"Nature normally hates power laws. In ordinary systems all quantities follow bell curves, and correlations decay rapidly, obeying exponential laws. But all that changes if the system is forced to undergo a phase transition. Then power laws emerge-nature's unmistakable sign that chaos is departing in favor of order. The theory of phase transitions told us loud and clear that the road from disorder to order is maintained by the powerful forces of self-organization and is paved by power laws. It told us that power laws are not just another way of characterizing a system's behavior. They are the patent signatures of self-organization in complex systems." (Albert-László Barabási, "Linked: How Everything Is Connected to Everything Else and What It Means for Business, Science, and Everyday Life", 2002)
"If you flip a coin three times and it lands on heads each time, it's probably chance. If you flip it a hundred times and it lands on heads each time, you can be pretty sure the coin has heads on both sides. That's the concept behind statistical significance - it's the odds that the correlation (or other finding) is real, that it isn't just random chance." (T Colin Campbell, "The China Study", 2004)
"Nonetheless, the basic principles regarding correlations between variables are not that difficult to understand. We must look for patterns that reveal potential relationships and for evidence that variables are actually related. But when we do spot those relationships, we should not jump to conclusions about causality. Instead, we need to weigh the strength of the relationship and the plausibility of our theory, and we must always try to discount the possibility of spuriousness." (Joel Best, "More Damned Lies and Statistics: How numbers confuse public issues", 2004)
"The basic concept of complexity theory is that systems show patterns of organization without organizer (autonomous or self-organization). Simple local interactions of many mutually interacting parts can lead to emergence of complex global structures. […] Complexity originates from the tendency of large dynamical systems to organize themselves into a critical state, with avalanches or 'punctuations' of all sizes. In the critical state, events which would otherwise be uncoupled became correlated." (Jochen Fromm, "The Emergence of Complexity", 2004)
"A correlation between two variables means they vary together. A positive correlation means that high values of one variable are associated with high values of the other, while a negative correlation means that high values of one variable are associated with low values of the other." (Steve McKillup, "Statistics Explained: An Introductory Guide for Life Scientists", 2005)
"Correlation is an exploratory technique used to examine whether the values of two variables are significantly related, meaning whether the values of both variables change together in a consistent way. (For example, an increase in one may be accompanied by a decrease in the other.) There is no expectation that the value of one variable can be predicted from the other, or that there is any causal relationship between them." (Steve McKillup, "Statistics Explained: An Introductory Guide for Life Scientists", 2005)
"Linear correlation analysis assumes that the data are random representatives taken from the larger population of values for each variable, which are normally distributed and have been measured on a ratio, interval or ordinal scale. A scatter plot of these variables will have what is called a bivariate normal distribution. If the data are not normally distributed, or the relationship does not appear to be linear, they may be able to be analysed by nonparametric tests for correlation [...]" (Steve McKillup, "Statistics Explained: An Introductory Guide for Life Scientists", 2005)
"Under certain circumstances, complex systems can demonstrate stronger types of particular correlation, some forming almost instantaneously to overwhelm their parent and transforming it into something completely and unexpectedly. This is the phenomenon we now know understand as 'emergence', the process by which complex systems transition into something that they once were not. Like complexity, emergence has a spectrum of disguises, being capable of manifesting great subtlety and power." (Philip Tetlow, "The Web’s Awake: An Introduction to the Field of Web Science and the Concept of Web Life", 2007)
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