glendower  20080802 Awesome submission. Does anyone know why this happens?

kelpfoot  20080802 Short answer: Because we start counting with small numbers, and work up to the big ones.
Long answer: Realworld values tend to span a range of magnitudes. For example, consider the number of people in an auditorium listening to a speaker  it could reasonably be anywhere between 1 and 1000. You could express that range [11000] as 10^x, with x between 0 and 3.
Pick any random value for x (between 0 and 3), using a flat probability curve. If your value is (roughly) in any of the ranges [0,0.3], [1,1.3] or [2,2.3], the leading digit of 10^x will be 1. These ranges include about 30% of all possible values of x, therefore there is a ~30% chance that 10^x will start with a 1.
If the value is (roughly) in the ranges [0.3,0.48], [1.3,1.48], or [2.3,2.48], the leading digit of 10^x will be 2. There's about an 18% chance of this.
If you have the least skill with logarithms, you can figure it out one your own from here.
The upshot of this is that Benford's Law only applies when variables span a range of magnitudes, and the probability of being of one magnitude is roughly the same as the probability of being another magnitude. (A "magnitude" is defined here as 10, since that's the base system we use for counting.)


kelpfoot  20080802 Wait I had an afterthough. I want to rephrase the "short answer." I should have said, "Benford's Law happens because our counting system is linear and the real world is exponential."
Also, I made a mistake in my post, but it's probably way too subtle for a nonmathematician to understand. (It has to do with the situations in which Benford's Law applies.)

kelpfoot  20080802 When I masturbate, I imagine manifolds, C* algebras, and computability theory.


kelpfoot  20080802 To be entirely honest, I've never heard of Benford's Law, I haven't bothered to look it up, and I didn't even watch the video past the first minute. Everything I wrote is conjecture. Plus I'm drunk.
Also, I ran the numbers and they worked out perfectly.
Math is so awesome.

halon  20080802 "and the probability of being of one magnitude is roughly the same as the probability of being another magnitude."
That kind of exactly the OPPOSITE of what Benford's Law is saying, actually. Your original "short answer" is also more accurateexponentiality, linearity, and logarithmic trends (the latter of which is expressed in Benford's Law) ALL occur in nature.

kelpfoot  20080802 Halon, do you know what "magnitude" means?

halon  20080803 Ok, yeah, my mistake. I thought about it for an extra few seconds after I made the comment and realized that I was totally mistaken and dumb there. My bad!
apologies on the internet, etc. I'm still not convinced that your revised "short answer" is better than the original, though.

Xenocide  20080802 The math guy sounds exactly like you'd expect a math guy to sound.

positively  20080802 I don't really get this. If you took, say, a data set for the size of lakes in Minnesota and converted it from metric to imperial, would both sets follow the Benford curve?

kelpfoot  20080802 Your ignorance of Mathematics is blasphemy and God will condemn you to the Lake of Fire for it.


SecretJunk  20080802 Apparently, according to math, the fact that the distribution of the size of lakes in Minnesota is independent of whether you measure it in metric or imperial (the lakes' sizes don't change even if the length of your measuring ruler does) IMPLIES that the distribution must follow the Benford curve
Stat! Fucking thing sucks!

SecretJunk  20080802 By math I mean wikipedia, the most authoritative source of math known to me

uekibachi  20080802 wow. this is the kind of math shit i like.

GiantAtomicFreak  20080802 Man will know the death of God, where wonder was before.

Knuckles  20080802 Yo, I know this Benford's Law shit forwards and backwards. Check it out...
I did one chick then I pointed at the door.
A girl entered in so that made it one.
I snapped one time and in came another one
Add it all up and that makes it one
The average age: 11.1
Now that's what I call gettin' some Benford!
One of the chicks wore oneinch heels
One of the one squealed like seals
111 was the area code
Quebec, Canada: my winter abode
In my 1.1 million dollar chalet
Benford's Law all night and all day


meamlegion  20080802 how did he export that table to excel so fast? is there a plugin for that?

meamlegion  20080802 nevermind  i now see this video is hocking the kirix data browser.

j lzrd / swift idiot  20080802 "The largest number is about 45,000,000,000, although mathematicians suspect that there may be even larger numbers."

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