# Red: the perfect unit of measurement?

If you're like me, when you write software that has to store distance information in floating point, you shudder because you know you have to pick either inches or millimeters, leading most common multiples of the other as numbers that are not exactly expressible in binary floating point.

So let me make a simple proposal: define red = 625nm, so called because light of 625nm is commonly perceived as red. Now, you can store all of the following as exact integers:

• Any binary fraction of an inch down to 1/64inch (1/64in = 635 red)
• Any 1/10 of an inch (1/10in = 4064 red)
• Any multiple of 5um (5um = 8 red)
Unfortunately, the following are still not exact:
• 1mil = 40.64 red
• 1pspt = 1/72in ~= 564.44 red
• 1/300in (common print resolution) ~= 135.46 red

Here are some other visible-light inspired fundamental distance units and the common distances they can express exactly as binary fractions:

Table of magic lengths
Color name Exact definition Wavelength (approximate) Exact binary fractions for multiples of
red 8192/11162109375m 733.91nm 1/64in mil pspt dpi nm
red 64/89296875m 716.71nm 1/64in mil pspt dpi 25nm
red 512/744140625m 688.04nm 1/64in mil dpi nm
red 4/5953125m 671.92nm 1/64in .01in dpi um
red 32/49609375m 645.04nm 1/64in mil 5nm
red 1/1587500m 629.92nm 1/64in .01in 5um
yellow 256/446484375m 573.37nm 1/64in mil pspt dpi 5nm
green 2/3571875m 559.93nm 1/64in .01in pspt 5um
green 2048/3720703125m 550.43nm 1/64in mil dpi nm
green 16/29765625m 537.53nm 1/64in mil dpi 25nm
green 128/248046875m 516.03nm 1/64in mil nm
green 1/1984375m 503.94nm 1/64in .01in um
blue 1024/2232421875m 458.69nm 1/64in mil pspt dpi nm
violet 8/17859375m 447.94nm 1/64in .01in pspt dpi um
violet 64/148828125m 430.03nm 1/64in mil dpi 5nm
violet 1/2381250m 419.95nm 1/64in .01in 5um
violet 512/1240234375m 412.83nm 1/64in mil nm
violet 4/9921875m 403.15nm 1/64in mil 25nm
computed by colors.py, frequency range for each colorname from wikipedia. Unlike the original 625nm "red" constant, common lengths are binary fractions rather than whole numbers. And of course these aren't nice integer multiples of nm either. I wonder why no oranges make the table.