Theosophical Reduction is the process of taking the digits of a number and adding them together to produce a smaller number. For example, the number 12 would be reduced to 1+2=3. The number 98 would reduce to 9+8=17, which would then further reduce to 1+7=8.
In some systems, the reduction is repeated until a number 1 through 9 is reached, and in some the numbers 11, 22 and 33 are also not further reduced.
An interesting effect occurs when Theosophically reducing a number resulting from a linear valuation system and the number of its AIK BEKAR variant for the same word or phrase; if you ignore the 11, 22 and 33 restriction, they always reduce to the same value. For example:
SOLEMNUS English-26: S O L E M N U S 19 + 15 + 12 + 5 + 13 + 14 + 21 + 19 = 118 Reduction: 1 + 1 + 8 = 10 Reduction: 1 + 0 = 1 English-9: S O L E M N U S 1 + 6 + 3 + 5 + 4 + 5 + 3 + 1 = 28 Reduction: 2 + 8 = 10 Reduction: 1 + 0 = 1
At first glance this seems as though the AIK BEKAR system operates in base 9, and so this shouldn't work out this way for a base 10 system of arithmetic, but what makes this work is that AIK BEKAR has no zero value -- and neither does the linear system, as it starts with the number 1 also. Hence, the AIK BEKAR variant is base 10 without the zeros, and thus the digits valuate the same under the linear system and under the AIK BEKAR variant.
Not that this detail is important, I just found it interesting.