The Anno Domini dating system and the Gregorian calendar that we now use are not zero-based numbering systems. There are no zeroth days, zeroth months or the zeroth year in these systems. That is because Europeans did not know zero as a number when they invented the AD dating system and the Roman calendar, the prototype of the Gregorian calendar. The numeral system we now use is, however, the zero-based decimal system. Identifying the time in reference to the current time system makes it difficult to calculate the functions whose variables include time. Although we should avoid unnecessary amendments, it is not desirable that we will continue to be bound by the numbering system which was formed when European mathematics was underdeveloped. Here I propose the best calendar that I can think of.
A Cartesian coordinate system is named after René Descartes. But Descartes did not first invent the Cartesian coordinate system nor did he first establish analytic geometry on the ground of the Cartesian coordinate system. Still it deserves its name, because the method of the Cartesian coordinate system is similar to that of Cartesian philosophy.