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hidden computational power of soap films. Say that you want to connect three poles with a wire. And you want to minimize how much wire you use. One option is to use trigonometry and linear algebra, another one is to use numerical simulations. But an elegant alternative is to create a model of the poles between two parallel planes and then submerge the structure in soapy water. Letting the natural energy-minimizing property of soap bubbles find the shortest connection between three poles is an interesting way of performing a computation. It is uniquely adapted to the problem without needing tweaks or adjustments – the self-organizing principle will work the same (within reason) wherever you place the poles. You are deriving computational power from physics in a very customized way that nonetheless requires no tuning or external memory. And it’s all done simply by each point of the surface wanting to minimize its tension. Any non-minimal configuration will have potential energy, which then gets transformed into kinetic energy and makes it wobble, and as it wobbles it radiates out its excess energy until it reaches a configuration where it doesn’t wobble anymore. So you have to make the solution of your problem precisely a non-wobbly state! In this way of thinking about computation, an intrinsic part of the question about what kind of thing a computation is will depend on what physical processes were utilized to implement it. In essence, we can (and I think should) enrich our very conception of computation to include what kind of internal bound states the system is utilizing, and the extent to which the holistic physical effects of such inner states are computationally trivial or significant. We can call this paradigm of computing “Holistic Computing”. From Soap Bubbles to ISING-Solvers Meeting Schedulers Implemented with Lasers Let’s make a huge jump from soap water-based computation. A much more general case that is nonetheless in the same family as using soap bubbles for compute, is having a way to efficiently solve the ISING problem. In particular, having an analog physics-based annealing method in this case comes with unique computational benefits: it turns out that non-linear optics can do this very efficiently. You are in a certain way using the universe’s very frustration with the problem (don’t worry I don’t think it suffers) to get it solved. Here is an amazing recent example: Ising Machines: Non-Von Neumann Computing with Nonlinear Optics – Alireza Marandi – 6/7/2019 (presented at Caltech). The person who introduces Marandi in the video above is Kwabena Boahen, with whom I had the honor to take his course at Stanford (and play with the neurogrid!). Back in 2012 something like the neurogrid seemed like the obvious path to AGI. Today, ironically, people imagine scaling transformers is all you need. Tomorrow, we’ll recognize the importance of holistic field behavior and the boundary problem. One way to get there on the computer science front will be by first demonstrating a niche set of applications where e.g. non-linear

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optics ISING solvers vastly outperform GPUs for energy minimization tasks in random graphs. But as the unique computational benefits become better understood, we will sooner or later switch from thinking about how to solve our particular problem, to thinking about how we can cast our particular problem as an ISING/energy minima problem so that physics solves the problem for us. It’s like having a powerful computer but it only speaks a very specific alien language. If you can translate your problem into its own terms, it’ll solve it at lightning speed. If you can’t, it will be completely useless. Intelligence: Collecting and Applying Self-Organizing Principles This takes us to the question of whether general intelligence is possible without switching to a Holistic Computing paradigm. Can you have generally intelligent (digital) chatbots? In some senses, yes. In perhaps the most significant sense, no. Intelligence is a contentious topic (see here David Pearce’s helpful breakdown of 6 of its facets). One particular facet of intelligence that I find enormously fascinating and largely under-explored is the ability to make sense of new modes of consciousness and then recruit them for computational and aesthetic purposes. THC and music production have a long history of synergy, for instance. A composer who successfully uses THC to generate musical ideas others find novel and meaningful is applying this sort of intelligence. THC-induced states of consciousness are largely dysfunctional for a lot of tasks. But someone who utilizes the sort of intelligence (or meta-intelligence) I’m pointing to will pay attention to the features of experience that do have some novel use and lean on those. THC might impair working memory, but it also expands and stretches musical space. Intensifies reverb, softens rough edges in heart notes, increases emotional range, and adds synesthetic brown noise (which can enhance stochastic resonance). With wit and determination (and co-morbid THC/music addiction), musical artists exploit the oddities of THC musicality to great effect, arguably some much more successfully than others. The kind of reframe that I’d like you to consider is that we are all in fact something akin to these stoner musicians. We were born with this qualia resonator with lots of cavities, kinds of waves, levels of coupling, and so on. And it took years for us to train it to make adaptive representations of the environment. Along the way, we all (typically) develop a huge repertoire of self-organizing principles we deploy to render what we believe is happing out there in the world. The reason why an experience of “meditation on the wetness of water” can be incredibly powerful is not because you are literally tuning into the resonant frequency of the water around you and in you. No, it’s something very different. You are creating the conditions for the self-organizing principle that we already use to render our experiences with water to take over as the primary organizer of our experience. Since this self-organizing principle does not, by its nature, generate a center, full absorption into “water consciousness” also

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text:
has a no-self quality to it. Same with the other elements. Excitingly, this way of thinking also opens up our mind about how to craft meditations from first principles. Namely, by creating a periodic table of self-organizing principles and then systematically trying combinations until we identify the laws of qualia chemistry. You have to come to realize that your brain’s relationship with self-organizing principles is like that of a Pokémon trainer and his Pokémon (ideally in a situation where Pokémon play the Glass Bead Game with each other rather than try to hurt each other– more on that later). Or perhaps like that of a mathematician and clever tricks for proofs, or a musician and rhythmic patterns, and so on. Your brain is a highly tamed inner space qualia warp drive usually working at 1% or less. It has stores of finely balanced and calibrated self-organizing principles that will generate the right atmospheric change to your experience at the drop of a hat. We are usually unaware of how many moods, personalities, contexts, and feelings of the passage of time there are – your brain tries to learn them all so it has them in store for whenever needed. All of a sudden: haze and rain, unfathomable wind, mercury resting motionless. What kind of qualia chemistry did your brain just use to try to render those concepts? We are using features of consciousness -and the self-organizing principles it affords- to solve problems all the time without explicitly modeling this fact. In my conception of sentient intelligence, being able to recruit self-organizing principles of consciousness for meaningful computation is a pillar of any meaningfully intelligent mind. I think that largely this is what we are doing when humans become extremely good at something (from balancing discs to playing chess and empathizing with each other). We are creating very specialized qualia by finding the right self-organizing principles and then purifying/increasing their quality. To do an excellent modern day job that demands constraint satisfaction at multiple levels of analysis at once likely requires us to form something akin to High-Entropy Alloys of Consciousness. That is, we are usually a judiciously chosen mixture of many self-organizing principles balanced just right to produce a particular niche effect. Meta-Intelligence David Pearce’s conception of Full-spectrum Superintelligence is inspiring because it takes into account the state-space of consciousness (and what matters) in judging the quality of a certain intelligence in addition to more traditional metrics. Indeed, as another key conceptual engineering move, I suggest that we can and need to enrich our conception of intelligence in addition to our conception of computation. So here is my attempt at enriching it further and adding another perspective. One way we can think of intelligence is as the ability to map a problem to a self-organizing principle that will “solve it for you” and having the capacity to instantiate that self-organizing principle. In other words, intelligence is, at least partly, about efficiency: you are successful to the extent that you can

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text:
take a task that would generally require a large number of manual operations (which take time, effort, and are error-prone) and solve it in an “embodied” way. Ultimately, a complex system like the one we use for empathy mixes both serial and parallel self-organizing principles for computation. Empathy is enormously cognitively demanding rather than merely a personality trait (e.g. agreeableness), as it requires a complex mirroring capacity that stores and processes information in efficient ways. Exploring exotic states of consciousness is even more computationally demanding. Both are error-prone. Succinctly, I suggest we consider: One key facet of intelligence is the capacity to solve problems by breaking them down into two distinct subproblems: (1) find a suitable self-organizing principle you can instantiate reliably, and (2) find out how to translate your problem to a format that our self-organizing principle can be pointed at so that it solves it for us. Here is a concrete example. If you want to disentangle a wire, you can try to first put it into a discrete datastructure like a graph, and then get the skeleton of the knot in a way that allows you to simplify it with Reidemeister moves (and get lost in the algorithmic complexity of the task). Or you could simply follow the lead of Yu et al. 2021(Yu et al. 2021) and make the surfaces repulsive and let this principle solve the problem for you. These repulsion-based disentanglement algorithm are explained in this video. Importantly, how to do this effectively still needs fine tuning. The method they ended up using was much faster than the (many) other ones tried (a Full-Spectrum Superintellligence would be able to “wiggle” the wires a bit if they got stuck, of course): This is hopefully giving you new ways of thinking about computation and intelligence. The key point to realize is that these concepts are not set in stone, and to a large extent may limit our thinking about sentience and intelligence. Now, I don’t believe that if you simulate a self-organizing principle of this sort you will get a conscious mind. The whole point of using physics to solve your problem is that in some cases you get better performance than algorithmically representing a physical system and then using that simulation to instantiate self-organizing principles. Moreover physics simulations, to the extent they are implemented in classical computers, will fail to generate the same field boundaries that would be happening in the physical system. To note, physics-inspired simulations like [Yu et al 2021] are nonetheless enormously helpful to illustrate how to think of problem-solving with a massively parallel analog system. Are Neural Cellular Automata Conscious? The computational success of Neural Cellular Automata(Mordvintsev et al. 2020) is primarily algorithmic. In essence, digitally implemented NCA are exploring a paradigm of selection and amplification of self-organizing principles, which is indeed a very different way of thinking about computation. But critically any NCA will still lack sentience. The main reasons are that they (a) don’t use physical fields with weak

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downward causation, and (b) don’t have a mechanism for binding/boundary making. Digitally-implemented cellular automata may have complex emergent behavior, but they generate no meaningful boundaries (i.e. objective, frame-invariant, causally-significant, and computationally-useful). That said, the computational aesthetic of NCA can be fruitfully imported to the study of Holistic Field Computing, in that the techniques for selecting and amplifying self-organizing principles already solved for NCAs may have analogues in how the brain recruits physical self-organizing principles for computation. Exotic States of Consciousness Perhaps one of the most compelling demonstrations of the possible zoo (or jungle) of self-organizing principles out of which your brain is recruiting but a tiny narrow range is to pay close attention to a DMT trip. DMT states of consciousness are computationally non-trivial on many fronts. It is difficult to emphasize how enriched the set of experiential building blocks becomes in such states. Their scientific significance is hard to overstate. Importantly, the bulk of the computational power on DMT is dedicated to trying to make the experience feel good and not feel bad. The complexity involved in this task is often overwhelming. But one could envision a DMT-like state in which some parameters have been stabilized in order to recruit standardized self-organizing principles available only in a specific region of the energy-information landscape. I think that cataloguing the precise mathematical properties of the dynamics of attention and awareness on DMT will turn out to have enormous computational value. And a lot of this computational value will generally be pointed towards aesthetic goals. To give you a hint of what I’m talking about: A useful QRI model (indeed, algorithmic reduction) of the phenomenology of DMT is that it (a) activates high-frequency metronomes that shake your experience and energize it with a high-frequency vibe, and (b) a new medium of wave propagation gets generated that allows very disparate parts of one’s experience to interact with one another. 3D Space Group (CEV on low dose DMT) At a sufficient dose, DMT’s secondary effect also makes your experience feel sort of “wet” and “saturated”. Your whole being can feel mercurial and liquidy (cf: Plasmatis and Jim Jam). A friend speculates that’s what it’s like for an experience to be one where everything is touching everything else (all at once). There are many Indra’s Net-type experiences in this space. In brief, experiences where “each part reflects every other part” are an energy minimum that also reduces prediction errors. And there is a fascinating non-trivial connection with the Free Energy Principle, where experiences that minimize internal prediction errors may display a lot of self-similarity. To a first approximation, I posit that the complex geometry of DMT experiences are indeed the non-linearities of the DMT-induced wave propagation medium that appear when it is sufficiently energized (so that it transitions from the linear to the non-linear regime). In other words, the complex hallucinations are energized patterns of non-linear resonance trying to radiate out their excess energy. Indeed, as you come down you experience the phenomenon of condensation

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text:
of shapes of qualia. Now, we currently don’t know what computational problems this uncharted cornucopia of self-organizing principles could solve efficiently. The situation is analogous to that of the ISING Solver discussed above: we have an incredibly powerful alien computer that will do wonders if we can speak its language, and nothing useful otherwise. Yes, DMT’s computational power is an alien computer in search of a problem that will fit its technical requirements. Vibe-To-Shape-And-Back Michael Johnson, Selen Atasoy, and Steven Lehar all have shaped my thinking about resonance in the nervous system. Steven Lehar in particular brought to my attention non-linear resonance as a principle of computation. In essays like The Constructive Aspect of Visual Perception(Lehar 2003) he presents a lot of visual illusions for which non-linear resonance works as a general explanatory principle (and then in The Grand Illusion(Lehar 2010) he reveals how his insights were informed by psychonautic exploration). One of the cool phenomenological observations Lehar made based on his exploration with DXM was that each phenomenal object has its own resonant frequency. In particular, each object is constructed with waves interfering with each other at a high-enough energy that they bounce off each other (i.e. are non-linear). The relative vibration of the phenomenal objects is a function of the frequencies of resonance of the waves of energy bouncing off each other that are constructing the objects. In this way, we can start to see how a “vibe” can be attributed to a particular phenomenal object. In essence, long intervals will create lower resonant frequencies. And if you combine this insight with QRI paradigms, you see how the vibe of an experience can modulate the valence (e.g. soft ADSR envelopes and consonance feeling pleasant, for instance). Indeed, on DMT you get to experience the high-dimensional version of music theory, where the valence of a scene is a function of the crazy-complex network of pairwise interactions between phenomenal objects with specific vibratory characteristics. Give thanks to annealing because tuning this manually would be a nightmare. But then there is the “global” vibe… Topological Pockets So far I’ve provided examples of how Holistic Computing enriches our conception of intelligence, computing, and how it even shows up in our experience. But what I’ve yet to do is connect this with meaningful boundaries, as we set ourselves to do. In particular, I haven’t explained why Holistic Computing would arise out of topological boundaries. For the purpose of this essay I’m defining a topological segment (or pocket) to be a region that can’t be expanded further without this becoming false: every point in the region locally belongs to the same connected space. The Balloons’ Case In the case of balloons this cashes out as: a topological segment is one where each point can go to any other point without having to go through connector points/lines/planes. It’s essentially the set of contiguous surfaces. Now, each of these pockets can have both a rich set of connections to other pockets as well as intricate internal

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boundaries. The way we could justify Computational Holism being relevant here is that the topological pockets trap energy, and thus allow the pocket to vibrate in ways that express a lot of holistic information. Each contiguous surface makes a sound that represents its entire shape, and thus behaves as a unit in at least this way. The General Case An important note here is that I am not claiming that (a) all topological boundaries can be used for Holistic Computing, or (b) to have Holistic Computing you need to have topological boundaries. Rather, I’m claiming that the topological segmentation responsible for individuating experiences does have applications for Holistic Computing and that this conceptually makes sense and is why evolution bothered to make us conscious. But for the general case, you probably do get quite a bit of both Holistic Computing without topological segmentation and vice versa. For example an LC circuit can be used for Holistic Computing on the basis of its steady analog resonance, but I’m not sure if it creates a topological pocket in the EM fields per se. At this stage of the research we don’t have a leading candidate for the precise topological feature of fields responsible for this. But the explanation space is promising based on being able to satisfy theoretical constraints that no other theory we know of can. But I can nonetheless provide a proof of concept for how a topological pocket does come with really impactful holism. Let’s dive in! Getting Holistic Behavior Out of a Topological Pocket Creating a topological pocket may be consequential in one of several ways. One option for getting holistic behavior arises if you can “trap” energy in the pocket. As a consequence, you will energize its harmonics. The particular way the whole thing vibrates is a function of the entire shape at once. So from the inside, every patch now has information about the whole (namely, by the vibration it feels!)2. One possible overarching self-organizing principle that the entire pocket may implement is valence-gradient ascent. In particular, some configurations of the field are more pleasant than others and this has to do with the complexity of the global vibe. Essentially, the reason no part of it wants to be in a pocket with certain asymmetries, is because those asymmetries actually make themselves known everywhere within the pocket by how the whole thing vibrates. Therefore, for the same reason a soap bubble can become spherical by each point on the surface trying to locally minimize tension, our experiences can become symmetrical and harmonious by having each “point” in them trying to maximize its local valence. Self Mirroring From Lehar’s Cartoon Epistemology And here we arrive at perhaps one of the craziest but coolest aspects of Holistic Computing I’ve encountered. Essentially, if we go to the non-linear regime, then the whole vibe is not merely just the weighted sum of the harmonics of the system. Rather, you might have waves interfere with each other in a concentrated fashion

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in the various cores/clusters, and in turn these become non-linear structures that will try to radiate out their energy. And to maximize valence there needs to be a harmony between the energy coming in and out of these dense non-linearities(Gómez Emilsson 2021). In our phenomenology this may perhaps point to our typical self-consciousness. In brief, we have an internal avatar that “reflects” the state of the whole! We are self-mirroring machines! Now this is really non-trivial (and non-linear) Holistic Computing. Cut From the Same Fabric So here is where we get to the crux of the insight. Namely, that weakly emergent topological changes can simultaneously have non-trivial causal/computational effects while also solving the boundary problem. We avoid strong emergence but still get a kind of ontological emergence: since consciousness is being cut out of one huge fabric of consciousness, we don’t ever need strong emergence in the form of “consciousness out of the blue all of a sudden”. What you have instead is a kind of ontological birth of an individual. The boundary legitimately created a new being, even if in a way the total amount of consciousness is the same. This is of course an outrageous claim (that you can get “individuals” by e.g. twisting the electric field in just the right way). But I believe the alternatives are far crazier once you understand what they entail. In a Nutshell To summarize, we can rule out any of the current computational systems implementing AI algorithms to have anything but trivial consciousness. If there are topological pockets created by e.g. GPUs/TPUs, they are epiphenomenal – the system is designed so that only the local influences it has hardcoded can affect the behavior at each step. The reason the brain is different is that it has open avenues for solving the boundary problem. In particular, a topological segmentation of the EM field would be a satisfying option, as it would simultaneously give us both holistic field behavior (computationally useful) and a genuine natural boundary. It extends the kind of model explored by Johnjoe McFadden (Conscious Electromagnetic Information Field(McFadden 2020)) and Susan Pockett (Consciousness Is a Thing, Not a Process(Pockett 2000)). They (rightfully) point out that the EM field can solve the binding problem. The boundary problem, in turn, emerges. With topological boundaries, finally, you can get meaningful boundaries (objective, frame-invariant, causally-significant, and computationally-useful). This conceptual framework both clarifies what kind of system is at minimum required for sentience, and also opens up a research paradigm for systematically exploring topological features of the fields of physics and their plausible use by the nervous system. See also: physicalism.com by David Pearce Against Functionalism by Michael Johnson The Binding Problem by Steven Lehar Lots of links on LaMDA / Key questions about artificial sentience: an opinionated guide by Robert Long Non-Linear Wave Computing: Vibes, Gestalts, and Realms on my YouTube channel Acknowledgements Many thanks to Michael Johnson, David Pearce, Anders & Maggie, and Steven Lehar for many discussions about the boundary/binding problem. Thanks to

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Anders & Maggie and to Mike for discussions about valence in this context. And thanks to Mike for offering a steel-man of epiphenomenalism. Many thank yous to all our supporters! Much love! Infinite bliss! Tags Consciousness, Effective Altruism, STV, Valence, Marr, Ethics Chalmers, D. 2006. “Strong and Weak Emergence.” In. Chalmers, David J. 2007. “The Hard Problem of Consciousness.” In. Gómez Emilsson, Andrés. 2021. “Healing Trauma with Neural Annealing.” Qualia Computing. https://qualiacomputing.com/2021/05/08/healing-trauma-with-neural-annealing/. Johnson, Michael. 2017. “Why We Seek Out Pleasure: The Symmetry Theory of Homeostatic Regulation.” OpenTheory. https://opentheory.net/2017/05/why-we-seek-out-pleasure-the-symmetry-theory-of-homeostatic-regulation/. Lehar, Steven. 2003. The Constructive Aspect of Visual Perception: http://slehar.com/www/ConstructiveAspect/ConstructiveAspect.html. ———. 2010. The Grand Illusion: A Psychonautical Odyssey into the Depths of Human Experience. http://slehar.com/wwwRel/GrandIllusion.pdf. McFadden, Johnjoe. 2020. “Integrating Information in the Brain’s EM Field: The Cemi Field Theory of Consciousness.” Neuroscience of Consciousness 2020 (1): niaa016. https://doi.org/10.1093/nc/niaa016. Mordvintsev, Alexander, Ettore Randazzo, Eyvind Niklasson, and Michael Levin. 2020. “Growing Neural Cellular Automata.” Distill 5 (2): 10.23915/distill.00023. https://doi.org/10.23915/distill.00023. Pockett, Susan. 2000. The Nature of Consciousness: A Hypothesis. San Jose, Calif.: Writers Club Press. Yu, Chris, Caleb Brakensiek, Henrik Schumacher, and Keenan Crane. 2021. “Repulsive Surfaces.” ACM Trans. Graph. 40 (6). See the “Self Mirroring” section to contrast the self-blindness of a lookup table and the self-awareness of sentient beings.↩︎ More symmetrical shapes will tend to have more clean resonant modes. So to the extent that symmetry tracks fitness on some level (e.g. ability to shed off entropy), then quickly estimating the spectral complexity of an experience can tell you how far it is from global symmetry and possibly health (explanation inspired by: Johnson’s Symmetry Theory of Homeostatic Regulation(Johnson 2017)).↩︎ References Citation For attribution, please cite this work as Gómez-Emilsson (2022, June 20). Digital Sentience Requires Solving the Boundary Problem. Retrieved from https://www.qri.org/blog/digital-sentience BibTeX citation @misc{gómez-emilsson2022digital, author = {Gómez-Emilsson, Andrés}, title = {Digital Sentience Requires Solving the Boundary Problem}, url = {https://www.qri.org/blog/digital-sentience}, year = {2022} } The Hyperbolic Geometry of DMT Experiences: Symmetries, Sheets, and Saddled Scenes Content Warning: Trying to understand the contents of this essay may be mindwarping. Proceed with caution. Andrés Gómez-Emilsson ../people/andrés-gómez-emilsson (Qualia Research Institute)https://www.qri.org/ December 12, 2016 Contents The Geometry of DMT States Conceptual Framework: Algorithmic Reduction What is Hyperbolic Geometry? We Can Only Remember What We Can Reconstruct What about DMT Suggests Hyperbolic Geometry? The Phenomenology of DMT Experiences: The Six Levels Threshold The Chrysanthemum The Magic Eye Level Waiting Room Breakthrough Amnesia Level Recalling the Immemorial DMT Objects DMT Space Expansion DMT Entities Modeling the Hyperbolic Geometry of DMT Control Interruption + Symmetry detection = Change in Metric Dynamic System Account: Energy Sources, Sinks and Invariants Hyperbolic Micro-Structure of Consciousness Generalizing hyperbolization to non-spatial experiential fields Getting a handle on the DMT state Unifying Your Space Applications to Qualia Computing and Closing Thoughts Mathematics post-hyperbolic consciousness Acknowledgements Tags The following research was conducted by synthesizing high-quality, anonymous, first-person reports from psychedelic forums and reports sent directly to us. We do not condone the use of psychedelics because fully positive states cannot be guaranteed. For further reading on

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our views of psychoactive substances in the study of consciousness, see our research lineages. Content Warning: Trying to understand the contents of this essay may be mind-warping. Proceed with caution. Friends, right here and now, one quantum away, there is raging a universe of active intelligence that is transhuman, hyperdimensional, and extremely alien. —Terence McKenna The Geometry of DMT States This is an essay on the phenomenology of DMT. The analysis here presented predominantly uses algorithmic, geometric and information-theoretic frameworks, which distinguishes it from purely phenomenological, symbolic, neuroscientific or spiritual accounts. We do not claim to know what ultimately(Emilsson 2015c) implements the effects here described (i.e. in light of the substrate problem of consciousness), but the analysis does not need to go there in order to have explanatory power. We posit that one can account for a wide array of (apparently diverse) phenomena present on DMT-induced states of consciousness by describing the overall changes in the geometry of one’s spatiotemporal representations (what we will call “world-sheets” i.e. 3D + time surfaces; 3D1T for short). The concrete hypothesis is that the network of subjective measurements of distances we experience on DMT (coming from the relationships between the phenomenal objects one experiences in that state) has an overall geometry that can accurately be described as hyperbolic (or hyperbolic-like). In other words, our inner 3D1T world grows larger than is possible to fit in an experiential field with 3D Euclidean phenomenal space (i.e. an experience of dimension R2.5 representing an R3 scene). This results in phenomenal spaces, surfaces, and objects acquiring a mean negative curvature. Of note is that even though DMT produces this effect in the most consistent and intense way, the effect is also present in states of consciousness induced by tryptamines(“Erowid Online Books : "TIHKAL" - the Continuation" by Alexander and Ann Shulgin,” n.d.) and to a lesser extent in those induced by all other psychedelics. Conceptual Framework: Algorithmic Reduction We will use the reduction framework originally proposed in the article Algorithmic Reduction of Psychedelic States(Emilsson 2016a). This means that we will be examining how algorithms and processes (as experienced by a subject of experience) can explain the dynamics of people’s phenomenology in DMT states. We do not claim “the substrate of consciousness” is becoming hyperbolic in any literal sense (though we do not discard that possibility). Rather, we interpret the hyperbolic curvature that experience acquires while on DMT as an emergent effect of a series of more general mechanism of action that can work together to change the geometry of a mind. These same mechanisms of action govern the dynamics of other psychedelic experiences; it is the proportion and intensity of the various “basic” effects that lead to the different outcomes observed. In other words, the hyperbolization of phenomenal space may not be a fundamental effect of DMT, but rather, it may be an emergent effect of more simple effects combined (not unlike how our seemingly smooth macroscopic space-time emerges from the jittery yet fundamental interactions that happen in

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text:
a microscopic high-dimensional quantum foam). In particular, we will discuss three candidate models for a more fundamental algorithmic reduction: (1) the synergistic effect of control interruption(“The Control Interrupt Model of Psychedelic Action,” n.d.) and symmetry detection resulting in a change of the metric of phenomenal space (analogously to how one can measure the geometry of hyperbolic graph embeddings), (2) the mind as a dynamic system with energy sources, sinks and invariants, in which curvature stores potential energy, and (3) a change in the underlying curvature of the micro-structure of consciousness. These models are not mutually-exclusive, and they may turn out to be compatible. More on this later. What is Hyperbolic Geometry? Perhaps the clearest way to describe hyperbolic space is to show examples of it: Saddle Inside a hyperbolic cube In hyperbolic 3D space dodecahedra can have right corners. The picture to the left shows a representation of a “saddle” surface. In geometry, saddle surfaces are 2-dimensional hyperbolic spaces (also called “hyperbolic planes” or H2(“Visualizing the Sphere and the Hyperbolic Plane: Five Projections of Each,” n.d.)). For a surface to have “constant curvature” it must look the same at every point. In other words, for a saddle to be a geometric saddle, every point in it must be a “saddle point(“Saddle Points,” n.d.)” (i.e. a point with negative curvature(“Negative Curvature, Surface of - Encyclopedia of Mathematics,” n.d.)). As you can see, saddles have the property that the angles of a triangle found in them add up to less than 180 degrees (compare that to surfaces with positive curvature such as the 2-sphere, in which the angles of a triangle add up to more than 180 degrees). Generalizing this to higher dimensions, the middle image above shows a cube in H3 (i.e. a hyperbolic space of three dimensions). This cube, since it is in hyperbolic space, has thin edges and pointy corners. More generally, the corners of a polyhedra (and polytopes) will be more pointy in Hn than they are in Rn. This is why you can see in the right image a dodecahedron with right-angled corners, which in this case can tile H3 (cf. Not Knot(“Not Knot,” n.d.)). Such a thingpeople of the past might say- is an insult to the imagination. Times are changing, though, and hyperbolic geometry is now an acceptable subject of conversation. An important property of hyperbolic spaces is the way in which the area of a circle (or the n-dimensional volume of a hypersphere) increases as a function of its radius. In 2D Euclidean space the area grows quadratically with the radius. But on H2, the area grows exponentially as a function of the radius! As you may imagine, it is easy to get lost in(“Hyperbolic Geometry in HyperRogue,” n.d.) hyperbolic space. A few steps take you to an entirely different scene. More so, your influence over the environment is greatly diminished as a function of distance. For example, the habitable region of solar systems in hyperbolic spaces (i.e. the Goldilocks zone) is extremely thin.

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text:
In order to avoid getting burned or freezing to death you would have to place your planet within a very narrow distance range from the center star. Most of what you do in hyperbolic space either stays as local news or is quickly dissipated in an ever-expanding environment. We Can Only Remember What We Can Reconstruct We cannot experience H2 or H3 manifolds under normal circumstances, but we can at least represent some aspects of them through partial embeddings(Weisstein, n.d.) (i.e. instantiations as subsets of other spaces preserving properties) and projections(“Hyperbolic Space,” n.d.) into more familiar geometries. It is important to note that such representations will necessarily be flawed. As it turns out, it is notoriously hard to truly embed H2 in Euclidean 3D space, since doing so will necessarily distort some properties(“Visualizing the Sphere and the Hyperbolic Plane: Five Projections of Each,” n.d.) of the original H2 space (such as distance, angle, area, local curvature, etc.). As we will discuss further below, this difficulty turns out to be crucial for understanding why DMT experiences are so hard to remember. In order to remember the experience you need to create a faithful and memorable 3D Euclidean embedding of it. Thus, if one happens to experience a hyperbolic object and wants to remember as much of it as possible, one will have to think strategically about how to fold, crunch and deform such object so that it can be fit in compact Euclidean representations. What about DMT Suggests Hyperbolic Geometry? Why should we believe that phenomenal space on DMT (and to a lesser extent on other psychedelics) becomes hyperbolic-like? We will argue that the features people use to describe their trips as well as concrete mathematical observations of such features point directly to hyperbolic geometry. Here is a list of such features (arranged from least to most suggestive… you know, for dramatic effect): Perception of far-out travel (as we said, small movements in hyperbolic space lead to huge changes in the scene). Feelings of becoming big (you can fit a lot more inside a circle of radius r in hyperbolic space). The space experienced is often depicted as “more real and more dense than normal.” The use of terms like “mind-expanding” and “warping” to describe the effects of the drug are very common. People describing it as “a different kind of space” and frequently using the word “hyperspace” to talk about it. Difficulty integrating/remembering the objects and scenes experienced (e.g. “they were too alien to recall”). Constant movement/acceleration and change of perspectives which are often described as “unfolding scenes and expanding patterns” (cf. the chrysanthemum(“Chrysanthemum - First Steps in Hyperspace - Welcome to the DMT-Nexus,” n.d.), jitterbox(“The Jitterbox: 3d Auxetic Material,” n.d.)). Continuous change of the scene’s context through escape routes: A door that leads to a labyrinth that leads to branching underground tunnels that lead to mirror rooms that lead to endless windows, and the one you take leading you to a temple with thirty seven gates which lead you

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