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C and 12

2019 February 135 min read

This blog post is brought to you by the letter C and the number 12! My favourite letter and number respectively, and I explained why in a text chat with some friends a while back. Thought I'd adapt those logs into a brief little manifesto here - be warned; if you're attached to your own personal favourite letter/number, you should stop reading now.


C is fun because it has many different sounds in many different languages, but the sound is always more or less consistent within the language - in some languages it's a consistent "k", others a "s", still others a "ts" or a "ch". In English it's cool because it can be either a "s" or a "k", but unlike most English rules which have hundreds of exceptions, the rule about what sound a C makes is pretty set in stone, and depends only on the vowel, if any, after the C.

The edge cases for when this rule breaks down have produced some interesting results. Normally, C makes a "s" sound if and only if it comes before an E, I or Y, but what about the plural of the word "focus"? That word comes from Latin, where C always makes the "k" sound, so its Latin plural "foci" would be pronounced "foh key". But in English, that C would typically make a "s" sound, because it comes before an I, not a U, so both pronunciations are typically accepted.

In French, they get around this problem with the cedilla - the little comma thing under the C in words like "garçon". And indeed in English we use "garçon", and it's one of the few English words that can have a cedilla. Another example is "Çaesar" - another Latin word where the C would have made a "k" sound cause it comes before an A - and in English sometimes Çaesar is spelled with a cedilla because for whatever reason we pronounce it "seezer".

Another exception to the soft/hard rule is (funnily enough) the word "flaccid". Here, the first C would normally make a "k" sound, because it's before a consonant, but it doesn't - and this is the only word I can think of where this happens. Words like "accent" and "succinct" behave more predictably, and are a rare case of a double consonant where each consonant makes a different sound. No other consonants do this regularly in english, including G which also has a hard and soft version.


12 is an important number both mathematically and culturally - the dozenal (base 12) system is hypothesized to be an optimal base for place value numbers and one we may very well have picked if not for the fact we have 10 fingers. Mostly cause unlike 10, 12 is divisible by 3 and 4. 12 is a "highly composite" number meaning it has more divisors than any number below it, making it uniquely suited to be a base for a place value system. (And yes, before you ask, I'm fond of the number 6 as well. It's like the fun-sized version of 12.)

A lot of our counting systems use 12 anyway - months in a year, hours on a clock, inches in a foot, members on a jury, function keys on a keyboard, default text size in pixels, highest grade in a school education, size of an egg carton, etc. It's why we have the words "dozen" and "gross" - 12 is like the "legacy base system" that we almost used but not quite.

12 is also a "sublime number", meaning both the number of its divisors (6) and the sum of its divisors (28) are perfect numbers. The only other known sublime number has 76 digits. Also, of course, 12 is the negative reciprocal of the sum 1 + 2 + 3 + 4 + .... (yes I know it's "nonstandard", but I have yet to hear a good reason not to make it standard. Euler's equation was still true before complex numbers were invented. Change my mind :p)

It's important in Pythagorean triples: in ancient times when they wanted to produce a right angle, they would tie 12 knots in a rope and then make a 3-4-5 triangle, which has perimeter 12. In fact, you can show that in any Pythagorean triple, at least one of the legs (not the hypotenuse) must be divisible by 3, and at least one must be divisible by 4, meaning their product must be divisible by 12!

In physics, 12 shows up by itself in a bunch of formulas for moments of inertia. Particularly, the general formula for a cuboid, rotated about any axis, has a constant factor of 1/12, as do the special cases where the axis is perpendicular to one of the faces. 12 also appears in the same way in the formulas for a cylinder rotating about its center and a hollow tetrahedron.

In music, 12 is very important - there are 12 tones in the chromatic musical scale, because the powers of the 12th root of 2 do a great job of approximating simple fractions like 3/2, 4/3, etc, which produce the most pleasing harmonies. And 12's multitude of factors also means that an octave in music can be subdivided a number of different ways to create cool chords and modulation sequences. (Also, let's not forget about the "12 bar blues" classic chord progression!)

In art, 12 is the number of colours on a typical colour wheel (primary, secondary, and tertiary) and otherwise very prominent in graphic design, because of its divisibility. Most graphics are made with either 72, 96, or 300 dots per inch - all multiples of 12.

There are too many more examples of the number 12 in culture to mention. The 12-step program, 12 days of Christmas, 12 Years a Slave, the list goes on... but this is probably a good place to stop for now.

Wrapping Up

In case you're not sold yet on C and 12, get this - they are the hexadecimal and decimal representations of the same number.

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