[Content Warning: Trying to understand the contents of this essaymay be mind-warping. Proceed with caution.]

Friends, right here and now, one quantum away, there is raging a universeof activeintelligence that is transhuman, hyperdimensional, and extremely alien.

Terence McKenna

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 spiritualaccounts. We do not claim to know what ultimately implements the effects heredescribed (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 onDMT-induced states of consciousness by describing the overall changes in the geometry of ones spationtemporal representations (what we will call world-sheets i.e. 3D + time surfaces;3D1T for short). The concrete hypothesis is that the network of subjective measurementsof distances weexperience on DMT (coming from the relationships between the phenomenal objects one experiencesin 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 tofit in an experiential field with 3D Euclidean phenomenal space (i.e. an experience of dimension R2.5 representing anR3scene). This results in phenomenal spaces, surfaces, and objects acquiring amean negative curvature. Of note is that even though DMT produces this effect in the most consistent and intense way, theeffect is also present in states of consciousness induced by tryptaminesand to a lesser extentin those induced by all other psychedelics.

We will use the reductionframework originally proposedin the articleAlgorithmic Reductions of Psychedelic States. This means that we will be examining how algorithms and processes (as experienced by a subject of experience) can explain the dynamics of peoples 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 onDMT as an emergent effect of a series of moregeneral mechanism of action that can work together to change the geometry of a mind. These same mechanisms of action govern the dynamicsof other psychedelic experiences; it is the proportion and intensityof the various basic effectsthat lead to the differentoutcomes observed. In other words, the hyperbolization of phenomenal space may notbe a fundamental effectof 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 amicroscopic high-dimensionalquantum foam).

In particular, we will discuss three candidate models for a more fundamental algorithmic reduction: (1) the synergistic effect of control interruption and symmetry detection resulting in a change ofthe 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 potentialenergy, and (3) a changein 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.

Perhaps the clearest way to describe hyperbolic spaceis to show examples of it:

Saddle

Inside a hyperbolic cube

In hyperbolic 3D space dodecahedra can have right corners.

The picture tothe left shows a representation of a saddle surface. In geometry, saddle surfaces are 2-dimensional hyperbolic spaces (also calledhyperbolic planes orH2). 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 itmust be a saddle point (i.e. a point withnegative curvature). As you cansee, saddles havethe property that the angles of a triangle found in themadd up to less than 180 degrees (compare that to surfaceswith positive curvature such asthe 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 apolyhedra (and polytopes) will be more pointy in Hn than they are in Rn. This is whyyou can see in the right imagea dodecahedron with right-angled corners, which in this case can tile H3(cf. Not Knot). Such a thing- people of the past might say- is an insult to the imagination. Times are changing, though, and hyperbolic geometryis now an acceptable subject of conversation.

An important property of hyperbolic spaces is the way in which the areaof a circle(or the n-dimensional volumeof a hypersphere) increasesas a function of its radius. In 2D Euclidean space the areagrows quadraticallywith the radius. But on H2, the areagrows exponentially as a function of the radius! As you may imagine, it is easy to get lost in 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 extremelly thin. In order to avoidgetting burned orfreezing to death you would have to place your planet within a very narrowdistance range from the centerstar. Most of what you do in hyperbolic space either stays as local news or is quickly dissipated in an ever-expanding environment.

We cannot experience H2 or H3 manifoldsunder normal circumstances, but we can at leastrepresent some aspects of themthrough partialembeddings(i.e. instantiationsas subsets of otherspaces preserving properties) and projections 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 embedH2 in Euclidean 3D space, since doing so will necessarily distort some properties of the original H2 space (such as distance, angle, area, local curvature, etc.). As we will discuss further below, this difficultyturns out to be crucialfor understanding why DMT experiences are so hard to remember. In order to remember the experience you need to create afaithful and memorable 3D Euclidean embedding of it. Thus, ifone 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 itcan be fit in compact Euclideanrepresentations.

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 describetheir trips as well as concrete mathematical observations of such features point directly tohyperbolic geometry. Here is a list of such features (arranged from least to most suggestive you know, for dramatic effect):

This article goes beyond claiming a mere connection between DMT and hyperbolic geometry. We will be more specific by addressing theaspects of the experience that can be interpreted geometrically. To do so, let us now turn to a phenomenological description of the way DMT experiences usuallyunfold:

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 levelsareperceived as the stages of the experience). If one takes just enough DMT to cross over to the highest level one reaches duringthe journey for only a brief moment, then that level will probablybe 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 missthe 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-experimenteris in good physical 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 costswhile you are drunk, depressed, angry, suicidal, irritable, etc.). The full geometry is best appreciated on a mentally and emotionally balanced set and settings.)

The very first alert of something unusual happening may take between 3 to30seconds after inhaling the DMT, depending on the dose consumed. Rather than a clear sensorial or cognitivechange, the very first hint is a change in the apparentambiance of ones 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?Theres nothing overt or specific about it. The ambianceof a place is more of an overall gestaltthan a localized feeling. An ambiancesomehow 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 DMTvibe you feel on a given session canbe one of a million different flavors. That said, whether you feel like you entered a circus or joineda 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 thefirst 150 seconds or so of the journey. Interestingly, thechange in ambianceis shorter-lived than the trip itself; it seems to go away before the visuals vanish quickly declining once the the peak is over.

Within secondsafter the change in ambiance, one feels a sudden sharpening of all the senses. Some people describe this as upgradingones experience to an HD versionof it. The level of detail inones experience is increased, yet the overall semantic content is still fairly intact.People say things like: Reality around me seems more crisp and its like Im really grasping my surroundings, you know? fully in tune with the smallesttextures of the things around me. Terence Mckenna describedthis stateas 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.

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 berecruited for a variety of computational 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 ones awareness ofones surroundings (possibly at the expense of consuming many calories). I find ithard to imagine thatartists willnot be able to use this state for anything valuable.

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 calledthe Chrysanthemum. This usually manifests as a surface saturated with a sort oftextured fabric composed ofintricate symmetrical relationships, bright colors, shifting edges and shimmering pulsing superposition patternsof 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 thisstate of consciousness may looklike.

2D Chrysanthemum

2.5D Chrysanthemum

Chrysanthemum with multuple symmetry channels

The visual component of the Chrysanthemum is often described as the best screen saver ever, and if you happen to experience it in a good mood you will almost certainly agree with that description, as it is usually extremelly harmonious, symmetric and beautiful in uncountable ways. No external input can possibly replicate the information density and intricate symmetry of this state; such statehas to be endogenously generatedas a a sort of harmonicattractor 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 replicationis one of my all-times favorite).

In Algorithmic Reduction of Psychedelic Stateswe 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 psychedelicvisuals, DMTs vibrational frequency forces such visuals to evolve at a speed that makes it difficult for most people to spotthe implicitsymmetry elementsthat give rise totheoverall mathematicalstructure underneath ones experience. For this reason it has been difficult to verify that all 17 wallpaper groups are possible in DMT states. Fortunatelywe were recently able to confirm that this is infact the case thanks tosomeone who trained himself to do just this. I.e. detecting symmetry elements in patterns at an outstanding speed.

Ananonymous psychonaut (whomwe will call researcherA) sent a series of trip reportto Qualia Computing detailing the mathematical properties of psychedelic visualsunder various substances 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 artor 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 thatthe symmetrical textures that arise in psychedelic states canexhibit any one of the 17 wallpaper symmetry groups. Likewise, he has been able to confirmthat every possible spherical symmetry groupcan also be instantiated in ones mind on these states.

The images belowshowsome examples of the visuals thatA has experienced on 2C-B, LSD, 4-HO-MET and DMT (sources: top left, top middle, the rest were made withthis service):

The Chrysanthemum level interacts with sensory input in an interesting way: thetexture 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 (i.e. statistical texture), it will symmetrifybeyond recognition. A explains that at this level DMT visuals share some qualities withthose of, say, LSD, mescaline, andpsilocin. Like other psychedelics, DMTs Chrysanthemum level can instantiate any 2-dimensional symmetry, yet there are importantdifferences fromother psychedelics at this dose range. These include the consistentchange 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 reaching up to 30 hertz, compared to 10-20 hertz for mostpsychedelics). 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 ballparkof 8 to 12 mg), the Chrysanthemum will start doing something new and interesting

A great way to understand the Magic Eye level of DMT effects is to think of the Chrysanthemum as the texture of anautostereogram (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 processas a sort of hand-shake between bottom-up perception and top-down modeling.

In everyday conditions one solves the depth-map problem within a second of opening ones 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 thatconstantly 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:

The image on the left is a lobster, the one on the center is a cone and the one tothe 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.

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 actualautostereograms). This texture is indeed the Chrysanthemum completely contorted to accommodateall 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 formore than a millisecond needs to have effective strategies for surviving in an ecosystem of other objects adapted to that level. Given the extremelly loweredinformation copying threshold,whatever is good at making copies of itself will begin to tesselate, mutate and evolve, stealing as much of your attention as possible in the way. Cyclic transitions occupy ones 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 atleast someof the 230 space groupsas objects represented in the world-sheet. For example, A reports having stabilized a structure with aPm-3m symmetry structure, not unlike the structure of ZIF-71-RHO. Visualizing such complex 3D symmetries, however, doesseem to require previous training and high levels of mentalconcentration (i.e. in order to ensure that all the symmetry elements are indeed what they are supposed to be).

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 itisprone to overflow ifyou focus too much on it. What does thismean? If you focus too much on, for example, the number 6, your mind mightrepresent the various ways in which you can arrange six balls in a perfectly symmetrical way. Worlds made of hexagons andoctahedrons interlocked in complex but symmetrical ways may begin to tesselate your experiential field. With every second you findmore and more ways of representing the number six in interesting, satisfying, metaphorically-sound synesthetic ways (cf. Thinking in Numbers). 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). Thus the resulting symmetrical patterns willseem to overflow the plane (which is often felt as a folding and fluid re-arrangement, andwhen there is no space left in a region it either expands space or it is felt as some sort of synesthetictension or stress, like a sense of crackling under a lot of pressure).

Heptagonal tiling of the Poincar disk representing the 2D hyperbolic space.

Triheptagonal tiling

Order-7-3 rhombille tiling

In particular, A claims that inthe lowerranges of the DMT Magic Eye level the texture of the Chrysanthemum tendstoexhibitheptagonal 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. 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 ones horizon in all directions and see oneself and ones 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 applied to the qualia patterns on the Magic Eyelevel. This concentrated hyperbolic synesthetic texture is what becomes the walls of the 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 curvaturepresent (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 describingthis transition is as follows: The curvature of the world-sheet gets to be so extremethat in order to accommodateit ones 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 meinto a bigger world.

DMT Waiting Room

Changes in the connectivity of the micro-structure of the texture

Constant flow of interlocking symmetry elements tile the texture.

The images above, taken together, are meant as animpressionistic replication of what a Waiting Room experience may feellike. On the left you see the textured world-sheet curved in several ways resulting in an enclosed room with shimmering walls andan entity looking ata 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 ofbeingtelepathic. 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 asecond-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 dont 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 Wating Roomas a temporary stopgap. Indeed more poetry could ever be written about the Waiting Room states of consciousness than about most human activities, for itsstate-space is larger, more diverse and more hedonicallyloaded. 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 asa stepping stonesto the real deal

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 as40mg). 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 ones experience on such high doses. Based on As observations we postulate that DMT breakthroughs are the result of a world-sheet with a curvatureso extreme that topological bifurcationsstart to happen uncontrollably. In other words, the very topology of ones world-sheet is forced to change in order to accommodate all of the intense curvature.

The geometry of space you experience maysuddenly 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 ones 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 toyour 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.

Unlike 5-MeO-DMT,normal DMT experiences are not typically so mind-warping that they dissolve ones self-model completely. On the contrary, many people report DMT as having surprisingly little effect on ones sense of self except at very high doses relative tothe overall intensity of the alteration. Thus, DMT usually does not produce amnesia due toego death directly. Rather, the amnesic properties of DMT at high doses can be blamed onthe difficulty ofinstantiating 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).

We postulate that the difficultypeople have remembering the phenomenal qualityof aDMT experience is in part the result of not being able to access the geometry required to accurately relive their hallucinations.The few and far apartelements 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). Unfortunatelymost 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 revealsan intrinsic limitation that comes from living in a community of intelligences (i.e. contemporaryhumans) who are constrainedin the range of state-spaces of consciousness that they can access. This realization calls for a new epistemological paradigm, one that incorporate state-specific representationsinto a globally accessible database of states of consciousness, together withthe network that emerges fromtheir mutual (in)intelligibility.

The increased curvature of ones 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 qualiaavailable 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 stabilizegiven the omnipresent symmetry enhancementfound 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. 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 condensewithin them complex networks of interlocking structures sustaining an overallsuperlative curvature. Here are some example objects that one can experience on Waiting Room and Breakthrough level experiences:

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 extremelly 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.

The expansion of space responsible for the increased curvature happens anywhere you direct your attention (including the objects you see). Here you can see what it may look like to stare at a DMT object: This is called the jitterbox mechanism.

DMT entities come in many forms, andtheir overall quality is extremelly dose-dependent. Rather than describing any specific manifestation we will instead briefly characterize the rough properties of the entities experienced based on the level reached.

How can we explain the drastic geometric changes of phenomenal space onDMT? As mentioned earlier, we will discuss three (non-mutually exclusive) hypothesis. These hypothesis work at the level of an algorithmic reduction, which means that we will godeeper than just describinginformation processing andphenomenology. 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 onDMT states by postulatingunderlying processes. Here are the three reductions:

Recall that on a previous article we algorithmically reduced general psychedelic states. The building blocks of that reduction were:

Using this framework one can argue that DMT makes space more hyperbolic in the following way: in high amounts the synergistic effect of control interruptiontogether with extremelly lowered symmetry detection thresholdsexperienced 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 usualquasi-Euclidean space we experience is an emergent effect of anequilibrium betweenthese two forces. Even in normal circumstances our world-sheet is continuously regenerated; the rate at which symmetrical relationships in the scene are detectedis 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 quick succession and thiscreates 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 ones 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 regionsfocus 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 to3D or even 3D1T (i.e.branching out the temporal component of ones experience). The result is that the totalcurvature of ones 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 totalcurvature 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 issimply 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 itsjump from onemodality 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).

Let usdefine a notion of energy in consciousnessso 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 weightedsum ofthe intensity and the information content of an experience. For instance, the brightness of a point of colored light in ones 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 ones geometry. All of these features require energy to be instantiated.

Under normal circumstances the brain has many clever and (evolutionarily) appropriate ways of modulating the amount of energy present in different modules of ones mind. That is, we have many programs that work asenergy switches for different mental activities depending on the context. When we think, we have allocated a certain amount of energy to finding a shape/thought-form that satisfies a number of constraints. When it shape-shifting that energy in various ways andfinding a solution, we either allocate more energy to it or perhaps give up. However, on DMT the energy cannot be switched off, and it can only pass from one modality into another. In other words, whereas in normal circumstances one uses strategically ones ability to give energy limits to different tasks, on DMT one simply has constant high energy globally no matter what.

More formally, this model of DMT action says that DMT modifies the structure of ones mind so that (1) energy freely passes from one form into another, and (2) energy floodsthe entire system. Lets talk about energy sources and sinks.

In this algorithmic reduction DMT increases the amount of consciousness in ones mind by virtue of impairing our normal energy sinks while increasing the throughput of its energy sources. This may frequently manifests asphenomenal spaces becoming hyperbolic in the mathematical-geometric sense of increasing its negative curvatureas such curvature is one manifestation of higher levels of energy. Energy sinks are still present and they struggle to capture as much of the energy as possible. In particular, one energy sink is recognition of objects on the world-sheet.

This model postulates that attention functions as an energy source, whereas pattern recognitionfunctions as an energy sink.

The total energy in ones consciousness increases on DMT, and there is a constant flow between different ways for this energy to take form. That said, one can analyze piecewise the various components of ones experience, specially if the network of energy exchange clusters well. In particular, we can postulate that world-sheets are fairly self-contained. Relative to other parts of the environment the mind is simulating, the world-sheet itself has a very high within-cluster energy exchange and a relatively low cross-cluster energy exchange. Ones world-sheet is very fluid, and little deformations propagate almost linearly throughout it. In a given dose plateau, if you add up the acceleration, the velocity, the curvature, and so on of every point in the world-sheetyou will comeup with a number that remains fairly constant over time. Thus studying the Hamiltonian of a world-sheet (i.e. the state-space given by a constant level of energy) can be very informative in describing both theinformation content and the experiential intensity of DMT experiences.

You can deform a surface without changing its local curvature. (Source: Gauss Remarkable Theorem [seriously not my quotes]). Thus on a DMT trip plateau there is still a lot of room for transformations of the world-sheet into different shapes with similar curvature.

It takes effort and wakefulness to focus on a complex scene with many intricate details. (Reading and trying to comprehend this essaymay itself require significant conscious energy expenditure). For this reason we might say that DMT is an exceedingly effective arouser of consciousness.

One essential property of our minds is that our level of mental arousal decreases when we interpret our experience as expected. People who can enjoy their own minds do so, in part, by finding unexpected ways of understandingexpected things. In the presence of new information that one cannot easily integrate, however, ones level of energy is adjusted upwards so that we try out a variety of different models quickly and try to sort out a model that does make the new information expected (though perhaps integrating new assumptions or adding content in other ways). When we cannot manage togenerate a mental model that works outa likely model of what weare experiencing we tend toremain in an over-active state.

This general principle applies to the world-sheet. One of the predominant ways in which a world-sheetreduces its energy (locally) is by morphing into something you can recognize or interpret. Thus the world-sheet in some way keeps on producing objects, at first familiar, but in higher energies the whole process can seemdesperate or hopeless: one can only recognize things with a stretch of the imagination. Since humans in general lack much experience with hyperbolic geometry, we usually dont manage to imagine objects that are symmetric on their own native geometry. But when we do, and we fill them up with resonant light-mind-energy, then BAM! New harmonics ofconsciousness! New varieties of bliss! Music of the angels! OMG! Laughter till infinity and more- shared across the galaxy- in a hyperbolic transpersonal delight! Its like LSD and N2O! Wow!

Forgive me, it is my first day. Lets carry on. As one does not know any object that the world-sheet can reasonably be able to generate in high doses, and the world-sheet has so much energy on its own, energy can seem to spiralout of control. This explains in part the non-linear relationship between experienced intensity and DMT dose.

Like all aspects of ones consciousness, the negativecurvature of phenomenal space tends to decay over time (possibly through inhibition by the cortex). In this case, the feeling is one of smoothing out the curves andembedding the phenomenal objects in 3D euclidean space. However, this is opposed by the effect that attention and (degrees of) awareness have on our phenomenal sheet, which is to increase its negative curvature. On DMT, anything that attention focuses on will begin branching, copying itself and multiplying, a process that quickly saturates the scene to the point of filling more spatial relationships than would fit in Euclidean 3D.The rate at which this happens is dose-dependent. The higher the dose, the less inhibiting control there is and the more intensethe folding property of attention will be. Thus, for different dosages one reaches different homeostatic levels of overall curvature in ones phenomenal space. Since attention does not stop at any point during a DMT trip (it keeps being bright and intense all throughout) there isnt really any rest period tosit back and see the curvature get smoothed out on its own. Everything one thinks about, perceives or imagines branches out and bifurcate at a high speed.

Every moment during the experience is very hard to grasp because the way one normally does that in usual circumstances is by focusing attention on it and shaping ones world-sheet to account for the input. But here that very attention makes the world-sheetwobble, warp and expand beyond recognition. Thus one might say that during a solid DMT experience one never sees the same thing twice, as the experience continues to evolve. That is, of course, as long as you do not stumble upon (or deliberatively create) stable phenomenal objects whose structure can survive the warping effect of attention.

Subjectively, A says, negative curvature is associated with more energy. Perhaps this curvature happens at a very low level? An example to light up the imagination is using heat to folda sheet of metal(thanks to thermal expansion). Whatever your attention focuses on seems to get heated up (in some sense) and expand as a result. The folding patterns themselvesseem to storepotential energy. Left on their own, this extra energy stored as negative curvature usually dissipates, but on DMT this process is lowered (while the effect of increasing the energy is heightened). Could this be the result of some very very fine-level micro-experiential change that gradually propagates upwards? With the help of our normal mental processes the change in the micro-structure may propagate all the way into seemingly hyperbolic 2D and 3D surfaces.

Perhaps the most important difference between DMT in high doses and other psychedelics is that the micro-structure of consciousness drifts in such a way that tiny Drosteeffectsbubble up into large Mbius transforms.

As noted already, these three algorithmic reductions are not incompatible. We just present them here due to their apparent explanatory power. A lot more theoretical work will be needed to make them quantitative and precise, but we are optimistic. The aim is now to develop an experimental framework to distinguish between the predictions that each candidate algorithmic reduction makes(including many not presented here). This is a work in progress.

In the case of experiential fields such as body feelings, smells and concepts, the hyperbolization takes different forms depending on the algorithmic reduction you use. I prefer the very general interpretation that one experiences hyperbolic information geometry rather than just hyperbolic space. In other words, when we talk about body feelings and so on, on a psychedelic one organizes such information in a hyperbolic relational graph, which also exhibits a negative curvature relative to its normal geometry. Arguing in favor of this interpretation would take another article, so we will leave that for another time.

Gluinga 1-handle is easy on a 2-sphere. Tongue in cheek, stickinga little doughnuton a big ballallows you to grab the sphere and control it in some way. But how do you get a handle on hyperbolic space? The answer is to build hyperbolic manifolds at the core of ones being, by imagining knots very intensely. The higher one is, the more complex the knot one can imagine in detail. Having practiced visualizations of this sort while sober certainly helps. If you imagine the knot with enough detail, you can then stress the environment surrounding it to represent a warpedhyperbolic space. This way yougive life to the complement of the knot(which is almost always hyperbolic!). We postulate that it is possible tostudy in detail the relationship between the knots imagined, and the properties of the experiential worlds that result from their inversion (i.e. thinking about the geometry of the space surrounding the knot rather than the knot itself). A reports that different hyperbolic spaces generated this way (i.e. imagining knots on tryptamines) have different levels of energy, and have unique resonant properties. Different kinds of music feel better in different kinds of hyperbolic manifolds. It takes more energy to light up a hyperbolic space like that, mostly due to its openness. Thisis why using small doses of 2C-B can be helpful to create a positive backbone to the experience (providing the necessary warmth to light up the hyperbolic space). Admittedly MDMA tends to work best, but its use is unadvisable for reasons we will not get into (related to the hedonic treadmill). A healthy combination that both enablesthe visualization of the hyperbolic spaces in a vivid way and also lights them up with positive hedonic tone healthily and reliably has yet to be found.

Relatedly Get a handle on your DMT trip by creating a stabilizing 4Dhyperbolic manifold in four easy steps:

God, the divine, open individualism, the number one, an abstract notion of self, or the thought of existence itself are all thoughts that work as great unifiers of large areas of phenomenal space. Indeed these concepts can allow a person to connect the edges of the hyperbolic space and create a pocket of ones experience that does not seem to have a boundary yet is extremelly open. This may be a reason why such ideas are very common in high levels ofpsychedelia. In a sense, depending on the mind, they have at times the highest recruiting power for your multi-threaded attention.

Beyondmeredesigner synesthesia, the future of consciousness research contains the possibility of exploring alternative geometries for the layout of our experiences. Ones overall level of energy, its manifestation, the allowed invariants, the logic gates, the differences in resonance, the granularity ofthe patterns, and so on, are all parameters that we will get to change in our minds to see what happens (in controlled and healthy ways, of course). The exploration of the state-space of consciousness is sure to lead to a combinatorial explosion. Even with good post-theoretical quantitative algorithmic reductions, it is likely that qualia computing scientists will still find an unfathomable number of distinct prime permutations. For some applications it may be more useful to use special kinds of hyperbolic spaces (like the compliment of certain class of knot), but for others it may suffice to be a little sphere. Who knows. In the end, if a valence economy ends up dominating the world, then the value of hyperbolic phenomenal spaces will be proportional to the level of wellbeing and bliss that can be felt in them. Which space in which resonant mode generates the highest level of bliss? This isan empirical question with far-reaching economicimplications.

I predict that some time in the next century or so manyof the breakthroughs in mathematics will take place in consciousness researchcenters. The ability to utilize arbitrary combinations of qualia with programablegeometry and information content (in addition to our whole range of pre-existing cognitive skills) will allow people to have new semantic primitives related to mathematical structures and qualia systems currently unfathomable to us. In the end, studyingthe mathematics of consciousness and valence is perhaps the ultimate effective altruist endeavor in a world filled with suffering, since reverse-engineering valence would simplify paradise engineering But even in a post-scarcity world, consciousness research will also probablybethe ultimate past time given the endless new discoveries awaiting to be found inthe state-space of consciousness.

*On the unexpected side effects of staring at a cauliflower on DMT: You can get lost in the hyperbolic reality of the (apparent) life force that spirals in a scale-free fractal fashion throughout the plant. The spirals may feel like magnetic vortexes that take advantage of your state to attractyour attention. The cauliflower may pull you into its own world of interconnected fractals, and as soon as you start to trust it, it begins trying to recruit you for the cauliflower cause. The cauliflower may scare you into not eating it, and make you feel guilty about frying it. You may freak out a little, but when you come down you convince yourself that itwas all just a hallucination. That said, you secretly worry it was for real. You may never choose toabstain from eating cauliflowers, but you will probably drop the knife when cooking it. You will break it apart with your own hands in the way you think minimizes its pain. You sometimeswonder whether it experiences agony as it is slowly cooked in the pan, and you drink alcohol to forget. Damn, dont stare at a cauliflower while high on DMT if you ever intend to eat one again.

P.S. Note onOriginality:The onlymention I have been able to find that explicitly connects hyperbolic geometry in a literal sense with DMT (rather than just metaphorical talk of hyperspace) is a 2014 post in the Psychonaut subredit. To my knowledge, no one has yet elaborated to any substantial degree on this interesting connection. That said, Im convinced that during the days that follow a strong trip, psychedelic self-experimentersmay frequently wonder about the geometry of the places they explored. Yet they usually lack any conceptual framework to justify their intuitions or even verbalize them, so they quickly forget about them.

P.S.S. ExampleSelf-Dribbling Basketball:

Self-dribbling basketball

To the right you can see what a self-dribbling basketball looks like. The more you try to grasp what it is, the more curved it gets. Thats because you are adding energy with you attention and you do not have enough recognition ability in this space to lower its energy and reduce the curvature to stabilize it. The curvature is so extreme at times that it produces constant context switches. This is the result of excess curvature being pushed towards the edge of your experience and turning into walls and corridors.

P.S.S.S.: Exampleon world-sheet bending:

See more here:

The Hyperbolic Geometry of DMT Experiences: Symmetries ...