Calendars and Pi

Yesterday was the 52nd day of 2014 by the calendar I use. Since there are about 52 weeks in a year, that means if the year were a week, we just got through Monday. 2014 is 1/7 gone, and it seems like it just got here.

Pi by Mehran Moghtadaei (Own work) [GFDL (http://www.gnu.org/copyleft/fdl.html), CC-BY-SA-3.0 (http://creativecommons.org/licenses/by-sa/3.0/) or CC-BY-SA-2.5-2.0-1.0 (http://creativecommons.org/licenses/by-sa/2.5-2.0-1.0)], via Wikimedia Commons

By Mehran Moghtadaei (Own work) [GFDL, CC-BY-SA-3.0 or CC-BY-SA-2.5-2.0-1.0], via Wikimedia Commons

Coming up in about three weeks is Pi Day, so called because in the usual American style of writing dates in the usual calendar we use, one of the dates resembles the beginning of the decimal representation of π: 3/14 is rather like 3.14… Normally you wouldn’t see all those qualifications (usual style, usual calendar, resembles, beginning of, decimal representation), but I want to illustrate how arbitrary Pi Day is. If we wrote our dates with the days before the month (European style), Pi Day is 14/3/14 this year, so at least there’s a “3/14″ in there somewhere, as long as we don’t use the four-digit year. But I like the four-digit year, having been through the great avoided-event of Y2K. Since April doesn’t have 31 days and there’s no 14th month of the year, the European style of date notation doesn’t yield much for pi-philes.

Under the American style, however, next year is going to be the media bonanza: there will be a 3/14/15. Never mind that you should round that 5 to a 6; I’m willing to bet that the media coverage for 3/14/16 will not be as great. But then again, if you want to write it in this order, next year there will be a 3/14/15 9:26:53.58979… The prefect representation of pi!

As long as you use that calendar, clock, date notation, time notation, and sequence of date and time. The clock is based on an arbitrary division of the day into hours, the arbitrary hours into an arbitrary number of minutes, the arbitrary minutes into an arbitrary number of seconds, while the calendar is based on a “close-enough” alignment of Earth-rotations to Earth-revolutions, with a “best guess (at the time)” of the nativity of Christ.

Which is all well and good for most media coverage, but is there an option for selecting temporal units other than the arbitrary or Earth-centric seconds, minutes, hours, days, months, and years, and a 0-point (or “epoch”) other than a guess at the nativity? There is!

The metric system uses seconds (and so kiloseconds, megaseconds, teraseconds, and otherwise), but those are based on a particular definition of “second”, the duration of 9,192,631,770 periods of the radiation corresponding to the transition between two hyperfine levels of the ground state of the caesium 133 atom at rest at a temperature of 0 K. Since I don’t understand that, I won’t rely on it, and I wouldn’t expect the same selection to be made independently.

No, what we need are natural units, units whose definitions are based on universal constants. I think Planck time (tP) would do admirably. It’s tiny, about 5.39106×10−44 seconds. If a ZettaPlanck time (ZtP) is a sextillion Planck times, 20 sextillion ZtP would be just over a second. Without a change in our understanding of physics, there’s no such thing as a fraction of a Planck time. I don’t understand everything else around it, but it makes more sense than the definition of a second.

OK, so what about the selection of the start of our counting point? I think the Big Bang should serve here. It is estimated at 13.798 ± 0.037 billion years ago. So:

13,798,000,000 years × 31,556,952 seconds in the average Gregorian year ÷ 5.39106×10−44 seconds per tP puts us at about 8.0767571×1060 tP. So we’re waiting for 3.14159265358979…×1061 tP to celebrate the next “Pi Planck Time” (πtP). That will happen around 39,872,000,000 AD (rounding off to five significant figures). The Big Bang is closer to us than that. Similarly, the last πtP was closer to the Big Bang than to us. It happened in 8,431,000,000 BC. Sigh. So I can see why the media will use the usual calendars and clocks instead.

—jhunterj

P.S. Any math or formula errors are mine. Please point them out in the comments.

Further Reading

Bang! The Complete History of the Universe Bang! The Complete History of the Universe, by Patrick Moore, by Patrick Moore

Complexity and the Arrow of Time Complexity and the Arrow of Time, by Charles H. Lineweaver, by Charles H. Lineweaver

Pi: A Biography of the World’s Most Mysterious Number Pi: A Biography of the World's Most Mysterious Number, by Alfred S. Posamentier, by Alfred S. Posamentier

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