To illustrate the point further, consider a task a program could not perform, involving creative, abstract thinking. Consider the “Betsy Ross Puzzle” [1]: “*Take a circular piece of paper and so fold it that with one cut of the scissors you can produce a perfect five-pointed star.*” To solve the puzzle, one has to fold the paper, a concept can be expressed using an algorithm, but it is challenging.

Fold the circular piece of paper in half along the dotted line shown in Fig. 1, and divide the upper half into five equal parts as indicated. Now fold the paper along the lines, and it will have the appearance shown in Fig. 2. If you want a star like Fig. 3, cut from A to B; if you wish one like Fig. 4, cut from A to C. Thus, the nearer you cut to the point at the bottom the longer will be the points of the star, and the farther off from the point that you cut the shorter will be the points of the star.

It will always be hard to achieve a sense of “creativeness” in machines. It is obviously possible to make them

[1] Amusements in Mathematics, puzzle 161.