Benford’s law, also called the first-digit law, states that in lists of numbers from many (but not all) real-life sources of data, the leading digit is distributed in a specific, non-uniform way. According to this law, the first digit is 1 almost one third of the time (as opposed to 11.11% of the time, or 1/9 of the time) and larger digits occur as the leading digit with lower and lower frequency, to the point where 9 as a first digit occurs less than one time in twenty. This distribution of first digits arises logically whenever a set of values is distributed logarithmically. Measurements of real world values are often distributed logarithmically (or equivalently, the logarithm of the measurements is distributed uniformly).
The discovery of this fact goes back to 1881, when the American astronomer Simon Newcomb noticed that in logarithm books (used at that time to perform calculations), the earlier pages (which contained numbers that started with 1) were much more worn than the other pages. Newcomb’s published result is the first known instance of this observation and includes a distribution on the second digit, as well. Newcomb proposed a law that the probability of a single number being the first digit of a number (let such a first digit be N) was equal to log(N + 1) − log(N).
The phenomenon was rediscovered in 1938 by the physicist Frank Benford, who checked it on a wide variety of data sets and was credited for it. In 1995, Ted Hill proved the result about mixed distributions mentioned above.
it made all too much sense to me—“if you want truth, and you want to be able to have a significant connection with people, and you want to find someone who will love you unconditionally, why would you ever be deceptive about who you are, or constrain yourself? there’s only so much time in this world, so we may as well get to know each other while we’re here. peace and love can only come with a genuine desire for mutual understanding; even if in the end i don’t understand me and you don’t understand you, taking the effort to try is the most significant thing that we can do. it’s of the most divine form of optimism, to try to do something in the face of a regressive pessimism—that our identities are shaped by context and are thus discontinuous, constantly shifting, unintelligible.” i never stopped to really consider how and why people would be afraid to be honest, or take the fear to an even more time/life-consuming level and prefer to exist under pretense, a field of identity comprised of row after row of scarecrows. row after row of scarecrows, and what do you have that you need to protect? is there even room anymore for that which you constructed so many straw men? it’s just terrifying, the prospect of digging through straw to find a pulsing heart. mine is for the birds
“It’s probably pretty easy to put together why somebody who grew up in Texas getting in fights a lot would not want to get up on the stage and start belting out songs at the top of their lungs. I’ve had enough of people yelling.”