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The antiscientifical revolution and mathematics \Lambda V.I. Arnold
 

Summary: The antiscientifical revolution and mathematics \Lambda
V.I. Arnold
I shall start describing an example of a mathematical theory that is easily explained
to non­mathematicians. Then, I shall discuss the aversion of the society to mathematics,
ending with some remarks on the specific problems of Russian mathematicians.
I consider the first digit of the number representing the area of a country. This digit
may be 1,2,...,9. The distribution of the countries of the world according to the first
digit of the area figure is extremely nonuniform. The countries for which the first digit
is 1 form about 30% of all the countries, and the number of those for which the first
digit is 9 is approximately 6 times smaller, with a gradual decline in between.
This distribution does not depend on the area units: you might measure the areas
in square kilometers, or square miles, or square inches and so on.
This nonuniform distribution of the first digits had been observed in many other
cases and is known as the empirical Benford law.
For instance, the first digits of the populations of countries of the world behave
similarly.
The contribution of mathematics to the explanation of these rather mysterious em­
pirical phenomena depends on ideas from the ergodic theory of dynamical systems.
Consider the sequence of the first digits of the powers of 2:
1; 2; 4; 8; 1; 3; 6; 1; 2; 5; 1; 2; :::

  

Source: Arnold, Vladimir Igorevich - Steklov Mathematical Institute

 

Collections: Mathematics