I decided to extend my previous post about a phenomenon called the Benford's Law (or distribution). You can find previous post here (the basics which can be handy reading part 2): Criminals who don't know Benford's law will always be caught!.
Surprisingly, Benford's law was not discovered by a person with that name, but astronomer Simon Newcomb. In 1881, he noticed an interesting thing - pages in the book with logarithmic tables, which had 1 as first digit in page number, were more worn than others. The law was named after Frank Benford when he noticed the the same fact later. The proof for the law was not known until 1995!
Benford's law versatility
Nature wanted so that this law appears in naturally created situations (preferably random).
- For example, it works well in the study of the surface of the countries. Even if the borders are created by man! We already know that most of the factors that influence people's decisions are random (more[PL, ENG soon]).
Scaling data does not affect the appearance of this distribution. Similarly, it doesn't depend on the number system used.
- This distribution unnaturally sharpens when examining the atomic masses of the particles. Digit 1 in the first positions appears in over 44% of cases.
It is more visible when random data is used to examine Benford's law. A sample of n particles was selected randomly from all known.
- Of course, by drawing numbers from Natural Numbers, Benford's law works perfectly. In the decimal system, a significant digit k appears with a frequency proportional to log (1 + 1 / k).
Widely known people, celebrities, must look more closely at their activities. A researcher once did check if Bill Clinton's 13-year tax returns are consistent with Benford's law. It turned out that yes!
Benford's distribution traps
This law is universal, but you should be aware of narrowing down the data. For example, law will not work if we check only whales payouts on steemit, without most small fishes that represents majority of the ecosystem.
It would be rare if known user earned only $ 1 or $ 11 on his/her post. It is possible that whales usually earn $ 100-200, and very rarely above this amount, and this law will also be unreliable. But when you take all the people publishing on the steemit, it should work perfectly. What's more I predict the same sharpness as in atom masses case.
Comments, opinions? I invite you to a conversation.
I publish mainly in polish, let me know if you want more crazy science articles :)
Previously:
- Would it be better to select politicians randomly in elections?!
- Criminals who do not know Benford's law will always be caught!
- Edge Sorting - design your game badly and I will win millions!
- How I won in Champions League betting contest with random picks ?!
- How to easy shuffle cards properly (in the matter of randomness)?
- My cryptographic ISAAC LOTTO generator wins more money than players!
Images: free pixabay and wikicommons