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innovative thinking. Multiple tasks, influences, and contexts can help to foster  an inventive frame of mind, and send the investigator in a  new and fruitful direction -- but they can also be distractions.  Failures of curiousity curiosity  or sagacity will undermine the process -- and although serendipity does not reduce to luck, there is some luck  involved as well. 
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\node (result) at (.055, .665) {\textbf{result}};  \node (result)[text width=2cm,align=center] at (.7, .71) {\textbf{prepared mind}};  \node (focus) at (.93, .88) {{\bf \textsc{focus shift}}};  \node (curiosity)[rotate=35] at (.44,.58) {curiousity}; {curiosity};  \node (sagacity)[rotate=-30] at (.72,.45) {sagacity};  \node (value) at (.04, .755) {value};  \node (influences)[text width=2cm,align=center,rotate=30] at (.99, .60) {{\small\baselineskip=2pt \emph{multiple influences}\par}}; 
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\caption{A heuristic map of the features of serendipity introduced in  Section \ref{sec:by-example}. The central black line traces first  the process of \emph{discovery} in which an initial trigger combines  with mounting curiousity curiosity  to effect a \emph{focus shift}, followed by a process of \emph{invention} in which a prepared mind draws on  various resources and makes use of its powers of sagacity to find a bridge to  a valuable result. In a typical chaotic fashion, paths that are initially nearby can have very different outcomes: some end