What is a Computer? A Survey

References (169)

1. computer because nature is discrete, but Lloyd's intermediate premises differ from Wolfram's. Lloyd argues as follows (Lloyd and Ng 2004):
2. Nature is discrete. (This is ''the central maxim of quantum mechanics'' (p. 54).)
3. In particular, elementary particles have a ''spin axis'' that can be in one of two directions.
4. They encode a bit.
5. Elementary particles store bits of information.
6. Because any physical system stores and processes information,) all physical systems are computers.
7. Also, the entire universe is a computer. Premise 1 matches Wolfram's fundamental premise and would seem to be a necessity for anything to be considered a digital computer. The next four premises also underlie quantum computing. But the most serious problem with Lloyd's argument as presented here is premise 6. Is the processing sufficient to be considered to be TM-equivalent computation? Perhaps; after all, it seems that all that is happening is that cells change from 0s to 1s and vice versa. But that's not all that's involved in computing. (Or is it? Isn't that what Hayes's magic-paper hypothesis says?) What about the control structures-the grammar-of the computation? 39 The easiest way to think of a cellular automaton is as a two-dimensional TM tape for which the symbol in any cell is a function of the symbols in neighboring cells (https://en.wikipedia.org/wiki/Cellular_ automaton). On cellular automata, see Burks (1970).
8. For more on Wolfram, see http://www.stephenwolfram.com/ and Wolfram (2002a). For a critical review, see Weinberg (2002). Aaronson (2011) claims that quantum computing has ''overthrown'' views like those of Wolfram (2002b) that ''the universe itself is basically a giant computer … by showing that if [it is, then] it's a vastly more powerful kind of computer than any yet constructed by humankind.'' References
9. Aaronson, S. (2011, December 9). Quantum computing promises new insights, not just supermachines. New York Times, D5. http://www.nytimes.com/2011/12/06/science/scott-aaronson-quantum- computing-promises-new-insights.html.
10. Adleman, L. M. (1998). Computing with DNA. Scientific American, 54-61. http://www.usc.edu/dept/ molecular-science/papers/fp-sciam98.pdf.
11. Aho, A. V. (2011, January). What is computation? Computation and computational thinking. Ubiquity, Article 1. http://ubiquity.acm.org/article.cfm?id=1922682.
12. Aizawa, K. (2010). Computation in cognitive science: It is not all about Turing-equivalent computation. Studies in History and Philosophy of Science, 41(3), 227-236. Reply to Piccinini (2004).
13. Anderson, D. L. (2006). The nature of computers. The Mind Project. http://www.mind.ilstu.edu/ curriculum/modOverview.php?modGUI=196.
14. Angier, N. (2010, February 2). Abtract thoughts? The body takes them literally. New York Times/Science Times, D2. http://www.nytimes.com/2010/02/02/science/02angier.html.
15. Bacon, D. (2010, December). What is computation? Computation and fundamental physics. Ubiq- uity 2010(December). Article 4, http://ubiquity.acm.org/article.cfm?id=1920826.
16. Bader, R. M. (2013). Towards a hyperintensional theory of intrinsicality. Journal of Philosophy, 110(10), 525-563.
17. Ballard, D. H. (1997). An introduction to natural computation. Cambridge, MA: MIT Press.
18. Benacerraf, P. (1965). What numbers could not be. Philosophical Review, 74(1), 47-73.
19. Biermann, A. (1990). Great ideas in computer science: A gentle introduction. Cambridge, MA: MIT Press.
20. Blum, L., Shub, M., & Smale, S. (1989). On a theory of computation and complexity over the real numbers: NP-completeness, recursive functions, and universal machines. Bulletin of the American Mathematical Society, 21(1), 1-46.
21. Borbely, R. (2005). Letter to the editor. Scientific American, 12, 15.
22. Bostrom, N. (2003). Are you living in a computer simulation? Philosophical Quarterly, 53(211), 243-255.
23. Burks, A. W. (Ed.). (1970). Essays on cellular automata. Urbana, IL: University of Illinois Press.
24. Buzen, J. P. (2011, January). Computation, uncertainty and risk. Ubiquity, Article 5. http://ubiquity.acm. org/article.cfm?id=1936886.
25. Care, C. (2007). Not only digital: A review of ACM's early involvement with analog computing technology. Communications of the ACM, 50(5), 42-45.
26. Carpenter, B., & Doran, R. (1977). The other Turing machine. The Computer Journal, 20(3), 269-279.
27. Chaitin, G. (2006). How real are real numbers? International Journal of Bifurcation and Chaos. http:// www.cs.auckland.ac.nz/*chaitin/olympia.pdf (2006 version); http://www.umcs.maine.edu/ *chaitin/wlu.html (2009 version).
28. Chalmers, D. J. (1996). Does a rock implement every finite-state automaton? Synthese, 108, 309-333. http://consc.net/papers/rock.html; Chalmers corrects ''an error in my arguments'' in Chalmers (2012, pp. 236-238).
29. Chalmers, D. J. (2011). A computational foundation for the study of cognition. Journal of Cognitive Science (South Korea), 12(4), 323-357.
30. Chalmers, D. J. (2012). The varieties of computation: A reply. Journal of Cognitive Science (South Korea), 13(3), 211-248.
31. Chirimuuta, M., Boone, T., & DeMedonsa, M. (2014, September 19). Is your brain a computer? (video). Instant HPS. https://www.youtube.com/watch?v=-8q_UXpHsaY.
32. Chow, S. J. (2015). Many meanings of 'heuristic'. British Journal for the Philosophy of Science, 66, 977-1016.
33. Churchland, P. S., & Sejnowski, T. J. (1992). The computational brain. Cambridge, MA: MIT Press.
34. Coffa, J. (1991). The semantic tradition from Kant to Carnap: To the Vienna Station. Cambridge: Cambridge University Press.
35. Copeland, B. J. (1996). What is computation? Synthese, 108, 335-359.
36. Copeland, B. J. (1997). The broad conception of computation. American Behavioral Scientist, 40(6), 690-716.
37. Copeland, B. J. (2002). Hypercomputation. Minds and Machines, 12(4), 461-502.
38. Copeland, B. J. (Ed.). (2004). The essential Turing. Oxford: Oxford University Press.
39. Copeland, B. J. (2013, August 12). What Apple and Microsoft owe to Turing. Huff[ington] Post Tech/The Blog. http://www.huffingtonpost.com/jack-copeland/what-apple-and-microsoft-_b_3742114.html.
40. Corry, L. (2017). Turing's pre-war analog computers: The fatherhood of the modern computer revisited. Communications of the ACM, 60(8), 50-58.
41. Davis, M. D. (2000). Overheard in the park. American Scientist, 88, 366-367.
42. Davis, M. D. (2004). The myth of hypercomputation. In C. Teuscher (Ed.), Alan Turing: The life and legacy of a great thinker (pp. 195-212). Berlin: Springer.
43. Davis, M. D. (2006a). The Church-Turing thesis: Consensus and opposition. In A. Beckmann, U. Berger, B. Lo ¨we, & J. Tucker (Eds.), Logical approaches to computational barriers: Second conference on computability in Europe, CiE 2006, Lecture notes in computer science (Vol. 3988, pp. 125-132), Swansea, UK, June 30-July 5, 2006. Berlin: Springer.
44. Davis, M. D. (2006b). Why there is no such discipline as hypercomputation. Applied Mathematics and Computation, 178, 4-7.
45. Daylight, E. G. (2013). Towards a historical notion of ''Turing-The father of computer science''. http:// www.dijkstrascry.com/sites/default/files/papers/Daylightpaper91.pdf.
46. Dennett, D. C. (2013). Intuition pumps and other tools for thinking. New York: W.W. Norton.
47. Dennett, D. C. (2017). From bacteria to bach and back: The evolution of mind. New York: W.W. Norton.
48. Edelman, S. (2008a). Computing the mind. New York: Oxford University Press.
49. Edelman, S. (2008b). On the nature of minds; or: Truth and consequences. Journal of Experimental & Theoretical Artificial Intelligence, 20(3), 181-196.
50. Egan, F. (2012). Metaphysics and computational cognitive science: Let's not let the tail wag the dog. Journal of Cognitive Science (South Korea), 13(1), 39-49.
51. Fortnow, L. (2010, December). What is computation? Ubiquity, Article 5. http://ubiquity.acm.org/article. cfm?id=1921573.
52. Gelenbe, E. (2011, February). Natural computation. Ubiquity, Article 1. http://ubiquity.acm.org/article. cfm?id=1940722.
53. Gigerenzer, G., & Goldstein, D. G. (1996). Mind as computer: Birth of a metaphor. Creativity Research Journal, 9(2-3), 131-144.
54. Go ¨del, K. (perhaps about 1938). Undecidable diophantine propositions. In S. Feferman, et al. (Eds.), Collected works (Vol. III, pp. 164-175). Oxford: Oxford University Press.
55. Goldin, D., Smolka, S. A., & Wegner, P. (Eds.). (2006). Interactive computation: The new paradigm. Berlin: Springer.
56. Goodman, N. D. (1987). Intensions, Church's thesis, and the formalization of mathematics. Notre Dame Journal of Formal Logic, 28(4), 473-489.
57. Gopnik, A. (2009). The philosophical baby: What children's minds tell us about truth, love, and the meaning of life. New York: Farrar, Straus and Giroux.
58. Guernsey, L. (2009). Computers track the elusive metaphor. Chronicle of Higher Education, 55, A11. Guzdial, M., & Kay, A. (2010, May 24). The core of computer science: Alan Kay's 'triple whammy'. Computing Education Blog. http://computinged.wordpress.com/2010/05/24/the-core-of-computer- science-alan-kays-triple-whammy/.
59. Haigh, T. (2013). 'Stored program concept' considered harmful: History and historiography. In P. Bonizzoni, V. Brattka, & B. Lo ¨we (Eds.), CiE 2013, Lecture notes in computer science (Vol. 7921, pp. 241-251). Berlin: Springer.
60. Harnish, R. M. (2002). Coda: Computation for cognitive science, or what IS a computer, anyway? In Minds, brains, computers: An historical introduction to the foundations of cognitive science (pp. 394-412). Malden, MA: Blackwell. https://www.amazon.com/Minds-Brains-Computers- Introduction-Foundations/dp/0631212604/.
61. Hartree, D. (1949). Calculating instruments and machines. Urbana, IL: University of Illinois Press.
62. Hayes, B. (2007). Trains of thought. American Scientist, 95(2), 108-113.
63. Hayes, P. J. (1997). What is a computer? Monist, 80(3), 389-404.
64. Hedger, L. (1998). Analog computation: Everything old is new again (Vol. 21). Indiana University Research & Creative Activity. http://www.indiana.edu/*rcapub/v21n2/p24.html.
65. Hidalgo, C. (2015). Planet hard drive. Scientific American, 313(2), 72-75.
66. Hintikka, J., & Mutanen, A. (1997). An alternative concept of computability. In J. Hintikka (Ed.), Language, truth, and logic in mathematics (pp. 174-188). Dordrecht: Springer.
67. Hogarth, M. (1992). Does general relativity allow an observer to view an eternity in a finite time? Foundations of Physics Letters, 5(2), 173-181.
68. Holst, P. A. (2000). Analog computer. In A. Ralston, E. D. Reilly, & D. Hemmendinger (Eds.), Encyclopedia of computer science (4th ed., pp. 53-59). New York: Grove's Dictionaries.
69. Jackson, A. S. (1960). Analog computation. New York: McGraw-Hill.
70. Kanat-Alexander, M. (2008, October 10). What is a computer? Code Simplicity. http://www. codesimplicity.com/post/what-is-a-computer/.
71. Kleene, S. C. (1995). Turing's analysis of computability, and major applications of it. In R. Herken (Ed.), The universal turing machine: A half-century survey (2nd ed., pp. 15-49). Vienna: Springer.
72. Kugel, P. (2002). Computing machines can't be intelligent (… and Turing said so). Minds and Machines, 12(4), 563-579.
73. Lamport, L. (2011). Euclid writes an algorithm: A fairytale. International Journal of Software and Informatics 5(1-2, Part 1), 7-20.
74. Langton, R., & D. Lewis (1998). Defining 'intrinsic'. Philosophy and Phenomenological Research, 58(2), 333-345.
75. Lewis, D. (1983). Extrinsic properties. Philosophical Studies, 44(2), 197-200.
76. Lewis, W. (1953). Electronic computers and telephone switching. Proceedings of the Institute of Radio Engineers, 41(10), 1242-1244.
77. Linker, D. (2015, July 1). No, your brain isn't a computer. The Week. http://theweek.com/articles/563975/ no-brain-isnt-computer.
78. Lloyd, S. (2000). Ultimate physical limits to computation. Nature, 406, 1047-1054.
79. Lloyd, S. (2002). Computational capacity of the universe. Physical Review Letters, 88(23), 237901-1-237901-4.
80. Lloyd, S. (2006). Programming the universe: A quantum computer scientist takes on the cosmos. New York: Alfred A. Knopf.
81. Lloyd, S., & Ng, Y. J. (2004). Black hole computers. Scientific American, 291(5), 52-61.
82. Marcus, G. (2015, June 28). Face it, your brain is a computer. New York Times Sunday Review, SR12. http://www.nytimes.com/2015/06/28/opinion/sunday/face-it-your-brain-is-a-computer.html.
83. Marshall, D. (2016). The varieties of intrinsicality. Philosophy and Phenomenological Research, 92(2), 237-263.
84. McCulloch, W. S., & Pitts, W. H. (1943). A logical calculus of the ideas immanent in nervous activity. Bulletin of Mathematical Biophysics, 7, 114-133. Reprinted in Warren S. McCulloch, Embodiments of mind (Cambridge, MA: MIT Press, 1965): 19-39.
85. McMillan, R. (2013, July 7). The end of digital tyranny: Why the future of computing is analog. Wired. http://www.wired.com/wiredenterprise/2013/07/analogfuture/.
86. Mitchell, M. (2011, February). What is computation? Biological computation. Ubiquity, Article 3. http:// ubiquity.acm.org/article.cfm?id=1944826.
87. Moor, J. H. (1978). Three myths of computer science. British Journal for the Philosophy of Science, 29(3), 213-222.
88. Morris, G. J., & Reilly, E. D. (2000). Digital computer. In A. Ralston, E. D. Reilly, & D. Hemmendinger (Eds.), Encyclopedia of computer science (4th ed., pp. 359-545). New York: Grove's Dictionaries.
89. Naur, P. (2007). Computing versus human thinking. Communications of the ACM, 50(1), 85-94.
90. O'Neill, S. (2015). The human race is a computer. New Scientist, 227(3029), 26-27. Interview with Ce ´sar Hidalgo.
91. Oommen, B. J., & Rueda, L. G. (2005). A formal analysis of why heuristic functions work. Artificial Intelligence, 164(1-2), 1-22.
92. Pasanek, B. (2015). The mind is a metaphor. http://metaphors.iath.virginia.edu/.
93. Perruchet, P., & Vinter, A. (2002). The self-organizing consciousness. Behavioral and Brain Sciences, 25(3), 297-388.
94. Piccinini, G. (2004). The first computational theory of mind and brain: A close look at McCulloch and Pitts's 'Logical calculus of ideas immanent in nervous activity'. Synthese, 141, 175-215. For a reply, see Aizawa (2010).
95. Piccinini, G. (2005). Symbols, strings, and spikes: The empirical refutation of computationalism. Abstract at https://philpapers.org/rec/PICSSA; unpublished paper at https://web.archive.org/web/ 20080216023546/http://www.umsl.edu/*piccininig/Symbols%20Strings%20and%20Spikes% 2019.htm. superseded by Piccinini and Bahar (2013).
96. Piccinini, G. (2006). Computational explanation in neuroscience. Synthese, 153(3), 343-353.
97. Piccinini, G. (2007a). Computational explanation and mechanistic explanation of mind. In M. Marraffa, M. D. Caro, & F. Ferretti (Eds.), Cartographies of the mind: Philosophy and psychology in intersection (pp. 23-36). Dordrecht: Springer.
98. Piccinini, G. (2007b). Computational modelling vs. computational explanation: Is everything a Turing machine, and does it matter to the philosophy of mind? Australasian Journal of Philosophy, 85(1), 93-115.
99. Piccinini, G. (2007c). Computing mechanisms. Philosophy of Science, 74(4), 501-526.
100. Piccinini, G. (2008). Computers. Pacific Philosophical Quarterly, 89, 32-73.
101. Piccinini, G. (2010). The mind as neural software? Understanding functionalism, computationalism, and computational functionalism. Philosophy and Phenomenological Research, 81(2), 269-311.
102. Piccinini, G. (2011). The physical Church-Turing thesis: Modest or bold? British Journal for the Philosophy of Science, 62, 733-769.
103. Piccinini, G. (2015). Physical computation: A mechanistic account. Oxford: Oxford University Press.
104. Piccinini, G. (2018). Computation and representation in cognitive neuroscience. Minds and Machines, 28(1), 1-6.
105. Piccinini, G., & Bahar, S. (2013). Neural computation and the computational theory of cognition. Cognitive Science, 34, 453-488.
106. Polya, G. (1957). How to solve it: A new aspect of mathematical method (2nd ed.). Garden City, NY: Doubleday Anchor.
107. Pour-El, M. B. (1974). Abstract computability and its relation to the general purpose analog computer (some connections between logic, differential equations and analog computers). Transactions of the American Mathematical Society, 199, 1-28.
108. Powell, C. S. (2006, April 2). Welcome to the machine. New York Times Book Review, 19. http://www. nytimes.com/2006/04/02/books/review/02powell.html.
109. Putnam, H. (1965). Trial and error predicates and the solution to a problem of Mostowski. Journal of Symbolic Logic, 30(1), 49-57.
110. Putnam, H. (1988). Representation and Reality. Cambridge, MA: MIT Press.
111. Randell, B. (1994). The origins of computer programming. IEEE Annals of the History of Computing, 16(4), 6-14.
112. Rapaport, W. J. (1988). Syntactic semantics: Foundations of computational natural-language under- standing.
113. In J. H. Fetzer (Ed.), Aspects of artificial intelligence (pp. 81-131). Dordrecht: Kluwer. http://www.cse.buffalo.edu/*rapaport/Papers/synsem.pdf; reprinted with numerous errors in Eric Dietrich (Ed.). (1994). Thinking machines and virtual persons: Essays on the intentionality of machines (San Diego: Academic Press): 225-273.
114. Rapaport, W. J. (1998). How minds can be computational systems. Journal of Experimental and Theoretical Artificial Intelligence, 10, 403-419.
115. Rapaport, W. J. (1999). Implementation is semantic interpretation. The Monist, 82, 109-130.
116. Rapaport, W. J. (2005a). Implemention is semantic interpretation: Further thoughts. Journal of Experimental and Theoretical Artificial Intelligence, 17(4), 385-417.
117. Rapaport, W. J. (2005b). Philosophy of computer science: An introductory course. Teaching Philosophy, 28(4), 319-341.
118. Rapaport, W. J. (2007). Searle on brains as computers. American Philosophical Association Newsletter on Philosophy and Computers, 6(2), 4-9.
119. Rapaport, W. J. (2012). Semiotic systems, computers, and the mind: How cognition could be computing. International Journal of Signs and Semiotic Systems 2(1), 32-71. Revised version published as Rapaport (2018b).
120. Rapaport, W. J. (2017a). On the relation of computing to the world. In T. M. Powers (Ed.), Philosophy and computing: Essays in epistemology, philosophy of mind, logic, and ethics (pp. 29-64). Cham: Springer. Paper based on 2015 IACAP Covey Award talk; preprint at http://www.cse.buffalo.edu/ *rapaport/Papers/rapaport4IACAP.pdf.
121. Rapaport, W. J. (2017b). Semantics as syntax. American Philosophical Association Newsletter on Philosophy and Computers, 17(1), 2-11.
122. Rapaport, W. J. (2017c). What is computer science? American Philosophical Association Newsletter on Philosophy and Computers, 16(2), 2-22. Paper based on 2017 APA Barwise Award talk. http://c. ymcdn.com/sites/www.apaonline.org/resource/collection/EADE8D52-8D02-4136-9A2A- 729368501E43/ComputersV16n2.pdf.
123. Rapaport, W. J. (2018a). Philosophy of computer science. Current draft in progress at http://www.cse. buffalo.edu/*rapaport/Papers/phics.pdf.
124. Rapaport, W. J. (2018b). Syntactic semantics and the proper treatment of computationalism. In M. Danesi (Ed.), Empirical research on semiotics and visual rhetoric (pp. 128-176). Hershey, PA: IGI Global.
125. Rescorla, M. (2012). How to integrate representation into computational modeling, and why we should. Journal of Cognitive Science (South Korea), 13(1), 1-38.
126. Rescorla, M. (2015). The computational theory of mind. In E. N. Zalta (Ed.), The Stanford encyclopedia of philosophy (Winter 2015 ed.). http://plato.stanford.edu/archives/win2015/entries/computational- mind/.
127. Richards, W. (1988). Natural computation. Cambridge, MA: MIT Press.
128. Robinson, J. A. (1994). Logic, computers, Turing, and von Neumann. In K. Furukawa, D. Michie, & S. Muggleton (Eds.), Machine Intelligence 13: Machine intelligence and inductive learning (pp. 1-35). Oxford: Clarendon Press.
129. Romanycia, M. H., & Pelletier, F. J. (1985). What is a heuristic? Computational Intelligence, 1(2), 47-58.
130. Rubinoff, M. (1953). Analogue vs. digital computers-a comparison. Proceedings of the IRE, 41(10), 1254-1262.
131. Sackur, J., & Dehaene, S. (2009). The cognitive architecture for chaining of two mental operations. Cognition, 111, 187-211.
132. Samuel, A. L. (1953). Computing bit by bit, or digital computers made easy. Proceedings of the IRE, 41(10), 1223-1230.
133. Scheutz, M. (2012). What it is not to implement a computation: A critical analysis of Chalmers' notion of implementation. Journal of Cognitive Science (South Korea), 13(1), 75-106.
134. Schmidhuber, J. (2002). Zuse's thesis: The universe is a computer. http://www.idsia.ch/*juergen/ digitalphysics.html.
135. Schmidhuber, J. (2006). The computational universe. American Scientist, 94, 364ff.
136. Schulman, A. N. (2009). Why minds are not like computers. The New Atlantis, 23, 46-68.
137. Searle, J. R. (1990). Is the brain a digital computer? Proceedings and Addresses of the American Philosophical Association, 64(3), 21-37. Reprinted in slightly revised form as Searle (1992, Ch. 9).
138. Searle, J. R. (1992). The rediscovery of the mind. Cambridge, MA: MIT Press.
139. Shagrir, O. (1999). What is computer science about? The Monist, 82(1), 131-149.
140. Shagrir, O. (2012). Can a brain possess two minds? Journal of Cognitive Science (South Korea), 13(2), 145-165.
141. Shapiro, E., & Benenson, Y. (2006). Bringing DNA computers to life. Scientific American, 294(5), 44-51.
142. Shapiro, S. (2009). We hold these truths to be self-evident: But what do we mean by that? Review of Symbolic Logic, 2(1), 175-207.
143. Shapiro, S. C. (2001). Computer science: The study of procedures. Technical report, Department of Computer Science and Engineering, University at Buffalo, Buffalo, NY. http://www.cse.buffalo. edu/*shapiro/Papers/whatiscs.pdf; see also http://www.cse.buffalo.edu/*shapiro/Courses/ CSE115/notes2.html.
144. Shepherdson, J., & Sturgis, H. (1963). Computability of recursive functions. Journal of the ACM, 10(2), 217-255.
145. Simon, H. A. (1996). Computational theories of cognition. In W. O'Donohue & R. F. Kitchener (Eds.), The philosophy of psychology (pp. 160-172). London: Sage.
146. Skow, B. (2007). Are shapes intrinsic? Philosophical Studies, 133, 111-130.
147. Squires, R. (1970). On one's mind. Philosophical Quarterly, 20(81), 347-356.
148. Sternberg, R. J. (1990). Metaphors of mind: Conceptions of the nature of intelligence. New York: Cambridge University Press.
149. Stewart, I. (1994). A subway named Turing. Scientific American, 104, 106-107.
150. Stoll, C. (2006). When slide rules ruled. Scientific American, 294(5), 80-87.
151. Suber, P. (1997). Formal systems and machines: An isomorphism. http://www.earlham.edu/*peters/ courses/logsys/machines.htm.
152. Thomason, R. H. (2003). Dynamic contextual intensional logic: Logical foundations and an application. In P. Blackburn (Ed.), CONTEXT 2003: Lecture notes in artificial intelligence (Vol. 2680, pp. 328-341). Berlin: Springer.
153. Turing, A. M. (1936). On computable numbers, with an application to the Entscheidungsproblem. Proceedings of the London Mathematical Society, 42, 230-265.
154. Turing, A. M. (1939). Systems of logic based on ordinals. Proceedings of the London Mathematical Society, S2-45(1), 161-228. Reprinted with commentary in Copeland (2004, Ch. 3).
155. Turing, A. M. (1947). Lecture to the London Mathematical Society on 20 February 1947. In B. J. Copeland (Ed.), The essential Turing (pp. 378-394). Oxford: Oxford University Press (2004). Editorial commentary on pp. 362-377. https://www.academia.edu/34875977/Alan_Turing_ LECTURE_TO_THE_LONDON_MATHEMATICAL_SOCIETY_1947_.
156. Turing, A. M. (1951, 1996). Intelligent machinery, a heretical theory. Philosophia Mathematica, 4(3), 256-260. http://viola.informatik.uni-bremen.de/typo/fileadmin/media/lernen/Turing-_Intelligent_ Machinery.pdf; typescripts and further bibliographic information at http://www.turing.org.uk/ sources/biblio1.html.
157. US National Library of Medicine. (2015). Dream anatomy. https://www.nlm.nih.gov/dreamanatomy/da_ g_IV-A-02.html.
158. Vardi, M. Y. (2013). Who begat computing? Communications of the ACM, 56(1), 5.
159. von Neumann, J. (1945 (1993)). First draft report on the EDVAC. IEEE Annals of the History of Computing, 15(4), 27-75
160. Wang, H. (1957). A variant to Turing's theory of computing machines. Journal of the ACM, 4(1), 63-92.
161. Weatherson, B., & Marshall, D. (2018). Intrinsic vs. extrinsic properties. In E. N. Zalta (Ed.), The Stanford encyclopedia of philosophy (Spring 2018 ed.). Metaphysics Research Lab, Stanford University. https://plato.stanford.edu/archives/spr2018/entries/intrinsic-extrinsic/.
162. Wegner, P. (1997). Why interaction is more powerful than algorithms. Communications of the ACM, 40(5), 80-91.
163. Weinberg, S. (2002). Is the universe a computer? New York Review of Books, 49(16), 43-47.
164. Weizenbaum, J. (1976). Computer power and human reason. New York: W.H. Freeman.
165. Wheeler, D. L. (1997, October 3). An ancient feud: Who invented the computer? Chronicle of Higher Education, B2.
166. Wolfram, S. (2002a). Introduction to A new kind of science. http://www.stephenwolfram.com/ publications/introduction-to-a-new-kind-of-science/.
167. Wolfram, S. (2002b). A new kind of science. Wolfram Media. http://www.wolframscience.com/nks/.
168. Zobrist, A. L. (2000). Computer games: Traditional. In A. Ralston, E. D. Reilly, & D. Hemmendinger (Eds.), Encyclopedia of Computer Science (4th ed.). New York: Grove's Dictionaries.
169. Zylberberg, A., Dehaene, S., Roelfsema, P. R., & Sigman, M. (2011). The human Turing machine: A neural framework for mental programs. Trends in Cognitive Science, 15(7), 293-300.