A 'second wave' connectionist (ANN) model with a hidden layer

Connectionism (coined by Edward Thorndike in the 1931[1]) is the name of an approach to the study of human mental processes and cognition that utilizes mathematical models known as connectionist networks or artificial neural networks.[2] Connectionism has had many 'waves' since its beginnings.

The first wave appeared 1943 with Warren Sturgis McCulloch and Walter Pitts both focusing on comprehending neural circuitry through a formal and mathematical approach,[3] and Frank Rosenblatt who published the 1958 book “The Perceptron: A Probabilistic Model For Information Storage and Organization in the Brain” in Psychological Review, while working at the Cornell Aeronautical Laboratory.[4] The first wave ended with the 1969 book about the limitations of the original perceptron idea, written by Marvin Minsky and Papert, which contributed to discouraging major funding agencies in the US from investing in connectionist research.[5] With a few noteworthy deviations, the majority of connectionist research entered a period of inactivity until the mid-1980s. The term connectionist model was reintroduced in the early 1980s in a Cognitive Science paper by Jerome Feldman and Dana Ballard.

The second wave blossomed in the late 1980s, following the 1987 book about Parallel Distributed Processing by James L. McClelland, David E. Rumelhart et al., which introduced a couple of improvements to the simple perceptron idea, such as intermediate processors (known as "hidden layers" now) alongside input and output units and used sigmoid activation function instead of the old 'all-or-nothing' function. Their work has, in turn, built upon that of John Hopfield, who was a key figure investigating the mathematical characteristics of sigmoid activation functions.[4] From the late 1980s to the mid-1990s, connectionism took on an almost revolutionary tone when Schneider,[6] Terence Horgan and Tienson posed the question of whether connectionism represented a fundamental shift in psychology and GOFAI.[4] Some advantages of the second wave connectionist approach included its applicability to a broad array of functions, structural approximation to biological neurons, low requirements for innate structure, and capacity for graceful degradation.[7] Some disadvantages of the second wave connectionist approach included the difficulty in deciphering how ANNs process information, or account for the compositionality of mental representations, and a resultant difficulty explaining phenomena at a higher level.[8]

The current (third) wave has been marked by advances in Deep Learning allowing for Large language models.[4] The success of deep learning networks in the past decade has greatly increased the popularity of this approach, but the complexity and scale of such networks has brought with them increased interpretability problems.[9]

Basic principle

The central connectionist principle is that mental phenomena can be described by interconnected networks of simple and often uniform units. The form of the connections and the units can vary from model to model. For example, units in the network could represent neurons and the connections could represent synapses, as in the human brain. This principle has been seen as an alternative to GOFAI and the classical theories of mind based on symbolic computation, but the extent to which the two approaches are compatible has been the subject of much debate since their inception.[9]

Activation function

Main article: Activation function

Internal states of any network change over time due to neurons sending a signal to a succeeding layer of neurons in the case of a feedforward network, or to a previous layer in the case of a recurrent network. Discovery of non-linear activation functions has enabled the second wave of connectionism.

Memory and learning

Main articles: Artificial neural networks and Deep learning

Neural networks follow two basic principles:

  1. Any mental state can be described as an (N)-dimensional vector of numeric activation values over neural units in a network.
  2. Memory and learning are created by modifying the 'weights' of the connections between neural units, generally represented as an N×M matrix. The weights are adjusted according to some learning rule or algorithm, such as Hebbian learning.[10]

Most of the variety among the models comes from:

Biological realism

Connectionist work in general does not need to be biologically realistic.[11][12][13][14][15][16][17] One area where connectionist models are thought to be biologically implausible is with respect to error-propagation networks that are needed to support learning,[18][19] but error propagation can explain some of the biologically-generated electrical activity seen at the scalp in event-related potentials such as the N400 and P600,[20] and this provides some biological support for one of the key assumptions of connectionist learning procedures. Many recurrent connectionist models also incorporate dynamical systems theory. Many researchers, such as the connectionist Paul Smolensky, have argued that connectionist models will evolve toward fully continuous, high-dimensional, non-linear, dynamic systems approaches.


Precursors of the connectionist principles can be traced to early work in psychology, such as that of William James.[21] Psychological theories based on knowledge about the human brain were fashionable in the late 19th century. As early as 1869, the neurologist John Hughlings Jackson argued for multi-level, distributed systems. Following from this lead, Herbert Spencer's Principles of Psychology, 3rd edition (1872), and Sigmund Freud's Project for a Scientific Psychology (composed 1895) propounded connectionist or proto-connectionist theories. These tended to be speculative theories. But by the early 20th century, Edward Thorndike was experimenting on learning that posited a connectionist type network.

Hopfield networks had precursors in the Ising model due to Wilhelm Lenz (1920) and Ernst Ising (1925), though the Ising model conceived by them did not involve time. Monte Carlo simulations of Ising model required the advent of computers in the 1950s.[22]

The first wave

The first wave begun in 1943 with Warren Sturgis McCulloch and Walter Pitts both focusing on comprehending neural circuitry through a formal and mathematical approach.[4] McCulloch and Pitts showed how neural systems could implement first-order logic: Their classic paper "A Logical Calculus of Ideas Immanent in Nervous Activity" (1943) is important in this development here. They were influenced by the work of Nicolas Rashevsky in the 1930s.

Hebb contributed greatly to speculations about neural functioning, and proposed a learning principle, Hebbian learning. Lashley argued for distributed representations as a result of his failure to find anything like a localized engram in years of lesion experiments. Friedrich Hayek independently conceived the model, first in a brief unpublished manuscript in 1920,[23][24] then expanded into a book in 1952.[25]

The Perceptron machines were proposed and built by Frank Rosenblatt, who published the 1958 paper “The Perceptron: A Probabilistic Model For Information Storage and Organization in the Brain” in Psychological Review, while working at the Cornell Aeronautical Laboratory. He cited Hebb, Hayek, Uttley, and Ashby as main influences.

Another form of connectionist model was the relational network framework developed by the linguist Sydney Lamb in the 1960s.

The research group led by Widrow empirically searched for methods to train two-layered ADALINE networks, with limited success.[26][27]

A method to train multilayered perceptrons with arbitrary levels of trainable weights was published by Alexey Grigorevich Ivakhnenko and Valentin Lapa in 1965, called the Group Method of Data Handling.[28][29][30] This method employs incremental layer by layer training based on regression analysis, where useless units in hidden layers are pruned with the help of a validation set. In 1972, Shun'ichi Amari made this architecture adaptive.[31][28]

The first multilayered perceptrons trained by stochastic gradient descent[32] was published in 1967 by Shun'ichi Amari.[33][28] In computer experiments conducted by Amari's student Saito, a five layer MLP with two modifiable layers learned useful internal representations to classify non-linearily separable pattern classes.[28]

The second wave

The second wave begun in late 1980s, following the 1987 two-volume book about the Parallel Distributed Processing (PDP) by James L. McClelland, David E. Rumelhart et al., which has introduced a couple of improvements to the simple perceptron idea, such as intermediate processors (known as "hidden layers" now) alongside input and output units and using sigmoid activation function instead of the old 'all-or-nothing' function. Their work has, in turn, built upon John Hopfield, who was a key figure investigating the mathematical characteristics of sigmoid activation functions.[4]

Connectionism vs. computationalism debate

As connectionism became increasingly popular in the late 1980s, some researchers (including Jerry Fodor, Steven Pinker and others) reacted against it. They argued that connectionism, as then developing, threatened to obliterate what they saw as the progress being made in the fields of cognitive science and psychology by the classical approach of computationalism. Computationalism is a specific form of cognitivism that argues that mental activity is computational, that is, that the mind operates by performing purely formal operations on symbols, like a Turing machine. Some researchers argued that the trend in connectionism represented a reversion toward associationism and the abandonment of the idea of a language of thought, something they saw as mistaken. In contrast, those very tendencies made connectionism attractive for other researchers.

Connectionism and computationalism need not be at odds, but the debate in the late 1980s and early 1990s led to opposition between the two approaches. Throughout the debate, some researchers have argued that connectionism and computationalism are fully compatible, though full consensus on this issue has not been reached. Differences between the two approaches include the following:

Despite these differences, some theorists have proposed that the connectionist architecture is simply the manner in which organic brains happen to implement the symbol-manipulation system. This is logically possible, as it is well known that connectionist models can implement symbol-manipulation systems of the kind used in computationalist models,[34] as indeed they must be able if they are to explain the human ability to perform symbol-manipulation tasks. Several cognitive models combining both symbol-manipulative and connectionist architectures have been proposed. Among them are Paul Smolensky's Integrated Connectionist/Symbolic Cognitive Architecture (ICS).[9][35] and Ron Sun's CLARION (cognitive architecture). But the debate rests on whether this symbol manipulation forms the foundation of cognition in general, so this is not a potential vindication of computationalism. Nonetheless, computational descriptions may be helpful high-level descriptions of cognition of logic, for example.

The debate was largely centred on logical arguments about whether connectionist networks could produce the syntactic structure observed in this sort of reasoning. This was later achieved although using fast-variable binding abilities outside of those standardly assumed in connectionist models.[34][36]

Part of the appeal of computational descriptions is that they are relatively easy to interpret, and thus may be seen as contributing to our understanding of particular mental processes, whereas connectionist models are in general more opaque, to the extent that they may be describable only in very general terms (such as specifying the learning algorithm, the number of units, etc.), or in unhelpfully low-level terms. In this sense, connectionist models may instantiate, and thereby provide evidence for, a broad theory of cognition (i.e., connectionism), without representing a helpful theory of the particular process that is being modelled. In this sense, the debate might be considered as to some extent reflecting a mere difference in the level of analysis in which particular theories are framed. Some researchers suggest that the analysis gap is the consequence of connectionist mechanisms giving rise to emergent phenomena that may be describable in computational terms.[37]

In the 2000s, the popularity of dynamical systems in philosophy of mind have added a new perspective on the debate;[38][39] some authors[which?] now argue that any split between connectionism and computationalism is more conclusively characterized as a split between computationalism and dynamical systems.

In 2014, Alex Graves and others from DeepMind published a series of papers describing a novel Deep Neural Network structure called the Neural Turing Machine[40] able to read symbols on a tape and store symbols in memory. Relational Networks, another Deep Network module published by DeepMind, are able to create object-like representations and manipulate them to answer complex questions. Relational Networks and Neural Turing Machines are further evidence that connectionism and computationalism need not be at odds.

Symbolism vs. connectionism debate

Smolensky's Subsymbolic Paradigm[41][42] has to meet the Fodor-Pylyshyn challenge[43][44][45][46] formulated by classical symbol theory for a convincing theory of cognition in modern connectionism. In order to be an adequate alternative theory of cognition, Smolensky's Subsymbolic Paradigm would have to explain the existence of systematicity or systematic relations in language cognition without the assumption that cognitive processes are causally sensitive to the classical constituent structure of mental representations. The subsymbolic paradigm, or connectionism in general, would thus have to explain the existence of systematicity and compositionality without relying on the mere implementation of a classical cognitive architecture. This challenge implies a dilemma: If the Subsymbolic Paradigm could contribute nothing to the systematicity and compositionality of mental representations, it would be insufficient as a basis for an alternative theory of cognition. However, if the Subsymbolic Paradigm's contribution to systematicity requires mental processes grounded in the classical constituent structure of mental representations, the theory of cognition it develops would be, at best, an implementation architecture of the classical model of symbol theory and thus not a genuine alternative (connectionist) theory of cognition.[47] The classical model of symbolism is characterized by (1) a combinatorial syntax and semantics of mental representations and (2) mental operations as structure-sensitive processes, based on the fundamental principle of syntactic and semantic constituent structure of mental representations as used in Fodor's "Language of Thought (LOT)".[48][49] This can be used to explain the following closely related properties of human cognition, namely its (1) productivity, (2) systematicity, (3) compositionality, and (4) inferential coherence.[50]

This challenge has been met in modern connectionism, for example, not only by Smolensky's "Integrated Connectionist/Symbolic (ICS) Cognitive Architecture",[51][52] but also by Werning and Maye's "Oscillatory Networks".[53][54][55] An overview of this is given for example by Bechtel & Abrahamsen,[56] Marcus[57] and Maurer.[58]

See also


  1. ^ Edward Thorndike (1931) Human Learning, page 122
  2. ^ "Internet Encyclopedia of Philosophy". iep.utm.edu. Retrieved 2023-08-19.
  3. ^ McCulloch, Warren S.; Pitts, Walter (1943-12-01). "A logical calculus of the ideas immanent in nervous activity". The Bulletin of Mathematical Biophysics. 5 (4): 115–133. doi:10.1007/BF02478259. ISSN 1522-9602.
  4. ^ a b c d e f Berkeley, Istvan S. N. (2019). "The Curious Case of Connectionism". Open Philosophy. 2019 (2): 190–205. doi:10.1515/opphil-2019-0018. S2CID 201061823.
  5. ^ Boden, Margaret (2006). Mind as Maniac: A History of Cognitive Science. Oxford: Oxford U.P. p. 914. ISBN 978-0-262-63268-3.
  6. ^ Schneider, Walter (1987). "Connectionism: Is it a Paradigm Shift for Psychology?". Behavior Research Methods, Instruments, & Computers. 19: 73–83. doi:10.1515/opphil-2019-0018. S2CID 201061823.
  7. ^ Marcus, Gary F. (2001). The Algebraic Mind: Integrating Connectionism and Cognitive Science (Learning, Development, and Conceptual Change). Cambridge, Massachusetts: MIT Press. pp. 27–28. ISBN 978-0-262-63268-3.
  8. ^ Smolensky, Paul (1999). "Grammar-based Connectionist Approaches to Language". Cognitive Science. 23 (4): 589–613. doi:10.1207/s15516709cog2304_9.
  9. ^ a b c Garson, James (27 November 2018). Zalta, Edward N. (ed.). The Stanford Encyclopedia of Philosophy. Metaphysics Research Lab, Stanford University – via Stanford Encyclopedia of Philosophy.
  10. ^ Novo, María-Luisa; Alsina, Ángel; Marbán, José-María; Berciano, Ainhoa (2017). "Connective Intelligence for Childhood Mathematics Education". Comunicar (in Spanish). 25 (52): 29–39. doi:10.3916/c52-2017-03. hdl:10272/14085. ISSN 1134-3478.
  11. ^ "Encephalos Journal". www.encephalos.gr. Retrieved 2018-02-20.
  12. ^ Wilson, Elizabeth A. (2016-02-04). Neural Geographies: Feminism and the Microstructure of Cognition. Routledge. ISBN 978-1-317-95876-5.
  13. ^ Di Paolo, E.A (1 January 2003). "Organismically-inspired robotics: homeostatic adaptation and teleology beyond the closed sensorimotor loop" (PDF). Dynamical Systems Approach to Embodiment and Sociality, Advanced Knowledge International. University of Sussex. S2CID 15349751. Retrieved 29 December 2023.
  14. ^ Zorzi, Marco; Testolin, Alberto; Stoianov, Ivilin P. (2013-08-20). "Modeling language and cognition with deep unsupervised learning: a tutorial overview". Frontiers in Psychology. 4: 515. doi:10.3389/fpsyg.2013.00515. ISSN 1664-1078. PMC 3747356. PMID 23970869.
  15. ^ Tieszen, R. (2011). "Analytic and Continental Philosophy, Science, and Global Philosophy". Comparative Philosophy. 2 (2): 4–22. Retrieved 29 December 2023.
  16. ^ Browne, A. (1997-01-01). Neural Network Perspectives on Cognition and Adaptive Robotics. CRC Press. ISBN 978-0-7503-0455-9.
  17. ^ Pfeifer, R.; Schreter, Z.; Fogelman-Soulié, F.; Steels, L. (1989-08-23). Connectionism in Perspective. Elsevier. ISBN 978-0-444-59876-9.
  18. ^ Crick, Francis (January 1989). "The recent excitement about neural networks". Nature. 337 (6203): 129–132. Bibcode:1989Natur.337..129C. doi:10.1038/337129a0. ISSN 1476-4687. PMID 2911347. S2CID 5892527.
  19. ^ Rumelhart, David E.; Hinton, Geoffrey E.; Williams, Ronald J. (October 1986). "Learning representations by back-propagating errors". Nature. 323 (6088): 533–536. Bibcode:1986Natur.323..533R. doi:10.1038/323533a0. ISSN 1476-4687. S2CID 205001834.
  20. ^ Fitz, Hartmut; Chang, Franklin (2019-06-01). "Language ERPs reflect learning through prediction error propagation". Cognitive Psychology. 111: 15–52. doi:10.1016/j.cogpsych.2019.03.002. hdl:21.11116/0000-0003-474F-6. ISSN 0010-0285. PMID 30921626. S2CID 85501792.
  21. ^ Anderson, James A.; Rosenfeld, Edward (1989). "Chapter 1: (1890) William James Psychology (Brief Course)". Neurocomputing: Foundations of Research. A Bradford Book. p. 1. ISBN 978-0-262-51048-6.
  22. ^ Brush, Stephen G. (1967). "History of the Lenz-Ising Model". Reviews of Modern Physics. 39 (4): 883–893. Bibcode:1967RvMP...39..883B. doi:10.1103/RevModPhys.39.883.
  23. ^ Hayek, Friedrich A. [1920] 1991. Beiträge zur Theorie der Entwicklung des Bewusstseins [Contributions to a theory of how consciousness develops]. Manuscript, translated by Grete Heinz.
  24. ^ Caldwell, Bruce (2004). "Some Reflections on F.A. Hayek's The Sensory Order". Journal of Bioeconomics. 6 (3): 239–254. doi:10.1007/s10818-004-5505-9. ISSN 1387-6996. S2CID 144437624.
  25. ^ Hayek, F. A. (2012-09-15). The Sensory Order: An Inquiry into the Foundations of Theoretical Psychology (1st ed.). The University of Chicago Press.
  26. ^ pp 124-129, Olazaran Rodriguez, Jose Miguel. A historical sociology of neural network research. PhD Dissertation. University of Edinburgh, 1991.
  27. ^ Widrow, B. (1962) Generalization and information storage in networks of ADALINE "neurons". In M. C. Yovits, G. T. Jacobi, & G. D. Goldstein (Ed.), Self-Organizing Svstems-1962 (pp. 435-461). Washington, DC: Spartan Books.
  28. ^ a b c d Schmidhuber, Juergen (2022). "Annotated History of Modern AI and Deep Learning". arXiv:2212.11279 [cs.NE].
  29. ^ Ivakhnenko, A. G. (1973). Cybernetic Predicting Devices. CCM Information Corporation.
  30. ^ Ivakhnenko, A. G.; Grigorʹevich Lapa, Valentin (1967). Cybernetics and forecasting techniques. American Elsevier Pub. Co.
  31. ^ Amari, Shun-Ichi (1972). "Learning patterns and pattern sequences by self-organizing nets of threshold elements". IEEE Transactions. C (21): 1197–1206.
  32. ^ Robbins, H.; Monro, S. (1951). "A Stochastic Approximation Method". The Annals of Mathematical Statistics. 22 (3): 400. doi:10.1214/aoms/1177729586.
  33. ^ Amari, Shun'ichi (1967). "A theory of adaptive pattern classifier". IEEE Transactions. EC (16): 279–307.
  34. ^ a b Chang, Franklin (2002). "Symbolically speaking: a connectionist model of sentence production". Cognitive Science. 26 (5): 609–651. doi:10.1207/s15516709cog2605_3. ISSN 1551-6709.
  35. ^ Smolensky, Paul (1990). "Tensor Product Variable Binding and the Representation of Symbolic Structures in Connectionist Systems" (PDF). Artificial Intelligence. 46 (1–2): 159–216. doi:10.1016/0004-3702(90)90007-M.
  36. ^ Shastri, Lokendra; Ajjanagadde, Venkat (September 1993). "From simple associations to systematic reasoning: A connectionist representation of rules, variables and dynamic bindings using temporal synchrony". Behavioral and Brain Sciences. 16 (3): 417–451. doi:10.1017/S0140525X00030910. ISSN 1469-1825. S2CID 14973656.
  37. ^ Ellis, Nick C. (1998). "Emergentism, Connectionism and Language Learning" (PDF). Language Learning. 48 (4): 631–664. doi:10.1111/0023-8333.00063.
  38. ^ Van Gelder, Tim (1998), "The dynamical hypothesis in cognitive science", Behavioral and Brain Sciences, 21 (5): 615–28, discussion 629–65, doi:10.1017/S0140525X98001733, PMID 10097022, retrieved 28 May 2022
  39. ^ Beer, Randall D. (March 2000). "Dynamical approaches to cognitive science". Trends in Cognitive Sciences. 4 (3): 91–99. doi:10.1016/s1364-6613(99)01440-0. ISSN 1364-6613. PMID 10689343. S2CID 16515284.
  40. ^ Graves, Alex (2014). "Neural Turing Machines". arXiv:1410.5401 [cs.NE].
  41. ^ P. Smolensky: On the proper treatment of connectionism. In: Behavioral and Brain Sciences. Band 11, 1988, S. 1-74.
  42. ^ P. Smolensky: The constituent structure of connectionist mental states: a reply to Fodor and Pylyshyn. In: T. Horgan, J. Tienson (Hrsg.): Spindel Conference 1987: Connectionism and the Philosophy of Mind. The Southern Journal of Philosophy. Special Issue on Connectionism and the Foundations of Cognitive Science. Supplement. Band 26, 1988, S. 137-161.
  43. ^ J.A. Fodor, Z.W. Pylyshyn: Connectionism and cognitive architecture: a critical analysis. Cognition. Band 28, 1988, S. 12-13, 33-50.
  44. ^ J.A. Fodor, B. McLaughlin: Connectionism and the problem of systematicity: why Smolensky's solution doesn't work. Cognition. Band 35, 1990, S. 183-184.
  45. ^ B. McLaughlin: The connectionism/classicism battle to win souls. Philosophical Studies, Band 71, 1993, S. 171-172.
  46. ^ B. McLaughlin: Can an ICS architecture meet the systematicity and productivity challenges? In: P. Calvo, J. Symons (Hrsg.): The Architecture of Cognition. Rethinking Fodor and Pylyshyn's Systematicity Challenge. MIT Press, Cambridge/MA, London, 2014, S. 31-76.
  47. ^ J.A. Fodor, B. McLaughlin: Connectionism and the problem of systematicity: Why Smolensky's solution doesn't work. Cognition. Band 35, 1990, S. 183-184.
  48. ^ J.A. Fodor: The language of thought. Harvester Press, Sussex, 1976, ISBN 0-85527-309-7.
  49. ^ J.A. Fodor: LOT 2: The language of thought revisited. Clarendon Press, Oxford, 2008, ISBN 0-19-954877-3.
  50. ^ J.A. Fodor, Z.W. Pylyshyn (1988), S. 33-48.
  51. ^ P. Smolenky: Reply: Constituent structure and explanation in an integrated connectionist / symbolic cognitive architecture. In: C. MacDonald, G. MacDonald (Hrsg.): Connectionism: Debates on psychological explanation. Blackwell Publishers. Oxford/UK, Cambridge/MA. Vol. 2, 1995, S. 224, 236-239, 242-244, 250-252, 282.
  52. ^ P. Smolensky, G. Legendre: The Harmonic Mind: From Neural Computation to Optimality-Theoretic Grammar. Vol. 1: Cognitive Architecture. A Bradford Book, The MIT Press, Cambridge, London, 2006a, ISBN 0-262-19526-7, S. 65-67, 69-71, 74-75, 154-155, 159-202, 209-210, 235-267, 271-342, 513.
  53. ^ M. Werning: Neuronal synchronization, covariation, and compositional representation. In: M. Werning, E. Machery, G. Schurz (Hrsg.): The compositionality of meaning and content. Vol. II: Applications to linguistics, psychology and neuroscience. Ontos Verlag, 2005, S. 283-312.
  54. ^ M. Werning: Non-symbolic compositional representation and its neuronal foundation: towards an emulative semantics. In: M. Werning, W. Hinzen, E. Machery (Hrsg.): The Oxford Handbook of Compositionality. Oxford University Press, 2012, S. 633-654.
  55. ^ A. Maye und M. Werning: Neuronal synchronization: from dynamics feature binding to compositional representations. Chaos and Complexity Letters, Band 2, S. 315-325.
  56. ^ Bechtel, W., Abrahamsen, A.A. Connectionism and the Mind: Parallel Processing, Dynamics, and Evolution in Networks. 2nd Edition. Blackwell Publishers, Oxford. 2002
  57. ^ G.F. Marcus: The algebraic mind. Integrating connectionism and cognitive science. Bradford Book, The MIT Press, Cambridge, 2001, ISBN 0-262-13379-2.
  58. ^ H. Maurer: Cognitive science: Integrative synchronization mechanisms in cognitive neuroarchitectures of the modern connectionism. CRC Press, Boca Raton/FL, 2021, ISBN 978-1-351-04352-6. https://doi.org/10.1201/9781351043526