A Brain That Works ?2% of the Time

I’m a bit chagrinned to admit that having been mired in details I failed to see the obvious.

In standard paper sizes (ISO 216) and pen-point sizes (ISO 128 &c), the square root of two is used as the interval between sizes, and between the short and long sides in the case of paper. This makes good sense for the purposes of mechanical enlargement or reduction. If you draw or write something with a #2 pen (0.70mm) on A4 paper (210×297mm) which is then reduced to A5 paper (148×210mm) you may write on the reduction with a #1 pen (0.50mm) while retaining consistency with the marks put down earlier. All these neat proportions, very nice.

It didn’t occur to me until several minutes ago that using a 1:?2 proportion as the interval is just a fancy way of saying even steps between sizes where two steps up means twice the original. The single increments then are «halfway» to double (though of course not literally half-way by linear measure).

It’s an obvious fact that has been staring me in the face for the better part of two decades. The more complicated products of that obvious fact have been evident to me all along. It feels a bit like realizing that words are made up of letters.