Normal numbers and its applications in real life

Bill Mance, PhD

Lecture of Free University on February 6th

Our guest is Bill Mance, PhD, mathematician from Adam Mickiewicz.

A real number is normal in base 10 if its decimal expansion is “random” in the sense that all the digits 0,1,..,9 occur with relative frequency 1/10, the pairs of digits 00,…,99 each occur with relative frequency 1/100, and so on. The “typical” real number is normal in base 10, but writing down specific examples is very difficult. For example, 0.2 3 5 7 11 13 … is normal in base 10, but it is unknown if numbers such as Pi, e, or sqrt{2} are normal in base 10.

Surprisingly, normality lies on the intersection of many different areas of mathematics. We will discuss some surprising connections between different areas of mathematics that involve normal numbers.