Unintelligent Number Biases

In this first section of chapter three in Douglas Hofstadter’s Fluid Concepts Daniel Defays discusses the workings of the program Numble. An adaption of the concept of a word jumble that chooses a random number goal (between 1 and 150) and attempts to computationally reach the target by picking random numbers (between 1 and 12) and using addition subtraction and multiplication to reach the number goal. While explaining the workings of the Numble program the author touches on a very interesting aspect of the mathematical solution process of people, which details that humans can see certain patterns and solutions immediately and other solutions elude us almost completely. He uses a good example in the text of a number goal of eighty seven and the set of numbers eight three nine ten and seven.

Target: 87
Bricks: 8 3 9 10 7

It seems almost immediate that most humans can recognize the solution of ((9 x 10) – 3) or ((8 x 10) + 7) mainly because we are accustomed to dealing with ten based numbers and for most people these are the easiest numbers to deal with in mathematical problems. However the solution (9 x 7) + (8 x 3) is rarely the first resolution to the problem detected by humans. The author makes another inference into why we prefer the ten based solution to this problem, because of our priori knowledge (familiar concepts and patterns pertaining to input) that eighty or ninety is close to the target number eighty seven. While testing a random crypto problem generator and solver program I noticed similar instances where I personally could immediately see a solution to the problem, usually one, zero, or ten based, yet the computer program picked a drastically different, usually shorter more quickly solvable solution. Having no bias or preference towards certain number patterns and priori, except what it was given, the computer program took a completely different path to solving the problem than I did. It is as if the lack of biases towards pattern recognition gave the program a different aspect of creativity and effectiveness. The section preceding chapter three, Hofstadter mentions that the randomness aspect of his Jumble construction program gives it a greater sense of intelligence and speed compared to a deductive reasoning or strictly pattern prediction method, as I put these theories to the test I am starting to clearly see the evidence and method to his madness.