The arguments herein are in large part owing to the Essentia Foundation’s “Entropy is in the eye of the beholder,” by Dr. Gabriel Proulx. A goal of this paper is to add to the arguments Dr. Proulx has already laid out in his essay. Credit is hereby given to Dr. Proulx and Essentia Foundation where it is due (Proulx, 2023).
Abstract
The Second Law of Thermodynamics, commonly known as the Second Law, posits that entropy or disorder in closed systems tends to increase over time (Smith, 2010). This paper challenges that conventional notion by proposing that such an observed increase in entropy is a product of conscious agents’ perception, which arises from their sequential simplification of an infinitely intricate reality. Furthermore, we contend that entropy is intricately connected to the limitations in bandwidth or computational capacities of conscious experiences, rather than being an inherent property of objective systems (Johnson & Brown, 2018). A deeper understanding of the Second Law necessitates an exploration of the concepts of consciousness and the computational boundaries that conscious agents operate within.
Introduction
Entropy encompasses the concepts of macrostates and microstates. A macrostate provides a broad, “low-resolution” depiction of a system, while a microstate offers a detailed description of the specific arrangement of particles within the system (Thompson, 2015). A given macrostate can correspond to numerous microstates, and systems tend to transition from macrostates with fewer possible microstates to those with a greater number of possible microstates.
To illustrate, consider a container divided into two sections, initially with 100 gas molecules on one side and a vacuum on the other. When the divider is removed, the system reaches a macrostate in which there are approximately 50 gas molecules in each section. Although it is theoretically possible for the system to remain in the initial macrostate, the number of microstates consistent with the evenly distributed macrostate significantly surpasses the microstates associated with the initial configuration. Consequently, the system undergoes a transition from a low-entropy macrostate (order) to a high-entropy macrostate (disorder) (Gibbs, 1873).
Recent challenges to the Second Law have predominantly revolved around the concepts of information and consciousness (Lloyd, 1997). These challenges emphasize the need to consider the impact of conscious agents’ information processing capabilities on the perception of entropy and the overall dynamics of thermodynamic systems.
Karl Friston, Markov blankets, and the free energy principle
The Markov blanket is a concept derived from probabilistic graphical models and Bayesian network theory. It refers to a set of variables within a larger network that acts as a protective barrier around a target variable, shielding it from the influence of all other variables outside the blanket (Pearl, 1988; Koller & Friedman, 2009). In essence, the Markov blanket encapsulates the minimal set of variables required to maintain conditional independence for the target variable. This means that if one knows the values of the variables within the Markov blanket, additional information about variables outside the blanket does not provide any extra information about the target variable.
Karl Friston’s Free Energy Principle is a theoretical framework in neuroscience that posits that the brain functions as a Bayesian inference machine, constantly seeking to minimize free energy, which represents the discrepancy between the brain’s predictions about its environment and the sensory inputs it receives (Friston, 2010). According to this principle, the brain aims to construct accurate, but not literal, models of the world to make effective predictions and adapt to its surroundings.
In the context of the Free Energy Principle, the Markov blanket can be seen as the set of sensory inputs and internal states that are relevant for an organism to minimize prediction errors and maintain an accurate model of its environment (Friston, 2010). These variables within the Markov blanket are crucial because they shield the brain from irrelevant or extraneous information while allowing it to focus on the essential aspects of the environment.
By concentrating its computational resources on the variables within the Markov blanket, the brain can efficiently process and update its internal models to minimize prediction errors. The Markov blanket helps ensure that the brain’s predictions remain accurate by preventing the incorporation of unnecessary information that could lead to incorrect modeling. In essence, the Markov blanket acts as a cognitive filter that separates the internal states essential for perception and action from the full complexity of external states, aligning with the overarching goal of minimizing free energy as proposed by Karl Friston’s Free Energy Principle.
So far, this seems to align with the prevailing physicalist worldview. However, these concepts pose that metaphysical theory a profound problem.
External states, which encompass the sensory inputs an organism receives from its environment, often exhibit high entropy (Friston, 2010). In other words, the external world is typically complex, uncertain, and filled with a vast amount of sensory information. If an organism’s internal states were to mirror the high entropy of the external states directly, as they would have to in order for us to perceive reality literally, the organism would face significant challenges:
- Overwhelm and Dissolution: Directly reflecting the high entropy of external states in internal states would lead to sensory overload and cognitive chaos. The brain would struggle to process and make sense of the sheer volume of incoming sensory data, potentially resulting in cognitive and perceptual breakdowns.
- Loss of Structural Integrity: Not only that, but the organism would dissolve into hot soup, as it would be unable to maintain structural integrity against the tide of essentially infinite entropy (Kastrup, 2019).
- Lack of Adaptation: High entropy in internal states would hinder an organism’s ability to adapt to changes in the environment. Adaptation relies on distinguishing relevant information from noise, which is made possible by maintaining a structured and relatively low-entropy internal representation.
To avoid these challenges, the brain employs the concept of the Markov blanket as a protective barrier between internal and external states (Friston, 2010). The Markov blanket effectively separates the organism’s internal models and expectations from the full complexity of external states. It filters and selects the most pertinent sensory information and internal representations needed to maintain a coherent worldview and make adaptive predictions. By doing so, it acts as a cognitive shield that shields the brain from the full impact of high external entropy.
Wolfram’s models of entropy
Stephen Wolfram, a physicist and computer scientist, has devoted his work to understanding the laws of physics as emergent phenomena arising from simple rules. He utilizes cellular automata, which are computational models involving grids of cells. These models begin with an initial state, often represented as a row of cells with varying shading, and they rely on straightforward rules to determine the shading of cells in subsequent rows. What’s intriguing is that some of these rules appear to produce immediate randomness, while others gradually lead to apparent randomness, some generate nested patterns, and yet others exhibit a mixture of organization and apparent randomness. Despite these diverse behaviors, all cellular automata are fundamentally deterministic, lacking any intrinsic randomness (Wolfram, 2002). This demonstrates how complex behavior can emerge from simplicity through the application of rules.
A pivotal concept in Wolfram’s models is the “ruliad,” which he defines as “the entangled limit of everything that is computationally possible: the result of following all possible computational rules in all possible ways.” Essentially, he likens reality to the ruliad, which encompasses all conceivable computational outcomes derived from simple rules. These rules are inherently complex, with no shortcuts available to reach the complete results without undergoing the computational process. However, within this complexity, there exist pockets of reducibility, which are patterns that can be observed and leveraged to gain some predictive understanding of the rules (Wolfrom, 2002).
Computationally bounded observers, such as humans, exist as subsets of the ruliad, meaning they cannot grasp the totality of its complexity. Instead, they can recognize patterns and create heuristic models of the ruliad. The extent to which they can reduce apparent chaos to predictable patterns depends on their computational limitations, specifically, the computing power of their perspective (Wolfram, 2002). One can also liken these computationally bounded observers to virtual machines running within an essentially infinite, relative to them, global computational information system.
In a paper from February 2023, Wolfram suggests that our perception of the Second Law of Thermodynamics arises from the irreducible complexity of the universe (Wolfram, 2023). Due to the constraints of our computational abilities as observers, we can model only a portion of the ruliad’s behavior. Over time, the discrepancy between our computational limitations and the universe’s irreducible complexity accumulates. While there are patterns that we can recognize and predict within our computational bounds, the patterns exceeding those bounds are interpreted as randomness and compound over time. This cumulative effect results in what we experience as the Second Law.
Wolfram emphasizes that observers are contained within and therefore experience the ruliad from within. Consequently, they possess a subset of its computational power, leading to computational bounds. This limitation implies that even if an observer recognizes a significant portion of a pattern and predicts behavior with high accuracy initially, each subsequent computational step leads to a constricted bandwidth. Over time, the overall accuracy approaches zero (Wolfram, 2002; 2023).
Wolfram’s models not only elucidate why information loss occurs over time but also shed light on how it is experienced. He introduces the concept of multiway graphs, which are akin to upside-down tree graphs representing all possible trajectories of a system, resembling the many-worlds interpretation. Initially, as computationally bounded observers, we start with a relatively high-fidelity understanding of a particular state, albeit not perfect. However, as time elapses, we must update our model to encompass numerous potential states. This necessitates a downsampling of our model, transitioning from fine-grained knowledge to coarse-grained knowledge. In essence, our initial high-resolution understanding progressively degrades into a more generalized, lower-resolution view (Wolfram, 2002; 2023).
Wolfram’s models collectively illustrate that the increase in entropy is not an inherent trait of systems but rather an outcome of observers repeatedly downsampling a high-fidelity stream of reality due to computational limitations. Additionally, Wolfram touches upon the concept of consciousness at various levels, from the microscopic scale of neurons to the macroscopic scale of planetary consciousness. While he refrains from drawing firm conclusions about the definition of computational bounds or the potential for expanding them, he emphasizes that our perception of the laws of physics is relative to our computational bounds, suggesting that different bounds would result in different laws of physics (Wolfram, 2002; 2023).
Entropy in Donald Hoffman’s Interface Theory of Perception
Donald Hoffman, a cognitive psychologist renowned for his investigations into visual perception, evolution, and consciousness, has introduced the Interface Theory of Perception (Hoffman, 2018). This theory, which aligns with idealism and converges with both Friston’s and Wolfram’s work, posits that reality is consciousness (specifically, phenomenal consciousness, to use the Western analytic terminology, as distinguished from meta-consciousness). Hoffman’s work, grounded in computational models, underscores the idea that, according to evolutionary game theory, the likelihood of reproductive fitness favoring an objective perception of reality is effectively zero (Hoffman, Singh, & Prakash, 2015). Instead, natural selection would have favored simplified and abstracted representations of reality to enhance survival and reproduction, which Hoffman and his colleagues worked out in the Fitness-Beats-Truth Theorem. He analogizes this to individuals unknowingly wearing VR headsets, emphasizing that our perception of reality is more akin to a shared, transpersonally subjective experience, where each observer encounters different perspectives of the same underlying fundamental reality (Hoffman & Prakash, 2014).
Within Hoffman’s framework, space and time are products of consciousness rather than foundational aspects of reality, a viewpoint consistent with quantum physics (Hoffman, 2017). Furthermore, he asserts that the hard problem of consciousness only arises within physicalism. Physicalists equate the correlations between physical brain activity and conscious experience with causation but struggle to explain a single conscious experience in terms of matter (Hoffman & Prakash, 2014). While physicalism entails two unexplained phenomena—matter and consciousness arising from matter—idealism necessitates only the existence of consciousness (Proulx, 2023). The experience of matter emanating from consciousness is a nightly occurrence during dreams, wherein we perceive matter, space, and time as products of consciousness (Hoffman, 2018). Although idealism presumes the a priori existence of consciousness, this is an assumption universally affirmed by human experience.
Hoffman’s model of conscious agents and his recognition that space-time is relative to the nature of a specific conscious agent align with Stephen Wolfram’s model of computationally bounded observers and the relativity of the laws of physics to those bounds (Hoffman, 2017). The conscious agent encompassing all conscious agents in Hoffman’s theory corresponds to what Wolfram terms the “ruliad” (Hoffman, 2018). Additionally, Karl Friston’s work on the free energy principle, which demonstrates the necessity of a Markov blanket between our internal and external states, points to the need for a perceptual interface that simplifies the essentially infinite complexity of reality, such that we, as subsets within that reality, can maintain our structural integrity. The physical world of our experience is the Markov blanket, including all of the physical laws. Of course, by recognizing that it is consciousness that renders the physical world, we resolve the paradoxes of the apparent fine-tuning problem and the unreasonable effectiveness of mathematics, both of which are relics of physicalism’s logical incoherence, internal inconsistency, and unavoidable dualism relating to the hard problem of consciousness.
Likewise within Hoffman’s framework, the perception of increasing entropy is attributed to the conscious agent rather than being an intrinsic property of objective systems (Hoffman, 2018). The transformation of a deeper fundamental reality beyond space-time into our perceptual experience is contingent on the capacity of the conscious agent and the optimization function of consciousness, which, according to evolution, is fitness (Hoffman, 2017). However, even the concept of evolution must, itself, be viewed as a projection of a deeper phenomenon beyond space-time within this framework. For that matter, so must the brain, thus adding new depth to Friston’s work. Hoffman invokes Gödel’s incompleteness theorem to argue for the infinite nature of reality, highlighting that any proof relies on at least one unprovable axiom (Hoffman, 2018). Analogous to Wolfram’s model, this suggests that conscious agents experience only a subset of reality and that this subset degrades over time due to the inherent loss of information in the filtration process.
The Gibsonian model of perception and affordances
Gibson’s ecological model of perception emphasizes that perception is not a passive process of receiving sensory information and then inferring meaning but rather an active process of perceiving meaning and then inferring objects (Gibson, 1979). In this view, perception is intimately tied to the ecological context in which it occurs, and it involves the detection of information-rich patterns that afford meaningful actions. Affordances, a central concept in Gibson’s framework, refer to the actionable properties of objects and the environment as they are perceived by an observer (Chemero, 2003). These affordances are not inferred based on sensory data but are perceived directly, guiding the observer’s actions. For example, a water bottle does not inherently possess the property of “graspability.” A conscious agent must first enter into an agent-arena relationship with the bottle. The agent can afford the bottle that property, while simultaneously, the bottle affords the conscious agent the property of being a “grasper.”
Connecting this to Hoffman’s Interface Theory of Perception, we can interpret that rather than perceiving objects and then inferring meaning, we perceive meaning and infer objects. In other words, our perception is geared towards extracting the meaningful aspects of our external state, and the objects we infer are a consequence of this perception. These inferred objects, which are part of the intersubjective reality described by Hoffman, can be seen as affordances, akin to narratives that our perceptual Markov blanket provides about survival fitness payoffs. In other words, they represent the actionable properties and meaningful features that our perceptual system detects.
This alignment between Hoffman’s theory and Gibson’s ecological model of perception highlights the idea that perception is not a mere reconstruction of objective reality but a process deeply intertwined with the meaningful aspects of the external state. In short, the physical world is a perceptual interface that serves as our Markov blanket, as it simplifies the infinite so that it can be experienced by the finite as patterns of meaning (affordances), akin to narratives.
Transpersonal subjectivity, not objectivity, describes the “physical” world
The perspective that entropy should be regarded as a characteristic of conscious agents rather than an inherent property of objective systems prompts inquiry into how different observers perceive entropy in a similar manner. Idealism offers valuable insights into comprehending this shared perception of entropy among observers.
The mainstream physicalist framework that still enjoys dominance in the Academy today, although influential, falls short in providing a satisfactory explanation for the common experience of entropy among observers. In contrast, Wolfram’s model suggests that observers can exhibit correlated experiences owing to their status as subsets of the same ruliad and due to sharing similar computational limitations (Wolfram, 2023). Similarly, Hoffman’s analogy involving a VR headset underscores how shared data sources can lead to observers having congruent observations (Hoffman, Singh, & Prakash, 2015).
Bernardo Kastrup, scientist and philosopher, advocates for a monistic and idealistic framework, analytic idealism, that furnishes a coherent explanation for the space between objective and solipsistic experiences. In this conceptualization, the universe is conceived as a singular mind, and the perception of separateness among conscious agents is attributed to the psychological phenomenon of dissociation (Kastrup, 2019). Much like in dreams, where a single mind generates dream avatars that appear distinct from the dream’s characters and backdrop, waking life is regarded as a transpersonally subjective reality fashioned by a greater mind.
Dissociative Identity Disorder (DID) provides a real-world manifestation of this dissociation, where an individual’s alter egos can recollect the same dream from different character perspectives. In this view, there exists no objective dream world; all elements of the dream emanate from the dreamer’s mind, each offering a unique observational vantage point. Waking reality operates along analogous lines, with each conscious agent contributing to the construction of a transpersonally subjective reality (Kastrup, 2019).
States of heightened awareness and non-dual experiences of universal oneness can be attained through various means such as meditation, spontaneous realizations, or the use of psychedelics. In these states, individuals often report receiving information from a source external to themselves. This corresponds with the idea that conscious agents can access information that was previously beyond their reach, potentially resulting in the perception of decreased entropy or increased order in their experiences.
Conclusion
In this paper, we have argued that entropy is not an inherent quality of objective systems but is rather tied to the limits of conscious awareness. An increase in entropy arises from an observer’s inability to fully capture and process information due to the necessary simplification of an infinitely complex reality, as described by Donald Hoffman’s Interface Theory of Perception, Karl Friston’s elucidation of the free energy principle in neuroscience, the Gibsonian ecological model of perception, and Stephen Wolfram’s concept of the ruliad and computational observer dynamics. Herein, we have provided a unified and promising viewpoint on a profound scientific enigma, the Second Law of Thermodynamics, which is ultimately explainable by means of consciousness.
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