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Vi 與 Sal 討論班佛定律的奧秘 (英): Vi Hart 拜訪可汗學院與 Sal 討論班佛定律
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- I am very excited to have Vi Hart visiting the office
- over here and we just having a very mathematical conversation
- earlier today and she mentioned something that is fascinating
- ya I was just telling Sal about a cool thing called
- Benford's Law. Benford's Law and what is Benford's law?
- it's this weird phenomenon that you get when you are looking at
- numbers in the real world. so for example we have got some
- graphs here. if you take the populations of all the
- countries and you say alright what is the first digit
- of the population of the country whether it is 1 million or
- 1 thousand or a hundred thousand. we'll say that okay
- starts with 1 . so we'll count up all, all of the countries
- that start with 1. and I guess here we have got 27
- of them. yes about 27. so really, like anything that
- starts with 1 here, so it could be a country that
- has a population of 1 or population of 17 or
- population of 1 billion three hundred million blah blah blah
- they would all fall into this bucket right over here
- Right and then if you start with 2 you fall in the second
- bucket and so on and so forth. better color oh ya go ahead
- ya better definitely better color. oh that's great.
- oh that's the Blue..better contrast.
- so the question is you'd think you'd have kind of
- random numbers here. yes! for that first digit like
- it's kind of random. Ya I mean there is huge differences
- in population of countries, some have billions and
- some have.. I don't know what the smallest population is.
- Yes. it's like Montenegro or something like that.
- Yea umm so. Montenegro is not a country.
- what am I thinking! I am thinking of what was the
- one on the French Riviera?. I mean..we can edit that out.
- [laughs] I don't know I'd be interested to see
- for populations of states and everything .
- The Vatican is the smallest country. I believe
- yea does that still count? I guess.. I think the Vatican
- counts, they have their own..yes. I don't know
- exactly what the requirements for it to be. But if we
- include the Vatican which I think would be like in the
- thousands. yea and so why would this happen? why would
- you see more 1s than 2s.. like what is going on
- and It's not some small chance I mean we were
- talking also about the idea that it is more likely to have
- odd numbered addresses than even numbered. you were
- talking about that earlier. yea I just learned about that
- recently. That's not a huge..that makes sense . that makes
- sense because every house will have a number 1 on it
- right. every street if your street starts you know with
- house number 1.. house number 2.. house number 3
- right. or or. If you have odd number of houses then your
- street has more odd numbers than.. exactly. and if
- you have an even number you have the same amount.
- right. right. but that starting with 1 which is odd whereas
- here a.. populations don't start with 1. exactly. and
- that phenomenon we are talking about the street numbers
- is not an extreme phenomenon. it's like 50 point some 0
- it's a slightly more, you have a slightly higher probability
- of having a odd numbered house or I guess a 1 house
- than everything else. yea it's kind of exactly what you'd
- expect. it's exactly what you'd expect. but here
- here it's a significantly higher probability of a random
- country's population that it's first digit is a 1 versus
- it's first digit as an 8 or a 9. I mean it seems
- it seems a little bit strange. yea and this just isn't in
- countries. yes. you see this if you're looking at a lot of
- financial stuff like how much money does a company make
- yes. the 1s show up as the first digit much more frequently
- much more frequently yea. and here we have another
- fancy graph which is like completely crazy it's the
- first digit of physical constants. so what would be the
- examples of some physical constants. like I am assuming
- that we weren't able to figure out exactly what they applied
- here but I am assuming it's things like the Gravitational
- constant, Planck's constant and this seems kind of
- crazy to me because it depends on the units that you are
- using and it depends on a whole bunch of you know
- things you assume about it. but even when you use
- these kind of arbitrary physical constants. which I am
- assuming they are doing here. the first the most significant
- digit in these physical constants is still much more
- likely to be 1. it almost exactly follows Benford's Law.
- and it's it's kind of gives you goose pimples. it's. yea
- so the challenge here is to. oh by the way Benford is
- the guy with the glasses. oh yes! yes you might be wondering
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