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Saturday, 2 March 2013


In Latin, a basis was a foot, a pedestal, the base of a statue or a column, though in architecture, it went from there to also mean the foundation of a building. In geometry, the Greeks and the Romans, as we do today, drew triangles with one horizontal line at the bottom when they could, and this is the base of a triangle, even today.

Somewhere along the way, 'basic' acquired the sense of just the fundamentals, the rudiments, the bare essentials, yet this sense, like "just the basics" is entirely ignored by the OED, which refers to the chemical meaning, where a base is the opposite of an acid, but the derivation of this use is not explored, and we are left hanging with the information that minerals deficient in silica are basic, as is steel which is deficient in phosphorus.

The base of chemistry seems to relate to the alchemists dismissal of cheaper and less valuable metals as base metals, unlike the royal metals like gold and silver. This was good marketing — like calling the mixture of hydrochloric acid and nitric acid that dissolved gold aqua regia. After all, if the name of the game was to get royal patronage to convert other metals to gold, you needed to get the right brand images!

To start teasing out the story of 'basic', we need to turn to the meaning of 'base', where we are reminded of the many uses of this term, mostly meaning something to do with the lower parts, although there seems to be a certain interweaving that confuses meanings originally assigned to various senses of 'bass'.

One of the common uses, the sense of a baseline, seems to have come to us from triangulation in surveying, when surveyors began with a meticulously measured straight line, and then measured the exact bearings from the ends of the base line to some other point. Using simple geometry and the sines of the angles, the lengths of these other lines could then be calculated, providing the bases for yet more triangles.

Some of the world's greatest surveying efforts of the 18th and 19th centuries involved triangulation on a large scale. Two surveyors called Charles Mason and Jeremiah Dixon plotted the line of the border between Maryland and Pennsylvania, giving us the Mason-Dixon line, while triangulation of meridians at different latitudes was used to demonstrate the true shape of the earth, a hot topic because Isaac Newton had asserted (correctly) that the earth was flattened at the poles, while various Europeans believed that the earth must be elongated at the poles.

People who knew their mathematics well enough to calculate the sizes of triangles knew also that our usual numbers are decimal, based on 10, while the binary numbers of computing are based on two, though many computerists make use of octal (base 8) and hexadecimal (base 16), while many rational engineers argue for more use of duodecimal (base 12) counting.

Logarithms are also calculated to a variety of bases, though these days, with the logarithms built into our electronic calculators, we are hardly aware of the difference between logarithms to the base 10, and those to the base e, which any good number hound can quote to 9 decimal places (2.718281828 . . .). We call logarithms to this base Napierian logarithms after their Scottish inventor, John Napier.

Even lumbering something with the name Basic does not guarantee that it will last. C. K. Ogden's Basic English, a collection of 850 fundamental words supposedly got its name from "British, American, Scientific, International, Commercial", just as the largely forgotten programming language BASIC was an acronym derived from "Beginners' All-purpose Symbolic Instruction Code", but both of these acronyms must surely have been contrived. There was a time when instruction in programming in BASIC was seen as an essential element in education, but that fad has passed away.

The use of slide rules (which offered a graphical version of logarithms, engraved into sliding pieces of finely-machined bamboo), like the use of log tables is a dying art, much to the annoyance of those crusty observers of education who tell us we need more basics.

Curiously, if these same people are asked to demonstrate the use of Napier's bones, another mechanical device from John Napier, contrived to assist multiplication, one which was replaced by logarithms, they are totally lost. One generation's 'basics', it seems, are the next generation's history of technology.


  1. e is 2.718281828.... not as you've suggested.

  2. As I very well know: my mobile number has as the last six digits 271828*. It was a typo, now fixed. Thanks!

    * The digits were selected, not a matter of chance.