Reflections on Fusions of Consciousness

Chris Percy (Qualia Research Institute)
Jan 15, 2024

Note: This review is based on a good faith reading of the original paper, but should not be taken to represent the HPP position. There may well be misunderstandings or ambiguities in either the original text or this review. I welcome opportunities through discussion and feedback to improve my understanding of the paper and the important issues it addresses.

Original paper citation (HPP): Hoffman, D.D.; Prakash, C.; Prentner, R. Fusions of Consciousness. Entropy 2023, 25, 129. (Hoffman, Prakash, and Prentner 2023)

1. Overview of paper claims and central claim for the review

This paper by Hoffman, Prakash, & Prentner (2023; hereinafter HPP) has four main contributions, which are presented as mutually reinforcing, but are helpfully addressed at least initially as separate contributions:

  1. An ontological claim that spacetime is not fundamental
  2. An epistemological claim that humans do not perceive the world as it really is
  3. A mathematical account to describe the fusing together of objects
  4. A philosophical position on the nature of consciousness.

I will comment briefly on all of these, but centre the discussion on (4). Their central philosophical claim is that a particular formulation of “conscious realism” (defined in s1.1) can (i) solve the combination or binding problem of phenomenal consciousness (defined in s1.2) and (ii) explain how apparent physical features of the world might emerge from the substrate of conscious realism, particularly space-time.

In some places, HPP makes strong assertions that have been off-putting to some readers (e.g. the ResearchHub conversation to which this review note responds). In particular, some sentences present what appear to be very strong positions on claims (1) and (2) and present as incontestable scientific consensus positions where at least some plausible alternatives are still being argued or alternative plausible definitions permit more nuanced statements. For instance: “Neurons have no causal powers.” “Spacetime Is Doomed”. “Our senses do not show us truths about objective reality.” Such bald statements seem designed to raise hackles. However, a patient reading of the text reveals both the reasoning behind the statements and the weaker versions that are nonetheless adequate for the paper’s philosophical claim. Unfortunately, time-poor readers may be quick to dismiss a paper that uses this kind of provocative language.

One load-bearing assumption of the paper is not discussed in as much detail as the claims (1) and (2). The mathematical formalism of the paper requires the assumption that if one mathematical object has the right isomorphisms to another mathematical object, it is reasonable to claim entities well-modelled by the former could “produce”, “give rise to”, or otherwise “ground” entities well-modelled by the latter. This assumption is not made explicit and is contestable, but is nonetheless one plausible assumption to use as the starting point for inquiry. I return to this in section 7.

My overall view is to welcome the creativity, ambition, and mathematical formalism in this paper, being three features of scientific endeavour that are much needed in the study of human consciousness. Cautious rather than bombastic language may help the paper gain more serious readership, although it may reduce its viral appeal and is, in any case, the right of the authors to determine. More importantly, I hope HPP continue their collaboration to investigate this topic and hope that the avenues for exploration discussed in this note and summarised in s7 identify some useful areas to work on.

Definitions and Perspectives in HPP Paper

1.1. Definitional aside: Conscious realism

Conscious realism is Hoffman’s preferred theory of consciousness, see (Hoffman and Prakash 2014) for details. To a first approximation, the theory states the ontological basis of all reality, including conscious experiences, is conscious agents networked together. In other words, everything we observe and experience - say a cat, a neuron, the propagation of gravitational wave, or a moment of pleasure – is an emergent phenomenon from an underlying reality of individual, discrete conscious agents interacting with each other. Such conscious agents are taken as fundamental entities and are not in turn constructed out of anything else, although they may have multiple, complex properties and multiple allowed interactions with each other, such that networks of such agents can give rise to considerable complexity.

1.2. Definitional aside: The combination/binding problem.

The authors present definitions and an account on pp10-11. To provide a complementary definition, to a first approximation, the binding problem asks how it is that human-style consciousness can experience multiple phenomena simultaneously, bound together as part of a single unified experience.

For instance, if applied to theories of consciousness that ground awareness in patterns of neurons firing, why is it that we often have a single experience corresponding to lots of individual neurons firing, rather than many individual experiences corresponding to each individual neuron or neuronal pattern firing? If applied to panpsychism, if certain micro-level, perhaps fundamental physical entities are conscious or proto-conscious, by what mechanism do they “combine together” their consciousnesses to create – at least at times - the larger, macro-style experiences that constitute everyday human conscious experiences?

“Feature binding” is a subset of this binding, such as why we can perceive one object with multiple features (e.g. a blue book is simultaneously book-shaped and blue), but the greater concern is “phenomenal binding”, in which our overall experiences unify disparate elements into a single complex subjective experience. For instance, we might be aware of neck discomfort while reading the blue book – while we might analytically separate the experiences of discomfort, perception, and cognition, nonetheless they are, at least at times, experienced as elements of a broader, single, unified experience.

1.3. A computationalist perspective on the binding problem and the resulting “boundary problem” challenge

There seems to be fairly broad consensus that bound and unified experiences are a feature of human consciousness at least at times, notwithstanding disagreement over whether these experiences are not what they seem in some respect or whether “non-bound” or non-unified experiences are even possible for humans (e.g. (Bayne 2010) and related work). Theorists therefore typically accept that the binding problem exists (once they have had occasion to understand it), but they disagree on the extent to which it is complex to address. A possible computationalist perspective is to stipulate any linkages between nodes on a network, informational concepts that connect via operations in an algorithm, or causally connected entities count as a form of binding (perhaps with several types of forms of binding with different features). From this perspective, very many physical phenomena are trivially bound together.

One argument against such trivial binding mechanisms constituting “true phenomenal binding” (at least in the case of human conscious experiences) is the related “boundary” problem. Human-level experience is boundaried, in that we are not aware of everything in the universe and there are typically private boundaries between your experience and mine, such that boundaries must also be created by the binding mechanism. To a first approximation, the boundary problem asks what non-arbitrary feature stops these proposed binding mechanisms from being too successful, in that they bind things together typically excluded from our conscious experiences, e.g. subconscious information processing in the brain is still causally and informationally connected with the conscious information processing.

Such theorists must explain why some causal connections create binding but not others. Potential such accounts can be constructed and computationalists should be encouraged to do so. It is particularly worthwhile as it leads potentially to empirical tests, manipulating the brain or causal connections as required to make information that is always present somewhere in the system pop in and out of conscious awareness.

One temptation in such accounts is to lean on complexity thresholds. For instance, in global workspace theories applied outside the specific structures of a modern human brain, we might assert that a certain “large” amount of information needs to be broadcast to at least a certain number of modules for it to count as a global workspace and for consciousness to “pop up”. Such accounts require at least one further detail to be convincing. One possibility is motivating a phase transition, with a corresponding mechanism and change in features that can be looked for. An alternative is to accept a broadly continuous scale of increasing complexity with no phase transitions, accepting in turn that even very simple objects that (for instance) “send at least some information to more than one receiver” would have consciousness, albeit perhaps only at a very “dim” level (i.e. many non-arbitrary, non-speciesist computationalist accounts implicitly tolerate a very broad range of conceivable micro-conscious entities, such as IIT).

If we further want these features to be non-subjective or frame invariant from the perspective of special relativity, additional constraints are placed on the plausible mechanisms, e.g. simultaneity of calculation can no longer be invoked since it is frame-dependent. For a fuller discussion and references on the combination/binding problem and boundary problem, please see our paper (Gómez-Emilsson and Percy 2023).

2. Philosophical outline of their central argument of interest

Caveating that the authors do not present such an outline explicitly, this is my reading of the structure of their central argument on consciousness. In some cases, I am drawing out assumptions that are implicit in the text, to the best of my understanding in order to produce a complete argument.

Note: This is presented as an assumption whose consequences are to be tested more than a claim to be argued for directly but p23 invokes an Ockham’s razor principle of parsimony. We know there exist at least conscious experiences (P4), science/senses cannot give us a comprehensive answer to the infinite recursion of “whys” about what is at the fundamental layer of we observe or what makes conscious experience a certain way, so it is simplest (arguably) to assume consciousness occupies the base layer and everything is constructed from it.

(Since there is nothing at the base layer of reality except conscious agents and their interactions, there is no need to further stipulate that these objects must be made up themselves of conscious agents.)

(these implications of P8-P9 appear to be taken axiomatically, see e.g., p12)

(This results in experiences that might typically be more complex than its constituents, but not necessarily. One mathematical argument is provided by which the prima facie complexity post-fusion might simplify to an extent, see eqns 17-29.)

3. Comment on the completeness of the project

In general, since HPP proposes a fundamental ontology, the goal is ultimately to account for all phenomena that we observe. Of course, such accounts can deny the phenomena are what they appear to be to some observers, but they should in this case explain both what they actually are and why some or many human experiences of them are misled. The two key target sets of physical phenomena are apparent physical laws as we know them today (including all features of quantum mechanics and relativity) and phenomenal consciousness as we appear to experience it. A full account would eventually cover both.

Nonetheless, it’s not reasonable or necessary to account for every phenomenon or solve every problem in a single paper. It would be attractive for a future paper to map out a research trajectory that would lead to such coverage and give readers confidence that with sufficient effort it could be achieved, at least to the limited extent that it has been achieved for other ontological positions. Most modern physical ontologies are focused on what the world might be such that we observe quantum mechanical effects, with theories differentiable in part by what assumptions/intuitions from classical mechanics they prefer to sacrifice.

Indeed, HPP does not claim this is a completed project. For instance, they write “It will be intriguing to see how physical properties such as mass, momentum, and spin arise as projections from Markov polytopes.”

HPP conjectures, as an aside, that the capacity of the fusion logic in P7 to extend through all agents might provide a rationale for claims that ultimately there is only one agent and that seemingly constituent or smaller agents are just projects of that “One” (universal) agent (p16). A further conjecture (p36) is that this perspective may naturally conclude that “entropic time is not a fundamental feature of reality, but merely an artifact of projection.” I do not pursue these conjectures further in this review, but welcome HPP’s intellectual ambition and creativity in the face of challenging questions. More may well be needed, but that should be no surprise to anyone.

4. Comment on the ontological claim that spacetime is not fundamental

The paper presents as scientific fact a physical position where significant alternatives and uncertainty is present: that spacetime is not fundamental. It may be the case or it may not, but the paper would do well to acknowledge the alternative explorations in this area in more detail. For instance, focusing just on a few recent papers, Zhang & Choi (2022) identify a modified space-time as fundamental in their ontology: 4D dual space as a unification of current 4D space-time and 4D momentum-energy properties; reciprocally interrelated via the Fourier transform. (Coffey 2021) identifies a spacetime orientation as one of the two fundamental properties of entities in their ontology, addressing how energy is an emergent property in the context of special relativity. Others are explicitly agnostic about Minkowski space-time ontology, such as the DQFT account of corpuscular particles by (Oldofredi and Öttinger 2021). Nonetheless, HPP is correct that many theories that address the question explicitly do treat space-time as emergent, with cites as covered in their paper.

Importantly, their argument about consciousness does not need to lean so heavily on the assumption about spacetime as HPP seem to suggest. Whether space-time is itself an interface or whether it is merely that our interactions with it occur via an interface is an important claim about physical reality, but less about consciousness. Indeed, P2 and C1 from the outline (and indeed variants of P4, C2 and P6) have been argued extensively to apply to empiricism and consciousness more generally, rather than specifically about space-time (see, e.g., (Russell 1927); (Jones 2010); (Goff 2020)). It is provocative and interesting to see space-time spelled out as a case study of this general argument, but ultimately the space-time case study does not make the general argument stronger or weaker from a philosophy of science perspective.

It would be interesting to understand how important HPP think the emergence of spacetime is to their ontology. If spacetime were fundamental and conscious agents have properties defining the relative positions along four or more dimensions of spacetime like fabrics, would their theory be materially different? Are there geometric isomorphisms to their model such that 6-tuples could be represented4 as embedded in 4-dimensional spaces of different geometries? Could there be a hierarchy of options for thinking about spacetime that are consistent with their ontology, beginning from fairly uncontroversial claims to more speculative ones? E.g.

Given such a hierarchy (with different options as required), what is the level of this hierarchy at which the HPP claim operates?

The ability of HPP’s mathematical formalism of conscious agents to produce mathematical formalisms of space-time is impressive mathematically, but not surprising philosophically and does not strengthen the paper’s philosophical argument. The reason simply being that HPP already claim that their conscious agent formalisation is Turing complete (p9) and therefore with sufficient effort any mathematical calculation that we currently use in physics can be modelled with their conscious agents. It may be possible to claim the conscious agent mathematics has a particularly smooth and natural manipulation to create the relevant decorated permutations, increasing the plausibility (or aesthetic appeal) of conscious agents as the basis of reality, but I did not see this claim advanced in the paper, which would need to include some discussion of naturalness and perhaps comparison against other mathematics which might be able to produce decorated permutations more or less “naturally”.

Similar to the space-time assertion, other claims about modern physics are asserted without even a brief nod to the debate and alternative interpretations. For instance, whether energy and mass are equivalent (p3) or merely co-translatable as argued by Coffey (2021). The existence of an equation implies the sides can be translated into each other via some relevant mechanism, not that both sides are necessarily identical in all their forms. Likewise, also on p3 whether the uncertainty principle describes ontological or epistemological uncertainty is also contested today (Bayne 2010) (Oldofredi and Öttinger 2021).

In another example, “if spacetime is not fundamental, neither are its particles, which are irreducible representations of the Poincaré symmetries of spacetime” assumes a very specific and contested interpretation of what particles are and what different types of spacetime might be assumed.

HPP puts heavy weight on the measurement problem and a strong interpretation that observation must require conscious observers to collapse the wave function rather than merely interaction with an environment or some other particles. Consider: “This applies to neurons and brains. They do not exist when they are not observed. We create them when we look and delete them when we look away. Thus, neurons create none of our behaviours or conscious experiences.” Another example on p5, “the conclusion of quantum physics that local realism and non-contextual realism are both false” - again perhaps a common interpretation, but not an uncontested one (see e.g. the maintenance of local realism via additional spatial dimensions in (Ney 2021)).

The HPP positions on these statements are not unreasonable or impossible (indeed, sometimes they are the mainstream position), but to assert such positions as fact without awareness of the debate around them weakens the paper’s standing. Quantum mechanics is not a finished project and presenting ontological claims about it as such are unhelpful. Nonetheless, the weakening of those claims does not affect any of the argument outline laid out in s2.

5. Comment on the paper’s criticism of other theories of consciousness

HPP argues from its position on space-time that many other theories of consciousness are flawed. This argument does not follow as directly as claimed, as it imposes unstated assumptions on those theorists – some may be willing to uphold the assumptions, but others might have alternatives.

Consider HPP: “despite this consensus that spacetime is not fundamental, most theories of consciousness in cognitive neuroscience, artificial intelligence, and philosophy of mind still include spacetime among their foundational entities.” However, in general, these theories do not make strong statements about a complete physical ontology. For instance, discussions of physical monism and dualism are happy to state that there is only one or two types of “stuff”. Implicitly, when a “physical stuff” type is indicated, that does not deny the possibility of subcategories, such as different fundamental particles, forces, fields, and yes, perhaps some form of dimensional fabric in which particles/fields can interact. However, the philosophical arguments about monism and dualism do not turn on whether space-time emerges from say particle interactions or whether space-time is itself fundamental - so long as it can all be lumped under the category of “physical stuff”, that is sufficient. There is a case to be made that this lack of specificity is a weakness and a missed opportunity for theories of consciousness, especially panpsychism, but that is a separate paper and not the target of HPP’s criticism.

As a second example, HPP claims that “a theory of consciousness that starts with spacetime, particles, neurons, or brains has little chance.” Why should this be so? Consider theories assuming consciousness is an emergent phenomenon, which is the neuroscientific mainstream today despite strong counter-arguments. If consciousness “emerges” (weakly) from neuronal activity and neurons themselves “emerge” (weakly) from underlying particle/force/space-time dynamics, which themselves “emerge” weakly from some other phenomenon, such as quantum loop gravity (Norton 2020) or informons (Sulis 2020) or even the conscious agents of HPP, the argument is not automatically made weaker by adding an extra layer of weak emergence. If emergence is adequate for consciousness, then it simply does not matter what the “base layer” of reality is - if such a concept even has ontological and epistemological value - provided that base layer is capable of giving rise to the necessary weakly emergent phenomena. The fact that neurons act “as if” they were in a space-time fabric is sufficient from an emergentists’ perspective; they do not need to assume that the 4D space-time we appear to observe is itself fundamental.

6. Reflections on the epistemological claim

The weak version of this claim is that we do not have perfect access to the world’s structure through our senses, even if enhanced by scientific instrument. The weak version needs little support, evidence such as infilling of peripheral vision, only partial visibility of the EM spectrum, and the limitations of our scientific instruments, and much more, is enough to make the case. This notion of “indirect realism” is sufficiently well-evidenced I will not argue for it any further in this review unless requested to do so.

HPP favours a strong version of this claim: “the probability is zero that any sensory system has ever been shaped to report any true structures of objective reality [34–36]. Our senses do not show us truths about objective reality. They simply guide adaptive action.” (emphasis added).

A truly strong interpretation is challenging here, since the co-authors of the paper relied on their sensory system to exchange ideas with each other, read the research they cited, and so on. At face value, such an absolute interpretation is self-defeating, such that even if it were true, we would be better off doing the best we can without it. The authors do concede that in math and logic (and perhaps other cognitive skills) there would be evolutionary pressure for some proficiency, but not in the senses. Unfortunately, except for entirely solipsistic and internal reflection, it is hard for us to make progress without some sensory data or exchange. We must row back, on the authors’ behalf, from the absolute interpretation in order to continue with our reading of their paper. Indeed on p10, HPP appears to take a softer stance: “our interface gives real access to some of the conscious experiences of these agents.” (i.e. what we perceive does convey some truth about the external environment).

The argument that what we perceive, despite being heavily filtered and processed, bears no relation to physical reality seems hard to support and is not evidenced in this paper. Something may not be 100% accurate — indeed, the paper presents good reasons that it is incentivised in natural selection to be deliberately less than 100% accurate — does not automatically mean it is 0% accurate. The probability of 100% accuracy may be 0%, but again, 0% accuracy does not follow.

Nonetheless, putting contrarian claims to one side, the only epistemological conclusion actually needed for the core philosophical argument is something like: just because we have evolved to perceive objects existing in a 3D physical space and persisting/changing through a single time dimension, does not mean there really is such a 4D reality underlying it. Such a claim is reasonable, although it does not constitute evidence against a 4D reality on its own — it just weakens some evidence that was in favour of a 4D reality, leaving us perhaps with no preferred hypothesis. Again though, the core argument in s2 does not require the space-time case study or the total inaccuracy of our senses.

7. Reflections on the core philosophical argument

The mathematical formalism of conscious agents and its proposed resolution of the combination/binding problem is the central novel contribution of HPP. Continuing to develop this idea is the key next step in terms of philosophy of mind. Some of these are natural extensions or clarifications, such as building on the work of Appendix 2 or deciding and arguing for whether a “principle of exclusion” applies (see this note’s FN2). Four other aspects of the mathematical formalism deserve particular attention, highlighted here as important topics for future work without criticism of the current paper – no one paper can or should be asked to answer every facet of a question.

First, HPP should be explicit about how they see the ontological relationship between the mathematical formalisms and conscious agents and what that means for assumptions in the philosophical argument as set out in s2.

In my reading of their text, the conscious agents are concrete entities in some respect, indeed they are the ontological bedrock of all reality. We then model how those entities interact using mathematics as a language/tool, similar to how we use mathematics to model (with degrees of approximation) the emergent physical phenomena we observe in physics. The argument is not that all mathematical objects are conscious agents, but rather that the former can model descriptively the latter via a subset of their conceivable structures (the relevant 6-tuples). To use a classical mechanics analogy, the equation that relates force, mass, and acceleration does not itself replace or metaphysically ground the actual physical objects whose behaviour can be described and predicted using the equation. There are alternative views, in which computations, information, or mathematical objects are the fundamental entities of reality (Sulis 2020), but that does not seem to be the position of “conscious realism”.

Under this reading, we need to be clear that modelling something mathematically tells us nothing yet about what it actually is, only how it behaves5. Effectively this is the familiar argument from (Goff 2020), (Jones 2010), inter alia, the famous “What is it that breathes fire into the equations and makes a universe for them to describe?” line from Stephen Hawking, and indeed the arguments that HPP marshal to support P1, P2, and C1.

P9 in section 2 reports how certain product algebras could cause micro-conscious binding under an assumption that anything describable by a particular mathematical object is definitionally conscious. HPP should consider whether they agree with how these assumptions are presented in s2 and, if not, how they would amend them or present an ontology of mathematical objects that leads to a complete argument.

Thinking constructively, given this binding mechanism solution, what responses would a complete HPP theory produce given the Slicing Problem (Gómez-Emilsson and Percy 2022) and the Boundary Problem (Gómez-Emilsson and Percy 2023)? Along with binding problem concerns (Bartlett 2012), these are more damaging challenges to computationalism-type accounts of consciousness than more commonly known ones such as the Chinese Room Argument, Mary’s Room, P-Zombies, fractional qualia, or the argument from abstract objects, where bullets can either be bitten or physicalist accounts designed to dissolve the threat. It is intriguing to consider whether designing constraints to meet the five subproblems in the Boundary Problem and to prevent the arbitrary “consciousness-multiplying exploits” in the Slicing Problem might help pin down the currently general mathematics of conscious agents into something more specific, perhaps eventually aiding empirical tests of the theory.

Second, and assuming mathematical objects do not replace conscious agents as fundamental in response to the first point, HPP should consider what are the mechanisms that are modelled by their mathematics. Most importantly for the combination/binding problem, what is actually happening that is modelled by the product algebra in P9. One response might be that we cannot possibly know that as it is too deep down the layer of perceivable reality. All we can say with confidence is that whatever mechanism it is, it must have the product algebra features. This is a reasonable philosophical position, but clearly it prevents the possibility of the latter being used as evidence for the former. If we assume the binding problem is solved by product algebra, then identifying one example mathematical object that obeys product algebra is only very weak evidence that there must be an ontological entity well-modelled by that mathematical object.

Third, how can we choose in a disciplined fashion between the alternatives to P6? For instance, could there be models of conscious agents and other non-conscious entities at the base layer that produces the same results? What methods might we use to differentiate such candidate arguments? An argument from parsimony is one approach but either needs to be formalised (parsimonious in what ways and why does that matter) or needs to be complemented with other epistemological principles.

For instance, the phenomena to account for and what qualifies as a good account could be expanded from the three examples given in P3 to a much wider list. We have a working list of 82 phenomena and thought experiments that theories of phenomenal consciousness should account for and several other lists exist – in any case, the three examples in P3 are just a start. An alternative approach would be to consider what types of mathematical derivation of objects used in modern physics (such as decorated permutations) might make one base layer set of mathematical objects more plausible than another (see discussion in s4).

Fourth, the strength of math modelling in physics is producing specific descriptions of diverse phenomena and predictions, which strengthen the case that the modelling is describing underlying mechanisms accurately. Without such value and without comment on what the mechanisms we’re modelling might actually be, it will be hard to convince newcomers to the idea. At the least, it has little to argue for it over Goff’s position on panpsychism as arrived at by similar logic to HPP. One valuable next step for HPP is to start to comment on what specific combinations of agent 6-tuples would represent specific experiences. Or, in a more general sense, if experiences combine via a product algebra, what does that imply for what humans should experience when we experience an increasing multiplicity of phenomena at the same time? Moving away from these philosophical meta-considerations and returning to the specifics of the 6-tuple mathematics and its potential explanatory power, it would be interesting to explore how might it be used to reproduce key properties of our conscious experience, even on the assumption those properties are not fundamental. After all, even illusions need to be accounted for.

For instance, day-to-day visual perception typically has a particular projective geometry (Williford et al. 2018) Steven Lehar’s thinking as summarised by (Gómez-Emilsson 2021). It would be powerful to find a simple mapping, in a moderate number of stages, from the structure of fundamental experiences and perceptions as envisaged by HPP to common geometric structures at the meso-level of human visual experience.

Likewise, certain solutions to the phenomenal binding problem could draw on path integral mathematics. Could the 6-tuple mathematical formalism be developed to embed binding mechanics at a fundamental level in the ontology? Or perhaps it can account for how a weakly-emergent binding mechanic nonetheless has sufficient causal power to shape human-level phenomenology?


Consciousness, Binding problem, Philosophy of mind, Mathematics, Physics

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Many thanks to Andrés Gómez-Emilsson for his dialogue and insightful commentary on drafts of this article, some of which made it into this final version. Appreciation to Hunter Meyer for organizational support and formatting this article.



For attribution, please cite this work as

Percy (2024, Jan. 15). Reflections on Fusions of Consciousness. Retrieved from

BibTeX citation

  author = {Percy, Chris},
  title = {Reflections on Fusions of Consciousness},
  url = {},
  year = {2024}