Minimal physicalism as a scale-free substrate for cognition and consciousness

The encoding of eigenvalues by qubits shown in Fig. 1 satisfies the requirements for a holographic encoding: the only information about B available to A, or vice versa, is the sequence of eigenvalues of HAB encoded by the qubit array. Hence we can consider the qubit array as a holographic screen B separating A from B. Any such holographic screen defines a classical communication channel, i.e. a channel via which A and B exchange finite bit strings (Fields and Marcianò 2020b; Fields et al. 2021). As no other system interferes with this channel, it is free of classical noise. However, it is characterized by quantum noise whenever A and B employ different reference frames (e.g. different z-axis reference frames in the case of qubits implemented by electron spins) to prepare and measure the qubits. The effect of such quantum noise is to impose a classical probability distribution Prob(measured|prepared) on each qubit; i.e. its observable effect is indistinguishable from classical noise.

If we now consider the internal (quantum) states |A> and |B> and the states |B> of the qubit array forming the holographic screen between them, we see that |A> affects |B> only via its effect on |B>, i.e. only via the action of HAB. This is, as noted above, a consequence of separability: separability implies conditional independence. Conditional independence of |A> from |B> and vice-versa is, however, also the MB condition (Pearl 1988; Friston 2013; Clark 2017); hence we can view B as an MB. Indeed, the generalization of the holographic principle stated by Equation (5) and illustrated in Fig. 1 implies that any holographic screen defines a classical information channel that functions as an MB, and vice versa (Fields and Marcianò 2020a; Fields et al. 2021).

As discussed in Friston (2013), MBs are ubiquitous features of living systems, and are indeed what distinguish living systems from their environments (see also Friston et al. 2015; Kuchling et al. 2020; Fields and Levin 2020c). Indeed MBs are ubiquitous features of all physical systems with ergodic behavior (Friston 2019). The MB concept is scale-free; Rubin et al. (2020) show, e.g. that it applies to Earth’s biosphere as a whole. The cell membrane, and in eukaryotic cells, organelle membranes, implement the most fundamental biological MBs. The blanket states of these MBs comprise the states of the embedded receptors, channels, and other exchange molecules, together with the permeability, elasticity, and other properties of the membrane itself. The existence of the MB enables the cell to have a well-defined state, conditionally independent of its environment; hence it enables homeostatic/allostatic processes. The information about the environment available to the cell, and vice-versa, is limited to that encoded by the state of the MB. A similarly strong conditional independence result has been obtained via evolutionary game theory by considering generic systems subjected to competition for environmental resources (Hoffman et al. 2015; Prakash et al. 2020a,b).

The central importance to the cell of the MB implemented by its membrane strongly suggests that enclosure by a membrane was the fundamental requirement for the origin of life (Friston 2013; Fields and Levin 2020c). What was enclosed by the MB/membrane of the last universal common ancestor (LUCA) represents the initial condition and oldest memory (Fields and Levin 2018) of all subsequent life. Viewed from an informational perspective, the state space of LUCA’s membrane-enclosed cytoplasm, including its nucleic-acid, protein, and small-molecule components, specifies the initial information about the environment available prior to membrane enclosure and hence physical separation from the environment. While the cytoplasmic conditions of later cells have diverged from these initial conditions, sometimes radically, they remain a fixed constraint with which all paths of divergence must be consistent. Here, the classical meaning of “separation” from the environment as the presence of a physical barrier accords with its quantum-theoretic meaning of state distinguishability. We can, indeed, see the former as implied by the latter.

The information that transits the cell membrane, and is thereby encoded on the MB implemented by the membrane, is actionable or meaningful to the cell: it “makes a difference” to what the cell does (Bateson 1972; Roederer 2005). When the cell’s interaction with its environment is represented as measurement as in Equation (5) or Fig. 1, what renders the information meaningful becomes clear: meaning requires measurement with respect to some reference frame (Fields and Levin 2020a; Fields et al. 2021). Viewed abstractly, a reference frame is a value, or more generally a vector, from which deviation is detectable. Consider, e.g. measuring the states of an array of qubits implemented by electron spins. Determining whether the spin of a qubit is up (+1) or down (–1) requires a reference frame that defines a particular z-axis, a vector in 3d space. Such a vector can be defined by, e.g. a Stern-Gerlach apparatus oriented in some particular way relative to the Earth’s gravitational field. Only the presence of a common reference frame allows multiple measurements to be compared, and hence makes any differences between them meaningful. Sequential measurements of electron spin with respect to a randomly varying z-axis merely yield noise.

While in classical physics a reference frame is an abstraction that can be completely described to arbitrary precision, this is not true in quantum theory (Bartlett et al. 2007). Quantum theory requires all reference frames to be implemented by physical systems, but forbids the description of any physical system to arbitrary precision. Hence quantum reference frames (QRFs) cannot be completely described to arbitrary precision; they encode, in virtue of their physical implementation, “unspeakable” (Bell 1987) or “nonfungible” (Bartlett et al. 2007) information. This is even true of meter sticks, the lengths of which become uncertain as the energies required to probe them become comparable to the binding energies of nucleii. It is much more obviously true of complex systems such as Stern-Gerlach apparatus or atomic clocks.

The intrinsically nonclassical nature of QRFs has some surprising consequences. Transferring a QRF from one observer to another requires transferring the physical implementation; transferring a finite bit string is provably insufficient (see Bartlett et al. 2007 for proof and examples). Any such transfer requires, moreover, that sender and receiver already share a QRF sufficient to identify the transferred system (Fields and Marcianò 2019). We can, therefore, without loss of generality regard all QRFs available to any observer, including any organism, as physically implemented by the dynamical structure of that system, i.e. by its internal Hamiltonian. All QRFs are, therefore, quantum informational processes, i.e. quantum computations, implemented by physical systems that act as observers. The computations that implement QRFs are, as we will see below, key to understanding both what organisms are aware of and how their awareness drives their cognition. They are, therefore, the central components of any scientific theory of consciousness and cognition that is mathematically consistent with quantum information theory.

The Che-Y system employed by bacterial chemotaxis, e.g. in Escherichia coli, provides a simple example of a biological QRF. If the concentration [Che-Y-P] of phosphorylated Che-Y is high, the flagellar motor spins counter-clockwise and the bacterium swims in a straight line; if [Che-Y-P] is low, the motor spins clockwise and the bacterium tumbles (Wadhams and Armitage 2004; Micali and Endres 2016). “High” and “low” concentrations of phosphorylated Che-Y are defined with respect to some default concentration ratio [Che-Y-P]/[Che-Y] of phosphorylated to unphosphorylated forms, which in turn depends on the balance of relevant kinases and phosphorylases. The default ratio [Che-Y-P]/[Che-Y] is the QRF for the Che-Y system; it fixes a particular value at which behavior switches from straight-line swimming to tumbling. Whether the measured [Che-Y-P]/[Che-Y] at any given time is above or below this fixed value effectively determines whether a stimulus is approached, i.e. is considered “good” by E. coli or avoided, i.e. considered “bad.”

In any electrically excitable cell, the resting membrane potential V0mem is a QRF for polarization: values of Vmem > V0mem are depolarized, while values of Vmem < V0mem are hyperpolarized. The setting of this reference frame is critical to cell behavior in both neurons and nonneural cells. In the planarian Dugesia japonica, altering V0mem of blastomere cells by blocking cell communication via gap junctions during regeneration can effect a homeotic transformation of the posterior from tail morphology to head morphology, including a complete functional brain (Oviedo et al. 2010; Durant et al. 2017). In both neurons and electrically excitable plant cells, blocking gap junctions via anesthetics induces cell quiescence (Baluška et al. 2016; Gremiaux et al. 2014; see also Kelz and Mashour 2019 for a general discussion of anesthetic effects across phylogeny).

The quantum theory of complex, macroscopic systems is generally intractable; hence investigating the general properties of biological QRFs requires an abstract, scale-free specification language. The category-theoretic formalism of Channel Theory, developed by Barwise and Seligman (1997) to describe networks of communicating information processors, provides a suitably general language for specifying the functions of QRFs without any specific assumptions about their implementation. The information processing elements in this representation are logical constraints termed “classifiers” that can be thought of as quantum logic gates; they are connected by “infomorphisms” that preserve the imposed constraints (numerous application examples, mainly in computer science, are reviewed in Fields and Glazebrook 2019a). Combinations of these elements are able to implement “models” in the sense of good-regulator theory (Conant and Ashby 1970). Suitable networks of classifiers and their connecting infomorphisms, e.g. provide a generalized representation of artificial neural networks (ANNs) and support standard learning algorithms such as back-propagation. Networks satisfying the commutativity requirements that define “cones” and “cocones” (“limits” and “colimits,” respectively, when these are defined) in category theory (Goguen 1991) provide a natural representation of both abstraction and mereological hierarchies (Fields and Glazebrook 2019b) and of expectation-driven, hierarchical problem solving, e.g. hierarchical Bayesian inference and active inference (Fields and Glazebrook 2020b,c). Commutativity within a cone—cocone structure, in particular, enforces Bayesian coherence on inferences made by the structure; failures of commutativity indicate “quantum” context switches (Fields and Glazebrook 2020c).

Theories of consciousness typically assume that the agent of interest is embedded in an environment that has observer-independent features and contains observer-independent objects. The visual system, e.g., is often described as using “inverse optics” to compute an “observer-independent” 3d layout from a 2d image (e.g. Pizlo 2001). Assuming observer-independent, ontological “givens” both restricts the agent of interest to some subset of our (typically assumed a priori) ontology and risks under-predicting the agent’s computational requirements. It makes von Uexküll’s (1957) question of defining the organism’s umwelt, and hence Nagel’s (1974) “what is it like?” question harder, and makes the Cartesian response that most organisms are aware of nothing, and hence have no umwelt easier.

Quantum theory itself forces MP to reject environmental “givens” on purely formal grounds. The Hilbert space HB in Equation (2) and internal Hamiltonian HB in Equation (3) can be decomposed in any arbitrary way without affecting the interaction HAB at all (Fields 2012, 2016); hence HAB can communicate no information to A about any such decompositions. This is the case for any bipartite interaction, and hence any interaction described by Equation (5), regardless of the physical makeup of the interacting components. It is the conditional independence between the inside and outside of an MB expressed in more fundamental physical terms.

By rejecting any a priori ontology for the environment, MP requires any perceived ontology to be fully supported by the information-processing capabilities of the perceiver. In particular, any perceived feature of, or perceived object embedded in, the environment B of any agent of interest A must be rendered both detectable and meaningful by a QRF implemented by A. This is illustrated in cartoon form in Fig. 2: detecting an environmental feature (a box) with a property (a color) requires a QRF for “box-ness” and a specific detector for the color. The box-detecting QRF encodes those properties (reference state observables) that boxes must have to qualify as boxes; hence it picks out boxes, and only boxes, against the general background of B. Informally, the QRF can be thought of as an attractor in an “interpretation space” associated with the system implementing the QRF. The property detector determines the value of some “pointer” observable that characterizes all systems that qualify as boxes; here, the box’s color. In quantum-theoretic language, identifying a bounded system (feature or object) having some specific property “decoheres” B relative to A (see Fields and Glazebrook 2020a; Fields and Marcianò 2020b for formal analysis). It is important to emphasize that A’s perceptual and cognitive capabilities have no effect on the physical state |B>, and in particular do not render it separable. The features or objects that A detects in B are strictly relative to A, not “objective” in any observer-independent sense (again see Mermin 2018; Müller 2020 for discussion from a purely quantum-theoretic perspective).

Specifying “objects of awareness” entirely in terms of QRFs, with no claims of observer-independent ontology, renders typical formulations of the “combination problem” ill-posed. Combination is well-defined for QRFs: two QRFs implemented by a single system can be combined if, but only if, all of the operators (i.e. the Barwise-Seligman infomorphisms) involved mutually commute (Fields and Glazebrook 2020c). This is the “combination” implemented by standard binding processes, e.g. feature or feature-motion binding during object categorization (Fields and Glazebrook 2019b). “Combination” of QRFs implemented by different systems is, on the hand, strictly undefined: the measurement operators implemented by different systems act on different environments, each of which by definition contains (at least partially) the other system. Hence what Chalmers (2017) calls the “quality” and “structure” combination problems cannot be coherently posed in MP. What Chalmers calls the “subject” combination problem is solved, for living systems, by their environments; systems that cannot maintain homeostasis/allostasis do not survive, and are unlikely to assemble at all. Systems that do survive are described by MP if they satisfy Equations (5) and (6), but they may implement only trivial QRFs. Hence we agree with the deflationary position advocated by Montero (2017), though for more technical reasons.

This universal requirement that awareness be supported by QRFs yields somewhat counter-intuitive predictions of minimality in basal organisms:

Prediction 1: Moving in 3d space does not require a QRF for 3d space, and hence does not require experiencing 3d space. E. coli chemotaxis provides an example. E. coli has a 1d spatial QRF: its body axis, with (mainly) anterior chemoreceptors and (mainly) posterior flagella. Directed “approach” motion is along this axis; undirected “tumbling” re-orients this axis randomly in the 3d “lab” frame of an observer equipped with a 3d QRF. E. coli has no known means of computing the relative angle between its pre- and post-tumbling linear motion, i.e. it has no known 3d QRF; hence tumbling appears to implement a 3d random walk (Wadhams and Armitage 2004). Colonial microbes living in planar mats, on the other hand, can potentially use differential cell–cell or cell–substrate interactions to distinguish left from right (Jauffred et al. 2017) and hence establish a 2d QRF; microbes inhabiting multi-species 3d mats with vertical division of labor may have 3d QRFs (Prieto-Barajas et al. 2018). Differentiated cells of multicellular eukaryotes clearly employ such QRFs (e.g. Bajpai et al. 2021); interestingly, multi-axis morphology correlates with the presence of neurons and appears to be directly instructed by neural signaling (Fields et al. 2020). How the representation of 3d space in migrating cells is coupled to the representations of cell- or extra-cellular surface characteristics, bioelectric and morphogen gradients, and other morphogenetic signals remains a central question in developmental biology (Grossberg 1978; Pezzulo and Levin 2015).

Prediction 2: Successful interaction with an object does not require a QRF that identifies that object, and hence does not require experiencing that object. E. coli mating provides an example: the mating pilus extends randomly in 3d space, and is tipped by an adhesin of unknown specificity (Cabezón et al. 2015). Commonplace lateral gene transfer (LGT) between members of distant microbial lineages (Robbins et al. 2016) suggests that mating without mate detection is routine in the microbial world; viral-mediated gene transfer and direct uptake of nucleic acids from the environment provide even more extreme examples. Communal microbes such as Myxococcus xanthus that differentiate kin from nonkin even below the species level, however, appear to have sophisticated, though yet uncharacterized, QRFs for other organisms (Muñoz-Dorado et al. 2016; Thiery and Kaimer 2020). Fungi that engage in differential anastomosis appear similarly equipped (de la Providencia et al. 2005). Cell-type identification QRFs appear to be implemented in part bioelectrically in multi-species microbial mats (Humphries et al. 2017; Yang et al. 2020); the ubiquitous use of bioelectric signaling in fungi suggests that this may be the case for fungal cell-type QRFs as well.

Prediction 3: Successful causation does not require a mechanism for detecting causation, and hence does not require experiencing causation. Hunting swarms of M. xanthus kill and eat other microbes, but appear to have separate, noncommunicating detection systems for prey species and edible prey components (Thiery and Kaimer 2020). Hence they have no way of causally associating the killing of prey with the subsequent availability of edible prey components.

These can be summarized by the following, which recognizes the key role of memory in enabling the experiences of space, objects, and causation:

Prediction 4: Having a memory does not require a QRF for linear time, and hence does not require experiencing time or retrievable memory. All organisms have genomes that record their phylogenetic history, but they have no mechanism for reading their previous genomic states. The genome does not, therefore, function as an internal QRF for linear time. This applies, in particular, to us, although we can employ the genomes of other organisms as external linear time QRFs (Kumar 2005).

If this last prediction is correct, microbes and perhaps other organisms lacking linear time QRFs may live in a “continuous present” characterized mainly by chemoreception (“taste”) and stress (see below). Their sensory capabilities may change radically via LGT or other mechanisms, but they cannot “notice” such changes.

Biological memories exist at multiple scales (Fields and Levin 2018). Characterizing the scales at which memories are encoded, and the QRFs that enable them, emerges as a central task for any theory of consciousness that assumes MP. Bioenergetic studies may provide a content-independent means of approaching these questions, as discussed below.

Actions by an organism on its environment are, in the language of Fig. 1, preparations of an MB state |B> that its environment observes. A swimming bacterium, e.g. prepares a new environmental state by expending energy to change its location. In Friston’s (2013) terms, this is active inference: acting on the environment to change its state alters, in consequence, the subsequent environmental states observed by the active system.

Actions are, by definition, thermodynamically irreversible: they transfer classical information, via B, from the organism to its environment. Transfers of classical information across boundaries such as B are, moreover, the only thermodynamically irreversible events in MP. As with the requirement for QRFs to enable awareness, this is a consequence of MP’s quantum theoretic foundation. The state |A> is not, in general, assumed to be separable; hence its Schrödinger evolution is time-reversible and incurs no energetic cost (Bennett 1982). Information can only be retrievable at some later time if it is irreversibly and hence classically encoded. Hence retrievable memories can, in MP, only be encoded on boundaries such as B. As experiencing a memory as such requires an ability to compare two experiences—either two memories or a memory and a current state—it requires retrieval. Any experienced memory must, therefore, be both encoded on, and retrievable via an appropriate QRF from B.

This fundamental thermodynamic constraint has immediate consequences for biological architecture and for the structure of QRFs for linear time:

Prediction 5: All retrievable biological memories are stigmergic. Beginning with bacteria (Gloag et al. 2015), biological systems ubiquitously employ stigmergic memories (Heylighen 2016). This is not a surprising observation to be explained, but rather an empirical confirmation in MP. The idea that the experiencing mind “extends” (Clark 1998) into the environment via stigmergic memory is a direct consequence of quantum theory.

The stigmergic nature of memory can be reconciled with the experience of memory as an internal, private phenomenon only if the agent A is compartmentalized by internalizing part of B to provide an internal boundary C on which classical information can be encoded. This internal boundary imposes a separability condition |A> = |A1>|A2> as shown in Fig. 3; A1 becomes part of the “environment” of A2 and vice-versa. The interaction between A1 and A2 can be written in the form of Equation (5); hence information flow across C is bidirectional classical communication between the components A1 and A2. If we view A2 as implementing perception and A1 as implementing action, this communication, together with the environment’s response, forms a closed loop. Hence we have:

Prediction 6: Internal awareness requires internal boundaries. Any system A capable of experiencing internal memories, in particular, has a separable internal state and positive integrated information Φ. Internal memories are built into all systems that qualify as conscious in IIT (Oizumi et al. 2014, see especially Fig. 19) and are the basis for such systems having Φ > 0. Here, we see this as a consequence of quantum information theory.

As discussed above in connection with MBs, this prediction links separability in its quantum-theoretic sense of state distinguishability with separability in its classical sense of separation by a boundary: the internal boundary C functions as an MB that encodes classical information and imposes conditional independence. It provides for a general expectation that living systems will be compartmentalized by internal boundaries on which classical information can be encoded. Because MBs limit, as well as enabling, information transfer, it also predicts a systematic inability to determine the source of a memory. In particular:

Prediction 7: Compartmentalized systems cannot determine the sources of their encoded memories. Systems can be expected to behave as if memories they encode reflect their own past experience, whether they do or not. Studies of memory transplantation (Pietsch and Schneider 1969) and false-memory induction (Ramirez et al. 2013) in nonhuman animals provide mechanistic support for this prediction (see Levin 2020 for additional examples and discussion), as does the psychology (Henkel and Carbuto 2008) and neuroscience (Straube 2012) of false-memory induction in humans.