Category Archives: Genius

Enrico Fermi: Tackle the Unknown

Source: MIT Tech Review, Apr 2013

He was always ready to tackle the unknown,” she recalls. “He would always ask questions about ‘What if this and this and this were true? What if we could make this—would it be interesting, and what could we learn?’”

Nobel Laureate, Physics (1938)

Geometric “Theory Space”

Source: Quanta, Feb 2017

I.J. Good on Super Intelligence

Source: Gizmodo, Oct 2013

I. J. Good happened to invent the idea of an intelligence explosion, and if it really was possible. The intelligence explosion was the first big link in the idea chain that gave birth to the Singularity hypothesis.

In the 1965 paper “Speculations Concerning the First Ultra-intelligent Machine,” Good laid out a simple and elegant proof that’s rarely left out of discussions of artificial intelligence and the Singularity:

Let an ultraintelligent machine be defined as a machine that can far surpass all the intellectual activities of any man however clever. Since the design of machines is one of these intellectual activities, an ultraintelligent machine could design even better machines; there would then unquestionably be an “intelligence explosion,” and the intelligence of man would be left far behind. Thus the first ultraintelligent machine is the last invention that man need ever make . . .

Thus the first ultraintelligent machine is the last invention that man need ever make, provided that the machine is docile enough to tell us how to keep it under control (emphasis mine).

In a 1996 interview with statistician and former pupil David L. Banks, Good revealed that he was moved to write his essay after delving into artificial neural networks. Called ANNs, they are a computational model that mimics the activity of the human brain’s networks of neurons. Upon stimulation, neurons in the brain fire, sending on a signal to other neurons. That signal can encode a memory or lead to an action, or both. Good had read a 1949 book by psychologist Donald Hebb that proposed that the behavior of neurons could be mathematically simulated.

In 1998, Good was given the Computer Pioneer Award of the IEEE (Institute of Electrical and Electronics Engineers) Computer Society. He was eighty-two years old. As part of his acceptance speech he was asked to provide a biography. He submitted it, but he did not read it aloud, nor did anyone else, during the ceremony. Probably only Pendleton knew it existed.

[The paper] “Speculations Concerning the First Ultra-intelligent Machine” (1965) . . . began:

“The survival of man depends on the early construction of an ultra-intelligent machine.” Those were his [Good’s] words during the Cold War, and he now suspects that “survival” should be replaced by “extinction.” He thinks that, because of international competition, we cannot prevent the machines from taking over. He thinks we are lemmings. He said also that “probably Man will construct the deus ex machina in his own image.”


Einstein’s Ulm Birthplace Motto: “The People of Ulm are Mathematicians”


Crazy Can Transform Lives

Source: The Verge, Oct 2013

“There’s often a long and tortured path to the final product, and it starts with theoretical thinking,” Dijkgraaf says. “But decades later, this work that can seem crazy has the potential to totally transform our lives.”

Einstein’s Office

Source: IAS, date indeterminate


Ramanujan – the Man who Knew Infinity

Source: Science and Non-Duality, 2016

Ramanujan was the first Indian professor to become a Fellow at Cambridge University. Hardy said: “He combined a power of generalization, a feeling for form, and a capacity for rapid modification of his hypotheses, that were often really startling, and made him, in his own peculiar field, without a rival in his day. The limitations of his knowledge were as startling as its profundity. Here was a man who could work out modular equations and theorems… to orders unheard of, whose mastery of continued fractions was… beyond that of any mathematician in the world, who had found for himself the functional equation of the zeta function and the dominant terms of many of the most famous problems in the analytic theory of numbers; and yet he had never heard of a doubly periodic function or of Cauchy’s theorem, and had indeed but the vaguest idea of what a function of a complex variable was…”

As for his place in the world of Mathematics, Paul Erdős of Israel’s Technion passed on Hardy’s personal ratings of mathematicians. Suppose that we rate mathematicians on the basis of pure talent on a scale from 0 to 100, Hardy gave himself a score of 25, J.E. Littlewood 30, David Hilbert 80 and Ramanujan 100.

While the beauty of the story has long impacted all students of mathematics, the nature of Ramanujan’s mathematical genius, and how he himself perceived it, tends to be less explored. Hardy called it some kind of deep ‘intuition’, but Ramanujan openly stated that he received the mathematical inspiration and sometimes whole formulas, through contacting the Hindu Goddess Namagiri while dreaming. Ramanujan was an observant Hindu, adept at dream interpretation and astrology. Growing up, he learned to worship Namagiri, the Hindu Goddess of creativity. He often understood mathematics and spirituality as one. He felt, for example, that zero represented Absolute Reality, and that infinity represented the many manifestations of that Reality.

Facebook founder Mark Zuckerberg recently named Ramanujan as one of his favourite scientists. He points out that all that genius – an intelligence that transformed mathematics and physics – could have been lost, had Hardy not responded in those early pre-war years. What would have happened if Ramanujan had access to the internet? He asks. How many more Ramanujans are out there?