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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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Even pulsars follow Benford's law (Image: NASA)

Curious mathematical law is rife in nature
Natural law?

Curious mathematical law is rife in nature

1 posted on 10/16/2010 5:27:29 PM PDT by SunkenCiv
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To: Ernest_at_the_Beach; Rurudyne; steelyourfaith; Tolerance Sucks Rocks; xcamel

I wonder if it crops up in University of East Anglia emails?


2 posted on 10/16/2010 5:28:21 PM PDT by SunkenCiv (The 2nd Amendment follows right behind the 1st because some people are hard of hearing.)
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To: AdmSmith; bvw; callisto; ckilmer; dandelion; ganeshpuri89; gobucks; KevinDavis; Las Vegas Dave; ...

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3 posted on 10/16/2010 5:28:47 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

God is one.


4 posted on 10/16/2010 5:32:00 PM PDT by Raycpa
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To: SunkenCiv

THANKS THANKS.


5 posted on 10/16/2010 5:35:05 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: SunkenCiv

One IS the lonliest number.


6 posted on 10/16/2010 5:36:53 PM PDT by paul in cape
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To: SunkenCiv
So, we've hacked God's PIN #. Starts with a one, and less than 4% chance the second one is a nine. 14xx.

What's the next clue? Any of the two numbers equals a prime?

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

/johnny

7 posted on 10/16/2010 5:37:19 PM PDT by JRandomFreeper (Gone Galt)
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To: SunkenCiv
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.

8 posted on 10/16/2010 5:37:39 PM PDT by eclecticEel (Life, Liberty, and the Pursuit of Happiness: 7/4/1776 - 3/21/2010)
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To: SunkenCiv

Do the percentages change if the number system is other than base 10? I presume they would have to.


9 posted on 10/16/2010 5:37:48 PM PDT by Pearls Before Swine (/s, in case you need to ask)
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To: SunkenCiv

Someone let me know if they figure out how to pick winning lottery numbers.


10 posted on 10/16/2010 5:40:34 PM PDT by Nachoman (Think of life as an adventure you don't survive.)
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To: JRandomFreeper

Well, that lets the Masons off the hook. Popular Mason conspiracies involve the digit string 195.


11 posted on 10/16/2010 5:44:47 PM PDT by Calvin Locke
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To: SunkenCiv
Wow. Thanks. Good one.

I've known this for, I think, 35 years when doing analysis of the early state lotteries. I never thought it to be remarkable. Didn't even know it had a name. I spent a good part of my childhood trying to figure what I knew that others did not. Stuff like the principle underlying this law. At some point I gave up on that effort.

12 posted on 10/16/2010 5:49:39 PM PDT by bvw
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To: JRandomFreeper
If God has a PIN number, it's 1.618.

Speaking of peculiarities, I recall a scientific study from several years back, that toast actually does fall buttered side down far more frequently than not, that carrying an umbrella actually decreases the chance of getting rained upon and forgetting it increases the chance, and that it actually does rain more frequently on the weekend. The universe really is stacked against us, lol.

13 posted on 10/16/2010 5:57:18 PM PDT by RegulatorCountry
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To: SunkenCiv

It doesn’t seem to apply to the price of cars, or houses (in US $).


14 posted on 10/16/2010 6:02:25 PM PDT by GregoryFul (Obama - Jim Jones redux)
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To: RegulatorCountry

I think more like pi, 3.14159


15 posted on 10/16/2010 6:05:51 PM PDT by GregoryFul (Obama - Jim Jones redux)
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To: JRandomFreeper

1492 ( pin hint : Ocean Blue)


16 posted on 10/16/2010 6:05:59 PM PDT by Waverunner (")
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Here's the String Theory keyword list, to date, chrono sorted newest to oldest 642 topics:
17 posted on 10/16/2010 6:06:10 PM PDT by SunkenCiv (The 2nd Amendment follows right behind the 1st because some people are hard of hearing.)
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To: Pearls Before Swine

The other commonly used number systems are binary and hexadecimal; a childhood friend of mine quite extravagantly claimed that modern decimal system mathematics was either overlooking or deliberately hiding something, and wanted to redo the whol thing from scratch using the Babylonians’ hexagesimal (base 60) system.

But anyway, I dunno. ;’)


18 posted on 10/16/2010 6:10:01 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

Computer scientists have been using this odd phenomena for some time now. Just about all computer floating point packages assume that the first number is a one, and so just throw it away. Ha! The hidden 1.


19 posted on 10/16/2010 6:10:24 PM PDT by GregoryFul (Obama - Jim Jones redux)
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To: Pearls Before Swine

Metrics are the result of having ten fingers.


20 posted on 10/16/2010 6:10:29 PM PDT by screaminsunshine (counter revolutionary)
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