Posted by hexnet -

"Ten is doubtless a convenient number of fingers to have, though men have gotten along with less and a few people have been born with more. But as the purely arbitrary unit which determines the form of our numbers, it was a miserable choice." – F. Emerson Andrews

"Do not disturb my circles." – Archimedes

Dozenal Pi Day It's that time of year again—time to start thinking about DOZENAL PI DAY.


Regardless of its radical prejudices, Pi Day has become, in recent years, an annual cultural event of some magnitude, and the occasion for a certain nominal enthusiasm about "math" that people seem to find meaningful. At the very least, it seems to remind us of our own cleverness, which is something I have nothing against in principle.

Yet I am more convinced than ever that, unless we remain firmly mindful of what separates the arbitrary and symbolic in mathematics from the truly meaningful, Pi Day will ultimately remain a rather vacuous and misguided holiday. Thus, I once again propose the observation of DOZENAL PI DAY on 18; March (decimal 20th), to raise awareness of the superior dozenal radix, while also bringing attention to the underlying meaninglessness of our present decimal notation.

As I wrote last year:

"I am not sure when exactly this 'Pi Day' thing became so fashionable, but for me it has come to symbolize everything that is wrong and unwholesome about modern society's relationship with numbers. You see, of late I find myself more and more perturbed by the extent to which people seem to take the primacy of decimal notation for granted in conceptualizing and comparing numbers. In the case of pi, there is NOTHING particularly universal or ontologically significant in the sequence of digits 3.14159265... except that they represent a certain way of parsing the value of pi by successive fractions of ten. THIS IS MAY BE INTERESTING IF YOU ARE REALLY INTO THE NUMBER TEN FOR SOME REASON. Otherwise it—like the entire decimal radix system—is fairly useless."

Again, I will take a moment here, as I did last year, to note PI IN SOME OTHER RADICES:

  • Binary: 11.00100100001111
  • Octal: 3.11037
  • Hexadecimal: 3.243F
  • DOZENAL: 3.184809493B

Why not celebrate "Pi Day" on, for instance, March 9th, as it would be in octal? (I can't even decide on the binary date—March 0th? And hex brings us straight into April.) Indeed, why not celebrate it on March 4th, when 0;18 (0.14) of March has elapsed?

Given that there are, notably, twelve months in our calendar, and in light of the natural superiority of the dozenal radix in practically all important matters, one begins to wonder why there would even be a decimal "Pi Day" at all. Should we not calculate such a silly, made-up holiday using a radix that is at least somewhat relevant to the calendrical structure it is derived from?

Thus I submit to you again, as I did last year, that Dozenal Pi Day makes more sense, on more levels, than decimal Pi Day ever will. Additionally it should be noted that, as in most years, Dozenal Pi Day this year falls on the vernal equinox, which is a pretty good day all around for celebrating crap. Moreover, this paricular Dozenal Pi Day falls agreeably on a Sunday, whereas decimal Pi Day falls on a Monday—and unless you're getting the day off, Monday is a pretty lame day for a holiday.

So, FOR ALL THESE REASONS AND MORE, wherever you are, in whater fashion you feel may or may not be appropriate, please join us in celebrating the SECOND ANNUAL DOZENAL PI DAY, on the nominal spring equinox, March one-dozen-and-eighth, in this the 11B7th (one-dozen-one-eleventy-seventh) year of the Common Era. Thank you.

Pi Day vs. Tau Day

Dozenal tau circle Several things have changed since last we celebrated this momentous day. Most notably perhaps, Michael Hartl's stirring Tau Manifesto gave voice to those of us long unhappy with the characterization of the circular constant as the ratio of circumference to diameter. Indeed, our HEXBLOG has fully endorsed Mr. Hartl's proposed adoption of τ as an alternate description of 2π (6;349419 or 6.283186). There are, however, two immediate problems with TAU DAY, at least as far as our purposes here are concerned:

  1. There is no day in the Gregorian year that even remotely corresponds to 6;34. Mr. Hartl, of course, is content to celebrate the antiquated decimal version of Tau Day on 28 June, but there is neither a 34th of June, nor a 63rd of April, in either decimal or dozenal.
  2. As the whole point of DOZENAL PI DAY is to bring attention more to dozenalism than to π or τ, moving it to a fairly obscure and esoteric day three months after the rest of the world celebrates its preferred circular constant day would not really advance our interests. Granted, τ seems to be catching on among the mathematical avant-garde (and rightly so), but I think it's still a few years away from getting any traction with the normals.

Anyway, the important point to consider here is that, unlike competing radices, and as the Tau Manifesto itself makes clear, τ and π are not mutually exclusive—they can exist side-by-side in the same environment, even in the same expression. One simply specifies one or the other with the appropriate symbol, and there is no confusion or ambiguity about it whatsoever. So I certainly feel that one can continue to fully support Tau Day and the tau movement without in any way renouncing π or π-related festivities. They are complementary manifestations of the same underlying geometrical principle.

The larger issue here, of course, is that the ideal occasions for observing either Pi Day or Tau Day would be according to some sort of radix-neutral orbital fraction. If we are to take, say, the winter solstice as an appropriate starting point, 1/τ of the year would bring us to, if my calculations are correct, February 15;th (decimal 17th) in most years. Likewise, doing the same with π would bring us to April 14;th (decimal 16th). Indeed, there is already a variant of this formulation that puts Pi Day on April 22;nd (decimal 26th), calculating from January 1. That's a fine system too, but as long as I'm reinventing shit for no apparent reason, I would rather stick with astronomically significant points of reference.

I could respect an Astronomical Pi or Tau Day of this sort. It might even be something I would legitimately enjoy celebrating. But again, it's a bit esoteric, and since it's radix-neutral it doesn't actually help us here at all.

Thus, in conclusion, we are once again left with Dozenal Pi Day as the only viable dozenal alternative to the bourgeois decimal supremacism of regular Pi Day.

Further reading

For a more in-depth treatment of the dozenal radix, please consult last year's rant on the subject, or even my own amazing Argument for Dozenalism (the latter of which actually includes, if I recall correctly, a fair amount of material from the former). Also, why not take advantage of the advent of this auspicious occasion to join the Dozenal Society of America (or even the Dozenal Society of Great Britain if that's more your thing).

(I am intending this post to serve as some sort of hub for DOZENAL PI DAY promotion on the internet, so it may evolve over time in response to changing needs. Or not. I don't know yet. Anyway, please feel free to post comments, questions, or thoughts you may have on WHAT DOZENAL PI DAY MEANS TO YOU in the comments section below. Thank you.)

Submitted by Jason Burrell ( - 2011-03-04 12:41

First off, I need to disclaim that I learned just enough to understand the significance of what you're doing here, but learned it just long enough ago that I can't remember how to translate a number from one base system to another. If I could, I could probably answer my own question myself.

I understand the preference of a base-12 system over a base-10 system in a basic way. If for no other reason than being more easily divisible internally. It's convenient. I get that. That's why we use it on our clocks and on our calendars. But with the whole thing being as arbitrary as it is, if we're going to takes cues from the heavens, since there are 13 (base 10) moon cycles in a year, shouldn't we use a base-13 system? I really wish I knew the adjective form of 13. Damn. Assuming this would yield a date we could apply to our calendar (even if it required we assume a 13 month year as well, which I think makes more sense under the circumstances), wouldn't that be the purest (though less convenient) cause to champion?

Triskadecimal pi day

Submitted by graham - 2011-07-17 11:02

What an exciting question.

Well, first of all: 3.1AC1049052...—which corresponds to March decimal 23rd. Also: tridecimal or triskadecimal (the latter form also occurring in the term triskaidekaphobia, &c.)—though these terms are still predicated on the underlying decimal prejudice of Greco-Latin language, which is of course why the dozenal movement no longer refers to itself as the "duodecimal" movement. Bakersdozenalism perhaps? I don't know.

I take it as a given that you understand why we wouldn't use base-thirteen for, you know, regular mathematical purposes. It is a prime number, thus it has no factors, thus it can't be broken down into any useful fractions, and so forth. But yes, there are compelling instances of thirteen in the local astronomical phenomena, and I guess if we are going to be having an arbitrary calendrical calculation for this, that would make as much sense as anything. I did think of this when I was invoking the twelve-month calendar as a justification for Dozenal Pi Day, but I didn't want to get off on some tangent about the lunar calendar so I didn't mention it.

There has been of course this whole idea in recent decades of reviving the lunar calendar, which Terence McKenna, among others, seemed very fond of. It certainly seems to be a recurring theme in a lot of the 2012 crap—at least it was back in the 80s, before it went mainstream. I myself do not particularly subscribe to this thinking. I mean, lunar calendars are fine, but at the end of the day, it's the solar calendar that tells us when to plant crops, &c., so while lunar cycles provide a pretty important independent, secondary timescale (such as days of the week are now), I don't think it would make sense to put too much calendrical stock in them, particularly in this day and age. I have nothing but the utmost respect for and fascination with ancient systems of timekeeping, of course, and I enjoy lunar calendars as a concept, and as a recurring mythocultural motif, I'm just not sure that, at this point in our history, proactively returning to them, for general calendrical purposes, makes much sense. Or perhaps any sense.

The bottom line though, as I try to make clear in my collected writings on the subject, is that I just don't take the idea of a positional-notation-derived Pi Day very seriously at all—Dozenal Pi Day is, for me at least, way more about dozenalism than it is about Pi Day. That is why I have the whole digression in this post about various alternate astronomical calculations—because I think, ultimately, if we as a society are going to celebrate an annual pi day, some sort of radix-neutral fractional system makes a lot more sense.

So I guess, if you find the idea of a positional-notation-based calendrical pi day more important than I do, and you are really looking for the ideal astronomical radix, then I think you're right, thirteen would make a lot of sense—though one could make the case for any number of other radices as well, based on planetary orbital resonances and such. I simply see twelve as representing the ideal intersection between universal arithmetical utility and our established, culturally dominant calendrical system. Also, of course, as my interest is in dozenalism, I wouldn't have any reason to promote a triskadecimal pi day. I assure you, however, HEXNET will fully support any movement to establish one, as long as it does not detract from Dozenal Pi Day.

Submitted by anonymous - 2014-12-14 11:43

Dec. 13 Dou.11 moon cycles in a year isn't entirely accurate yes it has them but they don't line up to our calendar year, the term "blue moon" is used if that number of (full) moons is reached in a year; which as the accompanying phase suggests isn't often. Even then they don't line up the way you imply.