Resumen de Predator arithmetic

Paul Shutler

• Modern Hindu-Arabic numeration is the end result of a long period of evolution, and is clearly superior to any system that has gone before, but is it optimal? We compare it to a hypothetical base 5 system, which we dub Predator arithmetic, and judge which of the two systems is superior from a mathematics education point of view. We find that complex calculations such as long multiplication can be carried out more efficiently in base 5 than in base 10, and that base 5 is in fact close to being optimal in this regard. We also show that base 5 is small enough so that the intuitiveness of simple grouping and the efficiency of fully ciphered numerals can be combined effectively in a single notation, something which Hindu-Arabic numeration tries but fails to achieve. Furthermore, as a consequence of these notational advantages, we show that the basic operations of arithmetic, addition and subtraction, also borrowing and carrying (regrouping), are easier to teach and to learn in base 5 than in base 10. Finally we show that, even though a shift from base 10 to base 5 may not be a realistic possibility, there are many ways in which the teaching of elementary arithmetic could be improved significantly, along the lines of Predator arithmetic, and which could be implemented at little cost within our current Hindu-Arabic system.