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All the Movies / 2009-10-17
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I thought it might be fun to compute the total number of possible movies, based on frame rate, resolution, and the number of possible colors on a standard high-definition digital blu-ray or something. So with some input from people who know more than I do about those things, I came up with the following numbers:
220^{3} = 10648000 colors/pixel 24 frames/second 1920*1080=2073600 pixels/frameAnd I want to calculate all of the possible movies with runnings times less than or equal to exactly four hours.
(4 hours = 14400 sec) * (24 frames/sec) = 345600 framesBased on the numbers for colors/pixel and pixels/frame, the number of possible frames should be
10648000^{2073600}So for any particular number of frames n, we should have exactly
(10648000^{2073600})^{n}possible movies. So for all possible movies less than or equal to four hours, we have to sum up these terms for all n from 0 to 345600. According to the appropriate summation formula, this is equal to exactly
(10648000^{2073600})^{n+1} |
10648000^{2073600}-1 |
(10648000^{2073600})^{345601} | = |
10648000^{2073600}-1 | |
10648000^{716638233600} | |
10648000^{2073600}-1 |
log_{10}(10648000^{716638233600}) = 716638233600(log_{10}10648000) = 5036008956987So we're talking about a number that has over five trillion digits. That's so many movies that if you watched a movie every day for the rest of the month, you still wouldn't be done!
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