the Signature of Tao

In the novel "Contact" Carl Sagan, astronomer, astrophysicist, astrochemist, great science writer and author, a founder of SETI Project, imagine a possible real "Signature of God".

In the story of Ellie (Jodie Foster in the movie) after a trip through a wormhole to get to meet an extraterrestrial intelligence that appears in the imagine of her father. At the end of the interview he is suggested to calculate pi much more thoroughly in the extension of digits than ever before, because it could be "very interesting".

Mosaic at entrance to math building, Technische Universität Berlin

pi is a number which is both irrational and transcendental, with infinite  decimal places after the point, that means that in base N the probability that in a certain position would appear any number between 0 and N is 1/N. Any statistical discrepancy from 1/N, for example a specific number repeated many times or a sequence of numbers repeated is a fact definitely worthy of note.

The calculation of decimal places of pi it's easy numerically through several series that approximate pi as much as desired, for example:

In computing the digits of pi several months later Ellie is warned by a statistical correlation that controls the figures calculated of a statistical anomaly that appears after several tens of billions of digits after the decimal point. Let us assume that the figures calculated are represented in binary mode with the 1 and 0, what appears is:

that is, arranging the 0s and 1s in a square shows a statistical anomaly of 0s and 1s that represents a circle. Deeply hidden after billions of digits of the number that represents, by definition, the circle there is a circle.

Since a circle is a circle everywhere (apart from very particular places where the geometry of the space-time is not  euclidean), and is an intrinsic property of our Universe, this means to Sagan that this sign has been placed before the creation of the Universe, in its very structure, a true "Signature of God."