Duodecimal (Base-Twelve) Counting
Nov 18, 2018 7:51:05 GMT 10
Post by RockyMountainExtreme on Nov 18, 2018 7:51:05 GMT 10
(yes I know I did a thread like this on inthe00s, who says I can't do one on Popedia as well?)
For those of you that don't know, Base-Twelve, or Duodecimal, refers to a numeric system where the Radix is twelve, where there are twelve unique digits to represent numbers in a positional numbering system.
The system we use currently is Base-Ten, or Decimal, where there are ten unique digits to represent numbers in a positional numbering system; 0, 1, 2, 3, 4, 5, 6, 7, 8, 9.
This is the system we've known so well since toddler hood, is used globally, and it all stems from the fact that we have ten fingers, 5 on each hand.
The problem with the Decimal system however is that there are only two non-trivial factors of ten; 2 and 5. Try to split it up any other way, and you're gonna end up with fractional notations.
Divide ten by 4, and you're gonna get 2.5, and ten divided by 3 is 3.3333→, where the 3's in the decimal place go on forever.
As stated before, in the Base-Twelve, or Duodecimal, system, there are twelve unique digits to represent numbers in a positional numbering system; 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, ↊, ↋.
"↊" and "↋" are the Base-Twelve counterparts to what we know as "10" and "11" in the Base-Ten system.
As for how they're pronounced, you could keep the "ten" and "eleven" spelling, but most duodecimal-fanatics instead use "dek" and "elv". I personally prefer "ten" for ↊ and "elv" for ↋
After ↋ comes 10, which is the Base-Twelve equivalent to Base-Ten's 12. It's pronounced "doh" (yeah yeah, cue the Homer GIFs), which is short for "dozen".
11 (13 in Base-Ten) is pronounced "doh-one", 12 (14 in Base-Ten) is pronounced "doh-two", 13 (15 in Base-Ten) is pronounced "doh-three", and so on all the way up to 1↋ (23 in Base-Ten), pronounced "doh-elv".
After 1↋ comes 20 (24 in Base-Ten), which is pronounced "two-doh". After that, you have 21 (25 in Base-Ten), which is pronounced "two-doh-one", then 22 (26 in Base-Ten), which is pronounced "two-doh-two", all the way up to 2↋ (35 in Base-Ten), which is "two-doh-elv".
Here's a guide, converting Base-Ten numbers to Base-Twelve numbers;
0 = 0 (zero)
1 = 1 (one)
2 = 2 (two)
3 = 3 (three)
4 = 4 (four)
5 = 5 (five)
6 = 6 (six)
7 = 7 (seven)
8 = 8 (eight)
9 = 9 (nine)
10 = ↊ (ten)
11 = ↋ (elv)
12 = 10 (doh)
13 = 11 (doh-one)
14 = 12 (doh-two)
15 = 13 (doh-three)
16 = 14 (doh-four)
17 = 15 (doh-five)
18 = 16 (doh-six)
19 = 17 (doh-seven)
20 = 18 (doh-eight)
21 = 19 (doh-nine)
22 = 1↊ (doh-ten)
23 = 1↋ (doh-elv)
24 = 20 (two-doh)
25 = 21 (two-doh-one)
26 = 22 (two-doh-two)
27 = 23 (two-doh-three)
28 = 24 (two-doh-four)
29 = 25 (two-doh-five)
30 = 26 (two-doh-six)
31 = 27 (two-doh-seven)
32 = 28 (two-doh-eight)
33 = 29 (two-doh-nine)
34 = 2↊ (two-doh-ten)
35 = 2↋ (two-doh-elv)
36 = 30 (three-doh)
48 = 40 (four-doh)
60 = 50 (five-doh)
72 = 60 (six-doh)
84 = 70 (seven-doh)
96 = 80 (eight-doh)
108 = 90 (nine-doh)
120 = ↊0 (ten-doh)
132 = ↋0 (elv-doh)
144 = 100 (groh)
145 = 101 (groh-one)
146 = 102 (groh-two)
147 = 103 (groh-three)
148 = 104 (groh-four)
149 = 105 (groh-five)
150 = 106 (groh-six)
151 = 107 (groh-seven)
152 = 108 (groh-eight)
153 = 109 (groh-nine)
154 = 10↊ (groh-ten)
155 = 10↋ (groh-elv)
156 = 110 (groh-doh)
157 = 111 (groh-doh-one)
158 = 112 (groh-doh-two)
159 = 113 (groh-doh-three)
160 = 114 (groh-doh-four)
161 = 115 (groh-doh-five)
162 = 116 (groh-doh-six)
163 = 117 (groh-doh-seven)
164 = 118 (groh-doh-eight)
165 = 119 (groh-doh-nine)
166 = 11↊ (groh-doh-ten)
167 = 11↋ (groh-doh-elv)
168 = 120 (groh-two-doh)
169 = 121 (groh-two-doh-one)
170 = 122 (groh-two-doh-two)
171 = 123 (groh-two-doh-three)
172 = 124 (groh-two-doh-four)
173 = 125 (groh-two-doh-five)
174 = 126 (groh-two-doh-six)
175 = 127 (groh-two-doh-seven)
176 = 128 (groh-two-doh-eight)
177 = 129 (groh-two-doh-nine)
178 = 12↊ (groh-two-doh-ten)
179 = 12↋ (groh-two-doh-elv)
180 = 130 (groh-three-doh)
192 = 140 (groh-four-doh)
204 = 150 (groh-five-doh)
216 = 160 (groh-six-doh)
228 = 170 (groh-seven-doh)
240 = 180 (groh-eight-doh)
252 = 190 (groh-nine-doh)
264 = 1↊0 (groh-ten-doh)
276 = 1↋0 (groh-elv-doh)
288 = 200 (two-groh)
300 = 210 (two-groh-doh)
312 = 220 (two-groh-two-doh)
324 = 230 (two-groh-three-doh)
336 = 240 (two-groh-four-doh)
348 = 250 (two-groh-five-doh)
360 = 260 (two-groh-six-doh)
372 = 270 (two-groh-seven-doh)
384 = 280 (two-groh-eight-doh)
396 = 290 (two-groh-nine-doh)
408 = 2↊0 (two-groh-ten-doh)
420 = 2↋0 (two-groh-elv-doh)
432 = 300 (three-groh)
576 = 400 (four-groh)
720 = 500 (five-groh)
864 = 600 (six-groh)
1008 = 700 (seven-groh)
1152 = 800 (eight-groh)
1296 = 900 (nine-groh)
1440 = ↊00 (ten-groh)
1584 = ↋00 (elv-groh)
1728 = 1000 (moh)
1729 = 1001 (moh-one)
1730 = 1002 (moh-two)
1731 = 1003 (moh-three)
1732 = 1004 (moh-four)
1733 = 1005 (moh-five)
1734 = 1006 (moh-six)
1735 = 1007 (moh-seven)
1736 = 1008 (moh-eight)
1737 = 1009 (moh-nine)
1738 = 100↊ (moh-ten)
1739 = 100↋ (moh-elv)
1740 = 1010 (moh-doh)
1752 = 1020 (moh-two-doh)
1764 = 1030 (moh-three-doh)
1776 = 1040 (moh-four-doh)
1788 = 1050 (moh-five-doh)
1800 = 1060 (moh-six-doh)
1812 = 1070 (moh-seven-doh)
1824 = 1080 (moh-eight-doh)
1836 = 1090 (moh-nine-doh)
1848 = 10↊0 (moh-ten-doh)
1860 = 10↋0 (moh-elv-doh)
1872 = 1100 (moh-groh)
1884 = 1110 (moh-groh-doh)
1896 = 1120 (moh-groh-two-doh)
1908 = 1130 (moh-groh-three-doh)
1920 = 1140 (moh-groh-four-doh)
1932 = 1150 (moh-groh-five-doh)
1944 = 1160 (moh-groh-six-doh)
1956 = 1170 (moh-groh-seven-doh)
1968 = 1180 (moh-groh-eight-doh)
1980 = 1190 (moh-groh-nine-doh)
1981 = 1191 (moh-groh-nine-doh-one)
1982 = 1192 (moh-groh-nine-doh-two)
1983 = 1193 (moh-groh-nine-doh-three)
1984 = 1194 (moh-groh-nine-doh-four)
1985 = 1195 (moh-groh-nine-doh-five)
1986 = 1196 (moh-groh-nine-doh-six)
1987 = 1197 (moh-groh-nine-doh-seven)
1988 = 1198 (moh-groh-nine-doh-eight)
1989 = 1199 (moh-groh-nine-doh-nine)
1990 = 119↊ (moh-groh-nine-doh-ten)
1991 = 119↋ (moh-groh-nine-doh-elv)
1992 = 11↊0 (moh-groh-ten-doh)
1993 = 11↊1 (moh-groh-ten-doh-one)
1994 = 11↊2 (moh-groh-ten-doh-two)
1995 = 11↊3 (moh-groh-ten-doh-three)
1996 = 11↊4 (moh-groh-ten-doh-four)
1997 = 11↊5 (moh-groh-ten-doh-five)
1998 = 11↊6 (moh-groh-ten-doh-six)
1999 = 11↊7 (moh-groh-ten-doh-seven)
2000 = 11↊8 (moh-groh-ten-doh-eight)
2001 = 11↊9 (moh-groh-ten-doh-nine)
2002 = 11↊↊ (moh-groh-ten-doh-ten)
2003 = 11↊↋ (moh-groh-ten-doh-elv)
2004 = 11↋0 (moh-groh-elv-doh)
2005 = 11↋1 (moh-groh-elv-doh-one)
2006 = 11↋2 (moh-groh-elv-doh-two)
2007 = 11↋3 (moh-groh-elv-doh-three)
2008 = 11↋4 (moh-groh-elv-doh-four)
2009 = 11↋5 (moh-groh-elv-doh-five)
2010 = 11↋6 (moh-groh-elv-doh-six)
2011 = 11↋7 (moh-groh-elv-doh-seven)
2012 = 11↋8 (moh-groh-elv-doh-eight)
2013 = 11↋9 (moh-groh-elv-doh-nine)
2014 = 11↋↊ (moh-groh-elv-doh-ten)
2015 = 11↋↋ (moh-groh-elv-doh-elv)
2016 = 1200 (moh-two-groh)
2017 = 1201 (moh-two-groh-one)
2018 = 1202 (moh-two-groh-two)
Interestingly enough, the Decimal year of 2016, the same 2016 that's two years ago, was the start of a new Duodecimal century, or the end of one if you take into account there being no year 0, the 12th Duodecimal Century would be from the Decimal years of 1873-2016, as they are the Duodecimal years of 1101-1200.
By the way, using the Duodecimal system, what's your age and birthyear?
I'd be 18 going on 19, and born December of 11↊5 (since in Base-Ten I'm 20 going on 21 and born December 1997). What about you?
Anyways, one major benefit of the Duodecimal system over the Decimal system is that unlike ten, twelve has four factors instead of just two; 2, 3, 4, and 6. This makes dividing it up way easier, and it also makes counting easier as well.
Counting by 3's in the Decimal system = 3, 6, 9, 12, 15, 18, 21, 24, 27, 30
Counting by 3's in the Duodecimal system = 3, 6, 9, 10, 13, 16, 19, 20, 23, 26, 29, 30
Counting by 4's in the Decimal system = 4, 8, 12, 16, 20, 24, 28, 32, 26, 40
Counting by 4's in the Duodecimal system = 4, 8, 10, 14, 18, 20, 24, 28, 30, 34, 38, 40
Counting by 6's in the Decimal system = 6, 12, 18, 24, 30, 36, 42, 48, 54, 60
Counting by 6's in the Duodecimal system = 6, 10, 16, 20, 26, 30, 36, 40, 46, 50, 56, 60
See how much cleaner and easier it is?
Splitting age groups would also be easier this way;
The single digit years of 0-↋ (0-11 in Base-Ten) would be one's childhood; with 0-5 being their early childhood (0-2 being infant/toddler, 3-5 being their "preschool" or "play age" years), and 6-↋ being their latter childhood (9-↋ would be "Pre-Adolescence").
10-1↋ (12-23 in Base-Ten) would be one's Adolescence or Youth period, with 10-15 (12-17) being the half when they're not of legal age, and 16-1↋ (18-23) being the half when they are of legal age. 20 (24) would roughly be the start of biological post-adolescent adulthood (biological, not legal).
As for counting, instead of counting individual fingers, you'd use your thumb to count the three phalanges on the other four fingers.
As for telling time, instead of 24 hours, 60 minutes, and 60 seconds, there'd instead be 24 hours, 12 minutes, and 300 seconds, or in duodecimal translation, 20 hours, 10 minutes, 260 seconds.
So, translated from decimal to duodecimal;
0:00 = 0:0:000
0:01 = 0:0:060
0:02 = 0:0:100
0:03 = 0:0:160
0:04 = 0:0:200
0:04:59 = 0:0:259
0:05 = 0:1:000
0:10 = 0:2:000
0:15 = 0:3:000
0:20 = 0:4:000
0:25 = 0:5:000
0:30 = 0:6:000
0:35 = 0:7:000
0:40 = 0:8:000
0:45 = 0:9:000
0:50 = 0:↊:000
0:55 = 0:↋:000
1:00 = 1:0:000
2:00 = 2:0:000
3:00 = 3:0:000
4:00 = 4:0:000
5:00 = 5:0:000
6:00 = 6:0:000
7:00 = 7:0:000
8:00 = 8:0:000
9:00 = 9:0:000
10:00 = ↊:0:000
11:00 = ↋:0:000
12:00 = 10:0:000
13:00 = 11:0:000
14:00 = 12:0:000
15:00 = 13:0:000
16:00 = 14:0:000
17:00 = 15:0:000
18:00 = 16:0:000
19:00 = 17:0:000
20:00 = 18:0:000
21:00 = 19:0:000
22:00 = 1↊:0:000
23:00 = 1↋:0:000
Finally, some gallery;
Finally, I know the duodecimal system isn't going to replace the decimal system anytime soon, since we're too used to the decimal system, and would get a headache trying to get used to a new numeral system.
But had we been used to the duodecimal system since toddlerhood, our lives regarding math would've likely been a lot easier.
Just imagine, had you been used to Base-Twelve instead of Base-Ten...
For those of you that don't know, Base-Twelve, or Duodecimal, refers to a numeric system where the Radix is twelve, where there are twelve unique digits to represent numbers in a positional numbering system.
The system we use currently is Base-Ten, or Decimal, where there are ten unique digits to represent numbers in a positional numbering system; 0, 1, 2, 3, 4, 5, 6, 7, 8, 9.
This is the system we've known so well since toddler hood, is used globally, and it all stems from the fact that we have ten fingers, 5 on each hand.
The problem with the Decimal system however is that there are only two non-trivial factors of ten; 2 and 5. Try to split it up any other way, and you're gonna end up with fractional notations.
Divide ten by 4, and you're gonna get 2.5, and ten divided by 3 is 3.3333→, where the 3's in the decimal place go on forever.
As stated before, in the Base-Twelve, or Duodecimal, system, there are twelve unique digits to represent numbers in a positional numbering system; 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, ↊, ↋.
"↊" and "↋" are the Base-Twelve counterparts to what we know as "10" and "11" in the Base-Ten system.
As for how they're pronounced, you could keep the "ten" and "eleven" spelling, but most duodecimal-fanatics instead use "dek" and "elv". I personally prefer "ten" for ↊ and "elv" for ↋
After ↋ comes 10, which is the Base-Twelve equivalent to Base-Ten's 12. It's pronounced "doh" (yeah yeah, cue the Homer GIFs), which is short for "dozen".
11 (13 in Base-Ten) is pronounced "doh-one", 12 (14 in Base-Ten) is pronounced "doh-two", 13 (15 in Base-Ten) is pronounced "doh-three", and so on all the way up to 1↋ (23 in Base-Ten), pronounced "doh-elv".
After 1↋ comes 20 (24 in Base-Ten), which is pronounced "two-doh". After that, you have 21 (25 in Base-Ten), which is pronounced "two-doh-one", then 22 (26 in Base-Ten), which is pronounced "two-doh-two", all the way up to 2↋ (35 in Base-Ten), which is "two-doh-elv".
Here's a guide, converting Base-Ten numbers to Base-Twelve numbers;
0 = 0 (zero)
1 = 1 (one)
2 = 2 (two)
3 = 3 (three)
4 = 4 (four)
5 = 5 (five)
6 = 6 (six)
7 = 7 (seven)
8 = 8 (eight)
9 = 9 (nine)
10 = ↊ (ten)
11 = ↋ (elv)
12 = 10 (doh)
13 = 11 (doh-one)
14 = 12 (doh-two)
15 = 13 (doh-three)
16 = 14 (doh-four)
17 = 15 (doh-five)
18 = 16 (doh-six)
19 = 17 (doh-seven)
20 = 18 (doh-eight)
21 = 19 (doh-nine)
22 = 1↊ (doh-ten)
23 = 1↋ (doh-elv)
24 = 20 (two-doh)
25 = 21 (two-doh-one)
26 = 22 (two-doh-two)
27 = 23 (two-doh-three)
28 = 24 (two-doh-four)
29 = 25 (two-doh-five)
30 = 26 (two-doh-six)
31 = 27 (two-doh-seven)
32 = 28 (two-doh-eight)
33 = 29 (two-doh-nine)
34 = 2↊ (two-doh-ten)
35 = 2↋ (two-doh-elv)
36 = 30 (three-doh)
48 = 40 (four-doh)
60 = 50 (five-doh)
72 = 60 (six-doh)
84 = 70 (seven-doh)
96 = 80 (eight-doh)
108 = 90 (nine-doh)
120 = ↊0 (ten-doh)
132 = ↋0 (elv-doh)
144 = 100 (groh)
145 = 101 (groh-one)
146 = 102 (groh-two)
147 = 103 (groh-three)
148 = 104 (groh-four)
149 = 105 (groh-five)
150 = 106 (groh-six)
151 = 107 (groh-seven)
152 = 108 (groh-eight)
153 = 109 (groh-nine)
154 = 10↊ (groh-ten)
155 = 10↋ (groh-elv)
156 = 110 (groh-doh)
157 = 111 (groh-doh-one)
158 = 112 (groh-doh-two)
159 = 113 (groh-doh-three)
160 = 114 (groh-doh-four)
161 = 115 (groh-doh-five)
162 = 116 (groh-doh-six)
163 = 117 (groh-doh-seven)
164 = 118 (groh-doh-eight)
165 = 119 (groh-doh-nine)
166 = 11↊ (groh-doh-ten)
167 = 11↋ (groh-doh-elv)
168 = 120 (groh-two-doh)
169 = 121 (groh-two-doh-one)
170 = 122 (groh-two-doh-two)
171 = 123 (groh-two-doh-three)
172 = 124 (groh-two-doh-four)
173 = 125 (groh-two-doh-five)
174 = 126 (groh-two-doh-six)
175 = 127 (groh-two-doh-seven)
176 = 128 (groh-two-doh-eight)
177 = 129 (groh-two-doh-nine)
178 = 12↊ (groh-two-doh-ten)
179 = 12↋ (groh-two-doh-elv)
180 = 130 (groh-three-doh)
192 = 140 (groh-four-doh)
204 = 150 (groh-five-doh)
216 = 160 (groh-six-doh)
228 = 170 (groh-seven-doh)
240 = 180 (groh-eight-doh)
252 = 190 (groh-nine-doh)
264 = 1↊0 (groh-ten-doh)
276 = 1↋0 (groh-elv-doh)
288 = 200 (two-groh)
300 = 210 (two-groh-doh)
312 = 220 (two-groh-two-doh)
324 = 230 (two-groh-three-doh)
336 = 240 (two-groh-four-doh)
348 = 250 (two-groh-five-doh)
360 = 260 (two-groh-six-doh)
372 = 270 (two-groh-seven-doh)
384 = 280 (two-groh-eight-doh)
396 = 290 (two-groh-nine-doh)
408 = 2↊0 (two-groh-ten-doh)
420 = 2↋0 (two-groh-elv-doh)
432 = 300 (three-groh)
576 = 400 (four-groh)
720 = 500 (five-groh)
864 = 600 (six-groh)
1008 = 700 (seven-groh)
1152 = 800 (eight-groh)
1296 = 900 (nine-groh)
1440 = ↊00 (ten-groh)
1584 = ↋00 (elv-groh)
1728 = 1000 (moh)
1729 = 1001 (moh-one)
1730 = 1002 (moh-two)
1731 = 1003 (moh-three)
1732 = 1004 (moh-four)
1733 = 1005 (moh-five)
1734 = 1006 (moh-six)
1735 = 1007 (moh-seven)
1736 = 1008 (moh-eight)
1737 = 1009 (moh-nine)
1738 = 100↊ (moh-ten)
1739 = 100↋ (moh-elv)
1740 = 1010 (moh-doh)
1752 = 1020 (moh-two-doh)
1764 = 1030 (moh-three-doh)
1776 = 1040 (moh-four-doh)
1788 = 1050 (moh-five-doh)
1800 = 1060 (moh-six-doh)
1812 = 1070 (moh-seven-doh)
1824 = 1080 (moh-eight-doh)
1836 = 1090 (moh-nine-doh)
1848 = 10↊0 (moh-ten-doh)
1860 = 10↋0 (moh-elv-doh)
1872 = 1100 (moh-groh)
1884 = 1110 (moh-groh-doh)
1896 = 1120 (moh-groh-two-doh)
1908 = 1130 (moh-groh-three-doh)
1920 = 1140 (moh-groh-four-doh)
1932 = 1150 (moh-groh-five-doh)
1944 = 1160 (moh-groh-six-doh)
1956 = 1170 (moh-groh-seven-doh)
1968 = 1180 (moh-groh-eight-doh)
1980 = 1190 (moh-groh-nine-doh)
1981 = 1191 (moh-groh-nine-doh-one)
1982 = 1192 (moh-groh-nine-doh-two)
1983 = 1193 (moh-groh-nine-doh-three)
1984 = 1194 (moh-groh-nine-doh-four)
1985 = 1195 (moh-groh-nine-doh-five)
1986 = 1196 (moh-groh-nine-doh-six)
1987 = 1197 (moh-groh-nine-doh-seven)
1988 = 1198 (moh-groh-nine-doh-eight)
1989 = 1199 (moh-groh-nine-doh-nine)
1990 = 119↊ (moh-groh-nine-doh-ten)
1991 = 119↋ (moh-groh-nine-doh-elv)
1992 = 11↊0 (moh-groh-ten-doh)
1993 = 11↊1 (moh-groh-ten-doh-one)
1994 = 11↊2 (moh-groh-ten-doh-two)
1995 = 11↊3 (moh-groh-ten-doh-three)
1996 = 11↊4 (moh-groh-ten-doh-four)
1997 = 11↊5 (moh-groh-ten-doh-five)
1998 = 11↊6 (moh-groh-ten-doh-six)
1999 = 11↊7 (moh-groh-ten-doh-seven)
2000 = 11↊8 (moh-groh-ten-doh-eight)
2001 = 11↊9 (moh-groh-ten-doh-nine)
2002 = 11↊↊ (moh-groh-ten-doh-ten)
2003 = 11↊↋ (moh-groh-ten-doh-elv)
2004 = 11↋0 (moh-groh-elv-doh)
2005 = 11↋1 (moh-groh-elv-doh-one)
2006 = 11↋2 (moh-groh-elv-doh-two)
2007 = 11↋3 (moh-groh-elv-doh-three)
2008 = 11↋4 (moh-groh-elv-doh-four)
2009 = 11↋5 (moh-groh-elv-doh-five)
2010 = 11↋6 (moh-groh-elv-doh-six)
2011 = 11↋7 (moh-groh-elv-doh-seven)
2012 = 11↋8 (moh-groh-elv-doh-eight)
2013 = 11↋9 (moh-groh-elv-doh-nine)
2014 = 11↋↊ (moh-groh-elv-doh-ten)
2015 = 11↋↋ (moh-groh-elv-doh-elv)
2016 = 1200 (moh-two-groh)
2017 = 1201 (moh-two-groh-one)
2018 = 1202 (moh-two-groh-two)
Interestingly enough, the Decimal year of 2016, the same 2016 that's two years ago, was the start of a new Duodecimal century, or the end of one if you take into account there being no year 0, the 12th Duodecimal Century would be from the Decimal years of 1873-2016, as they are the Duodecimal years of 1101-1200.
By the way, using the Duodecimal system, what's your age and birthyear?
I'd be 18 going on 19, and born December of 11↊5 (since in Base-Ten I'm 20 going on 21 and born December 1997). What about you?
Anyways, one major benefit of the Duodecimal system over the Decimal system is that unlike ten, twelve has four factors instead of just two; 2, 3, 4, and 6. This makes dividing it up way easier, and it also makes counting easier as well.
Counting by 3's in the Decimal system = 3, 6, 9, 12, 15, 18, 21, 24, 27, 30
Counting by 3's in the Duodecimal system = 3, 6, 9, 10, 13, 16, 19, 20, 23, 26, 29, 30
Counting by 4's in the Decimal system = 4, 8, 12, 16, 20, 24, 28, 32, 26, 40
Counting by 4's in the Duodecimal system = 4, 8, 10, 14, 18, 20, 24, 28, 30, 34, 38, 40
Counting by 6's in the Decimal system = 6, 12, 18, 24, 30, 36, 42, 48, 54, 60
Counting by 6's in the Duodecimal system = 6, 10, 16, 20, 26, 30, 36, 40, 46, 50, 56, 60
See how much cleaner and easier it is?
Splitting age groups would also be easier this way;
The single digit years of 0-↋ (0-11 in Base-Ten) would be one's childhood; with 0-5 being their early childhood (0-2 being infant/toddler, 3-5 being their "preschool" or "play age" years), and 6-↋ being their latter childhood (9-↋ would be "Pre-Adolescence").
10-1↋ (12-23 in Base-Ten) would be one's Adolescence or Youth period, with 10-15 (12-17) being the half when they're not of legal age, and 16-1↋ (18-23) being the half when they are of legal age. 20 (24) would roughly be the start of biological post-adolescent adulthood (biological, not legal).
As for counting, instead of counting individual fingers, you'd use your thumb to count the three phalanges on the other four fingers.
As for telling time, instead of 24 hours, 60 minutes, and 60 seconds, there'd instead be 24 hours, 12 minutes, and 300 seconds, or in duodecimal translation, 20 hours, 10 minutes, 260 seconds.
So, translated from decimal to duodecimal;
0:00 = 0:0:000
0:01 = 0:0:060
0:02 = 0:0:100
0:03 = 0:0:160
0:04 = 0:0:200
0:04:59 = 0:0:259
0:05 = 0:1:000
0:10 = 0:2:000
0:15 = 0:3:000
0:20 = 0:4:000
0:25 = 0:5:000
0:30 = 0:6:000
0:35 = 0:7:000
0:40 = 0:8:000
0:45 = 0:9:000
0:50 = 0:↊:000
0:55 = 0:↋:000
1:00 = 1:0:000
2:00 = 2:0:000
3:00 = 3:0:000
4:00 = 4:0:000
5:00 = 5:0:000
6:00 = 6:0:000
7:00 = 7:0:000
8:00 = 8:0:000
9:00 = 9:0:000
10:00 = ↊:0:000
11:00 = ↋:0:000
12:00 = 10:0:000
13:00 = 11:0:000
14:00 = 12:0:000
15:00 = 13:0:000
16:00 = 14:0:000
17:00 = 15:0:000
18:00 = 16:0:000
19:00 = 17:0:000
20:00 = 18:0:000
21:00 = 19:0:000
22:00 = 1↊:0:000
23:00 = 1↋:0:000
Finally, some gallery;
Finally, I know the duodecimal system isn't going to replace the decimal system anytime soon, since we're too used to the decimal system, and would get a headache trying to get used to a new numeral system.
But had we been used to the duodecimal system since toddlerhood, our lives regarding math would've likely been a lot easier.
Just imagine, had you been used to Base-Twelve instead of Base-Ten...
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