Man vs. Machine! Can't We All Just Along?

“Ideas came with explosive immediacy, like an instant birth. Human thought is like a monstrous pendulum; it keeps swinging from one extreme to the other.”
--Eugene Field

“Mistakes are at the very base of human thought, feeding the structure like root nodules. If we were not provided with the knack of being wrong, we could never get anything useful done.”
--Lewis Thomas


Defays continued his discussion on Numbo and how it functions and raises some interesting points. He reviewed how Numbo relates to human thought, which is something that I have rarely seen stated in learning about specific computer programs. He made some claims, most of which I agree with wholeheartedly, about how Numbo resembles human performance.

He stated that, "Ideas are not systematically explored, and in fact are often abandoned before having been fully examined"(pp.150). This is true not just to solving math problems but to nearly every aspect of human life. It seems ideas in all fields are subject, such as, but not limited to, social & economic reform, music & movie reviews, and even something so simple as deciding what to have for dinner. Humans just aren't always systematic and often give up on ideas before considering them fully, two characteristics which I often consider flaws.

Defays continued with, "The combinations created are not always strongly goal-driven, so that unmotivated-appearing avenues are occasionally embarked upon"(pp.150). This relation to human thought processes seemed so apparently obvious to me. The first thing that came to mind was, 'Numbo daydreams too?' and as silly as that sounds, the analogy made sense to me and helped clarify how the temperature and the urgency systems in Numbo operated. It also made me consider that not all 'unmotivated-appearing avenues' are irrelevant and sometimes Numbo's and our wandering avenues can lead to solutions.

A third observation Defays made was that, "Solutions are often found that involve the chaining of several arithmetical operations in a seemingly logical way"(pp.151). While I didn't have many vivid analogies at hand when reading this, I couldn't deny its truth. In his detailing of Numbo's processing, Defays has shown this and I know humans do it too. Not just in math, of course, humans come to solutions of problems by way of linking different thoughts together, such as by using analogies. For example: analogy to better clarify a misunderstanding.

Although I do agree with these three similarities, I do not agree with his fourth, "Obvious solutions are found at once"(pp.150). Which is kind of funny because neither does he. He states earlier, on the same page, that due to the randomness of Numbo, "...it is sometimes possible to miss an obvious solution." And this argument, I believe, could have made a better comparison because occasionally humans do miss an obvious solution to a problem.

Overall, I give much credit to Defays' work on the Numbo system, I found it to be extremely interesting. I also greatly appreciate his discussion on how the program is similar and different to human thought. In the computer science courses I've taken for my cognitive science major it is not often discussed how the programs we use and write mirror, or don't mirror, human thought.