Jeff Epler's blog

19 February 2014, 21:17 UTC

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.

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