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Curious Mathematical Law Is Rife In Nature
New Scientist ^ | Thursday, October 14, 2010 | Rachel Courtland

Posted on 10/16/2010 5:27:23 PM PDT by SunkenCiv

What do earthquakes, spinning stellar remnants, bright space objects and a host of other natural phenomena have in common? Some of their properties conform to a curious and little known mathematical law, which could now find new uses.

A subject of fascination to mathematicians, Benford's law states that for many sets of numbers, the first or "leading" digit of each number is not random. Instead, there is a 30.1 per cent chance that a number's leading digit is a 1. Progressively higher leading digits get increasingly unlikely, and a number has just a 4.6 per cent chance of beginning with a 9 (see diagram).

The law is named after physicist Frank Benford, who in 1938 showed that the trend appears in many number sets, from the surface area of rivers to baseball statistics to figures picked randomly from a newspaper. It later emerged that such distributions are "scale-invariant": if you convert the units of the numbers in the set, from metres to yards, say, the set will still conform to Benford's law.

Not all sets of numbers obey this law, but it crops up surprisingly often. As a result, mathematicians have put it to work, using deviations from it to detect cases of tax fraud, voter fraud and even digital image manipulation.

Now Malcolm Sambridge of the Australian National University in Canberra and colleagues have extended the list of natural phenomena with properties that follow Benford's law. Their new list includes the depths of almost 250,000 earthquakes that occurred worldwide between 1989 and 2009, the brightness of gamma rays that reach Earth as recorded by the Fermi space telescope, the rotation rates of spinning star remnants known as pulsars, and 987 infectious disease numbers reported to the World Health Organization in 2007.

(Excerpt) Read more at newscientist.com ...


TOPICS: Astronomy; Science
KEYWORDS: benfordslaw; stringtheory
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To: eclecticEel

K:’D


21 posted on 10/16/2010 6:12:01 PM PDT by SunkenCiv (The 2nd Amendment follows right behind the 1st because some people are hard of hearing.)
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To: SunkenCiv

Here’s an even stranger one: In binary numbers, 100% of numbers start with one.


22 posted on 10/16/2010 6:16:45 PM PDT by blindsangamon
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To: Nachoman

:’D

Hey, if anyone figures that out, they’ll keep it to themselves.

I was looking for the Powerball website one time and found a page written by a Minnesota math prof; he stated the odds of winning the PB, and then noted that, according to the Feds’ stats, the odds of being *involved* in a fatal auto crash during a three mile round trip to get the lottery ticket was twice as great as the odds of winning.

My response to that is, ya buy two or more tickets. Duh.


23 posted on 10/16/2010 6:16:53 PM PDT by SunkenCiv (The 2nd Amendment follows right behind the 1st because some people are hard of hearing.)
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To: All

The answer is 42.


24 posted on 10/16/2010 6:18:34 PM PDT by Ready4Freddy (Am working on plans for a Knights Templar Community Center next to the Kaaba in Mecca.)
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To: Raycpa; Quix; paul in cape; JRandomFreeper; bvw; RegulatorCountry; GregoryFul; Waverunner
The interesting thing to me is that our number system is itself a construct (despite our anthropocentric way of looking at it), and is merely our poor attempt at modeling the universe, which excels at having things like transcendental numbers (like π) and irrational square roots, just to tinkle all over us.
25 posted on 10/16/2010 6:18:49 PM PDT by SunkenCiv (The 2nd Amendment follows right behind the 1st because some people are hard of hearing.)
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To: blindsangamon

Only half of them do. Nyah nyah. ;’)


26 posted on 10/16/2010 6:20:19 PM PDT by SunkenCiv (The 2nd Amendment follows right behind the 1st because some people are hard of hearing.)
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To: JRandomFreeper

BTW, what do we do with it when we get it, besides realize that it’s His PIN #?

Free calling universe wide?
Reduced rates overnight and weekends?
Rollover minutes?


27 posted on 10/16/2010 6:20:26 PM PDT by tet68 ( " We would not die in that man's company, that fears his fellowship to die with us...." Henry V.)
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To: SunkenCiv

Bump to post #25.


28 posted on 10/16/2010 6:23:34 PM PDT by allmost
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To: GregoryFul
Obama loves pi.
29 posted on 10/16/2010 6:23:44 PM PDT by JPG (Sarah Palin says: "Buck-up or get out of the truck.")
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To: SunkenCiv

LOL.


30 posted on 10/16/2010 6:24:48 PM PDT by Quix (Times are a changin' INSURE you have believed in your heart & confessed Jesus as Lord Come NtheFlesh)
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To: tet68
Still gotta figure out the CC # to get the good stuff. I want anti-gravity panels, FTL, and non-gassy beans.

/johnny

31 posted on 10/16/2010 6:27:21 PM PDT by JRandomFreeper (Gone Galt)
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To: RegulatorCountry
I recall a scientific study from several years back, that toast actually does fall buttered side down far more frequently than not,

YEARS ago there was a very neat comic strip called "Prince Valiant" and, unlike many of the time, was richly drawn. PV's adventures, ca 500 AD, took him all over the world. In one series he was in China. One day the whole court was in an uproar as a horrible omen had appeared.

That morning, as the emperor prepared to eat, he dropped a piece of bread on the floor, and it landed dry side up - Super Bad Luck, according to the seers. They were wringing their hands trying to explain the disaster away, when PV took one of 'em aside and whispered in his ear.

The seer beamed and explained to the emperor that it was not the disaster everyone thought because it was obvious the bread was buttered (or whatever) on the WRONG side.

Hal Foster was the artist at the time and I don't know if he also did the story line, but I thought the solution was ingenious and reminded me of some politicians excuses years later.

32 posted on 10/16/2010 6:37:48 PM PDT by Oatka ("A society of sheep must in time beget a government of wolves." –Bertrand de Jouvenel)
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To: Oatka
YEARS ago there was a very neat comic strip called "Prince Valiant"

The comic strip "Prince Valiant" is still alive and well, the poor prince still hasn't found contentment.

33 posted on 10/16/2010 6:47:27 PM PDT by The Cajun
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To: eclecticEel
if you convert the units of the numbers in the set, from metres to yards

Well yes, picking units which are nearly equal to each other does help.

While it doesn't hold up quite so well converting meters to feet, it's flawless when converting from meters to kilometers, centimeters, etc. :=)

34 posted on 10/16/2010 6:53:58 PM PDT by Bob
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To: SunkenCiv

Bookmark


35 posted on 10/16/2010 6:56:28 PM PDT by Padams
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To: SunkenCiv

This must explain why I always end up with ONE sock that doesn’t have a match. It’s just the universe seeking its normal state.


36 posted on 10/16/2010 7:05:50 PM PDT by Yardstick
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To: SunkenCiv; decimon
Numerogomy ping.


Frowning takes 68 muscles.
Smiling takes 6.
Pulling this trigger takes 2.
I'm lazy.

37 posted on 10/16/2010 7:10:28 PM PDT by The Comedian (They Live. We Sleep.)
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To: screaminsunshine
Metrics are the result of having ten fingers.

How about yards?

38 posted on 10/16/2010 7:24:34 PM PDT by paudio (How could you be an open-minded person if you are a liberal?)
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To: SunkenCiv

Woah. “Anthropocentric” What do you mean by that?

I seem to remember that one theory says that observations create the universe, both back and forward from whatever the thing/event of an observation is called. I’ll call it the Beta point. So of course the universe is anthropocentric.


39 posted on 10/16/2010 7:28:24 PM PDT by bvw
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To: Yardstick

I’ve often wondered hose to blame for that problem.


40 posted on 10/16/2010 8:05:20 PM PDT by SunkenCiv (The 2nd Amendment follows right behind the 1st because some people are hard of hearing.)
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