Yakov Trachtenberg invented this mental computation system in order to remain sane in a Nazi concentration camp. He managed to survive, and got his invention published. The book is on sale on Amazon, and is even available as a Kindle Edition.
A week ago I began learning this computation method, starting with multiplication. As a general overview, the technique involves converting the problem of multiplication to a problem of addition. For example, the book begins describing a multiplication by 11, which is treated as multiplication by 10, followed by an addition of 1 copy of the number. Since multiplying by 10 is easy, the problem of multiplication is converted to a problem of addition of a number to itself, offset by one position. This works out to a rule prescribing to add adjacent digits in pairs to generate the answer.
In order to perform several additions mentally, a shortcut technique is taught: instead of naming all operations, only name intermediate accumulated results. For example, instead of mentally saying “nine plus three equals twelve”, say only “nine, twelve”. As an objectivist, I see that this is motivated by the crow epistemology.
In this fashion, the book gives algorithms to multiply by 11,12,6,7,5,9,8,4,3,2 in this order, and then proceeds to a completely different algorithm to multiply any number by any number. It then goes to division and even taking square roots.
Out of curiosity I wanted to know how the rules for each case were derived, but the derivation of the rules is not described in the book. I have, however, figured it out and posted the derivations on the method’s Wikipedia page.
If you play games like sudoku for mental exercise, I recommend this as a fun alternative.
