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to a kale salad world etc. (example(“Experience:30mg Smoked DMT - the Monolith,” n.d.)) Crowding of scene beyond the limits of Euclidean space (users frequently wondering “How was I able to fit so much in my mind? I don’t see any space for my experience to fit in here!”) Reported similarity with fractals. Omnipresence of saddles making up the structural constraints of the hallucinated scenes. For example, one often hears about experiencing scenes saturated with: joints, twists, bifurcations, curved alleys, knots, and double helixes. Looking at self-similar objects (such as cauliflowers) can get you lost in what seems like endless space. (Note: beware of the potential side effects of looking at a cauliflower on DMT1). PSIS-like experiences(Emilsson 2016c) where people seem to experience multiple alternative outcomes from each event at the same time (this may be the result of “hyperbolic branching” through time rather than space). Psychedelic replication pictures usually include features that can be interpreted as hyperbolic objects embedded in Euclidean 3D(“Embedding a Torus (John Nash) - Numberphile,” n.d.). People describe “incredibly advanced mechanisms” and “impossible objects” that cannot be represented in our usual reality (e.g. Terence McKenna’s self-dribbling basketballs). At least one mathematician has stated that what one experiences on DMT cannot be translated into Euclidian geometry (unlike what one experiences on LSD). We received a series of systematic DMT trip-reports by a math enthusiast and experienced psychonaut who claims that the surfaces experienced on DMT are typically composed of hyperbolic tilings (which imply a negative curvature; cf. wallpaper groups). This article goes beyond claiming a mere connection between DMT and hyperbolic geometry. We will be more specific by addressing the aspects of the experience that can be interpreted geometrically. To do so, let us now turn to a phenomenological description of the way DMT experiences usually unfold: The Phenomenology of DMT Experiences: The Six Levels In order to proceed we will give an account of a typical vaporized DMT experience. You can think of the following six sections as stages or levels of a DMT journey. Let me explain. The highest level you get to depends on the dose consumed, and in high doses one experiences all of the levels, one at a time, and in quick succession (i.e. on high doses these levels are perceived as the stages of the experience). If one takes just enough DMT to cross over to the highest level one reaches during the journey for only a brief moment, then that level will probably be described as “the peak of the experience.” If, on the other hand, one takes a dose that squarely falls within the milligram range for producing a given level, it will be felt as more of a “plateau.” Each level is sufficiently distinct from the others that people will rarely miss the transitions between them. The six levels of a DMT experience are: Threshold, Chrysanthemum, Magic Eye, Waiting Room, Breakthrough, and Amnesia. Let us dive in! (Note: The following description assumes that the self-experimenter is in good physical

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and mental health at the time of consuming the DMT. It is well known that negative states of consciousness can lead to incomprehensible hellscapes when “boosted” by DMT (please avoid DMT at all costs while you are drunk, depressed, angry, suicidal, irritable, etc.). The full geometry is best appreciated on a mentally and emotionally balanced set and settings.) Threshold The very first alert of something unusual happening may take between 3 to 30 seconds after inhaling the DMT, depending on the dose consumed. Rather than a clear sensorial or cognitive change, the very first hint is a change in the apparent ambiance of one’s setting. You know how at times when you enter a temple, an art museum, a crowd of people, or even just a well decorated restaurant you can abstract an undefinable yet clearly present “vibe of the place?” There’s nothing overt or specific about it. The ambiance of a place is more of an overall gestalt than a localized feeling. An ambiance somehow encodes information about the social, ideological and aesthetic quality of the place or community you just crashed into, and it tells you at a glance which moods are socially acceptable and which ones are discouraged. The specific DMT vibe you feel on a given session can be one of a million different flavors. That said, whether you feel like you entered a circus or joined a religious ceremony, the very first hint of a DMT experience is nonetheless always (or almost always) accompanied with an overall feeling of significance. The feeling that something important is about to happen or is happening is made manifest by the vibe of the state. This vibe is usually present for at least the first 150 seconds or so of the journey. Interestingly, the change in ambiance is shorter-lived than the trip itself; it seems to go away before the visuals vanish quickly declining once the the peak is over. Within seconds after the change in ambiance, one feels a sudden sharpening of all the senses. Some people describe this as “upgrading one’s experience to an HD version of it.” The level of detail in one’s experience is increased, yet the overall semantic content is still fairly intact. People say things like: “Reality around me seems more crisp” and “it’s like I’m really grasping my surroundings, you know? fully in tune with the smallest textures of the things around me.” Terence McKenna described this state as follows: “The air appears to suddenly have been sucked out of the room because all the colors brighten visibly, as though some intervening medium has been removed.” Threshold enhancement. “Enhancement of Color” by “Chelsea Morgan” is licensed under CC BY-SA 4.0. On a schedule of repeated small doses (below 4 mg; preferably i.m.) one can stabilize this sharpening of the senses for arbitrarily long periods of time. I am a firm believer that this state (quite apart from the alien experiences on higher doses) can already be recruited for a variety of computational

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text:
and aesthetic tasks that humans do in this day and age. In particular, the state itself seems to enable grasping complex ideas with many parameters without distorting them, which may be useful for learning mathematics at an accelerated pace. Likewise, the sate increases one’s awareness of one’s surroundings (possibly at the expense of consuming many calories). I find it hard to imagine that artists will not be able to use this state for anything valuable. The Chrysanthemum If one ups the dose a little bit and lands somewhere in the range between 4 to 8 mg, one is likely to experience what Terrence McKenna called “the Chrysanthemum.” This usually manifests as a surface saturated with a sort of textured fabric composed of intricate symmetrical relationships, bright colors, shifting edges and shimmering pulsing superposition patterns of harmonic linear waves of many different frequencies. Depending on the dose consumed one may experience either one or several semi-parallel channels. Whereas a threshold dose usually presents you with a single strong vibe (or ambiance), the Chrysanthemum level often has several competing vibes each bidding for your attention. Here are some examples of what the visual component of this state of consciousness may look like: 2D Chrysanthemum “Brick flower” by “dynamosquito” is licensed under CC BY-SA 2.0. 2.5D Chrysanthemum “Sun Red” by “阿橋 HQ” is licensed under CC BY-SA 2.0. Chrysanthemum with multiple symmetry channels. The visual component of the Chrysanthemum is often described as “the best screen saver ever(“Neuroscientist Describes Her DMT Trip,” n.d.),” and if you happen to experience it in a good mood you will almost certainly agree with that description, as it is usually extremely harmonious, symmetric and beautiful in uncountable ways. No external input can possibly replicate the information density and intricate symmetry of this state; such state has to be endogenously generated as a a sort of harmonic attractor of your brain dynamics. You can find many replications of Chrysanthemum-level DMT experiences on the internet, and I encourage you to examine their implicit symmetries (this replication(“Descent into Madness,” n.d.) is one of my all-times favorite). In Algorithmic Reduction of Psychedelic States(Emilsson 2016a) we posited that any one of the 17 wallpaper symmetry groups can be instantiated as the symmetries that govern psychedelic visuals. Unfortunately, unlike the generally slow evolution of usual psychedelic visuals, DMT’s vibrational frequency forces such visuals to evolve at a speed that makes it difficult for most people to spot the implicit symmetry elements that give rise to the overall mathematical structure underneath one’s experience. For this reason it has been difficult to verify that all 17 wallpaper groups are possible in DMT states. Fortunately we were recently able to confirm that this is in fact the case thanks to someone who trained himself to do just this. I.e. detecting symmetry elements in patterns at an outstanding speed. An anonymous psychonaut (whom we will call researcher A) sent a series of trip report to Qualia Computing detailing the mathematical properties of psychedelic visuals under various substances

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and dose regimens. A is an experienced psychonaut and a math enthusiast who recently trained himself to recognize (and name) the mathematical properties of symmetrical patterns (such as in works of art or biological organisms). In particular, he has become fluent at naming the symmetries exhibited by psychedelic visuals. In the context of 2D visuals on surfaces, A confirms that the symmetrical textures that arise in psychedelic states can exhibit any one of the 17 wallpaper symmetry groups. Likewise, he has been able to confirm that every possible spherical symmetry group can also be instantiated in one’s mind on these states. The images below show some examples of the visuals that A has experienced on 2C-B, LSD, 4-HO-MET and DMT (sources: top left(“Symmetry Stanford Vision and Neuro-Development Lab,” n.d.), top middle; the rest were made with this service(“PhiloGL - Wallpaper Groups,” n.d.)): 17 wallpaper symmetry groups Wallpaper symmetry chart (CC BY-SA 3.0) p1 pmm cmm pg p4 p3 p4g The Chrysanthemum level interacts with sensory input in an interesting way: the texture of anything one looks at quickly becomes saturated with nested 2-dimensional symmetry groups. If you took enough DMT to take you to this level and you keep your eyes open and look at a patterned surface(Emilsson 2015a) (i.e. statistical texture(Emilsson 2015b)), it will symmetrify beyond recognition. A explains that at this level DMT visuals share some qualities with those of, say, LSD, mescaline, and psilocin. Like other psychedelics, DMT’s Chrysanthemum level can instantiate any 2-dimensional symmetry, yet there are important differences from other psychedelics at this dose range. These include the consistent change in ambiance (already present in threshold doses), the complexity and consistency of the symmetrical relationships (much more dense and whole-experience-consistent than is usually possible with other psychedelics), and the speed (with a control interruption frequency(“The Control Interrupt Model of Psychedelic Action,” n.d.) reaching up to 30 hertz, compared to 10-20 hertz for most psychedelics). Thus, people tend to point out that DMT visuals (at this level) are “faster, smaller, more detailed and more globally consistent” than on comparable levels of alteration from similar agents. Now, if you take a dose that is a little higher (in the ballpark of 8 to 12 mg), the Chrysanthemum will start doing something new and interesting… The Magic Eye Level A great way to understand the Magic Eye level of DMT effects is to think of the Chrysanthemum as the texture of an autostereogram (colloquially described as “Magic Eye” pictures). Our visual experience can be easily decomposed into two points-of-view (corresponding to the feed coming from each eye) that share information in order to solve the depth-map problem in vision. This is to map each visual qualia to a space with relative distances so (a) the input is explained and (b) you get recognizable every-day objects represented as implicit shapes beneath the depth-map. You can think of this process as a sort of handshake(Alex and er 2016) between bottom-up perception and top-down modeling. In everyday conditions one solves the

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depth-map problem within a second of opening one’s eyes (minus minor details that are added as one looks around). But on DMT, the “low-level perceptions” looks like a breathing Chrysanthemum, which means that the top-down modeling has that “constantly shifting” stuff to play with. What to make of it? Anything you can think of. There are three major components of variance on the DMT Magic Eye level: 1. Texture (dependent on the Chrysanthemum’s evolution) 2. World-sheet (non-occluding 3D1T depth maps) 3. Extremely lowered information copying threshold. Lobster Cone Furniture The image on the left is a lobster, the one on the center is a cone and the one to the right contains furniture (a lamp, a chair and a table). Notice that what you see is a sort of depth-map which encodes shapes. We will call this depth-map together with the appearance of movement and acceleration represented in it, a world-sheet. World-sheet 1 World-sheet 2 World-sheet 3 The world-sheet encodes the “semantic content” of the scene and is capable of representing arbitrary situations (including information about what you are seeing, where you are, what the entities there are doing, what is happening, etc.). It is common to experience scenes from usually mundane-looking places like ice-cream stores, play pens, household situations, furniture rooms, apparel, etc.. Likewise, one frequently sees entities in these places, but they rarely seem to mind you because their world is fairly self-contained. As if seeing through a window. People often report that the worlds they saw on a DMT trip were all “made of the same thing.” This can be interpreted as the texture becoming the surfaces of the world-sheet, so that the surfaces of the tables, chairs, ice-cream cones, the bodies of the people, and so on are all patterned with the same texture (just as in actual autostereograms). This texture is indeed the Chrysanthemum completely contorted to accommodate all the curvature of the scene. Magic Eye level scenes often include 3D geometrical shapes like spheres, cones, cylinders, cubes, etc. The complexity of the scene is roughly dose-dependent. As one ups the highness (but still remaining within the Magic Eye level) complex translucid qualia crystals in three dimensions start to become a possibility. Whatever phenomenal objects you experience on this level that lives for more than a millisecond needs to have effective strategies for surviving in an ecosystem of other objects adapted to that level. Given the extremely lowered information copying threshold, whatever is good at making copies of itself will begin to tessellate, mutate and evolve, stealing as much of your attention as possible in the way. Cyclic transitions occupy one’s attention: objects quickly become scenes which quickly become gestalts from which a new texture evolves in which new objects are detected and so on ad infinitum. A reports that at this dose range one can experience at least some of the 230 space groups as objects represented in the world-sheet. For example, A reports having stabilized a structure with a Pm-3m symmetry structure, not

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text:
unlike the structure of ZIF-71-RHO. Visualizing such complex 3D symmetries, however, does seem to require previous training and high levels of mental concentration (i.e. in order to ensure that all the symmetry elements are indeed what they are supposed to be). Katoite hydrogarnet Reprinted with Permission from Frank Hoffmann of The Fascination of Crystals and Symmetry There is so much qualia laying around, though, at times not even your normal space can contain it all. Any regular or semi regular symmetrical structure you construct by focusing on it is prone to overflow if you focus too much on it. What does this mean? If you focus too much on, for example, the number 6, your mind might represent the various ways in which you can arrange six balls in a perfectly symmetrical way. Worlds made of hexagons and octahedrons interlocked in complex but symmetrical ways may begin to tesselate your experiential field. With every second you find more and more ways of representing the number six in interesting, satisfying, metaphorically-sound synesthetic ways (cf. Thinking In Numbers(Emilsson 2016e)). Now, what happens if you try to represent the number seven in a symmetric way on the plane? Well, the problem is that you will have too many heptagons to fit in Euclidean space (cf. Too Many Triangles(“Too Many Triangles - Numberphile,” n.d.)). Thus the resulting symmetrical patterns will seem to overflow the plane (which is often felt as a folding and fluid re-arrangement, and when there is no space left in a region it either expands space or it is felt as some sort of synesthetic tension or stress, like a sense of crackling under a lot of pressure). Heptagonal tiling of the Poincar´e disk representing the 2D hyperbolic space Triheptagonal tiling Order-7-3 rhombille tiling In particular, A claims that in the lower ranges of the DMT Magic Eye level the texture of the Chrysanthemum tends to exhibit heptagonal and triheptagonal tilings (as shown in the picture above). A explains that at the critical point between the Chrysanthemum and the Magic Eye levels the intensity of the rate of symmetry detection of the Chrysanthemum cannot be contained to a 2D surface. Thus, the surface begins to fold, often in semi-symmetric ways. Every time one “recognizes” an object on this “folding Chrysanthemum” the extra curvature is passed on to this object. As the dose increases, one interprets more and more of this extra curvature and ends up shaping a complex and highly dynamic spatiotemporal depth map with hyperbolic folds(“Crochet,” n.d.). In the upper ranges of the Magic Eye level the world-sheet is so curved that the scenes one visualize are intricate and expansive, feeling at times like one is able to peer through one’s horizon in all directions and see oneself and one’s world from a distance. At some critical point one may feel like the space around one is folding into a huge dome where the walls are made of whatever texture + world-sheet combination happened to win the Darwinian selection pressures

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text:
applied to the qualia patterns on the Magic Eye level. This concentrated hyperbolic synesthetic texture is what becomes the walls of the Waiting Room… Waiting Room In the range of 12-25mg of DMT a likely final destination is the so-called Waiting Room. This experience is distinguished from the Magic Eye level in several ways: first, the world-sheet at this level breaks into several quasi-independent components, each evolving semi-autonomously. Second, one goes from “partial immersion” into “full immersion.” The transition between Magic Eye and Waiting Room often looks like “finding a very complex element in the scene and using it as a window into another dimension.” The total 2D surface curvature present (by adding up the curvature of all elements in the scene) is substantially higher than that of the Magic Eye level, and one can start to see actual 3D hyperbolic space. Perhaps a way of describing this transition is as follows: Thecurvature of the world-sheet gets to be so extreme that in order to accommodate it one’s entire multi-modal experiential field becomes involved, and a feeling of total and complete synchronization of all senses into a unified synesthetic experience is inescapable (often described as the “mmmMMMMMMM+++++!!!” whole-body tone people report). Thus the feeling of entering into an entirely new dimension. This explains what people mean when they say: “I experienced such an intense pressure that my soul could not be contained in my tiny body, and the intense pressure launched me into a bigger world.” DMT Waiting Room Constant flow of interlocking symmetry elements tile the texture Changes in the connectivity of the micro-structure of the texture The images above, taken together, are meant as an impressionistic replication of what a Waiting Room experience may feel like. On the left you see the textured world-sheet curved in several ways resulting in an enclosed room with shimmering walls and an entity looking at a futuristic-looking contraption. The images on the right are meant to illustrate the ways in which the texture of the world-sheet evolves: you will find that the micro-structure of such texture is constantly unfolding in new symmetrical ways (bottom right), and propagating such changes throughout the entire surface at a striking speed (top right). DMT Waiting Rooms contain entities that at times do interact directly with you. Their reality is perceived as a much more intense and intimate version of what human interaction normally is, but they do not give the impression of being telepathic. That said, their power is felt as if they could radiate it. One could say that this level of DMT places you in such an intimate, vulnerable and open state that interpreting the entities in a second-person social mode is almost inevitable. It is like interacting with someone you really know (or perhaps someone you really really want to know… or really really don’t want to know), except that the whole world is made of those feelings and some entities inhabit that world. Serious hard-core psychonauts tend to describe the Waiting Room

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as a temporary stopgap. Indeed more poetry could ever be written about the Waiting Room states of consciousness than about most human activities, for its state-space is larger, more diverse and more hedonically loaded. But even so, it is important to realize that there are even weirder states. Serious psychonauts exploring the upper ranges of humanly-accessible high energy consciousness research may see Waiting Rooms as a stepping stones to the real deal… Breakthrough If one manages to ingest around 20-30mg of DMT there is a decent chance that one will achieve a DMT breakthrough experience (some sources place the dosage as high as 40mg). There is no agreed-upon definition for a “DMT breakthrough,” but most experienced users confirm that there is a qualitative change in the structure and feel of one’s experience on such high doses. Based on A’s observations we postulate that DMT breakthroughs are the result of a world-sheet with a curvature so extreme that topological bifurcations start to happen uncontrollably. In other words, the very topology of one’s world-sheet is forced to change in order to accommodate all of the intense curvature. Breakthrough 1 Breakthrough 2 Breakthrough 3 The geometry of space you experience may suddenly go from a simply connected space into something else. What does this mean? Suddenly one may feel like space itself is twisting and reconnecting to itself in complex (and often confusing) ways. One may find that given any two points on this “alien world” there may be loops between them. This has drastic effects on one’s every representation (including, of course, the self-other divide). The particular feeling that comes with this may explain the presence of PSIS-like experiences induced by DMT and high dose LSD (cf. LSD and Quantum Measurements). Since the topological bifurcations are happening on a 3D1T world-sheet, this may look like “multiple things happening at once” or “objects taking multiple non-overlapping paths at once in order to get from one place into another.” The entities at this level feel transpersonal: due to the extreme curvature it is hard to distinguish between the information you ascribe to your self-model and the information you ascribe to others. Thus one is all over the place, in a literal topological sense. While on the Waiting Room one can stabilize the context where the experience seems to be taking place, on a DMT breakthrough state one invariably “moves across vast regions, galaxies, universes, realities, etc.” in a constant uncontrollable way. Why is this? This may be related to whether one can contain the curvature of the objects one attends to. If the curvature is uncontrollable, it will “pass on to the walls” and result in constant “context switches.” In fact, such a large fraction of 3D space is perceived as hyperbolic in one way or another, that one seems to have access to vast regions of reality at the same time. Thus a sense of radical openness is often experienced. Amnesia Level Unlike 5-MeO-DMT, “normal DMT” experiences are not typically so mind-warping that

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text:
they dissolve one’s self-model completely. On the contrary, many people report DMT as having “surprisingly little effect on one’s sense of self except at very high doses” relative to the overall intensity of the alteration. Thus, DMT usually does not produce amnesia due to ego death directly. Rather, the amnesic properties of DMT at high doses can be blamed on the difficulty of instantiating the necessary geometry to make sense of what was experienced. In the case of doses above “breakthrough experiences” there is a chance that the user will not be able to recall anything about the most intense periods of the journey. Unfortunately, we are not likely to learn much from these states (that is, until we live in a community of people who can access other phenomenal geometries in a controlled fashion). Recalling the Immemorial We postulate that the diffculty people have remembering the phenomenal quality of a DMT experience is in part the result of not being able to access the geometry required to accurately relive their hallucinations. The few and far apart elements of the experience that people do somehow manage to remember, we posit, are those that happen to be (relatively) easy to embed in 3D Euclidean space. Thus, we predict that what people do manage to “bring back” from hyperspace will be biased towards those things that can be represented in R3. This explains why people remember experiencing intensely saddled scenes (e.g. fractals, tunnels, kale worlds, recursive processes, and so on). Unfortunately most information-rich and interesting (irreducible, prime) phenomenal objects one experiences on DMT are by their very nature impossible to embed in our normal experiential geometry. This problem reveals an intrinsic limitation that comes from living in a community of intelligences (i.e. contemporary humans) who are constrained in the range of state-spaces of consciousness that they can access. This realization calls for a new epistemological paradigm, one that incorporate state-specific representations into a globally accessible database of states of consciousness(Emilsson 2016b), together with the network that emerges from their mutual (in)intelligibility. DMT Objects The increased curvature of one’s world-sheet can manifest in endless ways. In some important ways, the state-space of possible scenes that you can experience on DMT is much bigger than what you can experience on normal states of consciousness. Strictly speaking, you can represent more scenes on DMT states than in most other states because the overall amount qualia available is much larger. Of course the very dynamics of these experiences constrains what can be experienced, so there are still many things inaccessible on DMT. For instance, it may be impossible to experience a perfectly uniform blue screen (since the Chrysanthemum texture is saturated with edges, surfaces and symmetrical patterns). Likewise, scenes that are too irregular may be impossible to stabilize given the omnipresent symmetry enhancement found in the state. What are the nature of the objects and entities one experiences on DMT? Magic Eye level experiences tend to include objects that are usually found in our everyday life.

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text:
It is at the DMT waiting room level and above that the “truly impossible objects” begin to emerge. In particular, all of these objects are often curved in extreme ways. They condense within them complex networks of interlocking structures sustaining an overall superlative curvature. Here are some example objects that one can experience on Waiting Room and Breakthrough level experiences: DMT Object 1 DMT Object 2 DMT Object 3 DMT Object 4 DMT Object 5 DMT Object 6 DMT Object 7 DMT Object 8 DMT Object 9 DMT Object 1, 2, 3, 5 - © Paul Nylander, http://bugman123.com DMT Object 8 - Copyright 2014 Robert Fathauer; robertfathauer.com Notice that all of these images have many saddles everywhere. Ultimately, the range of objects one can experience on such states includes many other features that are impossible to represent in R3. The objects that people do manage to bring back and recall later on, are precisely those that can be embedded in R3. Thus you often see extremely contorted wrapped-up objects. The most interesting ones (such as quasi-regular H3 tilings or irreducible objects) are next-to-impossible to bring back in any meaningful way, for now at least. DMT Space Expansion The expansion of space responsible for the increased curvature happens anywhere you direct your attention (including the objects you see). Here(“Jitterbox,” n.d.) you can see what it may look like to stare at a DMT object. This is called the “jitterbox” mechanism. DMT Entities DMT entities come in many forms, and their overall quality is extremely dosedependent. Rather than describing any specific manifestation we will instead briefly characterize the rough properties of the entities experienced based on the level reached. Threshold: Usually the ambiance change has a social feel to is. More similar to entering a room of people of an alien culture, than entering an empty cave or a warm pool on your own. In this sense the very beginning of a DMT experience may already frame the experience in social terms and facilitate the expectation of meeting entities. Chrysanthemum: One can feel perhaps the subtle presence of entities, but they are often interpreted as “feeling connected” to one’s friends, relatives and acquaintances. The feeling does not manifest in any clear spatial way, though. Other than that, this state is apersonal in the sense that one does not see any entity directly. Magic Eye: Here the entities can be roughly described as having an impersonal relationship with you. They are just there, hanging out on their own, often engrossed with whatever activities your world-sheet is capable of representing for them. Waiting Room: At this level entities start becoming able to interact with you. They feel like autonomous beings wrapped in mystery. Their intentions, what they know, and their emotional states can be guessed from their behavior, but they are not immediately obvious. Breakthrough: At this level the entities one meets seem to have what we might call a transpersonal relationship with you. They share their own internal states (emotions, knowledge, wishes, etc)

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text:
with you. It feels like they can communicate telepathically and “see through” you. One cannot hide one’s “private” mental contents from them at this level. Amnesia: One cannot remember, of course, exactly what happens here. But if trip reports are any indication, this level is reminiscent of highly “mystical” states in which one’s implicit beliefs about Personal Identity(Emilsson 2015e) are obliterated and replaced by the feeling of becoming an all-encompassing entity. “Union with God” and “Samadhi(Emilsson 2016d)” are terms that describe the subjective feeling of self in this state. In other words, at this level it is impossible to distinguish between oneself and other entities, for all is represented as one. (Beware of never trying to go here if you feel bad at the time since negative hedonic tone can be amplified just as much as a good feeling such as Samadhi). Modeling the Hyperbolic Geometry of DMT How can we explain the drastic geometric changes of phenomenal space on DMT? As mentioned earlier, we will discuss three (non-mutually exclusive) hypothesis. These hypothesis work at the level of an algorithmic reduction(Emilsson 2016a), which means that we will go deeper than just describing information processing and phenomenology. We will stop short of addressing the implementation level of abstraction. It is worth pointing out that describing the ways in which DMT experiences are hyperbolic is in itself an algorithmic reduction. What we are about to do is to develop a more granular algorithmic reduction in which we try to explain why hyperbolic geometry emerges on DMT states by postulating underlying processes. Here are the three reductions: Control Interruption + Symmetry detection = Change in Metric Recall that on a previous article(Emilsson 2016a) we algorithmically reduced general psychedelic states. The building blocks of that reduction were: Control Interruption(“The Control Interrupt Model of Psychedelic Action,” n.d.) (which amounts to a “longer half-life for all qualia”) Drifting (“breathing walls, eyes moving from their normal place, waving sensations”) Enhanced Pattern Recognition (pareidolia, cf. Getting Closer to Digital LSD(Emilsson 2015d)) Lowered Symmetry Detection Threshold (quasi-symmetric patterns tend to “lock into” perfectly symmetrical structures) Using this framework one can argue that DMT makes space more hyperbolic in the following way: in high amounts the synergistic effect of control interruption(“The Control Interrupt Model of Psychedelic Action,” n.d.) together with extremely lowered symmetry detection thresholds experienced in quick succession makes the subjective distance between the points in the phenomenal objects in the scene evolve a hyperbolic metric. How would this happen? The key thing to realize is that in this model the usual quasi-Euclidean space we experience is an emergent effect of an equilibrium between these two forces. Even in normal circumstances our world-sheet is continuously regenerated; the rate at which symmetrical relationships in the scene are detected is balanced by the rate at which these subjective measurements are forgotten. This usually results in an emergent Euclidean geometry. On DMT the rate of symmetry detection increases while the rate of “forgetting” (inhibiting control) decreases. Attention points out more relationships in

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quick succession and this creates a network of measured subjective distances that cannot be embedded in Euclidean 3D space. Thus there is an overflow of symmetries. We are currently working on a precise mathematical model of this process in order to reconstruct a hyperbolic metric out of these two parameters. In this model, control interruption is interpreted as a change in the decay for subjective measurements of distance in one’s mind, whereas the lowered symmetry detection threshold is interpreted as a change in the probability of measuring the distance between any two given points as a function of the network of distances already measured. The curvature increase is most salient where there is already a lot of measurements made, since highly-measured regions focus attention and attention drives symmetry detection. Thus, focusing on any surface will make the surface itself hyperbolic (rather than the 3D space, since measurements are mostly concentrated on the surface). On the other hand, if the curvature is too high to keep on a 2D surface, it will “jump” to 3D or even 3D1T (i.e. branching out the temporal component of one’s experience). The result is that the total curvature of one’s 3D1T world-sheet increases on DMT in a dose-dependent way. Different doses lead to different states of curvature homeostasis. Each part of the worldsheet has constantly-morphing shapes and sudden curvature changes, but the total curvature is nonetheless more or less preserved on a given dose. It is not easy to get rid of excess curvature. Rather, whenever one tries to reduce the curvature in one part of the scene one is simply pushing it elsewhere. Even when one manages to push most of the curvature out of a given modality (e.g. vision) it is likely to quickly return in another modality (e.g. kinesthetic or auditory landscape) since attention never ceases on a DMT trip. Such apparent dose-dependent global curving of the world-sheet (and its jump from one modality into another) constrains the shape of the objects one can represent on the state (thus leading to alien-looking highly-curved objects similar to the ones shown above). Dynamic System Account: Energy Sources, Sinks and Invariants Energy Invariants Let us define a notion of energy in consciousness so that we can formalize the way experiences warps and transforms on DMT. Assume that one needs “energy” in order to instantiate a given experience (really, this is just an implicit invariant and we could use a different name). Each feature of a given experience needs a certain amount of energy, which roughly corresponds to a weighted sum of the intensity and the information content of an experience. For instance, the brightness of a point of colored light in one’s visual field is energy-dependent. Likewise, the information content in a texture, the number of represented symmetrical relationships, the speed by which an object moves (plus its acceleration), and even the curvature of one’s geometry. All of these features require energy to be instantiated. Under normal circumstances the brain has many clever and (evolutionarily)

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