Robin's Interesting Thoughts

My intuition says that creativity is network-based and rational thought is hierarchy-based. Note that a hierarchical tree is simply one form of network or graph.

Also, there is no fundamental difference between graphs and matrices. This could explain why natural language researchers have not been so excited about latent semantic analysis (LSA), which is simply one way of representing a graph in a format that the computer can operate on naturally. This graph represents certain relationships in “meaning” between words.

Finally, an LSA/graph approach may or may not be more appropriate than a hierarchy/grammar approach, depending on the specific problem to be solved. Graphs are less constrained and therefore seem most powerful, though also potentially need a lot more computational resources. Also, human brains appear to be general networks, not constrained to hierarchies, but that may or may not be important to know.

This Interesting Thought came when I was thinking about the research I did this past summer. I was working on the problem of automatically finding sentence boundaries in a string of text. The big issue was that in a string of hundreds of sentences, there are on the order of 2^100 ways to place the sentence boundaries — only one of which is correct!! In other words, placing boundaries exhibits exponential complexity.

Our solution to this problem was to take high-probability boundaries as given. Such placements might be incorrect, but usually they aren’t and we were willing to sacrifice this little bit of precision. Because then, we only had to consider multiple possibilities for the boundaries in-between these high-probability boundaries. In mathematical terms, if we split the text into 10 high-probability segments of approximately 10 sentences each, the number of possibilities is only 10 times 2^10: about 10,000 possibilities, easy for a computer to consider. This is FAR, FAR smaller than the original 2^100, which is so big it is essentially impossible to comprehend. 2^100 is approximately the number of words that would be produced if every human being who EVER lived produced an entirely new academic research library every SECOND of their life.

But the point is, it occurred to me that all of science might be framed as a process of isolating a few variables from the vast network of interconnected variables that form the world. It is impossible to analyze more than a few variables at a time because if you assume that most variables affect most others, the number of “effects” (links between variables) exhibits exponential growth (combinations).

From this viewpoint you could say that if you want to make progress in science, you need to find a way to break down the problem you are solving into component parts with few enough interactions. If such small, useful units are found, you can then use them to build back up to the full size of the problem — where building back up has nice linear growth. This makes it possible to actually make progress. You just can’t get anywhere with 2^100 possibilities. Start writing those research libraries…

But these things come and go so quickly… that’s the whole point of the blog, to catch them while they last. hmmmm….

Rick Spalding (a man of wisdom) said that what made the biggest impression on him during the winter study trip to Nicaragua was that the people doing the hardest, most physically demanding (and demeaning) work were getting paid the least.

On the surface, this seems surely wrong. But ultimately whether this is moral seems to come down to the morality of a market economy in general. I think that the basics of such an economy make a lot of sense, but that additional measures are needed to protect the poor. There is some sense of “fairness” which makes it seem like hard physical labor should be rewarded more than skilled mental labor, but if you are doing hard physical labor that no one needs, than why should you be paid at all to do it? This is how the market allocates money “efficiently”.

So the real issue is not the market but that in Nicaragua there are a whole host of other problems, such as illegal maneuvers made possible because of extreme wealth disparities and poverty in general. Not the market but the fact that workers’ rights are not protected.

It’s ironic that the hardest workers are being paid the smallest sums, but what’s not “fair” is that they do not realistically have the option to change their work or improve their working conditions. A free and fair society is one where these opportunities do exist.

My mind has been swirling lately with interesting thoughts related to the book Zen and the Art of Motorcycle Maintenance. So as not to be overwhelmed I will try to post them as separate Interesting Thoughts at different Interesting Times.