2+2=11

2+2 = 11

I failed maths forever? Maybe, maybe not..

Every programmer worth the name knows at least that

8+7 = F

when one works with hexadecimal numbers, so there is also

F * F = E1

and

10 / 4 = 3
100/9=14
14/2=8

if you count on base twelve ( 10 = one dozen, it becomes clear).

Most people knows, nowadays, that you can represent numbers on a base of 2 digits:

0 and 1, the binary radix - the base of every computer's operation.
The latter detail is why what is otherwise a mere mathematical curiosity is so widely known.

In reality, humanity started using only one digit...

0
00
000
0000

the way of the abacus, but it is no very useful - not a compact representation for any number above 2, and to handle a multiplication is a mess

000 * 000 = 00000
0000*0000=0000000000
0000*000000= 0000000000000000

- better stick with, at least, a base of 2 digits

What most people ignore is that every choice of a base is somewhat arbitrary.

- we favor ten because we have ten digits in our hands... there are remnants of twenty-based systems, like in the way French names numbers between 80 and 99 quatre-vingt huit , and the time units are all 12 related.

The radices for representing a number, they are not bound to be even numbers... they can be odd.

Really, numbers do not care what is the radix you use to represent them.

Only, when they are odd numbers, even-ness ceases to appear as self-evident a property as we are used to see it.

If one uses a base of three digits, the first few numbers are

0
1
2
10
11
12
20
21
22
100
101
102
110
111
112
120
121
122
200

etc.

Now, you can spot the even-ness and oddnes of the numbers ?

No, t12, t102 and t122 - there - are all odd numbers.

- Note that these t12, t102 and t122 are also prime numbers, by the way, no matter how strong our brain screams that they must be divisible - they are 5, 11 and 17 in our familiar decimal base; also, we are used to call t21 seven, so he is not going to let anybody divide him either... by the way, decimal 111 is divisible by three, t111 goes by the name of 13 and is prime too.

Instead t11, t101 and t121 are all divisible by two.

When you use a base of 8 digits, every multiple of 7 can be recognized because the cascaded sum of its digits is 7... in base 16, multiples of F wind down to F, the same for 9 in base 10 and for B in base 12 - (if you use A and B as 11th and 12th digits), 5 in base 6 etc. ( you got the gist, I think).

Likewise, if you count in base 3, multiples of 2 can be recognized because they wind down to 2

121 => 1+2+1 => 11 => 1+1 => 2

Still simple, but not THAT simple - as saying "it ends on a multiple of 2" - any more.

As you can see, numbers don't really care that much about even-ness or oddness...

We like the distinction, being bilateral beings with two main sexes and all the rest, but that's our problem, not theirs.

But we really, really like it - I never saw an example with and odd number of digits as base.

It is one of the few certainties of life, if a number ends with a multiple of two, it is even... - alas, like most certainties in life, it is a form of collectively shared delusion.

By the way, when I see articles about using ternary state devices in the future computers, I know it is not going to happen.

It can be asked people to learn that binary 1101 => C hexadecimal, but you can't expect them to swallow that 12 is not divisible by 2...

Their mind will scream at the oddity.

- I hate when I have the flu. My mind gets stuck in the most horrible loops...

I let the reader the toil to verify that in base 15 (0-9, A-E) multiples of 3 ends with multiples of 3 (3,6,9,C), as well as multiples of 5 ends with multiples of five (0,5,A) .... Muahahahaha!!!!

If an alien species with trilateral symmetry and 15 fingers will ever contact ours, they could have a fixation in third-ness comparable to ours on even-oddness, and see divisibility by 2 as a secondary trait of some numbers.

Dedicated to my friends that already knew that two is just a number, like all the others, and not a pre-requisite for the magic in life.