Learning with Incomputable Algorithms and Soft Thought

• In Event: Learning Under Algorithmic Conditions: Critical Perspectives on AI and Curriculum

Abstract

Overview
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The term “soft thought” was introduced by Parisi & Portanova (2011) to characterize a kind of disruptive thought that lurked within software and its applications. Soft thought names the ubiquitous modes of learning in algorithmic programming constituted in mathematical incompleteness, randomness, and incomputable probabilities (Gödel, 1931/1992). Soft thought is the thought of number, in all its virtual potentiality, before it is enacted or encoded in what AI researchers call “machine curriculum”. This paper provides a brief history regarding ideas about soft thought and the axiomatic limits of mathematics—or, ‘incomputability’—in order to discuss how ideas of human and machine learning are changing.

Objectives
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The paper has two interrelated objectives. First, the paper discusses some of the conflicting approaches to human and machine learning that are currently at play in the field, and that rest on presuppositions of, on one hand, rule-based machine learning (RBML) often used in deductive logic, and rooted in philosophies of learning often discussed as cognitivism and computationalism. On another hand, in direct opposition to theories of computationalism, and aligned more with certain theories in curriculum studies, learning is discussed in terms of emergentism and enactivism. The second objective is to discuss how ‘mathematical incomputability’ interjects inconsistency into machinic learning processes. Incomputability signals a digital envelope that has ‘incorporated [randomness and contingency] into the body of computation, not excluded from it’ (Galloway, 2021, p. 21). These two objectives shed light on how ideas of chance, risk, and contingency become technical mediators in our contemporary image of learning.

Theoretical Framework
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The primary theory used in this analysis is critical media studies (Galloway, 2021; Parisi, 2013) which helps unpack the history of incomputability and the limits of computing (Gödel, 1931/1992) and shows how soft thought has shaped developments in artificial intelligence, machine learning, and ultimately, human learning and current images of curriculum.

Methods & Data
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The paper employs an exegetical approach, one that conducts a “close reading of a philosophical or literary text[s] with an eye more toward explication and understanding of its complex meanings than analysis or critique” (Burbules & Warnick, 2006, p. 491). The exegetical approach develops the idea of soft thought through a historical analysis of mathematical incomputability.

Findings and Scholarly Significance
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Curriculum studies can benefit from exploring the incomputable (Galloway, 2021; Parisi 2013), so as to identify and make sense of the soft thought framing our current investment in new theories of learning, derived from the AI revolution. Soft thought is an expression that signals that our contemporary moment is infused with distinct forms of digital technologies, and that these technologies operate through a kind of incompleteness. Incomputability arrives from a long history that has identified different axiomatic limits in systems like set theory, mathematics, and algorithmic computation, and can be leveraged to push back at regimes of algorithmic control.

Author

• P. Taylor Webb, University of British Columbia