Many are afraid of the complexity of the world. The sweeter to know that among the heaps of apparent coincidences have their own laws. Sometimes completely inexplicable. And it is even more frightening. In 1881 the American astronomer Simon New comb noticed that in the book of logarithmic tables, page numbers that start with one, worn out more than others. Upon reflection, the scientist suggested that the spread of numbers actually correspond to a logarithmic distribution: one occurs on average about 30% of cases, two – about 18% and so on up to nine, with its 5%. Although one would expect that all the figures there are approximately the same number of times.
In 1938 American physicist Frank Ben ford
Rediscovered this law, studied it in detail and formulate the corresponding equation. It is not universal, but it works surprisingly often: Benford checked it on the variety of data sets from the surface of rivers and the heat capacity of the physical connections to mathematical constants and baseball statistics.
The most interesting is that the law Benford can be used to detect financial fraud. People who plotted evil, it is believed that the random variations in the cover of their mischief, but he then gives them red-handed. It is sometimes said that the test results of the election shall include compliance with the law Benford, but, alas, it only works if the indicators cover several orders of magnitude. (Try it yourself.)
“Why the hell is going on?” – Angry scientists are asking.
Several years ago, researchers interested in whether the behavior of our planet Benford’s law. For example, an article published in 2010, described the analysis of such things as the time between geomagnetic reversals (when the magnetic “north” of the Earth is at the opposite geographical pole), the depth of earthquakes, greenhouse gas emissions, and even statistics of infectious diseases. They are all very good fit to Benford’s Law. (In the same way as before – speed and mass of the pulsar planets.)
In the new work a couple of Spanish researchers has increased the list by three sets of data – an area of volcanic calderas and the age and duration of volcanic eruptions in 1900-2009, respectively. This is not just a game of numbers, because science has passed the stage when the law demanded that Benford’s confirmation. The purpose of these Study now is to use it as a kind of validation of geological database for the truth. If they do not obey Benford, then it may be a sign that sets unrepresentative data contain errors or bias.
Benford’s Law very well come to the description of the duration of eruptions. Area calderas also proved good, although some deviations are seen, most likely occurred too indiscriminate rounding. But the age of the caldera is not entered in the law: too many numbers begin with the twos and threes. Peering into the data, scientists have realized the problem: too often North American caldera, formed 23-42 million years ago.
As it turned out, this is a known anomaly. It is not clear whether at that time have an unusually active formation of calderas or in North America, they are simply better understood. The removal of these calderas from the analysis of the situation has returned to the law Benford. The exception to the rule proves the rule.