The Australian is reporting on another breakthrough accomplishment made possible by advances in supercomputing. A group of researchers from the University of Newcastle, Lawrence Berkeley National Laboratory and IBM Australia used a BlueGene/P supercomputer to solve a mathematical calculation previously considered impossible. The team, lead by Newcastle’s Laureate Professor Jon Borwein, calculated digits beginning at the ten trillionth position (in two different number bases) of the mathematical constant pi squared, as well as Catalan’s constant. Widely used in the fields of geometry, physics and other mathematical analyses, pi is the ratio of the circumference of a circle to its diameter.
The computations involved a total of approximately 1:549 x 10^19 floating-point operations, which according to Professor Borwein, represents the largest single computation done for any mathematical object. He comments, “By combining human ingenuity with the awesome power of the BlueGene/P computer, we came up with an algorithm that allows us to identify potential weaknesses in computer system hardware and software. The scheme that we used enables one to compute digits of mathematical constants, including the square of the mathematical constant pi, without knowing any previous digits. It was like we stuck our hand deep into the mathematical universe and pulled out the exact data.”
The work was performed on a 4-rack IBM BlueGene/P system located at IBM’s Benchmarking Centre in Rochester, Minn. What would have taken a single CPU about 1,500 years to process, the Big Blue machine ran through in just months; and this is a shared machine. A dedicated machine of equal power would have taken less time. The researchers who were accessing the machine remotely from Australia did have the benefit of time-shifting. Due to the time-difference, they were able to use the system during its natural downtime.
Professor Borwein, a world-renowned expert in pi calculations, explains how this latest development applies to a new field of study known as quantum randomness, which he describes as “using natural processes to build random things.” The research could lead to better random number generators:
If we could prove pi squared was random in some sense then we could use it instead of all the expensive quantum random number generators or pseudo-random number generators that make all of our banking codes safe.
A prototype is in the works for later this year. The group’s paper, “The Computation of Previously Inaccessible Digits of π2 and Catalan’s Constant,” is available here.