The Beauty of Math in TV Shows

In the beginning of the third chapter, Hofstadter remembers the involvement of a Belgian colleague of his during the year 1986, Daniel Defays. He was part of the NARG but at the same time wrote a program called Numbo which would solve the sort of mental math task involved in crypto problems. The idea is to have a series of smaller integers (bricks) and one bigger target number and having to combine an arbitrary number of the bricks with the help of addition, subtraction or multiplication so they would equal the target integer.

The task is very similar to the crypto problem but the (human) computer is forced to partially use different strategies, since the number may be quite higher as in ordinary crypto problems. One of these strategies is rounding, so approximating a value close to the target and trying to go from there. Another is using analogies of the kind that 20*30=600 is similar to 2*3=6 which might be very obvious to the average mathematician among us but will not strike an infant immediately, not to speak of modeling such prior general knowledge to computer programs.

But it was exactly this kind of shortcuts we use in everyday situations that inspired Hofstadter and Defays in optimizing their programs accordingly. I must admit that these strategies, as subconscious as they might seem, are very vital to the speed and accuracy of our thought processes not necessarily only to solving math problems or figuring out words. It is very neat to think, somebody would realize such mechanisms in a real problem solving problem (even though, we are of course let alone in the dark about how this realization came about).