I'd advise everyone to watch the Netflix Series Connected and the episode on Digits. This is where I came across it.
What is Benfords Law? Its a law that states when you take a set of numbers from pretty much anything, the leading digit of those numbers will more or less follow this same curved distribution.
At first glance this doesn't make sense. You would assume it should all hover around 11% or 1 in 9. But seemingly EVERYTHING follows this same population. Some examples.
Take the populations of every country in the world. (numbers vary from the tens to the billions) It follows the distribution.
Take the front page of The Financial Times and pick out ALL the numbers on it. It follows.
Take the size of volcanoes around the world. It follows.
Take the distance between all members on ERA to the Statue of Liberty. It will likely follow.
Take the distance between stars in light years. It will follow. Convert those distances to miles. Still follows. Convert those distances to a made up unit like the length of my dog. It will follow.
Length of rivers. Death Rates. Covid Data. Election data. Tax numbers. It all follows.
Take the length of notes in a song. It will follow.
Seemingly every data set gathered in our world, no matter if its in log10 or 16 or whatever, no matter what unit it is even if its converted, it will follow. You ask 10000 people for a random number between 1 and 9999999... it will follow. The real world is supposed to be random but we see this pattern EVERYWHERE. Even in places without human influence.
Here is where it gets crazy though... If you manipulate that data... the law fails. So if you take all the numbers on a tax form, it will follow the law. If someone manipulates the numbers (tax fraud) the law will fail. Auditors literally use this law to see at a glance if someone is manipulating numbers. It's also been used to point out election fraud in Iran. It is used often to detect fraud or tampering etc. Interesting in elections, the law will follow if everyone votes for their first choice. The moment people start "playing politics" and voting strategically to prevent so and so from winning and whatnot, the law fails. People use to detect fake images/videos. Tax and accounting fraud. Scientific data fraud.
This guy explains it well and offers a somewhat intuitive explanation for why it behaves the way it does.
But even with this explanation its still wild to me. If you take a set of data that ranges a couple orders a magnitude (think populations of cities vs height of human adults which doesn't vary much) it will all fit. And when it doesn't it means its basically evidence someone tampered with the data. Even though the world is chaotic and random. People die, people are born, people move. The distribution of the leading digit in world city populations will still follow benfords law.
It's some Da Vinci Code shit.
Watch Connected | Netflix Official Site
Science journalist Latif Nasser investigates the surprising and intricate ways in which we are connected to each other, the world and the universe.
www.netflix.com
What is Benfords Law? Its a law that states when you take a set of numbers from pretty much anything, the leading digit of those numbers will more or less follow this same curved distribution.
Benford's law - Wikipedia
en.wikipedia.org
At first glance this doesn't make sense. You would assume it should all hover around 11% or 1 in 9. But seemingly EVERYTHING follows this same population. Some examples.
Take the populations of every country in the world. (numbers vary from the tens to the billions) It follows the distribution.
Take the front page of The Financial Times and pick out ALL the numbers on it. It follows.
Take the size of volcanoes around the world. It follows.
Take the distance between all members on ERA to the Statue of Liberty. It will likely follow.
Take the distance between stars in light years. It will follow. Convert those distances to miles. Still follows. Convert those distances to a made up unit like the length of my dog. It will follow.
Length of rivers. Death Rates. Covid Data. Election data. Tax numbers. It all follows.
Take the length of notes in a song. It will follow.
Seemingly every data set gathered in our world, no matter if its in log10 or 16 or whatever, no matter what unit it is even if its converted, it will follow. You ask 10000 people for a random number between 1 and 9999999... it will follow. The real world is supposed to be random but we see this pattern EVERYWHERE. Even in places without human influence.
Here is where it gets crazy though... If you manipulate that data... the law fails. So if you take all the numbers on a tax form, it will follow the law. If someone manipulates the numbers (tax fraud) the law will fail. Auditors literally use this law to see at a glance if someone is manipulating numbers. It's also been used to point out election fraud in Iran. It is used often to detect fraud or tampering etc. Interesting in elections, the law will follow if everyone votes for their first choice. The moment people start "playing politics" and voting strategically to prevent so and so from winning and whatnot, the law fails. People use to detect fake images/videos. Tax and accounting fraud. Scientific data fraud.
This guy explains it well and offers a somewhat intuitive explanation for why it behaves the way it does.
But even with this explanation its still wild to me. If you take a set of data that ranges a couple orders a magnitude (think populations of cities vs height of human adults which doesn't vary much) it will all fit. And when it doesn't it means its basically evidence someone tampered with the data. Even though the world is chaotic and random. People die, people are born, people move. The distribution of the leading digit in world city populations will still follow benfords law.
It's some Da Vinci Code shit.
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