Duodecimal Metric System: If only we had evolved with one less finger per hand!

{It’s Flashback Friday, when Professor Tertius’ comments from long ago get logged into the Bible.and.Science.Forum blog. Today’s flashback links Base 12 numerals, the Metric System, a Base 12 Metric System, algebra, and fear of Communism with the glory days of the early Young Earth Creationist movement in America. Enjoy.}

The following will never happen, but in an IDEAL WORLD, I would advocate a change not just to a Metric System but one based on Base 12 instead of Base 10 arithmetic. It would provide all of the usual advantages of the Metric System plus the natural advantages of more/simpler integer factoring and divisors.

If one works in Base 12, it is very simple to divide items in many ways without having to use complicated math and notations:

Half of 12 is 6.
One quarter of 12 is 3 and three quarters of 12 is 9.
One sextile of 12 is 2; two sextiles is 4, three sextiles is 6, etc.

In practical use, consider eggs, which are already sold in dozens:

To divide 12 eggs among various groups:

6 groups of 2
4 groups of 3
3 groups of 4
2 groups of 6

Compare that with dividing 10 eggs among various groups of people:

5 groups of 2
2 groups of 5
That’s it! It is very “indivisible”. And that is why the use of dozens has been popular since ancient times. The only reason we use a Base 10 number system is because of tradition, based upon the fact that we have 10 fingers and 10 toes. (Obviously, we call both our numerals and our finger “digits” because of their natural association in counting.)

Base 10 is very limiting. The only factors are 5 and 2. It makes dividing into equal parts of various sizes difficult and it requires long decimal numbers even for simple fractions. Consider in Base 10 that:

1/2 of 10 = 5 is not too bad, but….
1/3 of 10 = 3.33333_ never stops
1/4 of 10 = 2.5 not so simple
1/5 of 10 = 2 not too bad
1/6 of 10 = 1.66666_ never stops;
1/7 of 10 = 1.142857_ never stops
1/8 of 10 = 1.125 requires 4 digits to express

Consider the same fractions of 10 (i.e., 12 in Base 10) in Base 12 notations. However, first you must consider the need for two more “digits”. In my grade school days, computers were not yet changing how we looked at numbers. So most arithmetic books used “t” for ten and “e” for eleven. But there are many advantages to the notations used by computer scientists when dealing with hexadecimal numbers. So we will use the “A” for ten and “B” for eleven. So, counting in Base 12 means 1,2,3,4,5,6,7,8,9,A,B,10,11,12,13, 14…..19,1A,1B,20,21, etc. So now we can consider that in Base 12:

1/2 of 10 = 6 (remember, this is Base 12, where 10 is 1 dozen.)
1/3 of 10 = 4 still no fractional notations needed!
1/4 of 10 = 3 still no fractional notation needed.
1/5 of 10 = 2.497_ This is our first repeating fraction
1/6 of 10 = 2 no fractional notation needed!
1/7 of 10 = 1.86A35 _ Another repeating fraction.
1/8 of 10 = 1.6 only two digits needed

So, let’s compare them:

Base 10 produced:

2 simple integers
1 instance of 2 digit notations
1 instance of 4 digit notation
3 repeating fractions

Base 12 produced:

4 simple integers
1 instance of 2 digit notations
2 repeating fractions

Had I used examples of 2/N instead of the 1/N of the examples above, you would have seen similar savings in digits and avoidance of fractional notations.

CONSIDER THE ADVANTAGES OF A DUODECIMAL “METRIC SYSTEM”:

I won’t walk through the actual names of units but consider these facts:

1 egg
10 is a dozen eggs
100 is a dozen dozens of eggs

So you still have the advantage of adding a “0” to multiply the number by the base: 12. But “real world” division requires fewer fractions because of the phenomena we already observed in the 1/N examples.

You have nothing but whole units when dividing into two groups, three groups, four groups, and six groups! That is, you end up dealing in whole units (integer amounts) instead of fractions in those cases.

By dropping Base 10 and moving to Base 12, you lose the ability to divide 10 into 5 groups of 2……but in Base 12 you gain the ability to divide the NEW “10” into 6 groups of 2, 4 groups of 3, 3 of 4, 4 of 3, while still having groups of 2 (that is, 6 groups of 2.)

I hadn’t looked around before to see what was going on with DUODECIMAL (Base 12) METRIC SYSTEMS but here are some interesting examples of typical proposals:

Dozenal Metric Systems:
http://www.dozenal.org/drupal/content/dozenal-metric-systems  as presented by The Dozenal Society of America.

Here are some examples of proposals for Time, Linear Measure, and Weight:
http://duodecimal.net/archives/duodecimal/duodecimal.html

WHAT IF WE HAD EVOLVED WITH ONE LESS FINGER PER HAND?

Suppose that humans had evolved with three fingers plus a thumb on each hand. That would mean each human would have had two hands, each with four digits per hand (each hand consisting of three fingers plus one thumb.)  Assuming the usual symmetries, each foot would have had one big toe and three smaller toes. That’s a total of 4+4+4+4=16 fingers and toes for counting.

In that case, there would be a natural emphasis on the integers 1,2,3,4,6,8,12, & 16 because all of those come up naturally in counting by means of one’s available “digits”. So if that had been our evolution—where we had one less finger on each hand—I think we would have naturally gravitated toward the development of a Base 12 (duodecimal, aka dozenal) number system.

That’s just my spur-of-the-moment hypothesis. I haven’t looked to see if anyone based a dissertation on it.  (By the way, I think cartoon artists always use this 8-finger standard because it makes a cleaner cartoon image.)

 In the early 1960’s I recall some Young Earth Creationists also denouncing the Metric System as a “Communist plot” and “just as dangerous” because it would open up America to foreign imports. Does anyone else remember that?

So what does all of this have to do with evolution?

Believe it or not, in the early 1960’s I recall some Young Earth Creationists also denouncing the Metric System as a “Communist plot” and even “godless” because it would open up America to foreign imports, such as inexpensive Asian automobiles which could try to destroy Detroit’s prominence in supplying the world with automobiles! And later in that same decade, public education in the USA was “revolutionized” by what was touted as a major change in how mathematics was taught. Reformers called it “The New Math”. It was claimed to be a better foundation for teaching students algebra once they reached high school. But The New Math also included several mathematical concepts not previously taught at the elementary school arithmetic level. Among those were the alternative bases number systems.

All of these “radical changes” were way too much for many Fundamentalist Christians of the American Bible Belt, coming as it did right in the middle of the Cold War, fallout shelters, campus unrest due to the rising body count of the Vietnam War, and a series of shocking assassinations which further elevated the tensions and fears of the era.

Considering how Morris & Whitcomb’s THE GENESIS FLOOD (1961) had warned Young Earth Creationists of the dangers and evils of The Theory of Evolution and “billions of years”, YECs were told that they had the “authority of Science” (i.e., “creation science” and all other “valid” Science) behind them.  Yes, conservatives were flexing their muscles and the Civil Rights era brought huge losses to the Democratic Party (i.e., the entire South went Republican.)

So if one takes into account the context of the times, it shouldn’t be too surprising that the Metric System would be looked down upon by so many American conservatives, especially Bible Belt Fundamentalist Christians. So when their children brought home their math homework and parents had no idea how to help them do Base 12 arithmetic, you can imagine how a Duodecimal Metric System would have been considered a diabolical Communist plot right up there with The Theory of Evolution!

Those were the good ol’ days indeed.

(c) 2011. Professor Tertius & the Bible.and.Science.Forum at Gmail.com.
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1 Comment

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One response to “Duodecimal Metric System: If only we had evolved with one less finger per hand!

  1. I didn’t delve into the topic in my blog but plenty of civilizations did not focus on the fingers in selecting the base for their numeric system. The Babylonians used a base 60 system. In the pre-Columbian Americas, the Mayans used base 20, some others used base 60, but the Incas used base 10. Before decimal money was introduced, the British liked to use base 12 in their money. So that tells us that the total number of our “digits” was not absolutely certain to be in our own hands, so to speak.

    So I wouldn’t want to leave the impression that the number of fingers absolutely dictated what would eventually be the base of our numeric system. The “predictive” nature of our anatomical endowment quantities was meant to be read tongue-in-cheek. A base 8 number system has practical limitations/deficiencies of its own, so we can only speculate as to what might have happened had evolution given us the finger (so to speak) in quantities of one less per hand.

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