AXIOM 2: NUMERACY

permutations and combinations

 9th march 2010

love / life                               inanimacy

1 x 1                                          1 + 1

and                                            and

1 ¸ Ö                                                     1 - ½

 october 2009

permutations                                                                          combinations

(note what happens when you do a permutation of the number 25)

there are two permutations of 1 and 2                                             there is one combination of 1 and 2

1/2 and 2/1                                                                                   1/2

1 x 2 = 2                                                                            1 + 1 = 2 - 1 = 1

there are six permutations of 1, 2 and 3                                         there are three combinations of 1, 2, and 3

1/2/3, 1/3/2, 2/1/3, 2/3/1, 3/1/2 and 3/2/1                                                        1/2, 1/3 and 2/3

1 x 2 x 3 = 6                                                                          1 + 2 + 3 = 6 - 3 = 3

there are twenty four permutations of 1, 2, 3 and 4                                    there are six combinations of 1, 2, 3, and 4

1/2/3/4, 1/2/4/3, 1/3/2/4, 1/3/4/2, 1/4/3/2, 1/4/2/1,                                         1/2, 1/3, 1/4, 2/3, 2/4, and 3/4

2/1/3/4, 2/1/4/3, 2/3/1/4, 2/3/4/1, 2/4/1/2, 2/4/1/3,                                             1 + 2 + 3 + 4 = 10 - 4 = 6

3/1/2/4, 3/1/4/2, 3/2/1/4, 3/2/4/2, 3/4/1/2, 3/4/2/1,                              there are ten combinations of 1, 2, 3, 4, and 5

4/1/2/3, 4/1/3/2, 4/2/1/3, 4/2/3/1, 4/3/1/2 and 4/3/2/1                        1/2, 1/3, 1/4, 1/5, 2/3, 2/4, 2/5, 3/4, 3/5, and 4/5

1 x 2 x 3 x 4 = 24                                                                   1 + 2 + 3 + 4 + 5 = 15 - 5 = 10*

*(10 minus half equals 5 and 15 minus half equals 7.5)

1 x 2 x 3 x 4 x 5 = 120

1 x 2 x 3 x 4 x 5 x 6 = 720

1 x 2 x 3 x 4 x 5 x 6 x 7 = 5040

1 x 2 x 3 x 4 x 5 x 6 x 7 x 8 = 40320

1 x 2 x 3 x 4 x 5 x 6 x 7 x 8 x 9 = 362880

1 x 2 x 3 x 4 x 5 x 6 x 7 x 8 x 9 x 10 = 3628800

1 x 2 x 3 x 4 x 5 x 6 x 7 x 8 x 9 x 10 x 11 = 39916800

1 x 2 x 3 x 4 x 5 x 6 x 7 x 8 x 9 x 10 x 11 x 12 = 479001600

1 x 2 x 3 x 4 x 5 x 6 x 7 x 8 x 9 x 10 x 11 x 12 x 13 = 6227020800

1 x 2 x 3 x 4 x 5 x 6 x 7 x 8 x 9 x 10 x 11 x 12 x 13 x 14 = 87178291200

1 x 2 x 3 x 4 x 5 x 6 x 7 x 8 x 9 x 10 x 11 x 12 x 13 x 14 x 15 = 1307674368000

1 x 2 x 3 x 4 x 5 x 6 x 7 x 8 x 9 x 10 x 11 x 12 x 13 x 14 x 15 x 16 = 20922789888000

1 x 2 x 3 x 4 x 5 x 6 x 7 x 8 x 9 x 10 x 11 x 12 x 13 x 14 x 15 x 16 x 17 = 355687428096000

1 x 2 x 3 x 4 x 5 x 6 x 7 x 8 x 9 x 10 x 11 x 12 x 13 x 14 x 15 x 16 x 17 x 18 = 6402373705728000

1 x 2 x 3 x 4 x 5 x 6 x 7 x 8 x 9 x 10 x 11 x 12 x 13 x 14 x 15 x 16 x 17 x 18 x 19 = 121645100408832000

1 x 2 x 3 x 4 x 5 x 6 x 7 x 8 x 9 x 10 x 11 x 12 x 13 x 14 x 15 x 16 x 17 x 18 x 19 x 20 =  2432902008176640000 (20 numbers)

1 x 2 x 3 x 4 x 5 x 6 x 7 x 8 x 9 x 10 x 11 x 12 x 13 x 14 x 15 x 16 x 17 x 18 x 19 x 20 x 21 = 51090942171709440000 (21 numbers)

1 x 2 x 3 x 4 x 5 x 6 x 7 x 8 x 9 x 10 x 11 x 12 x 13 x 14 x 15 x 16 x 17 x 18 x 19 x 20 x 21 x 22 = 1124000727777607680000 (22 numbers)

1 x 2 x 3 x 4 x 5 x 6 x 7 x 8 x 9 x 10 x 11 x 12 x 13 x 14 x 15 x 16 x 17 x 18 x 19 x 20 x 21 x 22 x 23 = 25852016738884976640000 (23 numbers)

1 x 2 x 3 x 4 x 5 x 6 x 7 x 8 x 9 x 10 x 11 x 12 x 13 x 14 x 15 x 16 x 17 x 18 x 19 x 20 x 21 x 22 x 23 x 24 = 594596384994354462720000 (24 numbers)

1 x 2 x 3 x 4 x 5 x 6 x 7 x 8 x 9 x 10 x 11 x 12 x 13 x 14 x 15 x 16 x 17 x 18 x 19 x 20 x 21 x 22 x 23 x 24 x 25 = 14864909624858861568000000 (26 numbers)

1 x 2 x 3 x 4 x 5 x 6 x 7 x 8 x 9 x 10 x 11 x 12 x 13 x 14 x 15 x 16 x 17 x 18 x 19 x 20 x 21 x 22 x 23 x 24 x 25 x 26 = 386487650246330400768000000 (27 numbers)

now imagine what happens when you permute 1 ^100 000 000 024 (the, current, number of beings in heaven)

if you keep on doing a permutation of large numbers (bigger than thousands) eventually the answer for each new permutation is more than twice the previous number even though you only add one more digit to the new number to be permuted. and when you get to very large numbers (millions) there isn't a computer in the world that can do the computation. the numbers become transcendental (beyond the range of human experience). that's the reality that love/life has carved out for itself

now try to imagine how many different times you could play all in tag and reverse tag if everyone has a turn at being "it"

it and we go on and on

the heavenly state is endless fun