Vi and Sal Talk About the Mysteries of Benford's Law
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Uploaded by khanacademy on Aug 23, 2011
Vi Hart visits Khan Academy and talks about Benford's Law with Sal
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pleaaaaase Sal don't bring anyone next time
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the baddest thing that u did is
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You were thinking of Luxembourg.
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Sealand is the country with the smallest population.
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Montenegro is a country.
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Hey guys, I wondered what would happen if this was shifted to another base, for example binary (hmm 100% on 1, how odd :D) and found an amazing thing when shifted to octal ... on 1000 iterations of 2^n 1,2 and 4 had equal (33.3333% odds) of being the first digit - not a single 3,5,6 or 7 I suppose this is the "why" you wanted us to ponder.... though what it means I'm not sure ... maybe counting with our thumbs was a bad idea?
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...At this point it is increasing ten times faster than it was originally, but has exactly ten times as much ground to cover between 10 and 20 as it did between 1 and 2, so it will spend the same time there, then the same amount of time between 20 and 30 as between 2 and 3 etc.
That should give you a good idea of the scale invariance problem, which is what most seem to struggle with.
I advise using Wolfram|Alpha to graph e^(-x) from x = 0 to 5, then (separately) from 5 to 10. ..Look familiar? ;p
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The logarithmic relationship should be true for every base, but the graphs would look different.
The relationship applies to numbers that are generated by most natural systems, and as Desrathedemon states, it's all about exponentiation.
Say a number is increasing a rate which is proportional to its own magnitude.
Starting at one, it will increase slowly, then increase double as fast at 2, then double as fast again at 4 etc until it reaches ten.... (read on in next comment)
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Would this still work in a non base-10 numeral system?
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It's so weird to hear Vi's voice when it's not at 1000 words per minute
UltimateRandomN3ss 5 months ago 38
Guys, Sal is married and has a son lol.
rinwhr 6 months ago 24