Wednesday, June 26, 2013

Hexadecimperial metrics

I was reminded recently of a conversation I had a while back about weights and measures.  Though I was raised bilingually, speaking both Imperial and Metric, I find myself admiring metric but using imperial day-to-day.  (Of course, there are some archaic units I have a fondness for... I love cubits because they are one of the few units of measure I've found that intrinsically imply a lack of precision)  While I do love metric units, the entire SI finds itself mired in a tradition of base 10 numbering (side note:  that's a really poor way to name numbering systems.  All numbering systems are base 10, they simply disagree on the value of 10-1.  Shouldn't it be called base 9+1?  But I digress) Why does anyone think it makes inherent sense for a kilogram to be equal to 0x3E8 grams? (OK, one more side note:  that number is highly frustrating to those, like me, who are fans of both hexadecimal and scientific E notation.)

There are so many places where imperial units get things so tantalizingly close to right.  Rulers are already generally marked off in 1/0x10ths of an inch.  0x10 ounces make a pound.  Of course, they then wander off into lala land with 0xE lbs to the stone, 0xB inches to the foot, etc.  But instead of dismissing entirely, I say let's fix what's broken.  I say let's make a new system of heximetric (HM) measures based on imperial units, so that those with a familiarity with imperial can easily transition because their mental approximations are still approximately right.

0x10 inches to the HM cubit (off by 2 inches)
0x20 inches to the HM yard (off by 4 inches)
0x100 inches to the HM rod (off by 58 inches)
 (call 0x1000 inches a HM half-furlong)
0x2000 inches in the HM furlong (off by 272 inches)
0x10000 inches in the HM mile (off by 2176 inches)

(I'm shocked that a mile is so close to 64k inches, it's only off by
about 3%.  That's kind of neat)

0x10 drachm in an oz (exact)
0x10 oz in a lb (exact)
0x10 lb in a HM stone (off by 2 lbs)
0x80 lb in a HM hundredweight (off by 16 lbs)
 0x100 lb in 2 HM hundredweight
0x800 lb in a HM ton (off by 152 lbs)
 0x1000 in 2 HM tons
0x10 tons in another day older and deeper in debt

One of the minor side-coolnesses to this that I noticed in my conversation is light speed.  To 2 significant digits, lightspeed would be 0x2C,000 HM miles per second.  That just strikes me as kind of cool, in a c=2c way.  (although I would say that I need a better means of notation for powers of 2.  0x2c * 0x10^7 inches/second just looks uglier than 3E8 m/s (dammit, there's that number again.  It's haunting me.))

So, who's with me?