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 3:00 PM (Monday). I hope to make substantial progress with my note making this morning.

Chapter 6 An Accidental Science

• "... all historians bring personal baggage to their practice of history, and this inevitably colors their interpretation of the past." [p. 89]
• "Too many accidents and chance events force their way onto the stage, each leaving a mark on the unfolding future, and so explanations take the form not of references to general laws, but of stories that connect events together and tell how things came to be." [p. 90]
• "The evolutionary biologist Stephen Jay Gould argued, quite rightly, that 'contingency' of this kind lies at the very core of history. 'I am not speaking of randomness,' Gould wrote, ' ... but of the central principle of all history - contingency. ... This final result is therefore dependent, or contingent, upon everything that came before." [p. 91]
• "... this is not to say that there is nothing to history but contingency." [p. 91]
• "... there is a flip side to contingency, and more form lurking within history than we might naively suspect." [p. 92]
• "Benard's experiment illustrates how order and pattern can emerge from featureless nothingness, from uniformity. What about order from pure chaos and randomness? This is possible too, proving that striking order can emerge even in the face of history and its contingencies." [p. 97]
• Dendretic river patterns and snowflake accretion are examples of pattern at a level not usually considered.

The statement that order form chaos "proves" that order can emerge even in the face of history" is a large leap and "proves" only that order can emerge from random patterns.

Chapter 7 The Rich Get Richer

• "The researches of many commentators have already thrown much darkness on this subject, and it is probable that, if they continue, we shall soon know nothing about it at all." Mark Twain [p. 106]
• "The principle message of our story so far is that small worlds are almost everywhere. ... that deep general principles must lie behind their emergence." [p. 118]
• "... the networks of Watts and Strogatz lack two striking features of many real-world networks. To begin with they do not grow. Every complex network in the real world has come to be through a history of growth. ... also lack the vital ingredient of history while at the same time lacking connectors, the few rare elements that possess a disproportionate share of all the links." [p. 119]
• "The historical mechanism of the rich getting richer leads without fail to connectors." [p. 119]
• "... these networks with humbs might be better described as 'aristocratic', as only a handful of elements possess most of the networks links." [p. 119]
• "So there are, it seems, two flaovors of small: egalitarian networks in which all the elements have roughly the same number of links, and aristocratic networks characterized by spectacular disparity." [p. 119]

The important idea of hub or connector has been introduced.

Chapter 8 Costs and Consequences

• "Everything is what it is because it got that way." [p. 121]
• "... what causes the difference between the two kinds of small-world networks?" [p. 123]
• "It is fair to say that a host of puzzling questions still remain, as is hardly surprising in a field of research that is even now barely four years old." [p. 126]
• "But the crucial role of coordination in any successful network attack emerges even more clearly from the perspective of small-world networks." [p. 130]
• "... a few well-conceived strikes might suffice to fragment the information infrastructure into hundreds of small, isolated, and nonfunctioning pieces." [p. 132]
• "Others believe, however, that complex networks can be safeguarded in a more sophisticated way by learning to copy the defence mechanisms of living things." [p. 132]
• "The network perspective suggests that bacteria and other microbes can be hit hardest by striking at the proteins most highly linked within the bio-chemical network." [p. 137]

The opening quote is a gem!

The question posed in the second bullet assumes that there are only two kinds of small-world networks. This is dangerous. What ever happened to continua? And multi-dimensionality?

It is both sobering and exciting to realize how young this field of network theory is.

The same idea of focusing on the hubs can be used to plan defences or to plan attacks. This becomes particularly exciting as an approach to medicine and disease.

Chapter 9 The Tangled Web

• "This is like blaming woodpeckers for deforestation." [p. 139]
• "Nature is not put off by fine words." [p. 140]
• "... order is often hidden, and different kinds of organization lead to different properties for the network as a whole." [p. 143]
• "Which are the weak links in an ecosystem, and which are the strong?" [p. 148]
• "Any hub or connector species has a huge number of links to other species. As a result, most of these links will be weak links; the two species interact infrequently." [p. 151]
• "Ecologists have long talked about 'keystone' species" [p. 153]

The woodpecker quote is delightful as a rebuttal for focusing on the insignificant.

The quote on words is similar to my phrase of "Gravity wins."

The flip side of the question about weak and strong links is to focus on the nodes: which are the weak and strong nodes in a network?

Aaah. The idea of a 'keystone' addresses the issue of nodes!

Mathematics Index