Today, counted five ways

A sun sign from Greece, a day pillar from China, a day name from the Maya count, a planetary day from Babylon, a life path from modern numerology. They look like five independent opinions about you. Three of them are the same number.

Nothing here is looked up in a database of birthdays. Four of the five are arithmetic on the date itself. The sun sign is the exception — it comes from the conventional cusp-date table every horoscope column uses.

Astronomers count days in one unbroken run from a fixed starting point, with no months and no years in the way. That count for your birthday is:

The first table already said what each of those three is counting: the same unbroken run of days, cut seven ways, cut ten and twelve ways, cut thirteen and twenty ways. Stop reading the traditions and read the numbers. Seven shares nothing with the rest, so the weekday really is free. Ten and twelve share a two. Twenty is two tens. Cuts that share a factor cannot surprise each other.

Four of the five systems here are counters: hand them a day number and they divide. The sun sign is the odd one out. It is a printed list of dates, and a list of dates has to pick one calendar day for a boundary the sun crosses at a different hour every year. Here is the size of that rounding, boundary by boundary.

Each bar is the share of the two centuries from 1900 to 2099 in which the sun did not cross that boundary on the date the table prints. A crossing that lands a day early or late only moves the sign of the birthdays caught in the gap, which is why these bars are large and the number under them is small. The crossings come from the same low-precision solar formula the first table on this page uses, good to about a hundredth of a degree — roughly a quarter of an hour of the sun’s motion. A sharper ephemeris would move a handful of the closest calls. It would not move the shape.

A life path number is the digits of the written date added up. That makes it the only reading here keyed to how the day is written rather than to the day itself. Write the same birthday in the Julian calendar — the one Europe used until 1582, and Russia until 1918 — and it is the same day, the same sunrise, the same everything:

Reduce the year, reduce the month, reduce the day, add the three, reduce again. Five steps, and every one of them is about your digits. Whatever you put in, what comes out is the year plus the month plus the day, divided by nine, remainder kept.

1. Julian day number. The standard integer day count, the same one astronomers use. Every figure below except the sun sign is arithmetic on it, so it is printed rather than hidden.
2. Planetary day. (JDN + 1) mod 7, counting 0 as Sunday. Julian day 0 was a Monday, which is where the +1 comes from; the planet is the classical name that weekday still carries in the Romance languages.
3. Day pillar. Stem (JDN + 9) mod 10, branch (JDN + 1) mod 12 — together a 60-day cycle. Checked against 1 October 1949, a recorded Jia-Zi day.
4. Tzolk’in. Number ((JDN + 5) mod 13) + 1, name (JDN + 16) mod 20, on the Goodman-Martinez-Thompson correlation that anchors 4 Ahau 8 Cumku to Julian day 584283. Other correlations exist and would shift the name; this is the one in general use.
5. Sun sign. From the conventional table of cusp dates — the one printed in every horoscope column, where Aries starts on 21 March every year. The sun does not keep to that schedule, so we also work out its true longitude for the date from the standard low-precision solar formula and say when the table has put a cusp birthday on the wrong side.
6. Life path. Year, month and day each reduced by adding digits until one remains, then those three added and reduced again. Master numbers 11, 22 and 33 are kept rather than pushed down to 2, 4 and 6. The schools disagree about when that is allowed; the section above measures what is actually at stake in the disagreement, which is the name and not the number.