Vi 與 Sal 討論班佛定律的奧秘 (英)

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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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