There is no doubt that cognition and intelligence are the result of neural activity --- but how?
How do molecules, neurons and synapses give rise to reasoning, language, plans, stories, art, math? Despite dazzling progress in experimental neuroscience, as well as in cognitive science, we do not seem to be making progress in the overarching question. The reason is that these two communities are separated by a huge gap --- not just in scale, but also in experimental methodology and mindset. As Richard Axel recently put it in an interview to Neuron: "We don't have a logic for the transformation of neural activity into thought [...]."
What kind of formal system would qualify as this "logic"?
I will introduce the Assembly Calculus, a computational system whose basic data structure is the assembly: assemblies are large populations of neurons representing concepts, words, ideas, episodes, etc.The Assembly Calculus is biologically plausible in the following two orthogonal senses: Its primitives are properties of assemblies observed in experiments, or useful for explaining other experiments, and can be provably (through both mathematical proof and simulations in biologically realistic platforms) "compiled down" to the activity of neurons and synapses. Furthermore, The Assembly Calculus can be shown both mathematically and experimentally to simulate simple high-level cognitive functions, such as parsing simple sentences, as well as planning. We believe that this formalism is well positioned to help in bridging the gap between the brain and the mind.
Christos Harilaos Papadimitriou is the Donovan Family Professor of Computer Science at Columbia University. Before joining Columbia in 2017, he was a professor at UC Berkeley for the previous 22 years, and before that he taught at Harvard, MIT, NTU Athens, Stanford, and UCSD. He has written five textbooks and many articles on algorithms and complexity, and their applications to optimization, databases, control, AI, robotics, economics and game theory, the Internet, evolution, and the brain. He holds a PhD from Princeton (1976), and eight honorary doctorates, including from ETH, University of Athens, EPFL, and Univ. de Paris Dauphine. He is a member of the National Academy of Sciences of the US, the American Academy of Arts and Sciences, and the National Academy of Engineering, and he has received the Knuth prize, the Go"del prize, the von Neumann medal, as well as the 2018 Harvey Prize by Technion. In 2015 the president of the Hellenic republic named him commander of the order of the Phoenix. He has also written three novels: “Turing ,” “Logicomix” and his latest “Independence.”