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Lost numbers
2008-Mar-31, Monday 11:16 amwarning: geek question impending
With the equivalent of a minimum wage job, it's going to take a while to get myself out of debt and save up money for classes. So what to do in the meantime? I've been pondering two things. A) Programming a game. (a decades-old interest of mine) B) Defining division by zero.
Division by zero is not "impossible", as I understand it, because it's merely "undefined" at the moment. That makes it an attractive topic of interest. A place to leave an intellectual mark, so to speak, by solving the problem. Here follows my attempts to find appropriate metaphors for what I imagine is division by zero.
I think the solution has something to do with rotation. When I imagine division, I end up "turning" my perspective. Division by zero is a really intensely fast rotation... so fast that my orientation is lost altogether. Is it possible to measure anything (scalar) without even a single dimension for orientation? Some information is lost but not all of it. Division by zero has a "place" (in my mind) but it lacks a "value" that I can measure in the usual way. It may take a bit of mental trickery to create a "placeholding marker" (like i for imaginary numbers) where division by zero occurs in a formula, with neat tricks for working it out of the formula again. So division by zero wouldn't necessarily make a formula unsolvable any more.
Zero, in my mind, has both a place (at the origin on a scale) and a value (distance measured from the origin along a dimension). Division by zero, however, has only a place (related to the origin) but no value. It has lost all dimensionality so it can't have a "value" in the usual sense. That information is lost.
question finally: So does this metaphor sound familiar to anyone? Could you point me in the direction of a book or an author (mathematician?) that describes stuff like this? Has somebody already explored the concept of Lost numbers? I'd like to learn more.
With the equivalent of a minimum wage job, it's going to take a while to get myself out of debt and save up money for classes. So what to do in the meantime? I've been pondering two things. A) Programming a game. (a decades-old interest of mine) B) Defining division by zero.
Division by zero is not "impossible", as I understand it, because it's merely "undefined" at the moment. That makes it an attractive topic of interest. A place to leave an intellectual mark, so to speak, by solving the problem. Here follows my attempts to find appropriate metaphors for what I imagine is division by zero.
I think the solution has something to do with rotation. When I imagine division, I end up "turning" my perspective. Division by zero is a really intensely fast rotation... so fast that my orientation is lost altogether. Is it possible to measure anything (scalar) without even a single dimension for orientation? Some information is lost but not all of it. Division by zero has a "place" (in my mind) but it lacks a "value" that I can measure in the usual way. It may take a bit of mental trickery to create a "placeholding marker" (like i for imaginary numbers) where division by zero occurs in a formula, with neat tricks for working it out of the formula again. So division by zero wouldn't necessarily make a formula unsolvable any more.
Zero, in my mind, has both a place (at the origin on a scale) and a value (distance measured from the origin along a dimension). Division by zero, however, has only a place (related to the origin) but no value. It has lost all dimensionality so it can't have a "value" in the usual sense. That information is lost.
question finally: So does this metaphor sound familiar to anyone? Could you point me in the direction of a book or an author (mathematician?) that describes stuff like this? Has somebody already explored the concept of Lost numbers? I'd like to learn more.