Feb 9, 2015 08:52 PM
http://nautil.us/issue/21/information/th...with-logic
EXCERPT: [...] Standing face to face, they were an unlikely pair. [Warren] McCulloch, 42 years old when he met Pitts, was a confident, gray-eyed, wild-bearded, chain-smoking philosopher-poet who lived on whiskey and ice cream and never went to bed before 4 a.m. Pitts, 18, was small and shy, with a long forehead that prematurely aged him, and a squat, duck-like, bespectacled face. McCulloch was a respected scientist. Pitts was a homeless runaway. He’d been hanging around the University of Chicago, working a menial job and sneaking into Russell’s lectures, where he met a young medical student named Jerome Lettvin.
It was Lettvin who introduced the two men. The moment they spoke, they realized they shared a hero in common: Gottfried Leibniz. The 17th-century philosopher had attempted to create an alphabet of human thought, each letter of which represented a concept and could be combined and manipulated according to a set of logical rules to compute all knowledge—a vision that promised to transform the imperfect outside world into the rational sanctuary of a library.
McCulloch explained to Pitts that he was trying to model the brain with a Leibnizian logical calculus. He had been inspired by the Principia, in which Russell and Whitehead tried to show that all of mathematics could be built from the ground up using basic, indisputable logic. Their building block was the proposition—the simplest possible statement, either true or false. From there, they employed the fundamental operations of logic, like the conjunction (“and”), disjunction (“or”), and negation (“not”), to link propositions into increasingly complicated networks. From these simple propositions, they derived the full complexity of modern mathematics.
Which got McCulloch thinking about neurons. He knew that each of the brain’s nerve cells only fires after a minimum threshold has been reached: Enough of its neighboring nerve cells must send signals across the neuron’s synapses before it will fire off its own electrical spike. It occurred to McCulloch that this set-up was binary—either the neuron fires or it doesn’t. A neuron’s signal, he realized, is a proposition, and neurons seemed to work like logic gates, taking in multiple inputs and producing a single output. By varying a neuron’s firing threshold, it could be made to perform “and,” “or,” and “not” functions....
[...] This universality made it impossible for Pitts to provide a model of the brain that was practical, and so his work was dismissed and more or less forgotten by the community of scientists working on the brain. [...] A purely logical, purely brain-centered vision of thought had its limits. Nature had chosen the messiness of life over the austerity of logic, a choice Pitts likely could not comprehend. He had no way of knowing that while his ideas about the biological brain were not panning out, they were setting in motion the age of digital computing, the neural network approach to machine learning, and the so-called connectionist philosophy of mind...
EXCERPT: [...] Standing face to face, they were an unlikely pair. [Warren] McCulloch, 42 years old when he met Pitts, was a confident, gray-eyed, wild-bearded, chain-smoking philosopher-poet who lived on whiskey and ice cream and never went to bed before 4 a.m. Pitts, 18, was small and shy, with a long forehead that prematurely aged him, and a squat, duck-like, bespectacled face. McCulloch was a respected scientist. Pitts was a homeless runaway. He’d been hanging around the University of Chicago, working a menial job and sneaking into Russell’s lectures, where he met a young medical student named Jerome Lettvin.
It was Lettvin who introduced the two men. The moment they spoke, they realized they shared a hero in common: Gottfried Leibniz. The 17th-century philosopher had attempted to create an alphabet of human thought, each letter of which represented a concept and could be combined and manipulated according to a set of logical rules to compute all knowledge—a vision that promised to transform the imperfect outside world into the rational sanctuary of a library.
McCulloch explained to Pitts that he was trying to model the brain with a Leibnizian logical calculus. He had been inspired by the Principia, in which Russell and Whitehead tried to show that all of mathematics could be built from the ground up using basic, indisputable logic. Their building block was the proposition—the simplest possible statement, either true or false. From there, they employed the fundamental operations of logic, like the conjunction (“and”), disjunction (“or”), and negation (“not”), to link propositions into increasingly complicated networks. From these simple propositions, they derived the full complexity of modern mathematics.
Which got McCulloch thinking about neurons. He knew that each of the brain’s nerve cells only fires after a minimum threshold has been reached: Enough of its neighboring nerve cells must send signals across the neuron’s synapses before it will fire off its own electrical spike. It occurred to McCulloch that this set-up was binary—either the neuron fires or it doesn’t. A neuron’s signal, he realized, is a proposition, and neurons seemed to work like logic gates, taking in multiple inputs and producing a single output. By varying a neuron’s firing threshold, it could be made to perform “and,” “or,” and “not” functions....
[...] This universality made it impossible for Pitts to provide a model of the brain that was practical, and so his work was dismissed and more or less forgotten by the community of scientists working on the brain. [...] A purely logical, purely brain-centered vision of thought had its limits. Nature had chosen the messiness of life over the austerity of logic, a choice Pitts likely could not comprehend. He had no way of knowing that while his ideas about the biological brain were not panning out, they were setting in motion the age of digital computing, the neural network approach to machine learning, and the so-called connectionist philosophy of mind...