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The instructional information processing account of digital computation

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Abstract

What is nontrivial digital computation? It is the processing of discrete data through discrete state transitions in accordance with finite instructional information. The motivation for our account is that many previous attempts to answer this question are inadequate, and also that this account accords with the common intuition that digital computation is a type of information processing. We use the notion of reachability in a graph to defend this characterization in memory-based systems and underscore the importance of instructional information for digital computation. We argue that our account evaluates positively against adequacy criteria for accounts of computation.

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Notes

  1. The distinction between x being computable and x being computational is addressed further in sect. 6.

  2. Flip-flops are basic memory cells. A flip-flop is a bistable element with a clock input. Its state changes only in response to a clock edge, say, when the clock signal rises from 0 to 1 (Harris and Harris 2013, p. 108).

  3. This notion is defined and explicated in the next section.

  4. In this paper the property of being discrete—or digital—implies having sharp and distinct boundaries.

  5. The evaluation of this last claim remains a task for further work.

  6. We thank an anonymous reviewer for identifying this potential conundrum.

  7. Incidentally, in passing it should be noted that, at least prima facie, using algorithmic information as an alternative to semantic content in our context inevitably yields a circular definition of computation. For algorithmic information is defined in terms of computational programs.

  8. If the semantic content is incorrect, by following it reliably the expected outcome is unlikely to be obtained. If it is correct but ambiguous, it is impossible to follow reliably, for there are at least two courses of possible action.

  9. Strictly, Floridi considers another type of instructional information that is based on what he calls “environmental information”. Environmental information is conveyed by data that might be meaningful independently of an intelligent producer (Floridi 2010, p. 32). This type of information is distinguished from semantic content. In this paper, we confine our discussion to instructional information as a subtype of semantic content. We make another observation regarding environmental information below in the context of analyzing Boolean gates.

  10. Events are of two types: deeds, performed by specific agents, and happenings, which are world effects (Reed and Norman 2007, p. 417).

  11. It should be noted that a generalized meta-computational space with a richer memory model can be used to model any system with a simpler one. For example, the generalized meta-computational space associated with TMs can be used to model the systems shown in Figs. 1 and 2. The advantage gained by considering different generalized meta-computational spaces is a clearer taxonomy of computational systems as is shown in Sect. 4.2 and 6.

  12. This approach allows for descriptions of capacities to potentially be infinite. While infinite descriptions may not be particularly useful, they do not impact the finiteness requirement of instructional information.

  13. Floridi defines an LoA as an object of study (e.g., a system) that consists of a finite, non-empty set of observables, which are interpreted typed variables (2011, p. 52). A typed variable is a variable qualified to hold only some declared kind of data. In this context, ‘interpreted’ means that the typed variable represents some feature of the system under consideration. Note that an analysis that relies on the data being structured should proceed using moderated LoAs. For more on LoAs see Floridi (2011, chap. 3). In the context of computational objects, higher and lower LoAs interrelate. The interpretation of an LoA in terms of the lower LoA remains of utmost importance and the interface among LoAs is also crucial (van Leeuwen forthcoming). See van Leeuwen (forthcoming) for a discussion of the differences between the usage of LoAs in computer science and the method described by Floridi.

  14. It can also be argued that, in some sense, every imperative can be expressed as a conditional. For example, “do X” can be expressed as “do X unless there is some exceptional circumstance”. The “exceptional circumstance” serves as a sanction imposed on the normal course of action. Still, this is the modus operandi of physical computational systems. The system computes as long as there is no failure.

  15. There are four two-input, one-output Boolean functions that operate on sd, including the function defined by the following four 3-tuples: (0,0,0); (0,1,0); (1,0,1); (1,1,0). The first two bits are the inputs and the last one is the output bit. The inputs (0,1) and (1,0) clearly show that the order of D matters (in contrast to, say, an OR-gate).

  16. A multiplexer is a combinational circuit that is used to choose an output among several possible inputs sd based on a value of a select signal (Harris and Harris 2013, p. 83).

  17. An arithmetic logical unit (ALU) is an essential component of most CPUs. It combines a variety of arithmetic and logical operations, such as addition, subtraction, conjunction and disjunction, into a single unit (Harris and Harris 2013, p. 248).

  18. The reader is referred to Copeland (1996) for complete details.

  19. We thank an anonymous referee for drawing our attention to such a curious situation.

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Acknowledgments

We thank Oron Shagrir and Luciano Floridi for their helpful comments on earlier drafts of this paper. We are grateful to the anonymous referees for their constructive critiques and suggestions that have significantly improved the paper. A preliminary version of this paper was presented at the 2012 CiE Turing Centenary Conference at Cambridge University, Cambridge, U.K. A significant part of this research was conducted while Nir Fresco was a visiting fellow at the School of Humanities & Languages, University of New South Wales, Australia. He gratefully acknowledges their support. The usual disclaimer applies: any remaining mistakes are the sole responsibility of the authors.

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Authors and Affiliations

  1. Faculty of Engineering and Information Sciences, University of Wollongong (UoW), Northfields Avenue, Wollongong, NSW , 2522, Australia

    Nir Fresco

  2. Department of Mathematics and Computer Science Hagg-Sauer 368, Bemidji State University #23, 1500 Birchmont Drive, Bemidji, MN , 56601-2699, USA

    Marty J. Wolf

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Fresco, N., Wolf, M.J. The instructional information processing account of digital computation. Synthese 191, 1469–1492 (2014). https://doi.org/10.1007/s11229-013-0338-5

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