Subash Khot: A grand vision for the impossible

Sources: Quanta Magazine and Simons Foundation

Subash Khot is this year’s winner of the Nevanlinna Prize. If his “Unique Games Conjecture is correct, then for many of the problems people would most like to solve, it’s hard not only to find an exact solution—finding even a good approximation of the solution is beyond the reach of a computer. This conjecture may seem, on the face of it, like a pretty parochial statement (though possibly hard to prove, or even false). Over the past decade, however, computer scientists have found to their surprise that if the conjecture is true, then a host of problems—some of them seeming to bear little resemblance to the original Unique Games problem—are also hard to approximate.” Simons Foundation

Source: Quanta Magazine

“For the problem of coloring the nodes of a network that has a collection of constraints about which color combinations are allowed (top left), it is sometimes possible to find a coloring that satisfies all the constraints (top right). But for some networks and constraints (bottom left), it is impossible to satisfy all the constraints simultaneously. The Unique Games Conjecture concerns the problem of finding a coloring that satisfies as many constraints as possible, such as the bottom right coloring, which satisfies all the constraints except the one for the thick edge.” Quanta Magazine.

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The myth of mirror neurons

Gregory Hickok: The myth of mirror neurons. The real neuroscience of communication and cognition. W. W. Norton 2014.

Source: Publisher

From publisher’s website: “In The Myth of Mirror Neurons, neuroscientist Gregory Hickok reexamines the mirror neuron story and finds that it is built on a tenuous foundation—a pair of codependent assumptions about mirror neuron activity and human understanding. Drawing on a broad range of observations from work on animal behavior, modern neuroimaging, neurological disorders, and more, Hickok argues that the foundational assumptions fall flat in light of the facts.”

Review by Patricia Smith Churchland in Nature 511, 532–533 (31 July 2014): “Hickok’s critique deserves to be widely discussed, especially because many scientists have bought into the mirror-neuron theory of action understanding, perhaps because they lack the time or inclination to peer into its workings themselves. Hickok performs a valuable service by laying out the pros and cons clearly and fairly. He ends by agreeing that although mirror neurons may well have a role in explaining communication and empathy, many other neural networks with complex responses are undoubtedly involved. Those networks and their roles are still to be clarified.”

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