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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 one’s world-sheet to account for the input. But here that very attention makes the world-sheet wobble, 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 deliberately create) stable phenomenal objects whose structure can survive the warping effect of attention. Hyperbolic Micro-Structure of Consciousness 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 fold a sheet of metal(“Thermal Expansion and Deformation of Aluminum Sheet,” n.d.) (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 themselves seem to store potential energy.

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text:
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 Droste effects bubble up into large M¨obius transforms(“Spherical Video Editing with Möbius Transformations,” n.d.). 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. Generalizing hyperbolization to non-spatial experiential fields In the case of experiential fields such as body feelings, smells and concepts, the

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text:
“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. Getting a handle on the DMT state Gluing a 1-handle is easy on a 2-sphere. Tongue in cheek, sticking a little doughnut on a big ball allows 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 one’s 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 warped hyperbolic space. This way you give life to the

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text:
complement of the knot(“Not Knot,” n.d.) (which is almost always hyperbolic!). We postulate that it is possible to study 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. This is 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 enables the 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

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text:
DMT trip by creating a stabilizing 4D hyperbolic manifold in four easy steps: Hyperbolic manifold 1 Hyperbolic manifold 2 Hyperbolic manifold 3 Hyperbolic manifold 4 Unifying Your Space 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 one’s experience that does not seem to have a boundary yet is extremely open. This may be a reason why such ideas are very common in high levels of psychedelia. In a sense, depending on the mind, they have at times the highest recruiting power for your multi-threaded attention. Applications to Qualia Computing and Closing Thoughts Beyond mere designer synesthesia, the future of consciousness research contains the possibility of exploring alternative geometries for the layout of our experiences. One’s overall level of energy, its manifestation, the allowed invariants, the logic gates, the differences in resonance, the granularity of the patterns, and so on, are all parameters that we will get to change in our minds to see what happens

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(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 well-being and bliss that can be felt in them. Which space in which resonant mode generates the highest level of bliss? This is an empirical question with far-reaching economic implications. Mathematics post-hyperbolic consciousness I predict that some time in the next century or so many of the breakthroughs in mathematics will take place in consciousness research centers. The ability to utilize arbitrary combinations of qualia with programable geometry 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

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text:
structures and qualia systems currently unfathomable to us. In the end, studying the 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 probably be the ultimate past time given the endless new discoveries awaiting to be found in the state-space of consciousness. P.S. Note on Originality: The only mention 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 subreddit(“R/Psychonaut - DMT, Hyperbolic Space, and Dodecahedrons,” n.d.). To my knowledge, no one has yet elaborated to any substantial degree on this interesting connection. That said, I’m convinced that during the days that follow a strong trip, psychedelic self-experimenters may 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. Example Self-Dribbling Basketball: Below you can see what a “self-dribbling basketball” looks like. The more you try to “grasp” what it is,

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the more curved it gets. That’s because you are adding energy with your 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. Acknowledgements Thank you James W. Sanders for converting this piece to Distill for R Markdown format. Tags Psychedelics, Philosophy, Qualia, Ethics, Experiment, Hedonic Tone, Psychophysics, Symmetry, Valence Alex, Scott, and er. 2016. “It’s Bayes All the Way Up.” Slate Star Codex. https://slatestarcodex.com/2016/09/12/its-bayes-all-the-way-up/. “Chrysanthemum - First Steps in Hyperspace - Welcome to the DMT-Nexus.” n.d. https://www.dmt-nexus.me/forum/default.aspx?g=posts&t=8595. “Crochet.” n.d. http://pi.math.cornell.edu/~dwh/papers/crochet/crochet.html. “Descent into Madness.” n.d. https://www.youtube.com/watch?v=TYLuk_QpQCU. “Embedding a Torus (John Nash) - Numberphile.” n.d. https://www.youtube.com/watch?v=5qu3WETuf6c. Emilsson, Andrés Gómez. 2015a. “Psychedelic Perception of Visual Textures.” Qualia Computing. https://qualiacomputing.com/2015/04/08/pattern-walk/. ———. 2015b. “Psychophysics for Psychedelic Research: Textures.” Qualia Computing. https://qualiacomputing.com/2015/04/20/psychophysics-for-psychedelic-research-textures/. ———. 2015c. “Why Not Computing Qualia?” Qualia Computing. https://qualiacomputing.com/2015/04/19/why-not-computing-qualia/. ———. 2015d. “Getting Closer to Digital LSD.” Qualia Computing. https://qualiacomputing.com/2015/06/19/getting-closer-to-digital-lsd/. ———. 2015e. “Ontological Qualia: The Future of Personal Identity.” Qualia Computing. https://qualiacomputing.com/2015/12/17/ontological-qualia-the-future-of-personal-identity/. ———. 2016a. “Algorithmic Reduction of

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text:
Five Projections of Each.” n.d. https://www.youtube.com/watch?v=xHvAqDuWG2M. Weisstein, Eric W. n.d. “Embedding.” Text. https://mathworld.wolfram.com/Embedding.html. 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 attract your 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 it was all just a hallucination. That said, you secretly worry it was for real. You may never choose to abstain 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 sometimes wonder whether it experiences agony as it is slowly cooked in the pan, and you drink alcohol to forget.

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text:
Damn, don’t stare at a cauliflower while high on DMT if you ever intend to eat one again.↩︎ References Citation For attribution, please cite this work as Gómez-Emilsson (2016, Dec. 12). The Hyperbolic Geometry of DMT Experiences: Symmetries, Sheets, and Saddled Scenes. Retrieved from https://www.qri.org/blog/hyperbolic-geometry-DMT BibTeX citation @misc{gómez-emilsson2016the, author = {Gómez-Emilsson, Andrés}, title = {The Hyperbolic Geometry of DMT Experiences: Symmetries, Sheets, and Saddled Scenes}, url = {https://www.qri.org/blog/hyperbolic-geometry-DMT}, year = {2016} } Logarithmic Scales of Pleasure and Pain Rating, ranking, and comparing peak experiences suggest the existence of long tails for bliss and suffering. Andrés Gómez-Emilsson ../people/andrés-gómez-emilsson (Qualia Research Institute)https://www.qri.org/ August 10, 2019 Contents TL;DR Introduction Weber’s Law Why This Matters General Ideas The Non-Linearity of Pleasure and Pain Deference-type Approaches for Experience Ranking Survey Setup Mechanical Turk: Participant Composition Bots (easy to spot–unless extremely sophisticated) Preprocessing Results Appearance Base Rates Average Ratings Deference Graph of Top Experiences Latent Trait Ratings Long-tails in the Responses to “How Many Times Better/Worse” Question Discussion Key Pleasures Surfaced Falling In Love Travel/Vacation MDMA/LSD/Psilocybin Key Pains Surfaced Future Directions for Methodological Approaches Closing Thoughts on the Valence Scale Additional Material Appendix A Acknowledgements Tags TL;DR Based on: the characteristic distribution of neural activity, personal

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accounts of intense pleasure and pain, the way various pain scales have been described by their creators, and the results of a pilot study we conducted which ranks, rates, and compares the hedonic quality of extreme experiences, we suggest that the best way to interpret pleasure and pain scales is by thinking of them as logarithmic compressions of what is truly a long-tail. The most intense pains are orders of magnitude more awful than mild pains (and symmetrically for pleasure). This should inform the way we prioritize altruistic interventions and plan for a better future. Since the bulk of suffering is concentrated in a small percentage of experiences, focusing our efforts on preventing cases of intense suffering likely dominates most utilitarian calculations. An important pragmatic takeaway from this article is that if one is trying to select an effective career path, as a heuristic it would be good to take into account how one’s efforts would cash out in the prevention of extreme suffering (see: Hell-Index), rather than just QALYs and wellness indices that ignore the long-tail. Of particular note as promising Effective Altruist careers, we would highlight working directly to develop remedies for specific, extremely painful experiences. Finding scalable

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