http://bit-player.org/2006/running-on-empty An amateur's outlook on computation and mathematics. Tue, 07 Feb 2012 07:50:31 +0000 http://wordpress.org/?v=2.6.3 http://bit-player.org/2006/running-on-empty#comment-1219 Barry Cipra Mon, 27 Nov 2006 04:59:42 +0000 http://bit-player.org/?p=69#comment-1219 I think there's a simpler way, at least in principle. All you need to do is keep track of the function O(g), which is the Odometer reading when the car has burned a total of g gallons of gas. (I'm thinking of g as representing ALL the gas you ever put in the car, from day 1, not just what you've burnt since the last fill-up, but it really doesn't much matter.) Unless you spend a lot of time driving in reverse, O(g) is a non-decreasing function of g. If the car has burned g gallons and, at the moment, has r gallons remaining in the tank, then a reasonable estimate for the remaining range is O(g)-O(g-r) -- i.e., the distance you've most recently driven on the amount of gas that remains. I think there’s a simpler way, at least in principle. All you need to do is keep track of the function O(g), which is the Odometer reading when the car has burned a total of g gallons of gas. (I’m thinking of g as representing ALL the gas you ever put in the car, from day 1, not just what you’ve burnt since the last fill-up, but it really doesn’t much matter.) Unless you spend a lot of time driving in reverse, O(g) is a non-decreasing function of g. If the car has burned g gallons and, at the moment, has r gallons remaining in the tank, then a reasonable estimate for the remaining range is O(g)-O(g-r) — i.e., the distance you’ve most recently driven on the amount of gas that remains.

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