Transcendental Number
A transcendental number is a real or complex number that is not algebraic—that is, it is not a root of a non-zero polynomial equation with rational coefficients. The most well-known examples are π (pi) and e.
Related Concepts
Patterns in pi in “Contact”
In Carl Sagan’s novel Contact, the main character Ellie Arroway is informed by an alien that certain megastructures in the universe were created by an advanced intelligence, which left messages embedded inside transcendental numbers. To investigate this claim, Arroway writes a program to compute π in various bases and discovers that its base 11 representation contains a sequence of ones and zeros forming a circular pattern when aligned properly.
- 2026 04 13 Patterns in pi in Contact
Pi: 39 Digits for Universe Measurement, Trillions for Computational Testing
Clip title: Pi and the size of the Universe Author / channel: James Grime, Numberphile URL: https://www.youtube.com/watch?v=FpyrF_Ci2TQ
Summary
- In this video, Richard Dawkins discusses a fascinating concept from Carl Sagan’s science fiction novel, Contact.
- He recounts a hypothetical scenario where an intelligent design, often attributed to a divine entity, is found embedded within the fundamental mathematical constant π.
2026 04 13 Sagans Contact Gods Signature in Pi and Dawkins Scientific View