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Sir Muir had a career in the civil service, becoming Permanent Secretary to the Scottish Office (1998) and the Scottish Executive (1999), and was then Principal of the University of Glasgow from 2003 until his retirement in 2009. He is Chairing Member of the Judicial Appointments Board for Scotland (until September 2016), Chairman of Trustees of the Royal Botanic Garden Edinburgh, a Non-executive Director of the National House-Building Council and Chairman of its Scottish Committee, Chairman of the Dunedin Concert Trust, Vice-chair of the Board of Governors of the Glasgow School of Art, and a Member of the Board of the Moredun Research Institute. He was a Council Member of the Royal Society of Edinburgh from 2012 to 2016. He was educated at the High School of Glasgow and the University of Glasgow, graduating with First Class Honours in Natural Philosophy in 1970.