDQ. Maybe it was too simple.

We fast-forward now to about the turn of the second millennium of our Common Era and zoom in on lat 151.16° by long 382.23° – a dark foreboding castle, somewhere in the Transylvanian Alps, the stomping grounds of the vampire and other scary creatures.

Out of the gloom comes forth this monster, and it spreads itself like wildfire and causes confusion all over the world. As you’ve probably guessed, this monster came to be known as the “feet n inches thing,” although its detractors seemed to prefer less complimentary names for it. And no wonder.

Oftentimes employing more forceful methods if treacherous cunning didn’t pull the trick, the feet n inches thing managed to weasel its way into, and make a mess out of, the established scientific/mathematical order of things in country after country.

First thing to go was the simple, well-ordered, tried-and-true metric system, replaced with a kind of devil’s hodgepodge of three feet to the yard, 12 inches to the foot, the inch divided into halves, quarters, eighths, etc., for carpenters and into 1,000ths for machinists, 1,760 yards or 5,280 feet to the mile – unless it’s a nautical mile, which is about 6,080 feet. The list goes on and on covering leagues, fathoms, bushels, furlongs and a host of other measuring units, all of which correlated poorly and made even less sense.

Next to go was the 400° circle, then the four-hour clock. These were replaced by a 360° circle with the degrees divided into 60ths and further irksome 60ths, then jump back and forth between fractions and decimals – one wonders how anyone found their way at sea or anywhere else. Then, they stuck 24 hours in the day and decreed that each hour should have 60 minutes or 60 times 60 seconds. Time zones, AM and PM, International date line, daylight savings time, occasionally. As a final insult, they not only slapped a complicated 360° based lat/long latticework on the globe, they also – this was probably just politics – moved the 0° prime meridian to a place called Greenwich.

Would you believe they even had the audacity to have taken New Year’s Day and move it from summer solstice in June all the way to Jan. 1?

Granted, the feet n inches thing did have a certain quaintness about it, and having no other redeeming feature, this had to be the reason that the world embraced this inferior concept so fervently.

Donald Artz is a freelance writer living in Billings, Mont., at roughly 120° by 205°.