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Desc:A law of statistics that says 'fuck you' to everything you'd expect
Category:Educational, Science & Technology
Tags:statistics, Benfords Law, the universe needs better random number generation
Submitted:fermun
Date:08/02/08
Views:1846
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Comment count is 23
glendower
Awesome submission. Does anyone know why this happens?
kelpfoot
Short answer: Because we start counting with small numbers, and work up to the big ones.

Long answer: Real-world 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 [1-1000] 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
*on your own

kelpfoot
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 non-mathematician to understand. (It has to do with the situations in which Benford's Law applies.)

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

ProfessorChaos
+5 stars for these posts alone.
Considering this was going to get 5 stars anways, that's pretty cool.

kelpfoot
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
"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 accurate--exponentiality, linearity, and logarithmic trends (the latter of which is expressed in Benford's Law) ALL occur in nature.

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

halon
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
The math guy sounds exactly like you'd expect a math guy to sound.
positively
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
Your ignorance of Mathematics is blasphemy and God will condemn you to the Lake of Fire for it.

RandomFerret
Yes. You can even multiply each number by three, and Benford's will still hold.

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

uekibachi
wow. this is the kind of math shit i like.
GiantAtomicFreak
Man will know the death of God, where wonder was before.
Knuckles
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 one-inch 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

FatFatuousNation
Good work Knuckles.

meamlegion
how did he export that table to excel so fast? is there a plug-in for that?
meamlegion
nevermind - i now see this video is hocking the kirix data browser.

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