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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: paudio

That’s the result of having 36 fingers. Wait, what?


41 posted on 10/16/2010 8:07:06 PM PDT by SunkenCiv (The 2nd Amendment follows right behind the 1st because some people are hard of hearing.)
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To: bvw

That’s one that I learned oh so long ago; it’s perhaps more familiarly “the anthropic principle”.

http://www.google.com/search?q=anthropocentric
http://www.google.com/search?q=anthropocentric+site:freerepublic.com

http://www.google.com/search?q=anthropic+principle
http://www.google.com/search?q=anthropic+principle+site:freerepublic.com


42 posted on 10/16/2010 8:08:52 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
That’s the result of having 36 fingers. Wait, what?

Nah. It's the result of having three feet!

43 posted on 10/16/2010 8:30:17 PM PDT by LexBaird (Tyrannosaurus Lex, unapologetic carnivore)
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To: Yardstick

Actually, the missing sock enters the ho-zone in order to preserve the primacy of number 1.


44 posted on 10/16/2010 8:41:00 PM PDT by pankot
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To: SunkenCiv

Dark Helmet: So the combination is... one, two, three, four, five? That's the stupidest combination I've ever heard in my life! The kind of thing an idiot would have on his luggage!

45 posted on 10/16/2010 9:04:03 PM PDT by JRios1968 (What is the difference between 0bama and his dog, Bo? Bo has papers.)
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To: SunkenCiv
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.

A poor attempt at "modeling the universe" indeed.

But since we are part of that "universe" -- that we are attempting to model -- the "modeling" becomes problematic.

Still(anthropocentric or not)one could argue that there is something of the universe in our selves, and something of our selves in the universe.

Perhaps man's search for order -- in an apparently chaotic universe -- is not so unnatural as it would appear?

STE=Q

46 posted on 10/16/2010 9:31:41 PM PDT by STE=Q ("It is the duty of the patriot to protect his country from its government" ... Thomas Paine)
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To: RegulatorCountry

There’s a simple explanation about the toast, it’s all about the height of fall and the number of times it can turn around before reaching the ground. If tables were taller by some exact amount it’d be the opposite.


47 posted on 10/16/2010 9:35:09 PM PDT by Moose Burger
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To: SunkenCiv

Bump....


48 posted on 10/16/2010 9:55:30 PM PDT by Intolerant in NJ
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To: SunkenCiv

The curves look a lot like inverse exponential functions, e-kx + C.

49 posted on 10/16/2010 10:02:40 PM PDT by Gideon7
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To: Moose Burger

The table is the height it is because the humans who use it are the height they are. It’s not arbitrary.

Maybe we should try smaller toast.


50 posted on 10/16/2010 10:08:11 PM PDT by RegulatorCountry
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To: SunkenCiv

Newscientist ran this article almost verbatim 10 years ago.


51 posted on 10/16/2010 10:11:20 PM PDT by Southack (Media Bias means that Castro won't be punished for Cuban war crimes against Black Angolans in Africa)
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To: SunkenCiv
and a number has just a 4.6 per cent chance of beginning with a 9

Oh yeah, tell that to the Beatles...

Number nine, Number nine, Number nine, Number nine ...
IMHO, John had waaaaay too much acid that day.

;-)

52 posted on 10/17/2010 4:27:39 AM PDT by Condor51 (SAT CONG!)
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To: Condor51

‘urn me on, deadman. ‘urn me on, deadman.


53 posted on 10/17/2010 7:50:22 AM PDT by SunkenCiv (The 2nd Amendment follows right behind the 1st because some people are hard of hearing.)
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To: Southack

It’s a big timesaver. :’)


54 posted on 10/17/2010 8:20:50 AM PDT by SunkenCiv (The 2nd Amendment follows right behind the 1st because some people are hard of hearing.)
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To: Southack

For that matter, and given my usual habits, I should have searched more thoroughly and revived an existing topic about it. :’) Maybe the original version. But I didn’t find one. ;’)


55 posted on 10/17/2010 8:21:46 AM PDT by SunkenCiv (The 2nd Amendment follows right behind the 1st because some people are hard of hearing.)
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To: SunkenCiv; Nachoman

Wasn’t there a math professor from Texas(?) who had won the lottery a couple of times? Obviously she wasn’t telling.


56 posted on 10/17/2010 8:30:14 AM PDT by ladyjane
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To: SunkenCiv

Do they use negative numbers for real calculations in the anti-matter universe?


57 posted on 10/17/2010 1:03:51 PM PDT by Waverunner (")
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To: JPG
Obama loves pi.

Would that be cow pi?

58 posted on 10/17/2010 4:54:52 PM PDT by dearolddad
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