Earthquakes and The Man Who Knew Infinity

It is rare to get a glimpse of individuals of extreme genius who also elude the fame that often comes with these rare abilities, yet Ramanujan was a man of such raw and rare mathematical talent, that over 100 years after his death he is being “rediscovered” in the West through a relatively new movie called “The Man Who Knew Infinity” (produced in 2015 but recently released in the United States).

This movie is one of many in a lineup of modern films that depict the lives of notable mathematicians, scientists and musicians including mathematician Alan Turing (The Imitation Game), mathematician John Nash (A Beautiful Mind), physicist Stephen Hawking (The Theory of Everything), pianist Wolfgang Mozart (Amadeus), pianist David Helfgott (Shine) among others.

Largely drawn from the book of the same title, The Man Who Knew Infinity – A Life of the Genius Ramanujan by Robert Kanigel, is a gripping story of a young self-taught mathematical prodigy who, from humble beginnings in Madras, India, was discovered by an eminent Cambridge mathematician in 1923 and invited to work in England under his tutelage.

By the time he was 26 years old, Ramanujan, had not only established himself among his British counterparts, but he became a Fellow of the Royal Society, one of the most prestigious honors in one of the most prestigious societies of the time.

Ramanujan’s talent lay in his ability to see complex patterns in sequences of numbers with little or no proof. He often attributed his ability to visions of numbers or divine inspiration.

Ramanujan had such an insight into the world of numbers that most of his work cannot be understood except for a handful of mathematicians. To this day, there are elements of his work that remain unproven and are still being investigated because of their sheer complexity. His ability to transcended the mathematics of his time and anticipate new fields of math is exemplified in cosmology with the development of theories for objects such as black holes.

Ramanujan and Earthquakes

Earthquake sequences have baffled seismologists for decades, particularly when it comes to forecasting earthquakes. There are many influences, both human-induced and natural, that make this problem particularly difficult. Much of the work in earthquake forecasting uses probabilistic models based on the premise of seemingly random earthquake activity.

This begs the question of whether Ramanujan could have done any better?

In his book on the Mathematics of Natural Catastrophes, Gordon Woo described how formulas in Ramanujan’s Lost Notebook describes a series of numbers that has found relevance in the interval between earthquake activity.

Woo describes how seismologists Bakun and Lindh attempted to forecast the occurrence of a major earthquake on the San Andreas fault in the vicinity of Parkfield, California. Their forecast was based on an apparent uniform interval between successive earthquakes. Unfortunately, their approach was based on a short sequence of only 6 earthquakes. In retrospect, this approximation was misleading since the next earthquake in the sequence did not behave according to their periodic prediction.

Curiously, the interval between the last two Parkfield earthquakes in the Bakun and Lindh research was 32 years which was the same number found in an unusual number sequence determined by Ramanujan.

It took decades for some of Ramanujan’s formulas to be rediscovered and applied in cosmology and quantum theory. Whether his work will find its way into seismology, or other sciences, that present unusual sequences of numbers is an open question. An area that is ripe for his work is encryption.

Random Numbers and Computers

Today’s computer’s rely on random number generators for encryption, yet no algorithm is perfectly random. Yet, Ramanujan has formulas that remain the most “unpredictable” of all in terms of generating seemingly random sets of numbers.

This speaks to Ramanujan’s uncanny ability to have recognized patterns in apparently unrelated sequences of numbers.

Those who comprehend his level of mathematics expect to find applications for his work for many decades or centuries to come. That is how special he was.

His work displays “astonishing individuality and power” and “India now possesses a pure mathematician of the first order”. Hardy