Something Like That

“And therefore education at the University mostly worked by the age-old method of putting a lot of young people in the vicinity of a lot of books and hoping that something would pass from one to the other, while the actual young people put themselves in the vicinity of inns and taverns for exactly the same reason.”
--Terry Pratchett


Daniel Defays' Numbo system is interesting but not quite as interesting, to me, as his rationalizing of why it operates the way it does. He claims that humans effortlessly use three types of knowledge to solve mathematical problems such as "rote small-number arithmetic (e.g., 6+1=7), ...knowledge of approximate sizes of numbers(e.g., multiplying 20 by 6 should bring us into the vicinity of 114), ...[and] procedural arithmetical knowledge (e.g., we can multiply 6 by 19)" (pp.135).

The third one mentioned somewhat surprised me because when doing math problems, such as crypto problems, I overlook that procedural knowledge I'm using because it is so basic. The second knowledge he mentions however, excited me in a nerdy way because it was something that I do often, not just in mathematics. "Just tell me how to get to NYC, we'll see if we can't find the hotel from there," is not an uncommon way to think about a problem for humans but I had never really considered it as a way to program a computer. This is just one way in which computer science has helped clarify my own ways of thinking. It amazes me how these simple thought patterns that humans use every day can turn into a year long programming project for a Belgian mathematician/psychologist.

Although Numbo is a wonderful work of art, it understandably still lacks many features which a human has when solving problems. One such feature is not having all learned processes always readily available to utilize when confronted with a problem. Another, which Defays specifically tried to correct, was that of association resulting in blindly-spreading activation leading to "uncontrolled, chaotic behaviors of the network"(pp.138). I'm not saying humans don't have some degree of control over their mind running through associations but instead that perhaps in some program, it should be embraced to better mimic humans. This happens all the time in humans, people losing focus or wandering off on some tangent. For example a typical student might be faced with a crypto problem, "Well, you can multiply 5 and 5, which is 25, which is like a quarter, four quarters in a dollar, that's equal to 100, I wonder how many licks does it really take to get to the center of a tootsie-pop, what was I doing?" Although something like this in a program would most likely never serve a purpose, other than to demonstrate association, I'm just saying that something error-like in a program doesn't always have to be rejected, especially when attempting to mimic human thought.