The Expert

There are many well-known orthogonal functions, such as Legendre polynomials and Chebyshev polynomials.

As a brief diversion from the main topic, I would like to share my thoughts about a famous YouTube video titled The Expert, where an expert is asked to draw seven perpendicular lines. The customers are portrayed as a group of weird and foolish individuals. The expert, looking embarrassed, explains that drawing more than two perpendicular lines is impossible.

In Euclidean geometry, a line is a straight path defined by two points. However, the term "line" can be used more loosely to describe a path or trajectory, which may include curves (curved lines). The following figure exemplifies seven Legendre polynomials, all of which are orthogonal (perpendicular) to each other. The issue isn't the customers being weird or foolish; it's about the bad expert.