In the realm of scientific inquiry, both experimentation and mathematical explanation play crucial roles. Experimentation allows researchers to observe phenomena and gather data, leading to new discoveries and insights. However, without mathematical reasoning, these findings can lack depth and understanding. Thus, experimentation alone can be considered directionless or "blind."

On the other hand, mathematical explanation provides a framework for interpreting and analyzing experimental results. It can reveal underlying principles and relationships but may fall short without empirical evidence to support it. In this sense, mathematical explanation without experimentation is "empty," highlighting the importance of a balanced approach in the scientific process.