Benfords law

>I am not a mathematician
Bummer. Proving probability laws requires rigour.

>>8271429
Well if you have any explanation to offer I could at least try to understand

It is easier for there to be one of something than there is for there to be 9 of something.

It is easier for there to be 10s of something than there is for there to be 90s of something.

And so on.

>>8271449
Yeah okay but how do you get to these exact probabilities? And shouldn't this be heavily influenced by the kind of data you're using?

>>8271461
You get to those exact probabilities by taking the right kind of data, and counting. The reason it's a law is that a lot of different types of data ( election numbers, stock prices, mathematical constants). The common point I see is that they measure a real life quantity, not theoretical.

>>8271416
Let's look at an example: 2^x

If 1 is the first digit then this means

1 =< 2^x < 2 or 10 =< 2^x < 20 or etc.

0 =< x < 1 or log2(10) < x < log2(20) or etc.

Now to find the probability of this occurring we simply measure the relative length of these intervals. Luckily these lengths are very easy to compute and uniform for all magnitudes of 2^x:

log2(2*10^n)-log2(10^n) = 1

log2((d+1)*10^n)-log2(d*10^n) = log2(1/d+1))

So the probability of 2^x beginning with d is log2(1/d+1)) / sum from n=1 to 9 of log2(1/n+1)) = log10(1/d+1))

Hence Benford's Law.

>>8271416
It's just the nature of logarithms

http://datagenetics.com/blog/march52012/index.html

>>8271416

https://www.youtube.com/watch?v=vIsDjbhbADY

https://www.youtube.com/watch?annotation_id=annotation_1875489451&feature=iv&src_vid=Az3kXCPZpYs&v=XXjlR2OK1kM

its not a real law since i can prov eit wrong:

199999999999

1 only occured once, 9 occured the most

law broken

>>8272430
You certainly Never heard of the term almost everywhere

>>8271511
>>8271481
>>8271515
>>8272386
I want to thank all of you. Helped me a lot.