In Praise of American Architectural Measurement

For building design, we use this seemingly arcane length measurement system. Most of the rest of the world uses the translatable metric system, US engineers use inches and decimals of inches, while American architects measure dwellings with feet, inches, and fractions of inches. Examples can be 4.68 meters, 184.252 inches, or 15’-4 ¼”.

The rational base ten metric system changes units every count of ten. The US customary system is based around the number four.

There are advantages for translation of units and measurement accuracy with the metric system. Ten millimeters equals one centimeter; and if you can’t quite get the measurement to fit on your ruler, you can add another decimal place. The piece is not quite 3.4 cm, but is more than 3.3 cm, then it can be more accurately 3.38 cm.

A primary advantage with the base four system is cutting things in half. Useful in architecture. Use your 12 inch measurement; easily cut in half to 6, then again to 3, then the fractions easily and accurately take it. Use your 10 cm measurement; cut in half to 5, then again to 2.5, and whoops, it goes off into another level of units. Halve that again and it goes up into another scale of units, 1.25.

Cutting fractions in half is also easy, merely double the denominator; half of 1/16 inch is 1/32 inch. The numbers are all base 2 and base 4, easy to get a feel for the pattern. It is strangely simpler to express 1/32” than .03125”.

I have been thinking about numbers in the natural world. While the base 2 system sometimes occurs in nature, it is the fundamental of our digital system; the absolute of on or off, one or zero. The base 4 system is fundamental to all life.

The fundamental molecule to all life is the self replicating DNA. It is composed of only 4 chemicals, which then yield only 64 different combinations. These then attach together in enormous strings to make the super complex variation we see from dandelion to influenza to elephant. The whole thing is constructed on the basis of only these 4 chemicals: adenine, cytosine, guanine, and thymine.

There is unintended symmetry between the archaic architectural system and the natural chemical world.

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