plum blossom method and trouble with divisibles of 8

[ancestorseyes]

Was doing some calculations and it seems it is mathmaticly impossible to divide a number by eight and get a remainder of four. If this is so than it would exclude trigram Thunder from appearing in any primary hexagram. Does anyone have any insight into this?

 

[pocossin]

Was doing some calculations and it seems it is mathmaticly impossible to divide a number by eight and get a remainder of four. If this is so than it would exclude trigram Thunder from appearing in any primary hexagram. Does anyone have any insight into this?

84 divided by 8 has a remainder of 4.
12 divided by 8 has a remainder of 4.

 

[ancestorseyes]

that's strange, I get 5 for each of those
84 / 8 = 10.5 and 12 / 8 = 1.5
the remainder string for whole numbers increasing with a factor of 1 and starting with 0 is
.0 .125 .25 .375 .5 .625 .75 .875 .0 all increasing by a value of .125 and 8 / .125 = 64. so the trigram sequence would seem to skip Thunder and have two incidences of Lake. I am using the rule of when there is no remainder the remainder is considered as 8.

 

[pocossin]

Two kinds of arithmetic are involved here, decimal and integer. In Plum Blossom, only integer arithmetic is used. That is, you cannot conveniently use a calculator unless you have a MOD function.

12 / 8 = 1.5 The decimal remainder is not 5 but .5 (point five), which means 1/2. Using a calculator you can get the integer remainder by multiplying the divisor by the decimal remainder. 8 * .5 = 4. If you have 12 sticks and take away 8, you will have 4 remaining.

 

[ancestorseyes]

oh yes, of course, thank you for clarifying my understanding, 8 multiplied by that decimal remainder string will give you all the trigrams, thank you pocossin.

 

[pocossin]

I should add that a remainder of 0 is taken as 8.