Sketches

At one point during my week-long obsession I managed to "reword" the problem of representing a year into that of representing this 7x7 table (Fig. 4) in the most intuitive format I could think of. Diagonal designs followed: here, here, here, and here.

I got the table from trying to see what exactly was happening with the week with every month-change. For me, with my mathish background, it came down to this: Every month, the month's modulo base 7 (the integer remainder of dividing the month's days by 7) shifted the week's starting day. January, for instance, has a modulo of 3 (31/7=4, with a remainder of 3), and thus, the next month after it, February, begins 3 days after, on a Thursday (January begins with a Monday). Since February has a modulo of 0 (28 has no remainder when divided by 7), March starts the same day. And so on.

So if you figure out each month's modulo, then its incremental modulo (last month's modulo added to last month's incremental modulo), and finally the incremental modulo's modulo (Fig. 1) you can see just what is happening during the year (Fig. 2), just what operation you're trying to make visible with your design. If you now reorder months to minimize repetition (Fig. 3) you get that 7x7 table (Fig. 4).

So you see, a calendar, every calendar, is just an instrument for solving graphically the operations described in Fig. 1. The more our prodigious visual capacities are exploited, the less we think of it as an operation at all, the better the calendar.