Number one rules in nature: study

February 17, 2011, Australian National University
Professor Malcolm Sambridge. Photo by Belinda Pratten.

( -- Researchers from The Australian National University have used a long-forgotten mathematical rule to reveal that in nature the number one dominates, as well as detect natural events like earthquakes for the first time ever.

The research, led by Professor Malcolm Sambridge in the Research School of Earth Sciences, shows that events as diverse as the rotation rates of dying stars and the surface areas of rivers all share one thing in common – in nature larger numbers are less likely to occur than smaller ones.

Professor Sambridge said that by applying an obscure mathematical theory called Benford’s law to a range of natural phenomena, he and his colleagues were able to reveal some remarkable relationships across the physical sciences.

“Most physicists would think that the likelihood of a beginning with a one would occur just as often with numbers beginning with a two or a three or so on,” said Sambridge. “But it turns out this is not the case in the natural world.

“Instead, as Benford’s law shows, roughly 30 per cent of numbers related to real-world events begin with the number one and only 17 per cent begin with a two. And it goes right down to roughly about four per cent beginning with a nine,” he said.

To test the theory the researchers tested 18 data sets containing over 750,000 numbers across a range of natural phenomena, including green-house gas emissions, the masses of giant planets outside our solar system, the number of infectious diseases reported by the World Health Organization, the time it takes a burst from a gamma ray to reach your eye and the periods between the flipping of the earth’s magnetic poles.

“Much to our surprise we found that Benford’s law largely holds true in all these areas,” said Professor Sambridge. “The natural world is littered with a surplus of the digit one.”

The study also led to the detection of a physical event for the first time ever – identifying a previously overlooked earthquake which took place in Canberra during the 2004 Asian tsunami.

“One of the things we are interested in is automated methods of detecting an earthquake,” said Sambridge. “We found that Benford’s law can be used for exactly that purpose.

“By taking the first digits of the counts of a seismometer, which measures motions in the ground caused by earthquakes, we can quite clearly see the onset of an earthquake.

“This also means that we can use computers to detect when waves from an earthquake arrive at a recording station in an entirely new way,” he said.

Explore further: Menominee County shakeup was an earthquake, says researcher

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5 / 5 (1) Feb 17, 2011
Pareto principle
not rated yet Feb 17, 2011
Wow, this is all pretty weird. I'd love to know why this law applies. I'm not sure I really understand the earthquake detection idea, could anyone explain that?
not rated yet Feb 17, 2011
Wow, this is all pretty weird. I'd love to know why this law applies. I'm not sure I really understand the earthquake detection idea, could anyone explain that?

A mathematician named Benfored accidentally discovered this relationship when studying a book of logarithm tables from back before computers were invented. He noticed that the number 1 was worn out disproportionately compared to other numbers, because people who had borrowed the book from the library previously used the number 1 so much more often than other numbers.

It turns out that a lot of data sets in the real world have their first digit distribution predicted by benfords's law.

Log ((n+1)/n)

predicts how often a digit from 1 to 9 occurs in the data set.

1 = 30.1%
2 = 17.6%
3 = 12.5%
4 = 9.7%
5 = 7.9%
6 = 6.7%
7 = 5.7%
8 = 5.1%
9 = remainder

Ok, so this isn't perfect to the digit, but it's short version due to character limit.
not rated yet Feb 17, 2011
Now what is interesting is that Benford's law holds regardless of arbitrary units of measurement.

If a data set follows benford's law in one measurement system, it will follow benford's law in all measurement systems.
not rated yet Feb 17, 2011
I have subsequently found a good explanation for why Benford's Law applies by following the link to Benford's Law in the article. The comments were helpful. However, I still don't get how this could predict earthquakes, the article was quite vague about this.
not rated yet Feb 17, 2011
I still don't get how this could predict earthquakes, the article was quite vague about this.

I should say that the "numbering system" should be considered "real" numbers, such that classifications are of equal size, so for example, hurricane categories on the Saffir-Simpson scale won't work, because different categories are different sizes.

As for quakes, I gave it some thought, and I really don't get it either. It may have something to do with the inverse square law for wave propagation.

Multiplying Benford's law by an appropriate scalar value produces a curve similar to the inverse square law, so it's possible that one could be mistaken for the other in some relevant data sets, or that they may be related in some data sets.
5 / 5 (1) Feb 17, 2011
This is not newly discovered, but in use for a long time to check your books by the tax departments. People who fix their bookkeeping are going wrong on this law.
3 / 5 (2) Feb 18, 2011
This is neither long-forgotten nor obscure. See "The power of one" in New Scientist 10-Jul-1999.
not rated yet Feb 22, 2011
Does anyone know how Benford's Law extends to other bases?

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