The other day I was explaining hominid evolution during the last 3 million years to a friend. Suppose we had two photos, one of me, and one of Fred Homo Erectus from three million years ago. Suppose further that we use a morphing program to morph Fred's photo into mine. But, suppose that we did this morphing process in 150,00 steps, because there are 150,000 generations between Fred and myself. It was a failure of her imagination to appreciate the vastness of evolutionary time.
Technological design is another area suffering from widespread failure of imagination.
However, it is capable of performing millions of such operations per second. Surely such a reformulation of the problem would be stupendously complicated, but if we could do so, then the computer could in fact solve it for us in a few seconds. Most people fail to imagine the celerity of computation, and so they dismiss the computer as hopelessly stupid, capable of only the most mindless exertions. It just so happened the location 1709 was the magic location that was always displayed by the KIM-1. I am not claiming that the human imagination is a wondrous entity, and if only we dismiss our pedestrian constraints, we could unleash the infinite power of the human imagination, blah, blah, blah.