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Abstract
This paper focuses on the significance of the concept of noise for cognition and computation. The concept of noise was massively transformed in the twentieth century with the advent of information theory, cybernetics, and computer science, all of which provide formal accounts of information and noise centrally concerned with contingency. We show how the concept has changed from these classical formulations, through developments in mathematics (topology and topos theory), computing (interactive computing and univalent foundations), and cognitive science (predictive processing and cognitive morphodynamics). Ultimately it argues for the central importance of noise not only within a topological conception of cognition and computation, but also in the transcendental-empirical torsion of image schemata and the social interactive elaboration of freedom.
disclosure statement
No potential conflict of interest was reported by the author.
Notes
1 The range of senses are given a more detailed treatment in my forthcoming book, also many parts of this “topos of noise” piece are fragments of an argument that is constructed more carefully and dealt with in more detail there. See Wilkins.
2 Topology is the study of the properties of objects that are preserved through various deformations of their structure.
3 The distinction between robustness and resilience to noise is inspired by Bravi and Longo’s argument against the importation of computational metaphors into the domain of biology.
4 Srnicek; Dyer-Witherford et al.; Zuboff; Joque.
5 Turing discussed interactive computing extensively and characterized the form of computing in cognition as one that displays variability and sensitivity to initial conditions, in distinction to the exactly iterating discrete state machines he was then developing. These are also major concerns for founding computational theorists such as McCullough and Pitts, Von Neumann, and Minksy.
6 See Goldin et al.
7 This statement is inspired by Anil Cavia’s book, which we’ll come back to in more detail later.
8 Baum; Tishby and Zaslavsky; Mehta and Schwab.
9 Greitzer.
10 Wiese and Metzinger.
11 Rao and Ballard.
12 Friston, “Hierarchical Models”; “Free-Energy Principle”; Hohwy; Clark, “Whatever Next?”
13 Clark, “Perception.”
14 Metzinger.
15 Feldman and Friston.
16 Ramstead et al.
17 Palmer et al.; Sands and Ratey.
18 James; Wiese and Metzinger.
19 Friston et al.
20 Wiese and Metzinger.
21 Swanson.
22 Badiou, Logic of Worlds 235.
23 Matherne, “Kantian Themes.”
24 Ibid.
25 Swanson.
26 Petitot et al.; Petitot, Cognitive Morphodynamics.
27 Petitot, “Sheaf Mereology.”
28 Husserl’s use of the terms Verschmelzung (meaning fusion or merging) and Sonderung (meaning separation or disjunction) comes from and is strongly influenced by Herbert’s psychophysics.
29 Petitot, “Sheaf Mereology”; “Morphological Eidetics” 344.
30 Merleau-Ponty 180.
31 Matherne, “Kantian Roots.”
32 Petitot et al. 54.
33 Thom, Stabilite Structurelle et Morphogenese; Mathematical Models of Morphogenesis; Semiophysics; Thom and Chumbley.
34 Thom, Mathematical Models of Morphogenesis.
35 Thom, Semiophysics.
36 Petitot, Cognitive Morphodynamics 17–28.
37 Ibid. 50.
38 Petitot et al. 371, 331.
39 Petitot, “Morphological Eidetics” 349.
40 The segregation of sound into “streams,” analogous to visual “objects,” was first theorized by Bregman. The theory of auditory cognition as a running autocorrelation was first developed by Licklider, and the synthesis of these theories within a computational account is well explained by Lyon. See Bregman; Licklider; Lyon 132.
41 Mumford and Shah.
42 Scale-space describes the morphological analysis of physical signals in local multiscale neighbourhoods, it differs from the infinitesimal neighbourhoods of points in the space of pure geometry. It was introduced by Witkin and Koenderink, and after Marr’s introduction of a multiscale version of a Laplacean operator allowing for the application of differential geometry to physical signals, and his algorithm for wavelet analysis, which is “a type of Fourier analysis that is spatially localized, multiscale, and capable of extracting the singularities encoded in a signal.” Marr; Witkin; Koenderink.
43 Petitot, Cognitive Morphodynamics 87.
44 Variations of this argument have been made in Negarestani; Cavia.
45 The notion of “doxastic conservativeness” comes from Novaes.
46 Simondon.
47 This borrows from Badiou:
For the phenomenologist, the real is in the final analysis consciousness. For me, consciousness is at best a distant effect of real assemblages and their evental caesura, and the subject is through and through […] not constituent, as it is for Husserl, but constituted. (Logic of Worlds)
48 Ibid. 37–38.
49 Ibid. 38. Similarly, when Badiou claims that mathematics is ontology, he is referring specifically to set theory, and what he calls the Cantor–Gödel–Cohen event, from which he maintains that being itself is pure inconsistent multiplicity; and from which it follows that all beings are multiples that are counted-as-one by the set-theoretical formalism. Badiou, Being and Event.
50 “The canonical model of classical logic is set theory, that of intuitionist logic is topos theory, and that of para-consistent logics is category theory” (Badiou, Logic of Worlds 532).
51 Ibid. 174.
52 Including Merleau-Ponty, Nancy, etc.
53 Badiou, Logic of Worlds 38.
54 Ibid. 195.
55 Subset of Theoretical Practice.
56 Badiou, Logic of Worlds 146–47.
57 Subset of Theoretical Practice; Nunes.
58 Badiou, Logic of Worlds 309.
59 Subset of Theoretical Practice.
60 Badiou, Logic of Worlds 359.
61 Ibid. 419.
62 Ibid. 295.
63 Subset of Theoretical Practice.
64 Ibid.
65 Ibid.
66 Ibid.
67 Ibid.
68 Cavia 10.
69 Though Brouwer positioned his intuitionist philosophy of mathematics against logicism, formalism, and Hilbert’s axiomatic method, intuitionistic logic is perfectly formalizable, as Heyting showed, and is not intrinsically temporal.
70 Cavia 29–30.
71 Ibid. 29.
72 Ibid. 89; Voevodsky.
73 Cavia is here referring to the Curry–Howard isomorphism. See Cavia 76; Sørensen and Urzyczyn.
74 Cavia 98; Grothendieck.
75 Cavia 102.
76 Ibid. 47–48.
77 Ibid. 142.
78 Ibid. 112.
79 Ibid. 111.
80 Ibid. 114.
81 Subset of Theoretical Practice.
82 The apparent immovability of the world referred to here has been theorized as “capitalist realism”: Fisher.