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youre on a hike trying to figure out how far away you are from your destination you pull out a map whose bar scale tells you that one inch equals half a mile and measuring two inches between your current location and your destination you conclude that youre one mile out basic math sure but whether you realize it or not youve just utilized a form of the metric tensor one of the most revolutionary revisions to our modern geometry but what is this idea exactly and how has it come to play such a crucial role in the theory of general relativity this is dialect and today were demystifying the metric tensor [Music] the equations of general relativity tell us that matter and energy alter the metric of space-time resulting in a four-dimensional curvature thats synonymous with gravity the key to understanding general relativity then is locked away somewhere in this notion of a metric which at every point across space and time is characterized by ten numbers in the form of a mathematical obj