It’s not really pi day

By George Johnson | March 14, 2013 4:39 pm

A mosaic outside the mathematics building at the Technische Universität Berlin. Wikimedia Commons

3.1415926535 . . .

When I heard that today is supposed to be pi day, 3/14, I found it hard to get very excited. If this were March 14, 1592 — giving four more digits of the decimal expansion — that would be a more interesting coincidence. But that day has come and gone. Or did pi day come and go today (and every March 14) at 1:59 am and 26 seconds? Or 26.535 seconds. That is still far from precise. With an infinite number of digits in the decimal expansion — a sequence that never repeats — pi day would last an infinitesimally short period of time.

When mathematicians say that pi is an irrational number, they don’t mean that there is anything inherently crazy about it. It’s just that it can’t be expressed as a ratio of two integers. 2/3 can be turned into an infinitely long decimal — .666666 — but the numbers conveniently repeat. It’s true that pi is the ratio of the circumference of a circle to its diameter, but you can’t compute it that way. You would have to know both the distance around and across the circle to infinite precision. Nothing in the physical world can measure anything so perfectly.

Why we should live in a universe where pi isn’t exactly 3 is very strange. But how many of those digits — mathematicians have calculated trillions of them — actually matter?

Thinking of this, I was reminded of something I wrote long ago for The New York Times: that knowing pi to just 61 decimal places is enough to describe a circle surrounding the visible universe with a deviation of less than a single Planck length — a unit 1020 times smaller than a proton. This seems as close to perfectly circular as a real circle can be. Do the rest of the decimal places have any meaning?

Postscript: As a reader, Dwayne J. Stephenson, suggests, March 4, 2015 at 9:26 and 53 seconds (54 if you round up) will be closer to the mark.

CATEGORIZED UNDER: select, top-posts
  • http://www.facebook.com/angus.bohanon Angus Bohanon

    But if it’s pi DAY, then the most precision we need is to the day. Which would be 3.14.

    • http://www.facebook.com/dwayne.stephenson Dwayne J. Stephenson

      The assignation of the day is somewhat arbitrary. We could, for instance, have a pi day on May 9th, 3141, depending on how we order the numbers. The most accurate pi moment of our lives is coming in two years: 3/14/15 9:27. Or 26. However you want to roll with it.

      • http://talaya.net George Johnson

        Now that is a day almost worth looking forward to.

      • chomps

        Just relax and make pie. Like, holy shit.

  • http://www.facebook.com/dwayne.stephenson Dwayne J. Stephenson

    With that said, I support an annual celebration of pi on the grounds that mathematics could do with more conviviality, and it might as well be March 14th.

  • Hapworth

    “With an infinite number of digits in the decimal expansion — a sequence that never repeats — pi day would last an infinitesimally short period
    of time.”

    That is true, but the first part of the statement is irrelevant to the conclusion. Even if pi were exactly 3.142, pi day last an infinitesimally short period
    of time.

    • chomps

      Both statements are spurious. Pi DAY would last a whole day, no matter what the digits, the same way you were born at a specific time, but you celebrate the whole day.

  • Caleb G.

    Of course that works here in the United States where conventions says that you list the month before the day (3/14), but many (most?) other countries list the day and then the year (14/3) which eliminates the correlation. Still, it’s appropriate that we celebrate mathematics so why not set aside a day that (at least in the USA) corresponds to the first 2 digits of pi and also happens to be Albert Einstein’s birthday.

  • http://www.facebook.com/all4kindness2all Leslie Bianchi

    “Do the rest of the decimal places have any meaning?”

    What has meaning depends on your perspective. Knowing they exist and are unknowable is profound to me.

    • http://www.facebook.com/dwayne.stephenson Dwayne J. Stephenson

      But they are knowable to any arbitrary level of precision. When I buy a pound of potatoes, it’s not exactly a pound. I could argue that there was something mysterious and profound about the unknowable depths of the “actual” weight of a given pound of potatoes. But most people wouldn’t take me very seriously.

  • RogerSweeny

    “Postscript: As a reader, Dwayne J. Stephenson, suggests, March 4, 2015
    at 9:26 and 53 seconds (54 if you round up) will be closer to the mark.”

    Alas, according to ISO 8601, the international standard for representing time, that will be 2015-03-14T9:26:53.

    • http://www.facebook.com/dwayne.stephenson Dwayne J. Stephenson

      Yeah, but who cares about ISO 8601? I think we’re entitled a little numerological manipulation here.

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About George Johnson

George Johnson writes about science for the New York Times, National Geographic Magazine, Slate, and other publications. His nine books include The Cancer Chronicles: Unlocking Medicine's Deepest Mystery (August 2013), The Ten Most Beautiful Experiments, A Shortcut Through Time, and Fire in the Mind. He is a winner of the AAAS Science Journalism Award and has twice been a finalist for the Royal Society science book prize. Co-founder and director of the Santa Fe Science Writing Workshop, he can be found on the Web at talaya.net. Twitter @byGeorgeJohnson.

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