The Case for Elv and Unqua: Why We Should be Counting in Dozens

dozenal header

Welcome to PART 3 of our ongoing series here at the slowlorisblog, 42 STEPS TO A BETTER WORLD. That time, it sure is flying. To think we’re already 1/14th done! At this rate, we’re looking at a finish date of 2019, and that’s way ahead of schedule. Today, we offer a radical proposal (accompanied by perhaps as many links as we’ve ever had in a single post): that we’ve been counting in a count(ha)er-productive way for millennia, and to offer an alternative way to do it and make the whole world a better place.

Here’s how most of us count:

1, 2, 3, 4, 5, 6, 7, 8, 9, 10

Here’s how dozenalists (also called duodecimalists) propose we should be counting. It is also the official sponsored counting system of the slowlorisblog from here onward:

1, 2, 3, 4, 5, 6, 7, 8, 9, X, E, 10

(many dozenalists represent the X as an upside down 2, and the E as a backwards 3)

Both the Dozenal Societies of America and Great Britain propose that we should be counting not in base-10, but in base-12. Phonetically, they’d sound like this:

one, two, three, four, five, six, seven, eight, nine, ten, elv, unqua

(It is, in my opinion, a massive failing of the movement that most of them insist on forcing us to replace, conceptually, the Roman number 10 in their number line with a set of numbers that is in fact “12-large,” while phonetically retaining “ten” for the numeral X. Others have suggested calling the numeral X do. Whatever the case, it’s obvious that one of the largest obstacles to adoption is going to be pronunciation. Especially when it comes to large numbers.[1] But if we can put this problem aside for just a moment, we’ll see many potential benefits).

Historically, the way we count is more or less based on the number of fingers and toes we have. Other societies have counted differently: the Babylonians counted in base-60, the Mayans in base-20, the people of Papua New Guinea are said to count in base-6, the Umbu-Ungu in base-24, and various positional and other computational systems favor base-36. So counting in tens isn’t some kind of incarnation of Natural Law. It just happened, and we stuck with it.

Proposing any kind of change like this is sure to ruffle some feathers. It would cost a good deal to do, in addition to annoying parents who thought they knew how to count, Especially when little Umlaut comes home asking why mommy didn’t teach her about the number elv.

There are really two, not necessarily mutually exclusive, cases to be made here: that switching to the dozenal system would be a beneficent move in terms of everyday convenience, and that it provides mathematical benefits with larger impacts in that field of praxis. The former of these is the easier one to make, but it’s also much less convincing to the average reader. Convincing one generation to re-learn how to count so as to (mostly) benefit the succeeding ones rarely works. This phenomena affects not only knowledge systems, but technology. Look at the arguments to be made for switching to the Dvorak (or other alternative) typing systems. The latter of these, the mathematical benefits, are murkier, but still titillating. Let’s dive in!

Mathematical benefits

  1. Fractional representation: Fractions, in total number, digit-length, and common-use ones are, I think, inarguably simplified when it comes to dozenal math. Compare them for yourself below. The big takeaway for me is that 1/3 stops being a mess, and most of the other common fractions go from two or three digits to one. The only real backward step is that 1/5 goes from .2 to 0.24972497 (recurring).
1/2 0.6 .5
1/3 0.4 .333 (repeating)
1/4 0.3 .25
1/5 0.24 (repeating) .2
1/6 0.2 .1666 (repeating)
1/7 0.1714285 (repeating) .142857 (repeating)
1/8 0.15 .125
1/9 0.1333 (repeating) .111 (repeating)
  1. Recurring digits: In the real world, problems with factors of 5 come up far less than problems with factors of 3, and the the dozenal system brings with it a host of inherent properties making it superior to the decimal system.[2] That means recurring digits (and the rounding inexactitude they often require) come up less often. Nevertheless, the real benefit that in the dozenal system when recurring digits do come up, they tend to be much shorter than in the decimal system. This is because 12 sits in the middle of two prime numbers (11, 13) rather than, as 10 does, next to a composite number (9).[3] It also is the result of their respective factorizations (the process of breaking numbers down into all the small numbers which, when multiplied together, get you to the large number), where dozenal offers further benefits. The prime number 2 shows up twice in the factorization of 12 (as opposed to once in 10), and the prime number 3 shows up once instead of not at all. Basically, more primes = good, less = bad.[4]
  2. Superior highly composite numbers are those which have a greater number of divisors relative to the number itself. 12 is one of these. 10 isn’t even a highly composite number (those positive numbers with more divisors than every smaller positive number). This means the math, including but not limited to the two cases above, gets cleaner all the way around.

Everyday benefits

Basically, it makes counting better all the way around, in terms of weights (pharmacists and jewelers use a 12-ounce pound), measures (a circle has 12 divisions of 30 degrees, there are 2 sets of 12 hours in a day, 12 months in a year, 12 inches in a foot for carpenters) or money (the British pound system, but also American financial markets as they are based around a 12-month year). There are a host of others, that if you are curious about you can check out at the American Dozenal Society Education Resources Page[5]

Thus, for children, it makes math easier to conceptualize and understand. For those of us raised on the decimal system, we can just use a calculator.

What a Dozenal World Would Look Like





Fans can join the movement and its (only semi-facetious) legislative proposal, the Dozenal Establishment Act.

Further Reading

Interview with Dozenal Society of American Don Goodman

The Dozenal Society of America

The Dozenal Society of Great Britain

A nice video introduction to base-12

Some other stuff






Energy and Power: The History of Hydroelectricity in the American Northwest

Hirt and Wilma book review

Paul W. Hirt. The Wired Northwest: The History of Electric Power, 1870s-1970s. (Lawrence: University Press of Kansas, 2012. Illustrations, notes, bibliography, index. ix, 462 pp. $49.95)

David W. Wilma, Walt Crowley, and the HistoryLink Staff. Power for the People: A History of Seattle City Light. (Seattle: HistoryLink in Association with University of Washington Press, 2010. Illustrations, notes, index. 131 pp. $29.95.

It is a rare opportunity to review two texts which complement one another so well with regards to theme and scope. Paul W. Hirt in The Wired Northwest presents to us an ambitious, comprehensive, and integrated history of the development of regional power in Washington, Utah, Oregon, and British Columbia from 1870-1970. David Wilma, Walt Crowley, and the HistoryLink staff, on the other hand, attempt to render in detail a microcosm of Hirt’s larger narrative—that of the history of Seattle City Light, a municipal electric utility that in numerous ways lies at the heart of Hirt’s story—during almost the same period. Together, they offer a compelling account of reification, rationalization, ideology, and regional identity.

Harnessing the region’s rivers and watersheds remains, from the beginning, central to both stories, as environmental historians of the Northwest have shown for decades. Wilma, et. al. traces the stuttering emergence of this new technology that promised to liberate the masses from the darkness in the quickly growing city of Seattle in 1886, with two dynamos generating enough electricity for just three hundred sixteen-candlepower lamps from a single hydroelectric power source. Though, as Hirt points out, initially uneven in adoption and  use, questions about who would control production, transmission, and consumption of the nascent resource would immediately engender debate between public utilities charged with providing low-cost energy to as many as possible and private companies who claimed to be the inheritors of the American capitalist spirit.

Hirt’s wonderfully rich narrative of the northwest emphasizes the region’s early adoption of the electrical revolution, pioneered by industry magnates who both lighted private residences and began the process of illuminating those job sites where artificial light promised to increase productivity and profits, like mines and shipping yards, as well as re-organize factories on both sides of the border. Subjects include the amalgamation of small utilities into ever larger ones, the enthusiastic optimism in the possibilities offered by this new technology (some of which were quickly tempered by unequal service and prices for residential and commercial customers), apprehension of growing monopolies, conflict between competing industries attempting to rationalize the river (hydroelectric versus fishing), and the distinctive nature of energy history in the Northwest,  uniquely marked by geography as hydroelectric boosters, entrepreneurs, cooperatives, and regulators followed the twisting rivers, gorges, and watersheds of the region.

Hirt tends to favor the machinations of the private utility and the needs of industry, yet given his charge to synthesize a hundred years of energy history this is not entirely his fault. Municipal utilities, as shown by Wilma, et. al., were, especially in the early years, mercurial and small in number. Indeed, Wilma, et. al. provides a balance to Hirt’s narrative of the ideological struggle which quickly developed between proponents of private and public power by reminding us of the development of a powerful electric sensibility by the masses of people that could only be sated by more reliable, lower-priced, and increasing amounts of electricity.

Together Hirt and Wilma, et. al. demonstrate the fear of “foreigners” held by West Coast citizens, as they saw bankers, financiers, and capitalists from Chicago, Boston and New York attempt to enter the electric utility market via direct and indirect avenues of influence. They both also agree that the 1915 victory of the National Electric Light Association, effectively prohibiting municipal electric utilities from selling power beyond city limits, was a serious blow to anti-corporate interests in the public-private war. This conflict would, over time, come to dominate the electric industry no just in the Northwest, but across the United States.

At the same time, they each bring independent subjects to bear. Hirt highlights the particularities of electric power in the United States and Canada, like the fact that for Canadians growth remained generally slower, government regulation less transformative (especially during the world wars), and the worldwide depression of the 1930s more inhibiting to rural electrification, technical progress, and large hydroelectric projects because of already-strained economies and cautious financiers. He also spends considerable time with the Bonneville Power Administration and the long-reaching effects of federally funded hydroelectric projects would have on shaping the industry. Wilma, et. al., on the other hand, traces in meticulous detail the Seattle City Light’s sometimes rocky growth into the largest publicly owned utility in the region. Particularly welcome are moments like Seattle City Light’s implementation of public tours from 1929-1940, designed to keep the utility in the public eye during economic hardship. Picturesque train rides, guided tours of the monumental engineering project at Skagit River, an overnight stay, and imported plant and animal life made the destination successful to the tune of twenty-two thousand visitors per year by the start of World War Two. Especially useful to the reader is Wilma, et. al.’s rendering of life as a City Light employee with respect not only to daily activities for linemen, sales people, and troubleshooters, but the extent to which they all formed a complex association of families who lived, learned, worked, voted, commiserated and celebrated together.

The two texts are not without their disagreements. For instance, Wilma, et. al argues that in the early years of Seattle City Light residential customers were charged eight cents per kilowatt hour, with reduced rates as usage increased, while for commercial customers, rates were “generally higher” (28). This is in contrast to the trend unearthed by Hirt, which without fail notices commercial customers who use far more electricity than the average residential customer enjoying significantly reduced rates. Such trends provided continuous ammunition for the multifarious interests publicly debating the merits of various degrees of public and private ownership.

Both Hirt and Wilma end their parallel narratives with the onset of the 1970s and how the philosophy of pushing unending consumption (on the basis that production would meet future needs) suffered a relatively quick, if not easy, death. Economic realities along with local and global politics changed the landscape of public and private power. New imperatives transformed what it meant to be a corporate or public electric power entity in the late twentieth century, as the advent of the environmental impact study and new definitions of conservation among bureaucrats together redefined the manner by which the public accepted the harnessing of nature’s energy for their own and future generations.


This review will be published in the upcoming issue of the Pacific Northwest Quarterly.

U.S.S. Nautilus (SSN-571)- A Photo Tour


A couple of weeks ago I visited the U.S.S. Nautilus (designation SSN-571) in Groton, CT. The Nautilus bears the distinction of being the first nuclear-powered submarine put in operation by the United States Navy. It was operational from 1954-1980, during which time, notably, it completed a “submerged transit” of the North Pole (1958) and participated in the blockade of Cuba (October 1962). The Nautilus broke a number of submarine records, largely rendered the anti-sub countermeasures of WWII obsolete, and represented a critical stage in the development of warfare during the Cold War. Feel free to read more about it here, here, and here. On to the pictures!

See the full 157-picture tour via google drive here.

1 plaque

2 schematics


3 1892 edition Jules Verne

the bridge

4 Bridge
crew mess

5 crew mess

A3 oxygen breathing apparatus

6 A3 Oxygen breathing apparatus

battery banks

7 battery banks

battery banks diagnostic equipment

7-2 battery banks diagnostics


7 kitchen

officer bunk

8 officer bunk


pinups everywhere


radio room

9 radio room

radio room 2

9-2 radio room 2

reactor room pressure gauge (probably pretty important)
10 reactor room pressure

opposite torpedo room

11 torpedo room guts


12  deck