Contents

1
.
Introduction
2
.
Computation, the Principle of Computational Equivalence, Computational Reducibility vs. Irreducibility, and Meta-Pancomputationalism
3
.
Wolfram Modeling: The Ruliad, Rulial Multiway Systems, and Ruliology
4
.
Sampling the Ruliad—The Observer as an Experiential Equivalence Engine
5
.
Specific Observer Theory: Recursive Experiential Equivalence Engines
6
.
Computational Pre-phenomenology

1. Introduction

Explaining how consciousness fits in the physical world remains the holy grail of science (Melloni et al., 2021). After a long hiatus, the neuroscientific study of consciousness is experiencing a revival, most likely due to technological advancements that have made it possible to study the human brain non-invasively in real time. The field is growing (Michel et al., 2019), and over the past 25 years, neuroscientific hypotheses, models, and theories have proliferated while also gaining empirical support (Northoff & Lamme, 2020; Sattin et al., 2021; Seth & Bayne, 2022; Signorelli et al., 2021). Nevertheless, consensus on a global approach is still missing. The core problem is methodological heterogeneity: the theories have diverging presuppositions about what it is to be explained, how, and according to what success criteria. The issue runs deep. Experimentally, theories continue a siloed development: each is preoccupied with pursuing the empirical consequences of their assumptions only, without cross-referencing to other models. That led to a lack of empirical discrimination among them, as the disparity in starting points engenders almost orthogonal results (Yaron et al., 2022). Philosophically, consciousness qua explanandum forces a reconsideration of the relation between third-person (physical) descriptors and first-person (phenomenological) data, which poses a Hard Problem (Chalmers, [1995]2010) and an explanatory gap (Levine, 1983). Because how to objectively explain a subjective phenomenon is an outstanding issue, the falsifiability and empirical character of some (Doerig et al., 2019) or most (Kleiner & Hoel, 2021) theories recently came under fire. In this work, we aim neither to propose a new consciousness theory nor a methodology to empirically adjudicate between them (Melloni et al., 2023; Chis-Ciure et al., submitted). Instead, we begin with the question, “What is the most fundamental description level for consciousness?” and explore some of the implications of attempting an answer. While we prioritize breadth over depth, we provide rigorous definitions for the new concepts introduced. What we call “computational pre-phenomenology,” characterized in more detail below, is an interdisciplinary research program geared toward a meta-theory of structures in which different scientific theories of consciousness can be formally investigated.

2. Computation, the Principle of Computational Equivalence, Computational Reducibility vs. Irreducibility, and Meta-Pancomputationalism

The obvious starting point of our project is the qualifier “computational.” Defining computation is theoretically challenging: not only are there multiple notions of computation—each with its history—but also adopting a specific one has downstream consequences, e.g., bounds on explanatory power, possible conflicts with the use in other domains, etc. It is a fact that computing predates the advent of any machine we might call a “computer:” for millennia, humans performed mathematical calculations using algorithms, which, informally, were finite mathematical recipes that could be followed mechanically. Alonzo Church (1936a, 1936b) and Alan Turing (1936) independently developed a formal concept of “algorithm” to provide a proof to the Entscheidungsproblem, i.e., whether there is an algorithm for determining whether any given statement is valid within an axiomatic language (Hilbert & Ackermann, 1999). Church introduced lambda calculus, a formal logical framework, and defined algorithms as everything possible within it (Church, 1936a, 1936b). Similarly, Turing introduced the concept of a Turing machine and described an algorithm as anything that could be done with it. Both mathematicians demonstrated that the Entscheidungsproblem has no solution using their definitions. Additionally, their definitions were proved mathematically equivalent (Turing, 1937). Numerous other effective computation models, e.g., cellular automata (von Neumann, 1951), have been proposed. Thus, computer scientists generally accept the Church-Turing thesis, which states that any algorithm can be implemented by a Turing machine (Copeland, 2020). To prove the absence of an algorithm, it is typically necessary to demonstrate that a Turing computer cannot solve the problem (Cook, 1992). Why is the formal definition of an “algorithm” important? Because it is presupposed by the formal definition of “computer.” In computer science, a “computable function” is precisely defined as a function whose values may be calculated using an algorithm. A “computer,” then, is a physical device capable of executing algorithms to solve computable functions. While the Turing-Church models were examples of abstract computation, they were soon followed by endless debates about the scope of concrete computation, i.e., the physical implementation of any model of abstract computation. “Is the brain a computer?” is probably the question that launched cognitive science, the mother of contemporary cognitive neuroscience and psychology. However, this focus on implementation derailed efforts from investigating a more generic notion of computation. Even more significant, it created a conceptual ecology where “the computational” species depends on the more widespread “physical” one. Since the leading question was “What kind of physical systems compute?” a physical substrate was assumed to be theoretically more fundamental than any computation—a physical system had to be “really” there for anything we might call computation to occur. Unmistakably, this priority order was a natural extension of physicalism, the corpus of (mostly implicit) metaphysical beliefs pervasive in science at the time—and still today:​​[A]re brains computers? The answer for most scientists should be yes. First, though there is disagreement in philosophy as to whether brains are purely physical systems and whether their operations rely solely on physical machinery, the perspective of physicalism is widely accepted by brain scientists and we are not aware of any brain scientists who doubt that the operations of the brain are fundamentally physical. Second, with the aid of a pencil and paper, a human brain can in theory implement any program that one could implement with modern digital computers. The only limits would be time and energy […]. (Richards & Lillicrap, 2022, 4)​​What if we challenge this order and start instead with a generic notion of computation? This is exactly what Stephen Wolfram did starting with the 1980s, culminating with the groundbreaking A New Kind of Science (NKS): “Just as the rules for any system can be viewed as corresponding to a program, so also its behavior can be viewed as corresponding to a computation” (Wolfram, 2002, 5). Thus, computation describes any systematic rule-governed state evolution irrespective of its medium. It can be viewed as the progressive working out of particular rules in terms of state sequences. Wolfram’s (2002) investigations started from the basic idea of following the consequences of the most minimal set of primitives that could be used to model a system. That meant dispensing with sophisticated mathematical tools and realistic physical implementation details and asking: “What happens if one instead just looks at simple arbitrarily chosen programs created without any specific task in mind?” (Wolfram, 2002, 23). He extended the traditional notion of computation beyond conventional computing machinery to include any system that systematically transforms its own states according to some program as a set of specifiable rules: ​​In a typical case, the initial conditions for a system like a cellular automaton can be viewed as corresponding to the input to a computation, while the state of the system after some number of steps corresponds to the output. And the key idea is then to think in purely abstract terms about the computation that is performed, without necessarily looking at all the details of how it actually works. (Wolfram, 2002, 637-8)​​​This extreme definitional scope encompasses abstract mathematical processes as well as natural systems. Therefore, computation is a broad framework for describing how the universe works—any process is, ultimately, a computation (Wolfram, 2002, ch. 11; 2021). Wolfram’s discoveries from exploring the computational universe of cellular automata were nothing short of revolutionary. A central one is the Principle of Computational Equivalence (PCE) (Wolfram, 2002, ch. 12). This principle posits that systems exhibiting non-trivial behavior have equivalent computational capabilities. PCE entails that simple rule-based systems can exhibit computational sophistication comparable to more complex systems. This, in turn, implies that computational universality is the rule rather than the exception since there are systems whose rules can be described in one sentence that are nevertheless universal. One can derive from the PCE another central discovery: the distinction between computational reducibility and irreducibility. PCE entails that the behavior of systems with very simple rules, e.g., cellular automata, cannot be simplified or predicted by any shortcut method more efficiently than simulating each step of the system’s evolution. In other words, these systems are computationally irreducible. ​​​So what this means is that systems one uses to make predictions cannot be expected to do computations that are any more sophisticated than the computations that occur in all sorts of systems whose behavior we might try to predict. And from this it follows that for many systems no systematic prediction can be done, so that there is no general way to shortcut their process of evolution […].” (Wolfram, 2002, 741)​​​In contrast, computational reducibility refers to systems where behavior can be predicted without simulating each step, allowing for shortcuts in understanding system dynamics. Given the evolution of a system of interest, a prediction can be viewed as running a competing computation that, e.g., can arrive at the final state with less computational effort than just running the candidate’s system evolution back-to-back. The pervasiveness of computational irreducibility is obviously a major obstacle to traditional scientific approaches that seek predictable, formulaic explanations for complex phenomena. Let us return to the contrast between Wolfram’s view of computation and the one prevalent in the computational cognitive science research program. Giving a precise answer to the question “What does it mean when a physical system performs computation?” means to defuse the triviality objection to computational theories of mind. More specifically, one central worry for such theories is the explanatory purchase of weakly restricted notions of computations. For example, the view that every physical system is a computing system is called limited pancomputationalism, while the one that every physical system implements every computation is known as unlimited computationalism (Colombo & Piccini, 2023). Since Wolfram claims that some, but not all, computing systems are universal, it would seem he is committed to limited pancomputationalism. However, this conclusion forgets the starting point, namely, rejecting the assumption of a priority of the physical over the computational. The Wolframian position could be better characterized as meta-pancomputationalism, with the particle “meta-“ signifying (i) the abstract stance regarding any implementation details, (ii) the metaphysically agnostic stance as to the ultimate nature of any purported substrate of computation, and (iii) the epistemologically geared stance to viewing computation as a coherent description of the universe. The view is a variety of pancomputationalism because it considers computation as pervasive in nature, though not all systems are of equivalent computational sophistication. In other words, the universe can be characterized as being computationally self-constructive in the sense of its evolution being a computation. Nevertheless, “computational” need not mean the universe is inherently computable for observers like us. Indeed, given computational irreducibility, it strictly is not: we are forced to sample only “pockets” of computational reducibility. If the universe is computational, what rules govern its state evolution? How many rules does it have? Well, the short answer is all of them. See the next section for the slightly longer answer.

3. Wolfram Modeling: The Ruliad, Rulial Multiway Systems, and Ruliology

4. Sampling the Ruliad—The Observer as an Experiential Equivalence Engine

5. Specific Observer Theory: Recursive Experiential Equivalence Engines

6. Computational Pre-phenomenology

CITE THIS NOTEBOOK

Computational Pre-phenomenology: A Meta-Structural Foundation of Consciousness Science​
by Robert Chis-Ciure​
Wolfram Community, STAFF PICKS, January 11, 2024
​https://community.wolfram.com/groups/-/m/t/3100969