You’re probably expecting the punch line of this post to be “APRIL FOOLS!”

**SORRY,** it’s not!

Indeed, although January 1 is New Year’s Day according to the Gregorian calendar, really when there are (quasi)periodic boundary conditions(1) on a year, any day is as good of a “New Year’s Day” as any other.

In the Hebrew calendar, there are a few different days in the year which are referred to as the “new year.” The most well-known “new year” is ראש השנה (*Rosh Hashanah*) in the Jewish calendar. Interestingly, though, in the Torah, that day is never referred to as the day of the new year. As it is written (Numbers 28:1):

בחודש השביעי באחד לחודש מקרא-קודש יהיה לכם מאלכת עבודה לא תעשו יום תרועה יהיה לכם

Roughly translated, “In the seventh month, on the first day of the month, there will be a holy assembly for thou: thou shalt do no servile work; it will be a day of the horn for thou.” Of course, the “horn” refers to the שופר (*shofar:* the ram’s horn). There is no mention of a “new year” at all! It is the beginning of the Days of Awe, up until יום כיפור (*Yom Kippur*). Despite being the seventh month of the year, this is where the “branch cut” of a year appears in the Jewish calendar.

Another well-known new year’s day in the Jewish calendar is ט”ו בשבט (the fifteenth of the month *Shevat, *the eleventh month of the year). This is the new year for the trees, and it is customary to plant trees in Israel on this day.

So what is the first day of the first month of the Jewish calendar? That is the first day of ניסן *(Nisan), *which is the month in which the Exodus from Egypt happened, so that this day is interpreted as the New Year for kings and feasts.

However, there is something to be said about how in the calendar, March may have been the first month a long time ago. Why is this? Well, take a look at the names of the ninth through twelfth months of the Gregorian calendar (emphases intentional):

*Septem*ber, *Octo*ber, *Novem*ber, *Decem*ber…

Those italicized letters are the Latin words for seven, eight, nine, and ten, respectively!

Let me get to the (1) that I mentioned earlier, as a part of the text. This is somewhat mathematical, but try to follow along, please! (Skip to the second line of equals signs if you’re not interested in the math stuff.)

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The calendar is set up as a set of multiple cyclical periods: days, weeks, months, years. Take a year in the solar calendar, for example. Let *x* be the number of days from some reference day (e.g. suppose *x* is how many days old you are.) Let *f*(*x*) be the month-day (or day-month) name of Day *x. *This is a periodic function, so that *f*(*x*+365)=*f*(*x*). For example, if *x* is 91 days since the beginning of the year, then *f*(*x*) = “April 1” (or “1 April”).

Suppose that *x* is as above, but that *g*(*x*) is the day-month-year name of Day *x. * Then, *g*(*x*+365) is NOT equal to *g*(*x*), since the year’s name (number) increments by 1. This is the idea of a branch cut of an infinitely-valued function: each branch looks the same, but is on a different “sheet.”

Branch cuts are usually arbitrary, as long as they connect two branch points.

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Non-mathematically, what I explained above is basically that the start of any year is arbitrary, and that each year according to its start is periodic within that choice.

So, a person’s birthday makes for a natural New Year’s Day for them as well!

I think I’ve rambled on for long enough. Please leave any comments or tell me if you got completely lost!

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Today is the ninety-first day of M.M.X.I.V. That makes thirteen weeks.

Fascinating, Noah – and, despite having learned Latin at school, I had never made that connection with month order before. Thank you for extending my knowledge.

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Idiosyncrasies always fascinate and amuse me, so clearly this was something that caught my attention. Did you skip over the region bounded by the equals signs, or did you read it? 🙂

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I did read it, Noah – but, having always been bottom set for Maths, struggled to understand it! I would love to have your mathematical ability!

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