Okay so recently I have heard of what is known as Benford's law, and this is the first time I absolutely cannot think of my own inutuion about how this is true. Just trying to think about it makes my head hurt. How is this law possible? How does this make sense? Why does it occur? How is this something mathematically true?
Yes I have tried google and wikipedia, but nothing really is explaining to me how this is actually true. ( Mostly I just find the result and its applications , etc)
So can anyone help to illuminate me on this?
Here is the statement (as wikipedia says it):n many naturally occurring collections of numbers the small digits occur disproportionately often as leading significant digits.
Thanks all
Let's say you have a sequence that increases exponentially. That is; the larger your amount, the faster it will grow.
143 will not grow as fast as 973, because 973 is a larger number. Therefore, the sequence will spend more time in the 100's range than it will in the 900's range. It will spend even less time in the 1100's range, but even lesser still in the 9000's range.
What we get is a logarithmic distribution in terms of the leading digits.
Benford's law is useful, because it allows us to check if a sequence is exponentially increasing using random terms from that sequence. What we find is that many sequences in life follow an exponential curve in some regard.