reduction
There is a technique in numerology known as reduction. It is employed when a mathematical operation—usually to find the sum of related numerical values—results in a value greater than
. The numerologist adds up the digits of the result; if their sum is greater than
, the digits of this sum are then added together. This is repeated until a number between
and
is obtained.
In truth this operation is not much different, mathematically speaking, from a method for finding the remainder when the original value is divided by
. If we consider the value to have divided evenly when it leaves a remainder of
rather than
, the two are exactly the same.
We can see this if we take any decimal number with a length of
digits,
, and subtract the sum of its digits,
.


is a multiple of
. The difference between a number and the sum of its digits will therefore be a multiple of
.
If we divide both sides of the above equation by
, the remainder on the right side will prove to be
. The remainder when the original value is divided by
is therefore equal to the remainder when the sum of its digits is divided by
.
From this we can see that the sum of the digits of the sum of the digits, when divided by
, will also leave a remainder equal to that left over when the original value is divided by
. So we can conclude that the number obtained by the reduction technique is equal to the remainder left over when the original value is divided by
(with the proviso that remainders of
and
are considered equivalent in numerological reduction.)
This approach is valid generally for numeral systems other than base–
. Reduction in a base–
system can be accomplished by finding the remainder of the original value divided by
, with
and
being equivalent results.
When we look to the binary world, however, something interesting happens. Reduction in a binary system consists in finding the remainder when a value is divided by
, and results of
and
would be considered equivalent. Since there are no numbers that cannot be divided evenly, all binary numbers end up reducing to
.
This suggests that binary numbers cannot distinguish between good fortune and ill fortune…meaning that luck has no bearing on hardware that operates on the binary system, such as CPUs and memory.
If we want reduction to produce at least two possible results we must turn our attention to the ternary numeral system, in which all numbers reduce to either
or
. One of these results would probably represent good fortune, while the other would point to ill fortune. To create a computer that operates on the ternary system, one would doubtless need a digit (we may refer to it as a trit) to adjust values so the results of reduction always point to good fortune.
Shannon's theorem leads us to expect extremely high efficiency from ternary computers—contingent, of course, on the development of a suitably high speed switching element. I hereby claim priority with regards to the addition of an extra trit to stabilize operation against the effects of fortune. Heh, heh.
(This is an English version of an original Japanese article published August 21, 1999.)