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orithms called threshold logic which split the inquiry into two distinct approaches one approach focused on biological processes in the brain and the other focused on the application of neural networks to artificial intelligence 2 biography edit warren sturgis mcculloch was born in orange new jersey in 1898 his brother was a chemical engineer and warren was originally planning to join the christian ministry as a teenager he was associated with the theologians henry sloane coffin harry emerson fosdick herman karl wilhelm kumm and julian f hecker he was also mentored by the quaker rufus jones 3 he attended haverford college then studied philosophy and psychology at yale university where he received a bachelor of arts degree in 1921 he continued to study psychology at columbia and received a master of arts degree in 1923 receiving his md in 1927 from the columbia university college of physicians and surgeons in new york he undertook an internship at bellevue hospital new york then he worked under eilhard von domarus at the rockland state hospital for the insane 4 he returned to academia in 1934 he worked at the laboratory for neurophysiology at yale university from 1934 to 1941 in 1941 he moved to chicago and joined the department of psychiatry at the university of illinois at chicago where he was a professor of psychiatry as well as the director of the illinois neuropsychiatric institute until 1951 5 from 1952 he worked at the massachusetts institute of technology in cambridge massachusetts with norbert wiener he was a founding member of the american society for cybernetics and its second president during 1967 1968 he was a mentor to the british operations research pioneer stafford beer mcculloch had a range of interests and talents in addition to his scientific contributions he wrote poetry sonnets and he designed and engineered buildings and a dam at his farm in old lyme connecticut mcculloch married ruth metzger known as rook in 1924 and they had three children 6 he died in cambridge in 1969 work edit he is remembered for his work with joannes gregorius dusser de barenne from yale 7 and later with walter pitts from the university of chicago he provided the foundation for certain brain theories in a number of classic papers including a logical calculus of the ideas immanent in nervous activity 1943 and how we know universals the perception of auditory and visual forms 1947 both published in the bulletin of mathematical biophysics the former is widely credited with being a seminal contribution to neural network theory the theory of automata the theory of computation and cybernetics 1 mcculloch was the chair of the set of macy conferences dedicated to cybernetics these greatly due to the diversity of the backgrounds of the participants mcculloch brought in became the foundation for the field in wiener s cybernetics 1948 he recounted an event in the spring of 1947 when mcculloch designed a machine to allow the blind to read by converting printed letters to tones he designed it so that the tone is invariant for the same letter viewed under different angles gerhardt von bonin saw the design and immediately asked is this a diagram of the fourth layer of the visual cortex of the brain 8 22 140 in his last days in 1960s he worked on loops oscillations and triadic relations with moreno díaz the reticular formation with kilmer and dynamic models of memory with da fonseca 9 his work in the 1960s was summarized in a 1968 paper 10 neuroscience edit he studied the excitation of the brain by strychnine neuronography which was a method to map brain connections applying strychnine in one point of the brain causes excitations in different points of the brain 11 bailey bonin and mcculloch conducted a series of studies in the 1940s that identified connections in the brains of macaque and chimpanzee that are consistent with modern understanding of vof 12 13 mathematical logic edit in 1919 he began to work mainly on mathematical logic and by 1923 he attempted to make a logic of transitive verbs his goal in psychology is to invent a psychon or least psychic event that are binary atomic events with necessary causes such that they can be combined to create complex logical propositions concerning their antecedents he noticed in 1929 that these may correspond to the all or nothing firings of neurons in the brain 3 in the 1943 paper they described how memories can be formed by a neural network with loops in it or alterable synapses these then encode for sentences like there was some x such that x was a ψ or x ψ x displaystyle exists x psi x and showed that looped neural networks can encode all first order logic with equality and conversely any looped neural networks is equivalent to a sentence in first order logic with equality thus showing that they are equivalent in logical expressiveness 3 the 1943 paper describes neural networks operating over time and logical universals there exists and for all for spatial objects such as geometric figures was further developed in their 1947 paper 14 he worked with manuel blum in studying how a neural network can be logically stable that is can implement a boolean function even if the activation thresholds of individual neurons are varied 15 64 they were inspired by the problem of how the brain can perform the same functions such as breathing under influence of caffeine or alcohol which shifts the activation threshold over the entire brain 3 he worked on triadic relations an extension of the calculus of relations to handle relations that relates 3 objects such as a gives b to c or a perceives b to be c he was convinced that such a logic is necessary for understanding brain activity 10 16 how we know universals edit in the 1947 paper how we know universals they studied the problem of recognizing objects despite changes in representation for example recognizing a square under different viewing angles and lighting conditions or recognizing a phoneme under different loudness and tones that is recognizing objects invariant under the action of some symmetry group this problem was partly inspired by a practical problem in designing a machine for the blind to read recounted in wiener s cybernetics see before 17 the paper proposed two solutions the first is in computing an invariant by averaging over the symmetry group let the symmetry group be g displaystyle g and the object to be recognized be x displaystyle x let a neural network implement a function t displaystyle t then the group invariant representation would be 1 g g g t g x displaystyle frac 1 g sum _ g in g t gx the group action average the second solution is in a negative feedback circuit that drives a canonical representation consider the problem of recognizing whether an object is a square the circuit moves the eye so that the center of gravity of brightness of the object is moved to the middle of the visual field this then effectively converts each object into a canonical representation which can then be compared with a representation in the brain 18 19 neural network modelling edit in the 1943 paper mcculloch and pitts attempted to demonstrate that a turing machine program could be implemented in a finite network of formal neurons in the event the turing machine contains their model of the brain but the converse is not true 20 that the neuron was the base logic unit of the brain in the 1947 paper they offered approaches to designing nervous nets to recognize visual inputs despite changes in orientation or size from 1952 mcculloch worked at the research laboratory of electronics at mit working primarily on neural network modelling his team examined the visual system of the frog in consideration of mcculloch s 1947 paper discovering that the eye provides the brain with information that is already to a degree organized and interpreted instead of simply transmitting an image with roberto moreno díaz he studied a formalized problem of memory given that neural networks can store memory by a pattern of oscillations in a circle they studied the number of possible oscillation patterns that can be sustained by some neural network with n displaystyle n neurons this came out to be k n 2 n k k 1 2 n 1 k displaystyle k n binom 2 n k sum _ k 1 2 n 1 k schnabel 1966 21 also they proved a universality theorem in that for each n displaystyle n there exists a neural network possibly with more than n displaystyle n neurons with log 2 k n displaystyle log _ 2 k n binary inputs such that for any oscillation pattern realizable by some neural network with n displaystyle n neurons there exists a binary input for this universal network such that it exhibits the same pattern 22 23 24 control edit mcculloch considered the problem of contradictory information and motives which he called a heterarchy of motives meaning that the motives are not linearly ordered but can be ordered like a b c a displaystyle a b c a 25 he posited the concept of poker chip reticular formations as to how the brain deals with contradictory information in a democratic somatotopical neural network specifically how the brain can commit the animal to a single course of action when the situation is ambiguous they designed a prototypic example neural network retic with 12 anastomatically coupled modules stacked in columnar array which can switch between unambiguous stable modes based on ambiguous inputs 26 16 his principle of redundancy of potential command 26 was developed by von foerster and pask in their study of self organization 27 and by pask in his conversation theory and interactions of actors theory 28 publications edit mcculloch wrote a book and several articles 29 1965 embodiments of mind mit press cambridge 1993 the complete works of warren s mcculloch intersystems publications salinas ca articles a selection 1943 a logical calculus of the ideas immanent in nervous activity with walter pitts in bulletin of mathematical biophysics vol 5 pp 115 133 1945 a heterarchy of values determined by the topology of nervous nets in bulletin of mathematical biophysics 7 1945 89 93 1959 what the frog s eye tells the frog s brain with jerome lettvin h r maturana and w h pitts in proc of the i r e vol 47 11 1969 recollections of the many sources of cybernetics published in asc forum volume vi number 2 summer 1974 papers published by the chicago literary club 1945 one word after another 1959 the past of a delusion 1959 the natural fit see also edit randolph diagram references edit 1 2 ken aizawa 2004 mcculloch warren sturgis in dictionary of the philosophy of mind retrieved may 17 2008 mcculloch warren walter pitts 1943 a logical calculus of ideas immanent in nervous activity bulletin of mathematical biophysics 5 4 115 133 doi 10 1007 bf02478259 1 2 3 4 mcculloch warren 1961 what is a number that a man may know it and a man that he may know a number pdf general semantics bulletin 26 27 7 18 abraham tara h 2002 physio logical circuits the intellectual origins of the mcculloch pitts neural networks journal of the history of the behavioral sciences 38 1 3 25 doi 10 1002 jhbs 1094 issn 0022 5061 pmid 11835218 smalheiser neil 2000 walter pitts perspectives in biology and medicine 43 43 2 217 226 doi 10 1353 pbm 2000 0009 pmid 10804586 s2cid 8757655 h abraham tara october 28 2016 rebel genius warren s mcculloch s transdisciplinary life in science cambridge massachusetts isbn 9780262035095 oclc 946160418 cite book cs1 maint location missing publisher link cs1 maint multiple names authors list link joannes gregorius dusser de barenne yale j biol med 12 6 742 2 746 1940 pmc 2602446 pmid 21433922 wiener norbert cybernetics or control and communication in the animal and the machine 1948 de blasio gabriel moreno díaz arminda moreno díaz roberto 2018 mcculloch s relation to connectionism and artificial intelligence in moreno díaz roberto pichler franz quesada arencibia alexis eds computer aided systems theory eurocast 2017 vol 10671 cham springer international publishing pp 41 48 doi 10 1007 978 3 319 74718 7_6 isbn 978 3 319 74717 0 retrieved october 12 2024 1 2 mcculloch w s 1968 logic and closed loops for a computer junket to mars in caianiello e r ed neural networks berlin heidelberg springer berlin heidelberg pp 65 91 doi 10 1007 978 3 642 87596 0_7 isbn 978 3 642 87598 4 retrieved october 12 2024 de barenne j g dusser mcculloch w s october 31 1939 physiological delimitation of neurones in the central nervous system american journal of physiology legacy content 127 4 620 628 doi 10 1152 ajplegacy 1939 127 4 620 issn 0002 9513 the isocortex of the chimpanzee by percival bailey gerhardt von bonin and warren s mcculloch urbana illinois university of illinois press 1950 takemura hiromasa pestilli franco weiner kevin s september 1 2019 comparative neuroanatomy integrating classic and modern methods to understand association fibers connecting dorsal and ventral visual cortex neuroscience research 146 1 12 doi 10 1016 j neures 2018 10 011 issn 0168 0102 pmc 6491271 pmid 30389574 pitts walter mcculloch warren s september 1 1947 how we know universals the perception of auditory and visual forms the bulletin of mathematical biophysics 9 3 127 147 doi 10 1007 bf02478291 issn 1522 9602 pmid 20262674 blum manuel properties of a neuron with many inputs bionics symposium living prototypes the key to new technology 13 14 15 september 1960 wadd technical report 60 600 1961 1 2 arbib michael a 2000 warren mcculloch s search for the logic of the nervous system perspectives in biology and medicine 43 2 193 216 doi 10 1353 pbm 2000 0001 issn 1529 8795 masani p r 1990 mcculloch pitts and the evolution of wiener s neurophysiological ideas norbert wiener 1894 1964 basel birkhäuser basel pp 218 238 doi 10 1007 978 3 0348 9252 0_16 isbn 978 3 0348 9963 5 retrieved october 13 2024 aizawa kenneth september 2012 warren mcculloch s turn to cybernetics what walter pitts contributed interdisciplinary science reviews 37 3 206 217 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