The first digit law, also known as Benford’s law or the significant digit law, is an empirical phenomenon that the leading digit of numbers from real world sources favors small ones in a form log(1 + 1/d), where d= 1...The first digit law, also known as Benford’s law or the significant digit law, is an empirical phenomenon that the leading digit of numbers from real world sources favors small ones in a form log(1 + 1/d), where d= 1, 2,..., 9.Such a law has been elusive for over 100 years because it has been obscure whether this law is due to the logical consequence of the number system or some mysterious mechanism of nature. We provide a simple and elegant proof of this law from the application of the Laplace transform, which is an important tool of mathematical methods in physics. It is revealed that the first digit law originates from the basic property of the number system, thus it should be attributed as a basic mathematical knowledge for wide applications.展开更多
基金Supported by the National Natural Science Foundation of China under Grant No 11475006
文摘The first digit law, also known as Benford’s law or the significant digit law, is an empirical phenomenon that the leading digit of numbers from real world sources favors small ones in a form log(1 + 1/d), where d= 1, 2,..., 9.Such a law has been elusive for over 100 years because it has been obscure whether this law is due to the logical consequence of the number system or some mysterious mechanism of nature. We provide a simple and elegant proof of this law from the application of the Laplace transform, which is an important tool of mathematical methods in physics. It is revealed that the first digit law originates from the basic property of the number system, thus it should be attributed as a basic mathematical knowledge for wide applications.
