Introduced to Numbo, I immediately connected the theme to the several Crypto assignments presented thusfar in COG 366. I think it only appropriate to assume we will be attempting similar artful implementations in solving Cryptos in the near future, however I am a little unsatisfied.
Daniel Defays, a professor in mathematics and psychology, contacted Douglas Hofstadter in 1985 with a research idea quite similar to Hofstadter’s Jumbo project. Sparking interest, the two of them worked together for a year starting in the good summer of 1986, resulting in the relative completion of the Numbo project. The goal of Numbo was to take a collection of bricks, numbers between 1 and 25, and a single target, a number between 1 and 150, and find a way to reach the goal by adding, subtracting of multiplying any of the bricks, at most, once.
Rather than brute forcing an answer as we had done with our Crypto problems, Defays and Hofstadter set out to solve Numbo problems similar to humans. Enters the concept of the permanent network (Pnet), where a basic or common knowledge of numbers and relations are stored. The Pnet stores declarative knowledge about the most commonly known numbers, such as 5 * 20 = 100, simple squares like 5 * 5 = 25 and watching for multiples of 10’s.
I find that the downfall of the permanent network is the more or less static design. We are assuming that every person has the same common knowledge. After an individual has versed themselves in solving number problems, they will become accustomed to recognizing patterns or rules that make solving the puzzles easy. I fit into the group of people can look at numbers like 841 and immediately recognize it as 29 squared and many number pattern recognition problems, but I used to struggle with easy Sudoku puzzles. After solving a few dozen puzzles, I’ve started to recognize the patterns in these puzzles, but I don’t believe that my ability to recognize number patterns has diminished by any means. I do believe that the Pnet must be dynamic, slowly changing as the software experiences more complex puzzles, but it does not make sense to see the Pnet ever destroy knowledge.
Reading through Defay’s introducting paragraph a second time, the phrase “Cognition equals Recognition” stands out. This makes for a clever shibboleth that claims that in order to be able to process a problem intelligently, we must first be able to recognize patterns in the problem based on some previous knowledge. The shortcoming of Numbo appears to be that there is a software and computational limitation on the size of their permanent network, which leaves a seemingly significant difference between Numbo and the human brain.