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.
Sumerians used sexagesimal numerals not only because the number 60 has many divisors or it is countable on the fingers of both hands but because 60 is the least common multiple of the number of fingers of both hands and the number of months in a year. The Chinese cycle of the Stems and Branches has the same structure as the Sumerian sexagesimal system and we can assume the Chinese sexagesimal cycle was imported from Mesopotamia to China. Today both the Mesopotamian sexagesimal system and the Chinese sexagenary cycle are apt to be explained in terms of the 60-year conjunction cycle of Jupiter and Saturn, such an interpretation of posterity should not conceal the original implication.