An Example of a "Learning Process" Journal (using the 2 colored box format)

Book: Nexus by Mark Buchanan.

Source: New York: W W Norton, 2002.

It is 8:00 am (Saturday). I read this book a couple of weeks ago, and am beginning to make a few notes.

Chapter Prelude

• "Science is built up with facts, as a house is with stones. But a collection of facts is no more a science than a heap of stones is a house." Poincaire [p. 11]
• "But it does suggest that many of the inherent complexities of human society actually have little to do with the complex psychology of humans; indeed, similar patterns turn up in many other settings where conscious beings play no role at all." [p. 12]
• "Milgram's findings became famous and passed into folklore in the phrase 'six degrees of separation' " [p. 13]
• Two mathematicians at Cornell University, Duncan Watts and Steve Strogatz, in 1998 drew a new type of graph that had properties that no one had examined before.
• "Social networks turn out to be nearly identical in their architecture to the World Wide Web. ... Each of these networks shares deep structural properties with the food webs of any ecosystem and with the network of business links underlying any nation's economic activity. Incredibly, all these networks possess precisely the same organization as the network of connected neurons in the human brain and the network of interacting molecules that underlies the living cell." [p. 15]
• "No amount of information at the level of the individual species or economic agent can hope to reveal the patterns of organization that makes the collective function as it does." [p. 15]
• "... there have been at least five great episodes of mass extinction, in each of which more than 50 percent of all species world wide were suddenly eradicated." [p. 18]
• "The study of networks is part of the general area of science known as complexity theory." [p. 18]
• "Some of the deepest truths of our world may turn out to be truths about organization, rather than about what kinds of things make up the world and how those things behave as individuals." [p. 19]
• "How does the living cell manage to go on living in the face of all kinds of errors and mistakes at the molecular level? Fundamental insights ... tumble straight out of the networks perspective." [p. 19]

The second quote is an important one. The idea is that some societal patterns may be the result of the mathematics of complexity rather than the underlying reality of human interactions.

The Milgram phrase refers to the idea that any two people can be connected by a path of friends that only involves about 6 links. Very counter-intuitive!

One of the delightful aspects of the story about Watts and Strogotz is that it is contemporary. It is so rare to encounter mathematics in the press, or in textbooks, that refers to something recent. Other subjects are not like that. Why is mathematics so pre-occupied with "old" math? A partial answer may have to do with the specialist nature of the subject. Only the very old topics are accessible to novices.

The difference between different levels of observation raises the idea of emergence. Each level has properties that one could not infer from the other levels. But it also refers to something else I read a long time ago (and cannot recall clearly!) that has something to do with different levels. Maybe it was something to do with systems theory and possibly Bertalanfy. ??? . levels of organization ... about 8 ... cell - organism - organization -culture. Is this also how we move from brain to mind?

The above lead to a search that resulted in a discussion of proteins. What is a protein? Googling informs me that it is a large molecule made of various amino acids (which are also large molecules) that are found in living matter. I wonder how long I will remember that? Perhaps a long time.

The quote on mass extinctions is an aside, and it also rings a (faint) bell. Now to find out more about them. Easily done. The BBC site is excellent.

I like the way different ideas crop up spontaneously while reading and that I can pursue them using Google at the moment they occur!

Mathematics Index