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Unfortunately when these units were devised science had not advanced to where it was generally known that the earth rotated; and hence, the connection between time and angles was not realized. The rotation of the earth is divided into 24 parts for time, and 360 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. So, I will.
But first, let me point out that for many years there has been a small academic group proposing, with many good arguments, that we should change our counting from base ten to base twelve. They call themselves the "Dosenal Society". Eventually, I will have links to what I think are the better writings on the subject; but for the time being use Google to find more information. Much of the best 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.
First, 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 we 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 04-03-16
Examples of Dozenal Square Root of 2 to 25 (Dozenal decimal) places.
Using for the additional two digits: ASCII natural, A & B (both cases)
and E & T (both cases). Which would you prefer to read?
1.4;79170:07;85737704;085486853
1.4b79170a07b85737704b085486853
1.4B79170A07B85737704B085486853
1.4e79170t07e85737704e085486853
1.4E79170T07E85737704E085486853
|
Based on this and other experiments I decided to call the smaller of
the new digits "col" and the larger "sem". Thus, leaving "10" to be called
"ten", 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. More about that later.
For more practice here is a table of small prime numbers in both decimal and dosenal:
First 200 (dosenal) 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 97 101 103 107 109 113 127 131 137 139 149 151 157 163 167 173 179 181 191 193 197 199 211 223 227 229 233 239 241 251 257 263 269 271 277 281 283 293 307 311 313 317 331 337 347 349 353 359 367 373 379 383 389 397 401 409 419 421 431 433 439 443 449 457 461 463 467 479 487 491 499 503 509 521 523 541 547 557 563 569 571 577 587 593 599 601 607 613 617 619 631 641 643 647 653 659 661 673 677 683 691 701 709 719 727 733 739 743 751 757 761 769 773 787 797 809 811 821 823 827 829 839 853 857 859 863 877 881 883 887 907 911 919 929 937 941 947 953 967 971 977 983 991 997 1009 1013 1019 1021 1031 1033 1039 1049 1051 1061 1063 1069 1087 1091 1093 1097 1103 1109 1117 1123 1129 1151 1153 1163 1171 1181 1187 1193 1201 1213 1217 1223 1229 1231 1237 1249 1259 1277 1279 1283 1289 1291 1297 1301 1303 1307 1319 1321 1327 1361 1367 1373 1381 1399 1409 1423 1427 1429 1433 1439 1447 1451 1453 1459 1471 1481 1483 1487 1489 1493 1499 1511 1523 1531 1543 1549 1553 1559 1567 1571 1579 1583 1597 1601 1607 1609 1613 1619 1621 1627 1637 1657 1663 1667 1669 1693 1697 1699 1709 1721 1723 1733 1741 1747 1753 1759 1777 1783 1787 1789 1801 1811 1823 1831 1847 1861 1867 1871 1873 1877 1879 |
First 200 (dosenal) primes in "Col, Sem" DOSENAL 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 59; 5;1 5;5 5;7 5;; 611 615 617 61; 637 63; 647 655 661 665 66; 675 687 68; 695 69; 6:7 6;1 701 705 70; 711 71; 721 727 735 737 745 747 751 767 76; 771 775 77; 785 791 797 7:1 7;; 801 80; 817 825 82; 835 841 851 855 85; 865 867 871 881 88; 8:5 8:7 8:; 8;5 8;7 901 905 907 90; 91; 921 927 955 95; 965 971 987 995 9:7 9:; 9;1 9;5 9;; :07 :0; :11 :17 :27 :35 :37 :3; :41 :45 :4; :5; :6; :77 :87 :91 :95 :9; ::7 ::; :;7 :;; ;11 ;15 ;1; ;21 ;25 ;2; ;31 ;37 ;45 ;61 ;67 ;6; ;71 ;91 ;95 ;97 ;:5 ;;5 ;;7 1005 1011 1017 1021 1027 1041 1047 104; 1051 1061 106; 107; 1087 109; 10;1 10;7 10;; 1101 1105 1107 |
To the many who have given this much 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 dosenal. I also converted a Prime number output routine to output in "dosenal". If you are interested.
My Home phone number is on the left and the Cell on the right.