the point i just can't seem to get across is the people who you are talking about, the terrified ones, are exactly the people who benefit
most from using base12 over base10.
Steven Hawking? he benefits the least as those types of people are doing calculations beyond what's even graspable, even as a concept, to the majority of people.. their formulas and calculations and whatnot are going to be crazy no matter what base they're using.. the base is nearly irrelevant after certain levels of math and i'm most definitely not saying anything anywhere near close to "we should switch to base 12 so scientists can work more easily".. it's not for them, it's for us.
(like- realize someone who is very well versed in mathematics can approach a problem with more of a mindset of "this formula will work well in base8.. so i'm going to use base8".. if society switched to base 12, complex calculations remain the exact same.. and they'll remain in the base they were calculated in or the one that are cleanest to communicate in.. you and i using base10 is holding back complex mathematics about 0%.. for
Will Hunting? he gains nothing and he loses nothing if we switch to base12 counting
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our four basic math operations needed in modern life are:
addition, subtraction, multiplication, and division.
of these, three of them will be unaffected in base 10 vs base 12:
addition, subtraction, and multiplication
none of these can change whole numbers (or integers) into decimal/fractions..
4 + 15 = 19
143 - 21 = 122
6 x 7 = 42
you will never end up with a fraction/decimal, or a scary number, with any of these operations unless you're faced with decimals before doing the calculation.
(in base 12, the same is true but that's not really the point)
it's
Division -- that's the weird one.. that's the confusing one.
it can turn simple looking numbers such as 5 & 3 into :
5 ÷ 3 = 1.666666666666_
???
what the heck is that : )
with base10, you are very likely to encounter a scenario while dividing which doesn't have a clean or simple solution even when the input numbers are seemingly very simple and common.
you can only divide Ten by 2 numbers cleanly... or- you only have a 1 out of 5 chance to get clean division using base 10 when using whole numbers to begin with.. further, only one of these 2 numbers is a
very common number (#2).. the other one is number 5..
this is what happens when you do division in base 10:
10 ÷ 1 = 10
10 ÷ 2 = 5
10 ÷ 3 = 3.333_
10 ÷ 4 = 2.5
10 ÷ 5 = 2
10 ÷ 6 = 1.666_
10 ÷ 7 = 1.428
10 ÷ 8 = 1.25
10 ÷ 9 = 1.1111_
as you can see, there are only 2 numbers that work well and give clean results.. 2 & 5..
4 is ok, it's a little more confusing since it brings a fraction into play but it's just a single digit decimal so still not to bad.. likewise, 8 isn't really too bad either.
7? that starts getting into scary zone.. it's a repeating decimal but still resolves ok if only going out 3 decimals.. now, #3, 6, and 9 are just horrible.. they are repeating decimals (as in, even if you understand mathematics, a repeating decimal is bad since you can never arrive at an exact answer with it..).. but not only that, they are repeating instantly.. the very first decimal point leaves you with an estimated value instead of an actual true number)
so, out of the 9 numbers, only 2 work well... of the most common numbers (1-4), only #2 works great, one of them is o.k, and one is horrible.
the rest? pretty much crap.
this is our current counting situation.. this is our agreed upon system and the one that's been taught for a few thousand years to most people.
if the system were instead base12, it would look like this:
10 ÷ 1 = 10
10 ÷ 2 = 6
10 ÷ 3 = 4
10 ÷ 4 = 3
10 ÷ 5 = 2.497
10 ÷ 6 = 2
10 ÷ 7 = 1.714
10 ÷ 8 = 1.6
10 ÷ 9 = 1.4
ALL of the most common numbers resolve very cleanly..
there are NO immediate repeating decimals.
#8 is better as it now resolves at one decimal.
#9 is waaayy better
#6 is waaayy way better
#7 is equally bad and only #5 takes a hit in base12 vs base10.
but most importantly, #4 now remains a whole number..
and finally #3.. the most improved of them all.
in this example, only 2 of the numbers
are problematic whereas in base10, only 3 of the numbers
aren't causing any problems.
further yet, the numbers 1-4 are our most used numbers.. percentage wise, most everyday calculations are going to be using these numbers in them.. all 4 of them work sweet here.
and these same types of results/comparison will happen when using all the other numbers beyond 10..
in decimal, odds are you're going to end up with a difficult number when dividing easy numbers.. in duodecimal, odds are you're going to end up with an easy number when dividing easy numbers.
likewise, odds go up that you'll end up with an easy number when starting with difficult ones and that same applies to multiplication as well.. there are some other neat thing that happen with multiplication in base12 but for now, i just want to point out the most advantageous.. that being Division..
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but to tie back into the thread regarding units and whatnot... all we're doing with a unit (such as a meter.. or an inch... or the number Ten (ie- one unit in base10)) is dividing it up into smaller pieces or multiplying it into larger pieces.. or adding units together or subtracting from each other.. when a measuring unit is in base12, you will experience the exact same advantages as i've shown in the simple division examples above over a measuring unit that has been divided up into ten pieces.
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in the same exact way as i'm saying "let's consider switching to base12 instead of base10"..
you're saying "let's consider switching to base 13 instead of base12"
it's just that you're saying it in a way that you understand so you're not even realizing you're saying it (point being, switching between bases isn't some far out concept.. we do it all the time.. every single day.
it's just the way i'm talking about it that makes it seem foreign and scary.. but for real, you switch between base10, base12, base60, & probably base8 every day.. sometimes within the same thought or sentence.. without even realizing it.. it's in the background and the switching is fluid and simple.
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anyway, that's not my point in quoting you here
base13 is bad news.. especially for a calendar.
you would have no 1/2 years.. no quarters (as in fiscal quarters.. school semesters.. etc).. no bi monthly events (well, you could still do that.. they'd just fall on odd months one year then even the next)..
13 is a prime number... no other numbers will divide into it other than 1 and itself.. and as i've tried to point out earlier, the more numbers that can divide cleanly into a base then the simpler daily math becomes..
but yeah, 13 months is quite possibly the worst way to divide up a year.. it's entirely unusable (i'm exaggerating there) or- everything you try to do with that number will end up something funky.