The Message of Pi: Platonic, Archetypal, Immutable?

Science fiction has played with the idea of a message being hidden within laws or constants of physics, as if a higher power encoded information within the fabric of this universe. To open-mindedly contemplate the possibility of this is sufficient to inspire awe about mathematics and its potential to present the platonic.

A constant such as pi seems even more fundamental and inherently constant than other physical constants such as the speed of light or mass of an electron. While those physical constants suggest a fine-tuned nature of the universe, it is more easily imagined that the universe could be tuned to different constants which govern its ways. In contrast to that, how can one imagine a mathematical constant such as pi being different than it is? It is of the nature of ideas, of geometric concepts (what we refer to as a circle and the relationship between its circumference and diameter). How can a constant which governs a mere idea be manipulated?

What do you think?