And make: Time & Angles measurements consistant.

Recent changes: More about our currnt use of 12.

Started: Sat 2004-03-27

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

- Twelve is used in many places
- Clock faces.
- Months in a year.
- Eggs and other things are sold in dozens.
- Days and nights each have 12 hours.
- England and USA have 12 inches in a foot.
- Multiply table on school notebooks went to 12x12.
- there was 12 pennys in a shilling.
- You can probably think of more.

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.**

- The new digits should not be confused with letters of the alphabet.
- They should be representable in the familiar 7 segment display.
- They should be on a standard computer keyboard.
- They should be easily written with a single stroke.
- The first [ which I would call "
**col**" and have the value of "nine plus one". - The second ] which I would call "
**sem**" and have the value of "nine plus two". - I would call "10" in the base twelve
syztem "
**zen**".*Which has a value of "nine plus three". Of course!* - Here is long WiKi discussion.

ASCII characters: **col**on, and **sem**icolon 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 |

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 [ |

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.".

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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