So where we left off in the last video, Vi and myself had posed a mystery to you. We had talked about
Benford's law, and we asked, "What is up with Benford's law?"
This idea that if you took just random countries and took their population and took the most significant
figures of their population and plotted
the numbers, the numbers of countries that their most significant figures were a 1 versus a 2 versus
a 3, you just had - it was much more likely that it was a 1.
Or that, if you took physical constants of the universe that they're most likely to have 1
as their most significant digit.
And that - I wish we had more graphs, because graphs are FUN -
but if you look at information from the stock market or ANYTHING
and it seemed to all follow this curve. And what was EXTREMELY mysterious -
and this is where we finished off the last video -
if you look at PURE, I would say, compounding phenomenon
like, say, the Fibbonaci sequence or powers of 2
that exactly fits the Benford distribution.
It exactly fits this. If you take all the powers of 2 exactly 30%, or I don't know if a little bit over 30%
of those powers of 2, all of those powers of 2 have 1 as their most significant digit.
A little bit - what is this? 17? Roughly 17% of all of them have 2 as their most significant digit.
Although in this case, there was an infinite number in every test case, so it was harder to graph.
But if you wanted to try it out, you could take the first million powers of 2 and then find the percentage
and that would probably give you a pretty good approximation of things.
So to me that's, like, less mysterious when you're looking at - I mean -
on the one hand, wow, this fits exactly with mathematics but that also gives you a really good handle
'cuz you realize, alright, there's something here I can actually take a look at.
You can take a look at and it becomes something you can dig deeper in.
We said in the last video we wanted you to pause it and think deeper
because frankly, we had to do the same thing,
and a big clue for us was when we looked at a logarithmic scale
and we're looking at one right over here, and just to be clear:
what's going on in this logarithmic scale is, you see equal spaces on the scale are powers of 10
so on a linear scale this would be a 1 and maybe this would be a 2 and then a 3
Or if we wanted to say this is a 2, you'd say this is a 1, this is a 10, this would be a 20 and a 30,
and so on and so forth, but on a logarithmic scale equal distances are times 10
or in this case if we're taking powers of 10
so this is 1:10 then 10:100 then 100:1000 and you see how the numbers in between fall out
so the space between 1 and 2 is pretty big and the space between 2 and 3 is still pretty big

班佛定律的解釋 (班佛定律奧妙的續集) (英)

班佛定律的解釋 (班佛定律奧妙的續集) (英) : Vi 與 Sal 談班佛定律背後的概念 (part 2)