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This lecture explores the concept of infinite space in urban planning, from ancient cosmologies to modern city designs. It delves into the transition from geocentric to heliocentric cosmologies, the visualization of celestial orbs, and the impact of infinite space on architectural vision and urban development, using historical examples like Vaux-le-Vicomte and Versailles. The presentation also discusses the American Land Ordinance of 1785 and Thomas Jefferson's urban planning ideas for the New World, emphasizing the grid system and the relationship between maps and territories.