Rules
July birthdays: research methods and useful context
July birthdays: day-of-year arithmetic, how the weekday walks from year to year, why age is a definition rather than a subtraction, and why none is shown.
A birth date is used for arithmetic far more often than it is used for cake. Ages, weekdays, day counts and eligibility all get computed from it, and each computation has a rule inside it that sits outside the date. This page is about those rules, because most wrong ages and most impossible claims are made by arithmetic done on a correct date.
What to take away
- Almost everything derived from a birth date depends on a convention that is easy to apply wrongly: whether the year is leap, which calendar is in use, when a year counts as completed.
- The weekday of a birthday walks forward one step each common year and two across a leap day. Nothing about the person moves with it.
- Where the rule is legal rather than arithmetical, the answer belongs to a jurisdiction, and a calendar page should not supply it.
Day of the year
An ordinal date counts days from the start of the year instead of naming a month. The fourth of July is day 185 in a common year and day 186 in a leap year, because the leap day sits in front of it. Every date from March onward shifts by one in a leap year under this notation. Every date in January and February does not.
That matters because some systems store dates in ordinal form, and a conversion that forgets the leap day moves every spring, summer and autumn birthday by one day in one year out of four. The error is invisible on a page and obvious in a spreadsheet. Any list that was ever passed through a day-of-year field deserves that check.
The weekday walks
A common year is 52 weeks and one day, so the weekday of any fixed date advances by one from one year to the next. A leap year is 52 weeks and two days, so across a leap day it advances by two. In the Gregorian calendar the pattern repeats exactly every 28 years, except where a span crosses a century year that is not a leap year.
The Doomsday rule makes use of a curiosity: within any one year, a handful of easily remembered dates, the fourth of the fourth month, the sixth of the sixth, the eighth of the eighth and so on, all fall on the same weekday. Find that weekday for the year and every other date is a short count away. It is a party trick with a serious use. If a source states the weekday of a birth, that weekday can be checked against the date, and a mismatch is evidence that one of the two is wrong.
| Question | Depends on | Typical mistake |
|---|---|---|
| Weekday of the birth | The date and the calendar it is in | Applying the Gregorian rule to a Julian date |
| Day of the year | Whether the year is leap | Forgetting the shift for dates after February |
| Age on a given day | The definition of a completed year | Counting the anniversary itself one day early or late |
| Half-birthday | Convention only | Assuming every date has one exactly six months away; the 31st of some months does not |
Age is a definition, not a subtraction
Subtracting years gives a number. Whether that number is the person's age on a given day depends on a rule about the boundary. In ordinary usage a person reaches the next age on the anniversary. Some legal systems have used, or still use, a rule under which the age is attained at the start of the day before the anniversary. Others define how a person born on a leap day counts in a common year. Those are questions for the law of the place concerned, and a birthday page should not answer them.
Two consequences follow for a directory. Any claim of the form "the youngest person ever to" rests on the exact day of birth, which as the April page shows may be the day of registration instead, and on a definition of age. It is only as good as both. And an age displayed on a page is a computed field with a rule inside it. The rule should be stated once somewhere on the site.
Why this site displays no age
An age is derived from a date. Publishing the age of a living person publishes the date to within a year, and pairing it with a month page narrows it to thirty-odd days. The February page explains why that pairing is a key to more than a birthday. The arithmetic here is offered for reading other sites, checking what they claim, and understanding what a computed field can mean. January covers the fields an entry needs, and the June page covers what a rendering step does to precision, which is where most bad ages are born.
Common questions
Does everyone's birthday fall on the same weekday every 28 years?
In the Gregorian calendar, yes, as long as the span does not cross a century year that skips its leap day. Across 1900 or 2100 the cycle breaks.
Is the day of the year a useful field to store?
For computation, yes. For display, no. Store it alongside the year it belongs to, or it cannot be turned back into a date.
Can the weekday of a birth be recovered from the date alone?
Only if the calendar the date belongs to is known. March explains why the calendar itself is an approximation with a history, and the same digits under a different calendar name a different day.