Visualize the annual calendar you use as a loop instead of a line or a series of rectangles within rectangles. A continuous circle you’re just going around and around. There’s no beginning or end, just more days, one after the other. Imagine yourself standing on today on this vast loop. If you could walk straight across the diameter to February, it would take around 116 days. Normally of course, we all just stick to the circumference, which takes about 365 days to complete.
Now, if you can, imagine a smaller circle within the larger one, touching only at the point where you are standing. This is my calendar. It would only take about 95 days to walk straight across the diameter to month 9, and it only takes 300 days to walk the circumference. As I move along the circumference of these two huge circles, it seems as though the inner one is rolling around the inside edge of the larger one, so that they always meet where I am standing. Now, my calendar is not designed to synchronize with yours, so when I have gone one full circumference of my calendar, I have only completed about 82% of the way around yours. When I have completed one path around your calendar, I have rounded mine one and a fifth times. That is, while today is 3.1.4 on my calendar, and August 5th on yours, those two dates will not meet for another 60 of your years (sort-of; your years have an extra not-quite-quarter-day which makes it more like 630 trillion years before they synchronize again).
Okay, that’s easy enough, but let’s look at how we can use this visualization model to show why my calendar is a little easier than yours. Take my calendar’s ring out of yours, and instead put a tiny, 7-day ring in its place, representing your week. (The diameter of this one is only 2 days, 5 hours, 28.5 minutes.) Imagine it rolling around the inside of your year as you travel around the big circumference, and it will spin 52 times and get almost to yesterday. It will actually take 14 trips around your year before it synchronizes properly again. That’s 728 rotations of the week within the year and about 5096 days. Really, the 7-day ring won’t do, because of how your calendar handles “leap years”; instead, imagine a much, much larger ring that your year is rolling around, 14 years in circumference just to keep track of the days of the week properly. The ring you need, just to keep track of what day of the week it is, is almost four and a half years in diameter.
Now let’s step over to my calendar’s ring again. We can put a tiny 5-day ring in this one to represent the five-day week in my calendar, and a 30-day ring to represent the constant 30-day month in my calendar. Imagine that both of these rings within the year ring roll along the inside edge as we imagined before, following you around the year. In my calendar, the week ring rotates exactly six times for every month that passes, and the month ring goes around exactly 10 times to bring you back to the same place on the year. The same day on the year ring is always the same day on the week ring every year, and the month to weekday ratio follows the same synchronicity. 3.1.4 will always be in the third day of the week, in year 0 the same as in year 1, and in year 14 and every other year. If you were born in the middle of the week on my calendar, your birthday would always be in the middle of the week. (Interestingly, because my calendar is not solar, your birthday would always be on the same day of the week, but not always in the same season.)
So, on your calendar it will be 14 years before the days of the month and the days of the week match this year’s, but in mine they match every month of every year. Oh, and the only way to correlate your months with your years is on that same huge 14-year ring, since your months all have a different number of days, and aren’t even self-consistant.
Okay, was this boring enough? This is the sort of thing my mind noodles awya on sometimes. The entire visualization took me but an instant, but I wanted to share it, which took ma quite a while to type. I wish I could have drawn animated diagrams for you.