We should use a base Twelve Counting and Metric System
And make: Time & Angles measurements consistant.

Last Up date: 2019 February 6 nuMacMini work/gd/lafarr/math
Recent changes: More about our currnt use of 12.
Started: Sat 2004-03-27

Dozenal is: A Base Twelve number system

Academics groups for years have proposed, with many good arguments, that we should change our counting from base ten to base twelve.

Twelve is mathematically a much better base than Ten because Twelve is divisible by: 2, 3, 4, and 6; while Ten is only divisible by: 2 and 5. By looking at only the last digit we can know if the number is divisable by 2, 5 or ten. It would be much better if the last digit could tell if the number is divisable by: 2, 3, 4, 6 or twelve. (Only n/5 and n/7 would be infinintly long. like n/3 and n/6 are in base ten.)

The "Dozenal Society" is a group advocating changing to base Twelve. To find more information just Google on the word Dozenal. Much of the best writing on the subject seems to be by a British group but unfortunately, in my opinion, too much of it is simply "anti-metric". All the world, except for the United States and a few British die-hards, realize it is dumb to not have your weights and measures consistent with your number system.

    For Dozenal: We need to add two more digits to our counting system.
  1. The new digits should not be confused with letters of the alphabet.
  2. They should be representable in the familiar 7 segment display.
  3. They should be on a standard computer keyboard.
  4. They should be easily written with a single stroke.
  5. The first [ which I would call "col" and have the value of "nine plus one".
  6. The second ] which I would call "sem" and have the value of "nine plus two".
  7. I would call "10" in the base twelve syztem "zen".
    Which has a value of "nine plus three". Of course!
  8. Here is long WiKi discussion.

ASCII characters: colon, and semicolon follow 9, that's the reason I chose these names.
We would have to learn and use Dozenal Add and Multiply tables.

Dozenal Square Root of 2 to 25 (Dozenal decimal) places.

         1.4]79170]07[85737704]085486853

Tables of small prime numbers in decimal and Dozenal.

First 100 (Dozenal) primes in decimal. Wed  03-24-2004

3    5    7    11   13   17   19   23   29   31   37   41
43   47   53   59   61   67   71   73   79   83   89   97
101  103  107  109  113  127  131  137  139  149  151  157
163  167  173  179  181  191  193  197  199  211  223  227
229  233  239  241  251  257  263  269  271  277  281  283
293  307  311  313  317  331  337  347  349  353  359  367
373  379  383  389  397  401  409  419  421  431  433  439
443  449  457  461  463  467  479  487  491  499  503  509
521  523  541  547  557  563  569  571  577  587  593  599
601  607  613  617  619  631  641  643  647  653  659  661
673  677  683  691  701  709  719  727  733  739  743  751
757  761  769  773  787  797  809  811  821  823  827  829
First 100 (Dozenal) primes in "Col, Sem" Dozenal
3    5    7    ]    11   15   17   1]   25   27   31   35
37   3]   45   4]   51   57   5]   61   67   6]   75   81
85   87   8]   91   95   [7   []   ]5   ]7   105  107  111
117  11]  125  12]  131  13]  141  145  147  157  167  16]
171  175  17]  181  18]  195  19]  1[5  1[7  1]1  1]5  1]7
205  217  21]  221  225  237  241  24]  251  255  25]  267
271  277  27]  285  291  295  2[1  2[]  2]1  2]]  301  307
30]  315  321  325  327  32]  33]  347  34]  357  35]  365
375  377  391  397  3[5  3[]  3]5  3]7  401  40]  415  41]
421  427  431  435  437  447  455  457  45]  465  46]  471
481  485  48]  497  4[5  4]1  4]]  507  511  517  51]  527
531  535  541  545  557  565  575  577  585  587  58]  591 

The last digit of a prime can not be a composite: 4 6 8 or [

Time and Angles

A day was divided into 12 hours, because 12 has many divisors, and similarly for a night. For shorter times, hours are divided into 60 minutes, and each minute is divided into 60 seconds. Now we find even one thousandth of a second, or a milisecond is large. When the units for time and angles were devised it was not known that the earth rotated.

Six is a very convient number. Most know that when we draw a circle, using a "compass" the radius of the circle can be stepped off exactly six times around the circle. If we connect each of these steps with the next one using a straight line we will have a hexagon. Six equlateral triangles fit inside the circle.

6 times 60 is 360 and it is used for angular measure. There has been an attempe to put 400 units (Grads) around a circle, but it never became popular I have not heard any arguments that we should change our units of: Time. But as any programer knows doing arithmetic on time, or angles, is a crazy mess. Especially if AM and PM are used!

Note: A year is near 365.24 days. In dozenal that would be slightly less than 265.3 days. It would be up to the calendar makers to decide if and when we would have "leap years" or "short years.".

Using Dozenal, Here is a much better system.

Angles would be measured in Revolutions. An angle of one complete revolution would be 1.0 Rev. Instead of our crazy 360 degrees. "Rev" replacing the word "degree" for angular measures. A straight line would be an angle of 0.6 revs remember in Dozenal 1/2 is 0.6. And a right angle would be half a straight line or 0.3 revs. What we now call a 30-60-90 triangle would be a 0.1 - 0.2 - 0.3 triangle. Elegantly simple! I used a leading zero to emphasize numbers less than one, just as we currently do, but it would not always be needed.

Time should be simply a measure of the angular rotation of the earth. Thus a day would be: 1.0 and a half day would be 0.6 and what we now call 2 hours would be 0.1 of a day. Midnight would be time 0.0 and noon would be 0.6 and half way between midnight and noon would be 0.3 Oh, yes what we now call an hour would be 0.06 and smaller time intervals would be just more digits to the right. Different but elegantly consistent.


The Longitude of where you are at would tell you your Time Zone! Think of how this would simplify the concept of "Greenwich Mean Time" or UTM.

I have in My Arithmetic Routines a calculator program to do variable precision integer arithmetic. With it you can change the input and output number bases. The above Square Roots were done with it. I also have a "tweaked" version where the defaults are Dozenal. I also converted a Prime number output routine to output in "Dozenal". If you are interested.

For anyone who wants to compair other number system bases, I have a page comparing them.


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