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

Last Up date: 2010 November 15
Recent changes: Made link to "how we say numbers" more prominent.
Started: Sat 2004-03-27

Dozenal: Base Twelve number system

First, let me point out that for many years there have been academics groups proposing, 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 is because Twelve is divisible by: 2, 3, 4, and 6; while Ten is only divisible by: 2 and 5. 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. These new digits should not be confused with letters of the alphabet, and they should be clearly representable in the familiar 7 segment displays we see on many electronic devices. Furthermore, they should be easily written with a single stroke. I would like to propose: a character that would look like a backwards capitol "L" for the first which I would call "col" and it would have the value of "nine plus one". The second which I would call "sem" whose value would be "nine plus two" would be the same with one additional up bar on the left, making it look somewhat like the capitol letter "J". The rational for these names and shapes is explained below.

As I set typing today, I am using a computer that uses the ASCII character set. Which leaves much to be desired, but what other choice do I have? It is also unfortunate that I am spelling words by a convention that is not phonetic and is FAR from optional; but what other choice do I have? If I want you to be able to read it? I decided to experiment with different ASCII options for the two new digits:
                      Dozenal Extra Digits Experiment
                             Tue  2004-03-16

Examples of Dozenal Square Root of 2 to 25 (Dozenal decimal) places.
 Using for the additional two digits: (ASCII characters: colon, and
 semi-colon which follow 9), A & B (both upper and lower case) and
 E & T (both cases).  Which do you find easier to read?

1.4;79170:07;85737704;085486853

1.4b79170a07b85737704b085486853

1.4B79170A07B85737704B085486853

1.4e79170t07e85737704e085486853

1.4E79170T07E85737704E085486853
If you print these samples. Then cover the lines up so you only see them one at a time. I think you will inadvertently find yourself using the first line to find the "new" digits. The first line is more distinct and easier to read. Agree???

Based on this and other experiments I decided to call the smaller of the new digits "col" and the larger "sem". After some thought, to avoid confusion I would call "10" in the base twelve syztem "zen", which has a value of "nine plus three". Of course!. (If you find it hard to remember which is larger, think: it takes more ink to make a semicolon, so it is the bigger.) Also, we need to be more systematic in how we "say" numbers of more than one digit.

For more practice here is a table of small prime numbers in both 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 

Time and Angles

Unfortunately when these units for time and angles were devised science had not advanced to where it was generally known that the earth rotated; hence, the connection between time and angles was not realized. Presently: The rotation of the earth is divided into 24 parts for time, and 360 degrees for angular measure. This is truly an unfortunate mistake of the past, and regrettably even though we think we are smart and progressive: I have not heard any arguments that we should change our units of: Time and Angles. But as any programer knows doing arithmetic on time or angles is a crazy mess. Especially if AM and PM are used! So, I will present a much better system.

If we were using Dozenal, I propose angles be measured in parts of a complete circle. Thus 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 have used leading zeros to emphasize numbers just as we currently do, but they 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.

To the many who have given this some thought, I would love to get your thoughts, ideas, corrections and suggestions. I would be nice to have links or pages with other ideas, arguments, and opinions.

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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