Explain the concept of an irrational base number system and its potential applications in computer science and mathematics.

An irrational base number system uses an irrational number (e.g., the golden ratio, φ) as its base, allowing for unique representations and properties. Such systems can potentially simplify certain mathematical problems, offering novel perspectives in number theory and algorithms. Applications include quasi-crystal structures in material science and alternative computational methods that exploit the unique properties of irrational bases for efficient calculations and data encoding.