W. Brian Arthur is best known for his theoretical work on increasing returns or positive feedbacks in the economy and their role in locking markets in to the domination of one or two players. He is one of the pioneers of the science of complexity and one of the founders of the Santa Fe Institute, where he served many years on its Science Board and Board of Trustees. Brian Arthur is the recipient of the inaugural Lagrange Prize in Complexity Science in 2008 and the Schumpeter Prize in Economics in 1990. He has been dean and Virginia Morrison Professor of Economics and Population Studies at Stanford, and Citibank professor at the Santa Fe Institute. Currently Brian is External Professor at the Santa Fe Institute, Visiting Researcher at the System Sciences Lab, PARC, and External Faculty at CSH.