Ramanujan’s old formulae for pi echo in modern cosmology, Pg13

Key Highlights:

• IISc professor Aninda Sinha and Faizan Bhat linked Ramanujan's formulae with turbulent fluids and the expansion of the universe using pi.
• Srinivasa Ramanujan discovered at least 17 fast formulae to calculate 1/π over a century ago.
• Some of Ramanujan’s formulae underpin the Chudnovsky algorithm, used to compute π to over 200 trillion digits.
• The research unexpectedly began in string theory, leading to the discovery of an infinite number of new formulae for π.

Detailed Insights:

• Ramanujan's equations are analogous to those in certain kinds of conformal field theories (CFTs), the mathematical language of critical phenomena.
• CFTs explain phenomena at critical points where systems are on the edge of change, such as when fluids become superfluid.
• The mathematical structure identified in the Ramanujan-CFT connection appears in models of an expanding universe.
• The work suggests that other transcendental numbers might have efficient representations rooted in physics.
• Riemannian geometry, developed as pure mathematics, later became the geometry of spacetime in Einstein’s general theory of relativity.
• Fourier transforms, developed to analyze heat flow, now support digital image and music compression.

Scientific/Technical Concepts Involved:

• Pi (π): The ratio of a circle's circumference to its diameter, approximately 3.14159.
• String Theory: A theoretical framework where fundamental particles are vibrations of tiny strings.
• Conformal Field Theories (CFT): Mathematical language describing critical phenomena and systems on the edge of change.
• Transcendental Number: A number that is not the root of any non-zero polynomial equation with integer coefficients.