What Makes Tinnitus, Depression, and the Sound of the Bay Area Rapid Transit (BART) so Awful: Dissonance

The Bay Area Rapid Transit (BART) is often criticized for its loudness. According to measurements made in 2010, the noise reaches up to 100 decibels, enough to cause permanent hearing loss in the long term. This is why you should always wear earplugs on the BART, which can decrease the volume by up to 30 or so decibels, making it tolerable and harmless.

And while pointing out that BART gets really loud is indeed important, I would claim that there is something even more important to note. Namely, that BART is not merely loud, but it is also distinctly dissonant. Talking only about the stretch that goes from Millbrae to Embarcadero, an analysis I conducted reveals that the single worst period of dissonance happens on the ride from Glen Park to Balboa Park (at around the 20 second mark after one starts). If you are curious to hear it, you can check it out for yourself here. That said, I do not recommend listening to that track on repeat for any length of time, as it may have a strong mood-diminishing effect.

Too bad that some of the beautiful patterns found at the entrance of the Balboa Park BART station are not equally matched by beautiful sounds in the actual ride:

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Balboa Park has some beautiful visual patterns (useful for psychophysics).

Ultimately, dissonance might be much more important than loudness, insofar as it tracks the degree to which environmental sound directly impacts quality of life. Thus, in addition to metrics that track how loud cities are, it might be a good addition to our sound contamination measurements to incorporate a sort of “dissonance index” into our calculations.

A General Framework for Valence

At the Qualia Research Institute we have pointed that the connection between dissonance and valence may not be incidental. In particular, we suggest that it falls out as a possible implication of the Symmetry Theory of Valence (STV). The STV is itself a special case of the general principle we call Valence Structuralism, which claims that the degree to which an experience feels good or bad is a consequence of the structures of the object whose mathematical properties are isomorphic to a system’s phenomenology. The STV goes one step further and suggests that the relevant mathematical property that denotes valence is the symmetry of this object.

valence_structuralism

In Quantifying Bliss, we postulated that a general framework for describing the valence of an experience could be constructed in terms of Consonance-Dissonance-Noise Signatures (“CDNS” for short). That is, the degree to which the given states have consonance, dissonance, and noise in them. As an implication of the Symmetry Theory of Valence we postulate that consonance will directly track positive valence, dissonance negative valence, and noise neutral valence. But wait, there is more! Each of these “channels” themselves have a spectrum. That is to say, one could be experiencing high degrees of low-frequency-dissonance at the same time as high-frequency-consonance and maybe a general full-spectrum background noise. Any combination is possible.

The Quantifying Bliss article describes how recent advancements in neuroscience might be useful to quantify people’s CDNS (namely, using the pair-wise interactions between people’s connectome-specific harmonics).

Many Heads But Just One Body

Richard Wu has a good article on his experience with tinnitus. One of the things that stands out about it is the level of detail used to describe his tinnitus. At its worst, he says, he does not only experience a single sound, but several kinds at once:

By the way, its getting louder isn’t even the worst. Sometimes I develop an entirely new tinnitus. […] Today, I have three:

  1. A very high-pitched CRT monitor / TV-like screech (similar to the one in the video).
  2. A deep, low, powerful rumbling.
  3. A mid-tone that adjusts its volume based on external sounds. If my environment is loud, it will be loud; if my environment is quiet, it will ring more softly.

As in the case of the BART and how people complain about how loud it is while missing the most important piece (its dissonance), tinnitus may have a similar reporting problem. What makes tinnitus so unbearable might not be so much the fact that there is always a hallucinated sound present, but rather, that such a sound (or clusters of sounds) is so unpleasant, distracting, and oppressive. The actual texture of tinnitus may be just as, if not more, important than its mere presence.

We believe that Valence Structuralism and in particular the Symmetry Theory of Valence are powerful explanatory frameworks that can tie together a wide range of disparate phenomena concerning good and bad feelings. And if true, then for every unpleasant experience we may have, a reasonable thing to ask might be: in what way is this dissonant? For example: Depression may be a sort of whole-body low-frequency dissonance (similar to, but different in texture, to nausea). Anxiety, on the other hand, along with irritation and anger, might be a manifestation of high-frequency dissonance.

Likewise, whenever a good or pleasant feeling is found, a reasonable question to ask is: in what ways is this consonant? Let’s think about the three kinds of euphoria uncovered in State-Space of Drug Effects. Fast euphoria (stimulants, exercise, anticipation, etc.) might be what high-frequency consonance feels like. Slow euphoria (relaxation, opioids, etc.) might be what low-frequency consonance feels like. And what about spiritual euphoria (what you get by thinking about philosophy, tripping, and taking dissociatives)? Well, however trippy this may sound, it might well be that this is a sort of fractal consonance, in which multiple representations of various spatio-temporal resolutions become interlocked in a pleasant dance (which may, or may not, allow you to process information more efficiently).

Now what about noise? Here is where we place all of the blunting agents. The general explanation for why anti-depressants of the SSRI variety tend to blunt feelings might be because their very mechanism of action is to increase neuronal noise and thus reduce the signal-to-noise ratio. Crying, orgasm, joy, and ragegasms all share the quality of being highly symmetric harmonic states, and SSRIs having a generalized effect of adding noise to one’s neuronal environment would be expected to diminish the intensity (and textural orderliness) of each of these states. We also know that SSRIs are often capable of reducing the subjective intensity of tinnitus (and presumably the awfulness of BART sounds), which makes sense in this framework.

The STV would also explain MDMA’s effects as a generalized reduction in both dissonance and noise across the full spectrum, and a generalized increase in consonance, also across the full spectrum. This would clarify the missing link to explain why MDMA would be a potential tool to reduce tinnitus, not just emotional pain. The trick is that both perceptual dissonance and negative affect may have a common underlying quality: anti-symmetry. And MDMA being a chief symmetrifying agent takes it all away.

Many further questions remain: what makes meaningful experiences so emotionally rich? Why do some people enjoy weird sounds? Why is emo music so noisy? What kind of valence can be experienced when one’s consciousness has acquired a hyperbolic geometry? I will address these and many other interesting questions in future posts. Stay tuned!

Mental Health as an EA Cause: Key Questions

Michale Johnosn and I will be hanging out at the EA Global (SF) 2017 conference this weekend representing the Qualia Research Institute. If you see us and want to chat, please feel free to approach us. This is what we look like:

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At EAGlobal 2016 at Berkeley

I will be handing out the following flyer:


Mental Health as an EA Cause Area: Key Questions

  1. What makes a state of consciousness feel good or bad?
  2. What percentage of worldwide suffering is directly caused by mental illness and/or the hedonic treadmill rather than by external circumstances?
  3. Is there a way to “sabotage the hedonic treadmill”?
  4. Can benevolent and intelligent sentient beings be fully animated by gradients of bliss (offloading nociception to insentient mechanism)?
  5. Can we uproot the fundamental causes of suffering by tweaking our brain structure without compromising our critical thinking?
  6. Can consciousness technologies play a part in making the world a high-trust super-organism?

symmetries

Wallpaper symmetry chart with 5 different notations (slightly different diagram in handout)

If these questions intrigue you, you are likely to find the following readings valuable:

  1. Principia Qualia
  2. Qualia Computing So Far
  3. Quantifying Bliss: Talk Summary
  4. The Tyranny of the Intentional Object
  5. Algorithmic Reduction of Psychedelic States
  6. How to secretly communicate with people on LSD
  7. ELI5 “The Hyperbolic Geometry of DMT Experiences”
  8. Peaceful Qualia: The Manhattan Project of Consciousness
  9. Symmetry Theory of Valence “Explain Like I’m 5” edition
  10. Generalized Wada Test and the Total Order of Consciousness
  11. Wireheading Done Right: Stay Positive Without Going Insane
  12. Why we seek out pleasure: the Symmetry Theory of Homeostatic Regulation
  13. The Hyperbolic Geometry of DMT Experiences: Symmetries, Sheets, and Saddled Scenes

Who we are:
Qualia Research Institute (Michael Johnson & Andrés Gómez Emilsson)
Qualia Computing (this website; Andrés Gómez Emilsson)
Open Theory (Michael Johnson)

Printable version:

mental_health_as_ea_cause

Why I think the Foundational Research Institute should rethink its approach

by Mike Johnson

The following is my considered evaluation of the Foundational Research Institute, circa July 2017. I discuss its goal, where I foresee things going wrong with how it defines suffering, and what it could do to avoid these problems.

TL;DR version: functionalism (“consciousness is the sum-total of the functional properties of our brains”) sounds a lot better than it actually turns out to be in practice. In particular, functionalism makes it impossible to define ethics & suffering in a way that can mediate disagreements.

I. What is the Foundational Research Institute?

The Foundational Research Institute (FRI) is a Berlin-based group that “conducts research on how to best reduce the suffering of sentient beings in the near and far future.” Executive Director Max Daniel introduced them at EA Global Boston as “the only EA organization which at an organizational level has the mission of focusing on reducing s-risk.” S-risks are, according to Daniel, “risks where an adverse outcome would bring about suffering on an astronomical scale, vastly exceeding all suffering that has existed on Earth so far.”

Essentially, FRI wants to become the research arm of suffering-focused ethics, and help prevent artificial general intelligence (AGI) failure-modes which might produce suffering on a cosmic scale.

What I like about FRI:

While I have serious qualms about FRI’s research framework, I think the people behind FRI deserve a lot of credit- they seem to be serious people, working hard to build something good. In particular, I want to give them a shoutout for three things:

  • First, FRI takes suffering seriously, and I think that’s important. When times are good, we tend to forget how tongue-chewingly horrific suffering can be. S-risks seem particularly horrifying.
  • Second, FRI isn’t afraid of being weird. FRI has been working on s-risk research for a few years now, and if people are starting to come around to the idea that s-risks are worth thinking about, much of the credit goes to FRI.
  • Third, I have great personal respect for Brian Tomasik, one of FRI’s co-founders. I’ve found him highly thoughtful, generous in debates, and unfailingly principled. In particular, he’s always willing to bite the bullet and work ideas out to their logical end, even if it involves repugnant conclusions.

What is FRI’s research framework?

FRI believes in analytic functionalism, or what David Chalmers calls “Type-A materialism”. Essentially, what this means is there’s no ’theoretical essence’ to consciousness; rather, consciousness is the sum-total of the functional properties of our brains. Since ‘functional properties’ are rather vague, this means consciousness itself is rather vague, in the same way words like “life,” “justice,” and “virtue” are messy and vague.

Brian suggests that this vagueness means there’s an inherently subjective, perhaps arbitrary element to how we define consciousness:

Analytic functionalism looks for functional processes in the brain that roughly capture what we mean by words like “awareness”, “happy”, etc., in a similar way as a biologist may look for precise properties of replicators that roughly capture what we mean by “life”. Just as there can be room for fuzziness about where exactly to draw the boundaries around “life”, different analytic functionalists may have different opinions about where to define the boundaries of “consciousness” and other mental states. This is why consciousness is “up to us to define”. There’s no hard problem of consciousness for the same reason there’s no hard problem of life: consciousness is just a high-level word that we use to refer to lots of detailed processes, and it doesn’t mean anything in addition to those processes.

Finally, Brian argues that the phenomenology of consciousness is identical with the phenomenology of computation:

I know that I’m conscious. I also know, from neuroscience combined with Occam’s razor, that my consciousness consists only of material operations in my brain — probably mostly patterns of neuronal firing that help process inputs, compute intermediate ideas, and produce behavioral outputs. Thus, I can see that consciousness is just the first-person view of certain kinds of computations — as Eliezer Yudkowsky puts it, “How An Algorithm Feels From Inside“. Consciousness is not something separate from or epiphenomenal to these computations. It is these computations, just from their own perspective of trying to think about themselves.

 

In other words, consciousness is what minds compute. Consciousness is the collection of input operations, intermediate processing, and output behaviors that an entity performs.

And if consciousness is all these things, so too is suffering. Which means suffering is computational, yet also inherently fuzzy, and at least a bit arbitrary; a leaky high-level reification impossible to speak about accurately, since there’s no formal, objective “ground truth”.

II. Why do I worry about FRI’s research framework?

In short, I think FRI has a worthy goal and good people, but its metaphysics actively prevent making progress toward that goal. The following describes why I think that, drawing heavily on Brian’s writings (of FRI’s researchers, Brian seems the most focused on metaphysics):

Note: FRI is not the only EA organization which holds functionalist views on consciousness; much of the following critique would also apply to e.g. MIRI, FHI, and OpenPhil. I focus on FRI because (1) Brian’s writings on consciousness & functionalism have been hugely influential in the community, and are clear enough *to* criticize; (2) the fact that FRI is particularly clear about what it cares about- suffering- allows a particularly clear critique about what problems it will run into with functionalism; (3) I believe FRI is at the forefront of an important cause area which has not crystallized yet, and I think it’s critically important to get these objections bouncing around this subcommunity.

Objection 1: Motte-and-bailey

Brian: “Consciousness is not a thing which exists ‘out there’ or even a separate property of matter; it’s a definitional category into which we classify minds. ‘Is this digital mind really conscious?’ is analogous to ‘Is a rock that people use to eat on really a table?’ [However,] That consciousness is a cluster in thingspace rather than a concrete property of the world does not make reducing suffering less important.”

The FRI model seems to imply that suffering is ineffable enough such that we can’t have an objective definition, yet sufficiently effable that we can coherently talk and care about it. This attempt to have it both ways seems contradictory, or at least in deep tension.

Indeed, I’d argue that the degree to which you can care about something is proportional to the degree to which you can define it objectively. E.g., If I say that “gnireffus” is literally the most terrible thing in the cosmos, that we should spread gnireffus-focused ethics, and that minimizing g-risks (far-future scenarios which involve large amounts of gnireffus) is a moral imperative, but also that what is and what and isn’t gnireffus is rather subjective with no privileged definition, and it’s impossible to objectively tell if a physical system exhibits gnireffus, you might raise any number of objections. This is not an exact metaphor for FRI’s position, but I worry that FRI’s work leans on the intuition that suffering is real and we can speak coherently about it, to a degree greater than its metaphysics formally allow.

Max Daniel (personal communication) suggests that we’re comfortable with a degree of ineffability in other contexts; “Brian claims that the concept of suffering shares the allegedly problematic properties with the concept of a table. But it seems a stretch to say that the alleged tension is problematic when talking about tables. So why would it be problematic when talking about suffering?” However, if we take the anti-realist view that suffering is ‘merely’ a node in the network of language, we have to live with the consequences of this: that ‘suffering’ will lose meaning as we take it away from the network in which it’s embedded (Wittgenstein). But FRI wants to do exactly this, to speak about suffering in the context of AGIs, simulated brains, even video game characters.

We can be anti-realists about suffering (suffering-is-a-node-in-the-network-of-language), or we can argue that we can talk coherently about suffering in novel contexts (AGIs, mind crime, aliens, and so on), but it seems inherently troublesome to claim we can do both at the same time.

Objection 2: Intuition duels

Two people can agree on FRI’s position that there is no objective fact of the matter about what suffering is (no privileged definition), but this also means they have no way of coming to any consensus on the object-level question of whether something can suffer. This isn’t just an academic point: Brian has written extensively about how he believes non-human animals can and do suffer extensively, whereas Yudkowsky (who holds computationalist views, like Brian) has written about how he’s confident that animals are not conscious and cannot suffer, due to their lack of higher-order reasoning.

And if functionalism is having trouble adjudicating the easy cases of suffering–whether monkeys can suffer, or whether dogs can— it doesn’t have a sliver of a chance at dealing with the upcoming hard cases of suffering: whether a given AGI is suffering, or engaging in mind crime; whether a whole-brain emulation (WBE) or synthetic organism or emergent intelligence that doesn’t have the capacity to tell us how it feels (or that we don’t have the capacity to understand) is suffering; if any aliens that we meet in the future can suffer; whether changing the internal architecture of our qualia reports means we’re also changing our qualia; and so on.

In short, FRI’s theory of consciousness isn’t actually a theory of consciousness at all, since it doesn’t do the thing we need a theory of consciousness to do: adjudicate disagreements in a principled way. Instead, it gives up any claim on the sorts of objective facts which could in principle adjudicate disagreements.

This is a source of friction in EA today, but it’s mitigated by the sense that

(1) The EA pie is growing, so it’s better to ignore disagreements than pick fights;

(2) Disagreements over the definition of suffering don’t really matter yet, since we haven’t gotten into the business of making morally-relevant synthetic beings (that we know of) that might be unable to vocalize their suffering.

If the perception of one or both of these conditions change, the lack of some disagreement-adjudicating theory of suffering will matter quite a lot.

Objection 3: Convergence requires common truth

Mike: “[W]hat makes one definition of consciousness better than another? How should we evaluate them?”

Brian: “Consilience among our feelings of empathy, principles of non-discrimination, understandings of cognitive science, etc. It’s similar to the question of what makes one definition of justice or virtue better than another.”

Brian is hoping that affective neuroscience will slowly converge to accurate views on suffering as more and better data about sentience and pain accumulates. But convergence to truth implies something (objective) driving the convergence- in this way, Brian’s framework still seems to require an objective truth of the matter, even though he disclaims most of the benefits of assuming this.

Objection 4: Assuming that consciousness is a reification produces more confusion, not less

Brian: “Consciousness is not a reified thing; it’s not a physical property of the universe that just exists intrinsically. Rather, instances of consciousness are algorithms that are implemented in specific steps. … Consciousness involves specific things that brains do.”

Brian argues that we treat conscious/phenomenology as more ‘real’ than it is. Traditionally, whenever we’ve discovered something is a leaky reification and shouldn’t be treated as ‘too real’, we’ve been able to break it down into more coherent constituent pieces we can treat as real. Life, for instance, wasn’t due to élan vital but a bundle of self-organizing properties & dynamics which generally co-occur. But carrying out this “de-reification” process on consciousness– enumerating its coherent constituent pieces– has proven difficult, especially if we want to preserve some way to speak cogently about suffering.

Speaking for myself, the more I stared into the depths of functionalism, the less certain everything about moral value became– and arguably, I see the same trajectory in Brian’s work and Luke Muehlhauser’s report. Their model uncertainty has seemingly become larger as they’ve looked into techniques for how to “de-reify” consciousness while preserving some flavor of moral value, not smaller. Brian and Luke seem to interpret this as evidence that moral value is intractably complicated, but this is also consistent with consciousness not being a reification, and instead being a real thing. Trying to “de-reify” something that’s not a reification will produce deep confusion, just as surely trying to treat a reification as ‘more real’ than it actually is will.

Edsger W. Dijkstra famously noted that “The purpose of abstraction is not to be vague, but to create a new semantic level in which one can be absolutely precise.” And so if our ways of talking about moral value fail to ‘carve reality at the joints’- then by all means let’s build better ones, rather than giving up on precision.

Objection 5: The Hard Problem of Consciousness is a red herring

Brian spends a lot of time discussing Chalmers’ “Hard Problem of Consciousness”, i.e. the question of why we’re subjectively conscious, and seems to base at least part of his conclusion on not finding this question compelling— he suggests “There’s no hard problem of consciousness for the same reason there’s no hard problem of life: consciousness is just a high-level word that we use to refer to lots of detailed processes, and it doesn’t mean anything in addition to those processes.” I.e., no ‘why’ is necessary; when we take consciousness and subtract out the details of the brain, we’re left with an empty set.

But I think the “Hard Problem” isn’t helpful as a contrastive centerpiece, since it’s unclear what the problem is, and whether it’s analytic or empirical, a statement about cognition or about physics. At the Qualia Research Institute (QRI), we don’t talk much about the Hard Problem; instead, we talk about Qualia Formalism, or the idea that any phenomenological state can be crisply and precisely represented by some mathematical object. I suspect this would be a better foil for Brian’s work than the Hard Problem.

Objection 6: Mapping to reality

Brian argues that consciousness should be defined at the functional/computational level: given a Turing machine, or neural network, the right ‘code’ will produce consciousness. But the problem is that this doesn’t lead to a theory which can ‘compile’ to physics. Consider the following:

Imagine you have a bag of popcorn. Now shake it. There will exist a certain ad-hoc interpretation of bag-of-popcorn-as-computational-system where you just simulated someone getting tortured, and other interpretations that don’t imply that. Did you torture anyone? If you’re a computationalist, no clear answer exists- you both did, and did not, torture someone. This sounds like a ridiculous edge-case that would never come up in real life, but in reality it comes up all the time, since there is no principled way to *objectively derive* what computation(s) any physical system is performing.

I don’t think this is an outlandish view of functionalism; Brian suggests much the same in How to Interpret a Physical System as a Mind“Physicalist views that directly map from physics to moral value are relatively simple to understand. Functionalism is more complex, because it maps from physics to computations to moral value. Moreover, while physics is real and objective, computations are fictional and ‘observer-relative’ (to use John Searle’s terminology). There’s no objective meaning to ‘the computation that this physical system is implementing’ (unless you’re referring to the specific equations of physics that the system is playing out).”

Gordon McCabe (McCabe 2004) provides a more formal argument to this effect— that precisely mapping between physical processes and (Turing-level) computational processes is inherently impossible— in the context of simulations. First, McCabe notes that:

[T]here is a one-[to-]many correspondence between the logical states [of a computer] and the exact electronic states of computer memory. Although there are bijective mappings between numbers and the logical states of computer memory, there are no bijective mappings between numbers and the exact electronic states of memory.

This lack of an exact bijective mapping means that subjective interpretation necessarily creeps in, and so a computational simulation of a physical system can’t be ‘about’ that system in any rigorous way:

In a computer simulation, the values of the physical quantities possessed by the simulated system are represented by the combined states of multiple bits in computer memory. However, the combined states of multiple bits in computer memory only represent numbers because they are deemed to do so under a numeric interpretation. There are many different interpretations of the combined states of multiple bits in computer memory. If the numbers represented by a digital computer are interpretation-dependent, they cannot be objective physical properties. Hence, there can be no objective relationship between the changing pattern of multiple bit-states in computer memory, and the changing pattern of quantity-values of a simulated physical system.

McCabe concludes that, metaphysically speaking,

A digital computer simulation of a physical system cannot exist as, (does not possess the properties and relationships of), anything else other than a physical process occurring upon the components of a computer. In the contemporary case of an electronic digital computer, a simulation cannot exist as anything else other than an electronic physical process occurring upon the components and circuitry of a computer.

Where does this leave ethics? In Flavors of Computation Are Flavors of Consciousness, Brian notes that “In some sense all I’ve proposed here is to think of different flavors of computation as being various flavors of consciousness. But this still leaves the question: Which flavors of computation matter most? Clearly whatever computations happen when a person is in pain are vastly more important than what’s happening in a brain on a lazy afternoon. How can we capture that difference?”

But if Brian grants the former point- that “There’s no objective meaning to ‘the computation that this physical system is implementing’”– then this latter task of figuring out “which flavors of computation matter most” is provably impossible. There will always be multiple computational (and thus ethical) interpretations of a physical system, with no way to figure out what’s “really” happening. No way to figure out if something is suffering or not. No consilience; not now, not ever.

Note: despite apparently granting the point above, Brian also remarks that:

I should add a note on terminology: All computations occur within physics, so any computation is a physical process. Conversely, any physical process proceeds from input conditions to output conditions in a regular manner and so is a computation. Hence, the set of computations equals the set of physical processes, and where I say “computations” in this piece, one could just as well substitute “physical processes” instead.

This seems to be (1) incorrect, for the reasons I give above, or (2) taking substantial poetic license with these terms, or (3) referring to hypercomputation (which might be able to salvage the metaphor, but would invalidate many of FRI’s conclusions dealing with the computability of suffering on conventional hardware).

This objection may seem esoteric or pedantic, but I think it’s important, and that it ripples through FRI’s theoretical framework with disastrous effects.

 

Objection 7: FRI doesn’t fully bite the bullet on computationalism

Brian suggests that “flavors of computation are flavors of consciousness” and that some computations ‘code’ for suffering. But if we do in fact bite the bullet on this metaphor and place suffering within the realm of computational theory, we need to think in “near mode” and accept all the paradoxes that brings. Scott Aaronson, a noted expert on quantum computing, raises the following objections to functionalism:

I’m guessing that many people in this room side with Dennett, and (not coincidentally, I’d say) also with Everett. I certainly have sympathies in that direction too. In fact, I spent seven or eight years of my life as a Dennett/Everett hardcore believer. But, while I don’t want to talk anyone out of the Dennett/Everett view, I’d like to take you on a tour of what I see as some of the extremely interesting questions that that view leaves unanswered. I’m not talking about “deep questions of meaning,” but about something much more straightforward: what exactly does a computational process have to do to qualify as “conscious”?

 

 

There’s this old chestnut, what if each person on earth simulated one neuron of your brain, by passing pieces of paper around. It took them several years just to simulate a single second of your thought processes. Would that bring your subjectivity into being? Would you accept it as a replacement for your current body? If so, then what if your brain were simulated, not neuron-by-neuron, but by a gigantic lookup table? That is, what if there were a huge database, much larger than the observable universe (but let’s not worry about that), that hardwired what your brain’s response was to every sequence of stimuli that your sense-organs could possibly receive. Would that bring about your consciousness? Let’s keep pushing: if it would, would it make a difference if anyone actually consulted the lookup table? Why can’t it bring about your consciousness just by sitting there doing nothing?

To these standard thought experiments, we can add more. Let’s suppose that, purely for error-correction purposes, the computer that’s simulating your brain runs the code three times, and takes the majority vote of the outcomes. Would that bring three “copies” of your consciousness into being? Does it make a difference if the three copies are widely separated in space or time—say, on different planets, or in different centuries? Is it possible that the massive redundancy taking place in your brain right now is bringing multiple copies of you into being?

 

 

Maybe my favorite thought experiment along these lines was invented by my former student Andy Drucker.  In the past five years, there’s been a revolution in theoretical cryptography, around something called Fully Homomorphic Encryption (FHE), which was first discovered by Craig Gentry.  What FHE lets you do is to perform arbitrary computations on encrypted data, without ever decrypting the data at any point.  So, to someone with the decryption key, you could be proving theorems, simulating planetary motions, etc.  But to someone without the key, it looks for all the world like you’re just shuffling random strings and producing other random strings as output.

 

You can probably see where this is going.  What if we homomorphically encrypted a simulation of your brain?  And what if we hid the only copy of the decryption key, let’s say in another galaxy?  Would this computation—which looks to anyone in our galaxy like a reshuffling of gobbledygook—be silently producing your consciousness?

 

When we consider the possibility of a conscious quantum computer, in some sense we inherit all the previous puzzles about conscious classical computers, but then also add a few new ones.  So, let’s say I run a quantum subroutine that simulates your brain, by applying some unitary transformation U.  But then, of course, I want to “uncompute” to get rid of garbage (and thereby enable interference between different branches), so I apply U-1.  Question: when I apply U-1, does your simulated brain experience the same thoughts and feelings a second time?  Is the second experience “the same as” the first, or does it differ somehow, by virtue of being reversed in time? Or, since U-1U is just a convoluted implementation of the identity function, are there no experiences at all here?

 

Here’s a better one: many of you have heard of the Vaidman bomb.  This is a famous thought experiment in quantum mechanics where there’s a package, and we’d like to “query” it to find out whether it contains a bomb—but if we query it and there is a bomb, it will explode, killing everyone in the room.  What’s the solution?  Well, suppose we could go into a superposition of querying the bomb and not querying it, with only ε amplitude on querying the bomb, and √(1-ε2) amplitude on not querying it.  And suppose we repeat this over and over—each time, moving ε amplitude onto the “query the bomb” state if there’s no bomb there, but moving ε2 probability onto the “query the bomb” state if there is a bomb (since the explosion decoheres the superposition).  Then after 1/ε repetitions, we’ll have order 1 probability of being in the “query the bomb” state if there’s no bomb.  By contrast, if there is a bomb, then the total probability we’ve ever entered that state is (1/ε)×ε2 = ε.  So, either way, we learn whether there’s a bomb, and the probability that we set the bomb off can be made arbitrarily small.  (Incidentally, this is extremely closely related to how Grover’s algorithm works.)

 

OK, now how about the Vaidman brain?  We’ve got a quantum subroutine simulating your brain, and we want to ask it a yes-or-no question.  We do so by querying that subroutine with ε amplitude 1/ε times, in such a way that if your answer is “yes,” then we’ve only ever activated the subroutine with total probability ε.  Yet you still manage to communicate your “yes” answer to the outside world.  So, should we say that you were conscious only in the ε fraction of the wavefunction where the simulation happened, or that the entire system was conscious?  (The answer could matter a lot for anthropic purposes.)

To sum up: Brian’s notion that consciousness is the same as computation raises more issues than it solves; in particular, the possibility that if suffering is computable, it may also be uncomputable/reversible, would suggest s-risks aren’t as serious as FRI treats them.

Objection 8: Dangerous combination

Three themes which seem to permeate FRI’s research are:

(1) Suffering is the thing that is bad.

(2) It’s critically important to eliminate badness from the universe.

(3) Suffering is impossible to define objectively, and so we each must define what suffering means for ourselves.

Taken individually, each of these seems reasonable. Pick two, and you’re still okay. Pick all three, though, and you get A Fully General Justification For Anything, based on what is ultimately a subjective/aesthetic call.

Much can be said in FRI’s defense here, and it’s unfair to single them out as risky: in my experience they’ve always brought a very thoughtful, measured, cooperative approach to the table. I would just note that ideas are powerful, and I think theme (3) is especially pernicious if incorrect.

III. QRI’s alternative

Analytic functionalism is essentially a negative hypothesis about consciousness: it’s the argument that there’s no order to be found, no rigor to be had. It obscures this with talk of “function”, which is a red herring it not only doesn’t define, but admits is undefinable. It doesn’t make any positive assertion. Functionalism is skepticism- nothing more, nothing less.

But is it right?

Ultimately, I think these a priori arguments are much like people in the middle ages arguing whether one could ever formalize a Proper System of Alchemy. Such arguments may in many cases hold water, but it’s often difficult to tell good arguments apart from arguments where we’re just cleverly fooling ourselves. In retrospect, the best way to *prove* systematized alchemy was possible was to just go out and *do* it, and invent Chemistry. That’s how I see what we’re doing at QRI with Qualia Formalism: we’re assuming it’s possible to build stuff, and we’re working on building the object-level stuff.

What we’ve built with QRI’s framework

Note: this is a brief, surface-level tour of our research; it will probably be confusing for readers who haven’t dug into our stuff before. Consider this a down-payment on a more substantial introduction.

My most notable work is Principia Qualia, in which I lay out my meta-framework for consciousness (a flavor of dual-aspect monism, with a focus on Qualia Formalism) and put forth the Symmetry Theory of Valence (STV). Essentially, the STV is an argument that much of the apparent complexity of emotional valence is evolutionarily contingent, and if we consider a mathematical object isomorphic to a phenomenological experience, the mathematical property which corresponds to how pleasant it is to be that experience is the object’s symmetry. This implies a bunch of testable predictions and reinterpretations of things like what ‘pleasure centers’ do (Section XI; Section XII). Building on this, I offer the Symmetry Theory of Homeostatic Regulation, which suggests understanding the structure of qualia will translate into knowledge about the structure of human intelligence, and I briefly touch on the idea of Neuroacoustics.

Likewise, my colleague Andrés Gómez Emilsson has written about the likely mathematics of phenomenology, including The Hyperbolic Geometry of DMT Experiences, Tyranny of the Intentional Object, and Algorithmic Reduction of Psychedelic States. If I had to suggest one thing to read in all of these links, though, it would be the transcript of his recent talk on Quantifying Bliss, which lays out the world’s first method to objectively measure valence from first principles (via fMRI) using Selen Atasoy’s Connectome Harmonics framework, the Symmetry Theory of Valence, and Andrés’s CDNS model of experience.

These are risky predictions and we don’t yet know if they’re right, but we’re confident that if there is some elegant structure intrinsic to consciousness, as there is in many other parts of the natural world, these are the right kind of risks to take.

I mention all this because I think analytic functionalism- which is to say radical skepticism/eliminativism, the metaphysics of last resort- only looks as good as it does because nobody’s been building out any alternatives.

IV. Closing thoughts

FRI is pursuing a certain research agenda, and QRI is pursuing another, and there’s lots of value in independent explorations of the nature of suffering. I’m glad FRI exists, everybody I’ve interacted with at FRI has been great, I’m happy they’re focusing on s-risks, and I look forward to seeing what they produce in the future.

On the other hand, I worry that nobody’s pushing back on FRI’s metaphysics, which seem to unavoidably lead to the intractable problems I describe above. FRI seems to believe these problems are part of the territory, unavoidable messes that we just have to make philosophical peace with. But I think that functionalism is a bad map, that the metaphysical messes it leads to are much worse than most people realize (fatal to FRI’s mission), and there are other options that avoid these problems (which, to be fair, is not to say they have no problems).

Ultimately, FRI doesn’t owe me a defense of their position. But if they’re open to suggestions on what it would take to convince a skeptic like me that their brand of functionalism is viable, or at least rescuable, I’d offer the following:

Re: Objection 1 (motte-and-bailey), I suggest FRI should be as clear and complete as possible in their basic definition of suffering. In which particular ways is it ineffable/fuzzy, and in which particular ways is it precise? What can we definitely say about suffering, and what can we definitely never determine? Preregistering ontological commitments and methodological possibilities would help guard against FRI’s definition of suffering changing based on context.

Re: Objection 2 (intuition duels), FRI may want to internally “war game” various future scenarios involving AGI, WBE, etc, with one side arguing that a given synthetic (or even extraterrestrial) organism is suffering, and the other side arguing that it isn’t. I’d expect this would help diagnose what sorts of disagreements future theories of suffering will need to adjudicate, and perhaps illuminate implicit ethical intuitions. Sharing the results of these simulated disagreements would also be helpful in making FRI’s reasoning less opaque to outsiders, although making everything transparent could lead to certain strategic disadvantages.

Re: Objection 3 (convergence requires common truth), I’d like FRI to explore exactly what might drive consilience/convergence in theories of suffering, and what precisely makes one theory of suffering better than another, and ideally to evaluate a range of example theories of suffering under these criteria.

Re: Objection 4 (assuming that consciousness is a reification produces more confusion, not less), I would love to see a historical treatment of reification: lists of reifications which were later dissolved (e.g., élan vital), vs scattered phenomena that were later unified (e.g., electromagnetism). What patterns do the former have, vs the latter, and why might consciousness fit one of these buckets better than the other?

Re: Objection 5 (the Hard Problem of Consciousness is a red herring), I’d like to see a more detailed treatment of what kinds of problem people have interpreted the Hard Problem as, and also more analysis on the prospects of Qualia Formalism (which I think is the maximally-empirical, maximally-charitable interpretation of the Hard Problem). It would be helpful for us, in particular, if FRI preregistered their expectations about QRI’s predictions, and their view of the relative evidence strength of each of our predictions.

Re: Objection 6 (mapping to reality), this is perhaps the heart of most of our disagreement. From Brian’s quotes, he seems split on this issue; I’d like clarification about whether he believes we can ever precisely/objectively map specific computations to specific physical systems, and vice-versa. And if so— how? If not, this seems to propagate through FRI’s ethical framework in a disastrous way, since anyone can argue that any physical system does, or does not, ‘code’ for massive suffering, and there’s no principled way to derive any ‘ground truth’ or even pick between interpretations in a principled way (e.g. my popcorn example). If this isn’t the case— why not?

Brian has suggested that “certain high-level interpretations of physical systems are more ‘natural’ and useful than others” (personal communication); I agree, and would encourage FRI to explore systematizing this.

It would be non-trivial to port FRI’s theories and computational intuitions to the framework of “hypercomputation”– i.e., the understanding that there’s a formal hierarchy of computational systems, and that Turing machines are only one level of many– but it may have benefits too. Namely, it might be the only way they could avoid Objection 6 (which I think is a fatal objection) while still allowing them to speak about computation & consciousness in the same breath. I think FRI should look at this and see if it makes sense to them.

Re: Objection 7 (FRI doesn’t fully bite the bullet on computationalism), I’d like to see responses to Aaronson’s aforementioned thought experiments.

Re: Objection 8 (dangerous combination), I’d like to see a clarification about why my interpretation is unreasonable (as it very well may be!).

 


In conclusion- I think FRI has a critically important goal- reduction of suffering & s-risk. However, I also think FRI has painted itself into a corner by explicitly disallowing a clear, disagreement-mediating definition for what these things are. I look forward to further work in this field.

 

Mike Johnson

Qualia Research Institute


Acknowledgements: thanks to Andrés Gómez Emilsson, Brian Tomasik, and Max Daniel for reviewing earlier drafts of this.

Sources:

My sources for FRI’s views on consciousness:
Flavors of Computation are Flavors of Consciousness:
https://foundational-research.org/flavors-of-computation-are-flavors-of-consciousness/
Is There a Hard Problem of Consciousness?
http://reducing-suffering.org/hard-problem-consciousness/
Consciousness Is a Process, Not a Moment
http://reducing-suffering.org/consciousness-is-a-process-not-a-moment/
How to Interpret a Physical System as a Mind
http://reducing-suffering.org/interpret-physical-system-mind/
Dissolving Confusion about Consciousness
http://reducing-suffering.org/dissolving-confusion-about-consciousness/
Debate between Brian & Mike on consciousness:
https://www.facebook.com/groups/effective.altruists/permalink/1333798200009867/?comment_id=1333823816673972&comment_tracking=%7B%22tn%22%3A%22R9%22%7D
Max Daniel’s EA Global Boston 2017 talk on s-risks:
https://www.youtube.com/watch?v=jiZxEJcFExc
Multipolar debate between Eliezer Yudkowsky and various rationalists about animal suffering:
https://rationalconspiracy.com/2015/12/16/a-debate-on-animal-consciousness/
The Internet Encyclopedia of Philosophy on functionalism:
http://www.iep.utm.edu/functism/
Gordon McCabe on why computation doesn’t map to physics:
http://philsci-archive.pitt.edu/1891/1/UniverseCreationComputer.pdf
Toby Ord on hypercomputation, and how it differs from Turing’s work:
https://arxiv.org/abs/math/0209332
Luke Muehlhauser’s OpenPhil-funded report on consciousness and moral patienthood:
http://www.openphilanthropy.org/2017-report-consciousness-and-moral-patienthood
Scott Aaronson’s thought experiments on computationalism:
http://www.scottaaronson.com/blog/?p=1951
Selen Atasoy on Connectome Harmonics, a new way to understand brain activity:
https://www.nature.com/articles/ncomms10340
My work on formalizing phenomenology:
My meta-framework for consciousness, including the Symmetry Theory of Valence:
http://opentheory.net/PrincipiaQualia.pdf
My hypothesis of homeostatic regulation, which touches on why we seek out pleasure:
http://opentheory.net/2017/05/why-we-seek-out-pleasure-the-symmetry-theory-of-homeostatic-regulation/
My exploration & parametrization of the ‘neuroacoustics’ metaphor suggested by Atasoy’s work:
http://opentheory.net/2017/06/taking-brain-waves-seriously-neuroacoustics/
My colleague Andrés’s work on formalizing phenomenology:
A model of DMT-trip-as-hyperbolic-experience:
https://qualiacomputing.com/2017/05/28/eli5-the-hyperbolic-geometry-of-dmt-experiences/
June 2017 talk at Consciousness Hacking, describing a theory and experiment to predict people’s valence from fMRI data:
https://qualiacomputing.com/2017/06/18/quantifying-bliss-talk-summary/
A parametrization of various psychedelic states as operators in qualia space:
https://qualiacomputing.com/2016/06/20/algorithmic-reduction-of-psychedelic-states/
A brief post on valence and the fundamental attribution error:
https://qualiacomputing.com/2016/11/19/the-tyranny-of-the-intentional-object/
A summary of some of Selen Atasoy’s current work on Connectome Harmonics:
https://qualiacomputing.com/2017/06/18/connectome-specific-harmonic-waves-on-lsd/

Quantifying Bliss: Talk Summary

Below I provide a summary of the Quantifying Bliss talk at Consciousness Hacking (video360 degree live feed record), which took place on June 7th 2017. I am currently working on a longer and more precise treatment of the topic, which I will be posting here as well. That said, since the talk already makes clear, empirically testable predictions, I decided to publish this summary as soon as possible. After all, there is only a small window of opportunity to publish one’s testable predictions online before the experiment is run and they turn into “retrodictions”. By writing this out and archiving it on time I’m enabling future-me to say “called it!” (if the results are positive) or “at least I tried” (if the experiment fails to show the predicted effects). Better do this quick, then, for science!

The Purpose of Life

We begin by asking the question “what is the purpose of life?”. In order to give a sense for where I am coming from, I explain that I think that the purpose of life is…

  1. To Understand the Universe
  2. To be Happy, and Make Others Happy

I admit that for the first half of my life I thought that the only purpose of life was to understand the universe. If anything, in light of this exclusive goal, happiness could be seen as a temporary distraction rather than something to pursue for its own sake. Thankfully, as a teenager I was exposed to philosophy of mind, was introduced to meditation, and experimented with psychedelics, all of which pointed me to the fact that (a) we don’t understand consciousness yet, and (b) happiness is really a lot more important than we usually think, even if one is only concerned with the most theoretical and abstract level of understanding possible.

I now regard “to understand the universe” and “to be happy and make others happy” on an equal footing. More so, these two life goals complement each other. On the one hand, understanding the universe will allow you to figure out how to make anyone happy. And on the other hand, being happy and making others happy can allow you to stay motivated in order to figure out the nature of reality. Hence one can think of these two life goals as synergistic rather than as being in opposing camps (of course, at the edges, one will be forced to choose one over the other, but we are nowhere near the point where this is a concern).

By taking these two “purposes of life” seriously we are then faced with a crucial question: What makes an experience valuable? In other words, for someone who is both trying to understand the universe and trying to make its inhabitants as happy as possible, the question “how do you measure the value of an experience?” becomes important.

At Qualia Computing we generally answer that question using the following criteria

  1. Does it feel good? (happy, loving, pleasant)
  2. Does it make you productive (in a good way)?
  3. Does it make you ethical?

That is to say, the value that we assign to an experience is guided by three criteria. In brief, a valuable experience is one that feels good (i.e. has positive hedonic tone), improves your productivity (in the sense of helping you pursue your own values effectively), and makes you more ethical – both towards yourself and others. That said, for the purpose of this talk, I make it explicit that I will only discuss how to measure (1). In other words, we will concern ourselves with what makes an experience feel good; ethics and productivity are discussed elsewhere.*

What is Bliss?

So what makes an experience feel good? The “feel good” quality of an experience is usually called valence in psychology and neuroscience (also described as the “pleasure-pain axis”). This quality is to be distinguished from arousal, which refers to the amount of energy expressed in an experience. Four examples: Excitement is a high-valence, high-arousal state. Serenity is a high-valence, low-arousal state. Anxiety is low-valence, high-arousal. And depression low-valence, low-arousal.

For some people valence and arousal are correlated (either negatively or positively as shown by Peter Kuppens). Likewise, one’s culture can have a large influence on the way one conceptualizes of valence (or ideal affect, as demonstrated in the extensive work of Jeanne Tsai). That said, valence is not a cultural phenomenon; even mice can experience negative and positive valence.

Even though valence and arousal do seem to explain a big chunk of the differences between emotions, we can nonetheless find many cases where the “texture” of two emotions feel very different even though their valence and their arousal are similar. Hence we ask ourselves: How do we explain and characterize the textural differences between such emotions?

And across all of the possible intensely blissful states on offer (encompassing all of the possible inner meanings present), what exactly is shared between them all at their very core?

Some interpret holistic feelings of wellbeing as a sort of spiritual signal. In this interpretation, feeling at a very deep level that the world is good, that things fall into place perfectly, that you don’t owe anything to anyone, etc. is a sign that you are on the right (spiritual) track. Undoubtedly many people use the (often extreme) positive shift in their valence upon religious conversion as evidence of the validity of their choice. Intense positive valence may not throw Bayesian purists off-balance, but for the rest of the world, blissful experiences are often found as cornerstones of worldviews.

Other people say that bliss is “just chemicals in your brain”. Some claim that it’s more a matter of the functional state of your pleasure centers (themselves affected by dopamine, opioids, etc.) rather than the chemicals themselves. Many others are focused on what usually triggers happiness (e.g. learning, relationships, beliefs, etc.) rather than on what, absolutely, needs to happens for bliss to take place in the simplest experiential terms possible. Most who study this closely become mystics.

Could it be that there’s something structural that makes the experiences feel good? Let’s say that there exists a good-fitting mathematical object that translates brain states to experiences. What mathematical property of that object would valence look like? Our proposal is very simple. In some sense it is the simplest possible theory for the important theory of consciousness. We propose the symmetry theory of valence.

(The important theory of consciousness is the question that asks why experience feels good and/or bad, vs. e.g. the hard problem of consciousness, why consciousness exists to begin with).

The Symmetry Theory of Valence

We are pretty confident that consciousness is a real and a measurable phenomenon. That’s why Consciousness Hacking is such a good venue for this kind of discussion. Because here we can talk freely about the properties of consciousness without getting caught up about whether it exists at all. Now, symmetry is a very general term, how is that precise?

Harmony feels good because it’s symmetry over time. In reality, our moments of experience contain a temporal direction. I call this a pseudo-time arrow, since its direction is likely encoded in the patterns of statistical independence between the qualia experienced. And by manipulating the symmetrical connectivity of the micro-structure of one’s consciousness, one can change the perception of time. It’s a change in the way one evaluates when one is and how fast one is going. 

In this model, the pleasure centers would work as “tuning knobs” of harmonic patterns. They are establishing the mood, the underlying tone to which the rest needs to adapt. And the emotional centers, including the amygdala, would be strategically positioned to add anti-symmetry instead. Hence, in this framework we would think of boredom is an “anti-symmetry” mechanism. It prevents us from getting stuck in shallow ponds, but it can be nasty if left unchecked. Cognitive activity may be in part explained by differences in boredom thresholds.

Connectome-Specific Harmonics

I was at the Psychedelic Science 2017 conference when I saw Selen Atasoy presenting about improvisation enhancement with LSD. She used a paradigm previously developed, whose methods and empirical tests were published in Nature in 2016 but now applied to psychedelic research. For a good introduction check out the partial transcript of her talk.

In her talk she shows how one can measure the various “pure harmonics” in a given brain. The core idea is that brain activity can be interpreted as a weighted sum of “natural resonant frequencies” for the entire connectome (white matter tracks together with the grey matter connections). They actually take the physical structure of a mapped brain and simulate the effect of applying the excitation-inhibition differential equations known for collective neural activity propagation. Then they infer the presence and prevalence of these “pure harmonics” in a brain at a given point in time using a probabilistic reconstruction.

Chladni plates here are a wonderful metaphor for these brain harmonics. This is because the way the excitation-inhibition wavefront propagates is very similar in both Chladni plates and human brains. In both cases the system drifts slowly within the attractor basin of natural frequencies, where the wavefront wraps around the medium an integer number of times. I was in awe to see her approach applied to psychedelic research. After all, Qualia Computing has indeed explored harmonic patterns in psychedelic experiences (ex. 1, ex. 2, ex. 3), and the connection was made explicit in Principia Qualia (via the concept of neuroacoustic modulation).

giphy-downsized-large

But how do these harmonics look like in the brain? Show me a brain!

 

Notice the traveling wave wrapping around the brain an integer number of times in each of these numerical solutions (source). The work by these labs is incredible, and they seem to show that the brain’s activity can be decomposed into each of these harmonics.

At the Psychedelic Science 2017 conference, Selen Atasoy explained that very low frequency harmonics were associated with Ego Dissolution in the trials that they studied. She also explained that emotional arousal, here defined as one’s overall level of energy in the emotional component (i.e. anxiety and ecstasy vs. depression and serenity), also correlated with low frequency harmonic states. On the other hand, high valence states were correlated with high frequency brain harmonics.

These empirical results are things that I claim we could have predicted with the symmetry theory of valence. I then thought to myself: let’s try to come up with other predictions. How should we consider the mixture of various harmonics, beyond merely their individual presence? How can we reconstruct valence from this novel data-structure for representing brain-states?

The Algorithm for Quantifying Bliss

Starting my reasoning from first principles (sourced from the Symmetry Theory of Valence), the natural way to take a data-structure that represents states of consciousness and recover its valence (in cases where samples occur across time in addition to space), is to try to isolate the noise, then proceed to quantify the dissonance, and what remains becomes what’s consonant. Basically, one will estimate the rough amount of symmetry (over time), as well as the degree of anti-symmetry, and the level of noise total.

In other words, I prophesize that we can get an “affective signature” of any brain state by applying an algorithm to fMRI brain recordings in order to estimate the degree of (1) consonance, (2) dissonance, and (3) noise within and across the brain’s natural harmonic states. This will result in what I call “Consonance-Dissonance-Noise Signatures” of brain states (“CDNS” for short) consisting of three histograms that describe the spectra of consonance, dissonance, and noise in a given moment of experience. The algorithm to arrive at a CDNS of a brain state is as follows:

Remove some of the noise in the brain state by applying the technique in Atasoy (2016) and recovering the distribution of the best approximation possible for the harmonics present (you may apply some further denoising on the harmonics when taken as a collective). Then estimate the total dissonance of the combination of harmonics by taking each pair of harmonics and quantifying their mutual dissonance. Finally, subtract the dissonance from “all of the interactions that could have existed” and what’s left ends up being the consonance. This way you obtain a Consonance, Dissonance, Noise Signature.

 

Each of these three components will have their associated spectral power distribution. The noise spectrum is obtained during the first denoising step (as whatever cannot be explained by the harmonic decomposition). Then the dissonance spectrum is a function of the minimum power of pairs of harmonics that exist within the critical band of each other (see slides 18; possibly upgraded by 20), as well as the frequencies of the beating patterns.

Quantifying Dissonance?

In order to quantify dissonance we use a method that may end up being simpler than what you need to calculate dissonance for sound! E.g. in Quantifying the Consonance of Complex Tones With Missing Fundamentals (Chon 2008) we learn that the human auditory system may at times detect dissonance even when there is no actual dissonance in the input. That is, there are auditory illusions pertaining to valence and dissonance. Based on the missing fundamental one can create ghost dissonance between tones that are not even present. That said, quantifying dissonance in a brain in terms of its harmonic decomposition may be easier than quantifying dissonance in auditory input, precisely because the auditory input (and any sensory input for that matter) contains many intermediary pre-processing steps. The auditory system is relatively “direct” when compared to, e.g. the visual system, but you will still see some basic signal processing done to the input before it influences brain harmonics. The sensory systems, being adapted to meet the criteria of both interfacing with a functioning valence system and representing the information adequately (in terms of the real-world distribution of inputs) serve the function of translating the inputs into usable signals. I.e. frequency-based descriptions, often log-transformed, in order to arrive at valence gradients. For this reason, the algorithm that describes how to extract valence out of a brain state may turn out to be simpler than what you need to predict the hedonic quality of patterns of sound (or sight, touch, etc).

In brief, we propose that we can compute the approximate amount of dissonance between these harmonics by seeing how close they are in terms of spatial and temporal frequencies. If they are within the critical window then they will be considered as dissonant. There is likely to be a peak dissonance window, and when any pair of harmonic states live within that window, then experiencing both at once may feel really awful (to quantify such dissonance more precisely we would use a dissonance function as shown in Chon 2008). If indeed symmetry is intimately connected to valence, then highly anti-symmetrical states such as what’s produced by overlapping brain harmonics within the critical band may feel terrible. Remember, harmony is symmetry over time. So dissonance is anti-symmetry over time. It’s worth recalling, though, that in the absence of dissonance and noise, by default, what remains is consonance.

Visualizing Emotions as CDNS’s of States of Consciousness

Above you can find two ways of visualizing a CDNS. Before we go on to the predictions, here we illustrate how we think that we will be able to see at a glance the valence of a brain with our method. The big circle shows the dissonance and consonance for each of the brain harmonics (the black dots surrounding the circle represent the weights for each state). If you want the overall dissonance in a given state, you add up the red-yellow arrows, whereas if you want the total consonance, you add the purple-light-blue arrows. The triangles on the right expand upon the valence diagram presented in Principia Qualia. Namely, we have a blue (positive valence/consonant), red (negative valence/dissonant), and grey (neutral valence/noise) component in a state of consciousness. Each of these components has a spectrum; the myriad textures of emotional states are the result of different spectral signatures for hedonically loaded patterns.

Testable Predictions

Quantifying Bliss (27)

We predict that intense emotions/experiences reported on psychedelics will result in states of consciousness whose harmonic decomposition will show a high amount of energy to be found in the pure harmonics (this was already found in 2017 as explained in the presentation, so let’s count that as a retrodiction). People who report being “very high” will have particularly high amounts of energy in their pure harmonics (as opposed to more noisy states).

The predicted valence for their experiences will be a function of the particular patterns (in terms of relative weights) of the various harmonics. Those which generate highly harmonic CDNS will be blessed with high valence experiences. And those who experience high dissonance, as empirically measured, will report negative feelings (e.g. fear, anxiety, nausea, weird and unpleasant body load, etc). In particular, we can explore the shape of highly harmonic states. In this framework, MDMA would be seen as likely to work by increasing the energy expressed by an exceptionally consonant set of harmonics in the brain.

A point to make here is that predicting “pure harmonics” on psychedelics (evidently simple and ordered patterns), would seem to go counter to the recently accrued empirical data concerning entropy in the tripping brain.** But we also know that the psychedelic brain can produce ridiculously self-similar near-informationless yet highly intense moments of experience preceded by a symmetrification process. Indeed, there are several symmetric attractors for the interplay of awareness and attention at various levels of “consciousness energy” and quality of mood. These states, in turn, not only are hedonically charged, but also allow the exploration of high-energy qualia research (since the implicit symmetry provides an energy seal). Highly energetic states of consciousness can be encapsulated in a highly symmetrical network of local binding. More about this in a future article.

On the other hand, we predict that people on SSRIs will show an enhanced amount of noise in their CDNS. A couple of slides back, this was represented as a higher loading of activity in the grey component of the triangular visualization of a CDNS. Likewise, some drugs will have various effects on the CDNS, such as stimulants inducing more consonance in high frequencies, whereas opioids and hypnotics having signatures of inducing high consonance in the low frequencies.

Summary of Predictions About Drug Effects

  1. Psychedelic substances will increase the overall power of the brain’s pure harmonics, and thus result in a CDN Signature characterized by: (a) high consonance of all frequencies, (b) high dissonance of all frequencies, and (c) low noise of all frequencies. Criticality will be observed by way of the CDNS having high variance.
  2. MDMA will produce a very specific range of states that have on the one hand very pure harmonic states of high frequencies, and on the other, very small collective dissonance and noise. In other words: (a) high amounts of high-frequency consonance, (b) low amounts of dissonance of all frequencies, and (c) low noise of all frequencies.
  3. Any “affect blunting” agent such as SSRIs, ibuprofen, aspirin, acetaminophen, and agmatine, will produce CDNS characterized by: (a) reduced consonance of all frequencies, (b) reduced dissonance of all frequencies, and (c) increased noise in either some or all frequencies. We further hypothesize that different antidepressants (e.g. citalopram vs. fuoxetine) will look the same with respect to reducing the C and D components, but may have differences in the way they increase the N spectrum.
  4. Opioids in euphoric doses will be found to (a) increase low frequency consonance, (b) decrease dissonance for all frequencies but especially the high frequencies, and (c) slightly increase noise across the board.
  5. Stimulants will be found to (a) increase medium and high frequency consonance, (b) leave dissonance fairly unaltered, and (c) reduce noise for all frequencies but especially those in the upper end of the spectrum.

Predictions About Emotions

For now, here are the specific predictions concerning emotions that I am making:

  1. The energy of the consonant (C) component of a CDNS will be highly correlated with the amount of euphoria (pleasure, happiness, positive feelings, etc.) a person is experiencing.
  2. The energy of the dissonant (D) component will have a high correlation with the amount of dysphoria (pain, suffering, negative feelings, etc.) a person feels.
  3. The energy of the noise (N) component will be correlated with flattened affect and blunted valence (i.e. feeling neither good nor bad, like there is a fog that masks all feelings).
  4. If one creates a geometric representation of the relationships between various brain states using their respective CDNS similarities as a distance metric for emotional states using Multi-Dimensional Scaling (MDS) techniques, one will be able to recover a really good approximation of the empirically-derived dimensional models of emotions (cf. dimensional models of emotionWire-heading Done Right). In other words, if you ask your participants to tell you how they feel during the fMRI sessions and then associate those emotions to their instantaneous CDNS, and then you apply multidimensional scaling to the resulting CDNS, you will be able to recover a good dimensional picture of the state-space of emotions. I.e. “subjective similarity between emotions” will be closely tracked by the geometric distance between their corresponding CDNS:
    1. Applying MDS scaling to the C component of the CDNS will result in a better characterization of the differences between positive emotions.
    2. Applying MDS to the D component will result in a better characterization of the differences between negative emotions. And,
    3. Applying MDS to the N component will result in a better characterization of the differences between valence-neutral emotions.

The Future of Mental Health

Quantifying Bliss (28)

Sir, your 17th harmonic is really messing up the consonance of your 19th harmonic, and it interrupts the creative morning mood you recently enjoyed. I suggest taking 1mg of Coluracetam, listening to a selection of Diamond songs, and RD23 [stretching exercise]. Here’s your expected CDNS.

Penfield mood organs may not be as terrible as they seem. At least not if you’re given a good combination of personalized settings, and a manual to wire-head in the proper manner. In such a situation, among the options available, you will have the ability to choose an experientially attractive, healthy, and sustainable set of moods indefinitely.

The “clinical phenomenologist” of the year 2050 might look into your brain harmonics, and try to find the shortest paths to nearby state-spaces with less chronic dissonance, fishing for high-consonance attractors with large basins to shoot for. The qualia expert would go on to provide you various options that may improve all sorts of metrics, including valence, the most important of them all. If you ask, your phenomenologist can give you trials for fully reversible treatments. You sample them in your own time, of course, and test them for a day or two before deciding whether to use these moods for longer.

Personalized Harmonic Retuning

I assume that people will be given just about enough retuning to get back to their daily routines as they themselves prefer them, but without any sort of nagging dissonance. Most people will probably continue on with their preference architectures relatively unchanged. Indeed, that will be a valued quality for a personalized harmonic retuning product. Having adequate mood devices that don’t mess up your existing value system might eventually become a highly understood, precision-engineered aspect of mainstream mental health. At least compared to the current (pre-psychedelic re-adoption 2017) paradigms. Arguably, even psychedelic therapy is pretty blunt in a way. Not in the sense of blunting the hedonic quality of your experience (on the contrary). But in the sense of applying the harmonization process indiscriminately.

For the psychonauts (hopefully they are not too rare by then), who still want to investigate consciousness even though human life is already full of love (in the future), we will have a different arrangement. They are free to explore themselves while being part of a research institute. Indeed, pursuing the purpose of understanding the big picture (including consciousness) will require the experimental method. More so, exploring the state-space of consciousness will, for the foreseeable future, be a way to find new ways of making others happy. People will continue to explore alien state-spaces in the search of highly-priced high-valence states. At least for some scores of generations valence engineering is bound to continue to be economically profitable. As we discover new drugs, new treatments, new philosophical trances, new interpretations and expressions of love, and so on, the economy will adapt to these inventions. We already live in an informational economy of states of consciousness, and the future is likely to be like that as well. Except that consciousness technologies will be immensely more powerful.

Barring the unlikely emergence of anti-hedonist Spartan self-punishing transhumanist social movements enabled with genetic technology, I don’t anticipate major obstacles in the eventual widespread use of mood organs. In fact, the wide adoption of SSRIs in some pockets of society shows that the general public is willing and interested in minor self-adjustments to deal with chronic negativity. Hedonic technology is in its early days, but with a root understanding of the nature of valence, the sky is the limit.

Case studies – SSRIs & Psychedelics

Let’s take a closer look at SSRIs and psychedelics in light of the Symmetry Theory of Valence.

SSRIs have an overall effect of blunting one’s experience at pretty much every level imaginable. Usually just a little, enough to help people re-establish a new order between their harmonics, in a more noisy, less intense range of moods. Some people may benefit from this sort of intervention. Now, also it’s worth pointing out the possible side effects, which have the common theme of reducing the structural integrity of the micro-structure of consciousness. Thus, the highly ordered pleasant and unpleasant experiences get softened. Whether this generalized softening is beneficial depends on many factors. Psychonauts usually avoid them as much as possible in order to protect the psychoacoustical potential of their brain, were they to desire to use this potential sometime in the future.

Psychedelics, in this framework, would be interpreted as neuroacoustic enhancers. These agents trigger, via control interruption, a more “echo-ey acoustic environment for one’s consciousness”. Meaning, any qualia experienced under the influence lasts for longer (the decay of intensity of experience as a function of time since presentation of stimuli becomes a lot “slower” or “fatter”). On high doses, the intensity of each component of a cycle of an experience can feel just as intense, and thus one might find oneself unable to locate oneself in time. Sometimes intense feelings return cyclically, and ultimately at strong doses, experiential feedback dominates every aspect of one’s experience, and there isn’t anything other than standing waves of synesthetic psychedelic feelings.

Peak symmetry states with their associated valence would be predicted to be far more accessible on highly harmonic states of consciousness. So psychedelics and the like could be carefully used to explore the positive extreme of valence: Hyper-symmetrical states. That said, for responsible exploration, a euphoriant will be needed to prevent negative psychedelic experiences.

Final Thoughts

A Harmonic Society is a place where everyone recognizes what makes other sentient beings love life. It’s a place in which everyone deeply understands the valence landscapes of other beings. People in such a society would know that a zebra, an owl, and a salamander all share the pursuit of harmonic states of consciousness, albeit in their own, often different-looking, state-spaces of qualia. We would understand each other far more deeply if we saw each other’s valence landscapes as part of a big state-space of possible preference architectures. Ultimately, the pursuit of existential bliss and the ontological question (why being?) would incite us to explore each other through consciousness technologies. We will have an expanded state-space of available possible moods, both individual and collective, increasing our chances of finding a new revolutionary understanding of consciousness, identity, and what’s possible for post-hedonium societies.


*I will note that to define what’s ethical one ultimately relies on beliefs about personal identity; truly frame-independent systems of morality are exceptionally hard to construct.

**The Entropic Brain theory portrays psychedelia in terms of increased entropy, but also, and most importantly, focuses on criticality. Just thinking about entropy would not distinguish between adding white noise and adding interesting patterns. In other words, from the point of view of simple entropy without any spectral (or nonlinear) analysis, SSRIs and psychedelics are doing pretty much the same thing. So the sense of “entropy” that matters will have to be a lot more detailed, showing you in what way the information encoded in normal states of consciousness changes as a function of entropy added in various ways.

On psychedelics one does indeed find highly ordered crystal-like states of consciousness (which I’ve described elsewhere as peak symmetry states), and as far as we know those states are also some of the most positively hedonically charged. Hence, at least in terms of describing the quality of the psychedelic experience, leaving symmetry out would make us miss an important big-picture kind of quality for psychedelics in general and their connection to valence variance.

 

***→ see quote →

My hypothesis strongly implies that ‘hedonic’ brain regions influence mood by virtue of acting as ‘tuning knobs’ for symmetry/harmony in the brain’s consciousness centers. Likewise, nociceptors, and the brain regions which gate & interpret their signals, will be located at critical points in brain networks, able to cause large amounts of salience-inducing antisymmetry very efficiently. We should also expect rhythm to be a powerful tool for modeling brain dynamics involving valence- for instance, we should be able to extend (Safron 2016)’s model of rhythmic entrainment in orgasm to other sorts of pleasure.

– Michael Johnson in Principia Qualia, page 52

Connectome-Specific Harmonic Waves on LSD

The harmonics-in-connectome approach to modeling brain activity is a fascinating paradigm. I am privileged to have been at this talk in the 2017 Psychedelic Science conference. I’m extremely happy find out that MAPS already uploaded the talks. Dive in!

Below is a partial transcript of the talk. I figured that I should get it in written form in order to be able to reference it in future articles. Enjoy!

[After a brief introduction about harmonic waves in many different kinds of systems… at 7:04, Selen Atasoy]:

We applied the [principle of harmonic decomposition] to the anatomy of the brain. We made them connectome-specific. So first of all, what do I mean by the human connectome? Today thanks to the recent developments in structural neuroimaging techniques such as diffusion tensor imaging, we can trace the long-distance white matter connections in the brain. These long-distance white matter fibers (as you see in the image) connect distant parts of the brain, distant parts of the cortex. And the set of all of the different connections is called the connectome.

selen_connectome_image

Now, because we know the equation governing these harmonic waves, we can extend this principle to the human brain by simply solving the same equation on the human connectome instead of a metal plate (Chladni plates) or the anatomy of the zebra. And if you do that, we get a set of harmonic patterns, this time emerging in the cortex. And we decided to call these harmonic patterns connectome harmincs. And each of these connectome harmonic patterns are associated with a different frequency. And because they correspond to different frequencies they are all independent, and together they give you a new language, so to speak, to describe neural activity. So in the same way the harmonic patterns are building blocks of these complex patterns we see on animal coats, these connectome harmonics are the building blocks of the complex spatio-temporal patterns of neural activity.

Describing and explaining neural activity by using these connectome harmonics as brain states is really not very different than decomposing a complex musical pieces into its musical notes. It’s simply a new way of representing your data, or a new language to express it.

What is the advantage of using this new language? So why not use the state-of-the-art conventional neurimaging analysis methods? Because these connectome harmonics, by definition are the vibration modes, but applied to the anatomy of the human brain, and if you use them as brain states to express neural activity we can compute certain fundamental principles very easily such as the energy or the power.

The power would be the strength of activation of each of these states in neural activity. So how strongly that particular state contributes to neural activity. And the energy would be a combination of this strength of activation with the intrinsic energy of that particular brain state, and the intrinsic energy comes from the frequency of its vibration (in the analogy of vibration).

So in this study we looked at the power and the energy of these connectome harmonic brain states in order to explore the neural correlates of the LSD experience.

We looked at 12 healthy participants who received either 75µg of LSD (IV) or a placebo, over two sessions. These two sessions were 14 days apart in counter-balanced order. And the fMRI scans consisted of 3 eyes-closed resting states scans, each lasting 7 minutes, in the first and the third scan the participants were simply resting, eyes closed, but in the second scan they were also listening to music. And after each scan, the participants rated the intensity of certain experiences.

activity_power_energy_scans.png

So if you look at, firstly, at the total power and the total energy of each of these scans under LSD and placebo, what we see is that under LSD both the power as well as the energy of brain activity increases significantly.

And if we compute the probability of observing a certain energy value on LSD or placebo, what we see is that the peak of this probability distribution clearly shoots towards high energy values under LSD.

energy_difference

And that peak is even slightly higher in terms of probability when the subjects were listening to music. So if we interpret that peak as, in a way, the characteristic energy of a state, you can see that it shifts towards higher energy under LSD, and that this effect is intensified when listening to music.

And then we asked, which of these brain states, which of these frequencies, were actually contributing to this energy increase. So we partitioned the spectrum of all of these harmonic brain states into different parts and computed the energy of each of these partitions individually. So in total we have around 20,000 brain states. And if you look at the energy differences in LSD and placebo, what we find is that for a very narrow range of low frequencies actually these brain states were decreasing their energy on LSD. But for a very broad range of high frequencies, LSD was inducing an energy increase. So this says that LSD alters brain dynamics in a very frequency-selective manner. And it was causing high frequencies to increase their energy.

So next we looked at whether these changes we are observing in brain activity are correlated with any of the experiences that the participants themselves were having in that moment. If you look at the energy changes within the narrow range of low frequencies, we found that the energy changes in that range significantly correlated with the intensity of the experience of ego dissolution. The loss of subjective self.

ego_dissolution

And very interestingly, the same range of energy change within the same frequency range also significantly correlated with the intensity of emotional arousal, whether the experience was positive or negative. This could be quite relevant for studies looking into potential therapeutic applications of LSD.

emotional_arousal

Next, when we look at a slightly higher range of frequencies, what we found was that the energy changes within that range significantly correlated with the positive mood.

higher_frequencies

In brief, this suggests that it’s rather the low frequency brain states which correlated with ego dissolution or with emotional arousal, and it’s the activity of higher frequencies that is correlated with the positive experiences.

Next, we wanted to check the size of the repertoire of active brain states. And if you look at the probability of activation for any brain state (so we are not distinguishing for any frequency brain states), what we observe is that the probability of a brain state being silent (zero contribution), actually decreased under LSD. And the probability of a brain state contributing very strongly, which corresponds to the tails of these distributions, were increased under LSD. So this suggests that LSD was activating more brain states simultaneously.

repertoaire

And if we go back to the music analogy that we used in the beginning, that would correspond to playing more musical notes at the same time. And it’s very interesting, because studies that have looked at improvising, those who have looked at jazz improvisation, show that improvising jazz musicians play significantly more musical notes compared to memorized play. And this is what we seem to be finding under the effect of LSD. That your brain is actually activating more of these brain states simultaneously.

cross-frequency

And it does so in a very non-random fashion. So if you look at the correlation across different frequencies. Like at the co-activation patterns, and their activation over time. You may interpret it as the “communication across various frequencies”. What we found is that for a very broad range of the spectrum, there was a higher correlation across different frequencies in their activation patterns under LSD compared to placebo.

So this really says that LSD is actually causing a reorganization, rather than a random activation of brain states. It’s expanding the repertoire of active brain states, while maintaining -or maybe better said- recreating a complex but spontaneous order. And in the musical analogy it’s really very similar to jazz improvisation, to think about it in an intuitive way.

Now, there is actually one particular situation when dynamical systems such as the brain, and systems that change their activity over time, show this type of emergence of complex order, or enhanced improvisation, enhanced repertoire of active states. And this is when they approach what is called criticality. Now, criticality is this special type of behavior, special type of dynamics, that emerges right at the transition between order and chaos. When these two (extreme) types of dynamics are in balance. And criticality is said to be “the constantly shifting battle zone between stagnation and anarchy. The one place where a complex system can be spontaneous, adaptive, and alive” (Waldrop 1992). So if a system is approaching criticality, there are very characteristic signatures that you would observed in the data, in the relationships that you plot in your data.

And one of them is -and probably the most characteristic of them- is the emergence of power laws. So what does that mean? If you plot one observable in our data, which for example, in our case would be the maximum power of a brain state, in relationship to another observable, for example, the wavenumber, or the frequency of that brain state, and you plot them in logarithmic coordinates, that would mean that if they follow power laws, they would approximate a line. And this is exactly what we observe in our data, and surprisingly for both LSD as well as for placebo, but with one very significant and remarkable difference: because the high frequencies increase their power on LSD, this distribution follows this power law, this line, way more accurately under LSD compared to placebo. And here you see the error of the fit, which is decreasing.

This suggests that LSD shoots brain dynamics further towards criticality.  The signature of criticality that we find in LSD and in placebo is way more enhanced, way more pronounced, under the effect of LSD. And we found the same effect, not only for the maximum power, but also for the mean power, as well as for the power of fluctuations.

criticality_signature

So this suggests that the criticality actually may be the principle that is underlying this emergence of complex order, and this reorganization of brain dynamics, and which leads to enhanced improvisation in brain activity.

So, to summarize briefly, what we found was that LSD increases the total power as well as total energy of brain activity. It selectively activates high frequency brain states, and it expands the repertoire or active brain states in a very non-random fashion. And the principle underlying all of these changes seems to be a reorganization of brain dynamics, right at criticality, right at the edge of chaos, or just as the balance between order and chaos. And very interestingly, the “edge of chaos”, or the edge of criticality, is said to be where “life has enough stability to sustain itself, and enough creativity to deserve the name of life” (Waldrop 1992). So I leave you with that, and thank you for your attention.

[Applauses; ends at 22:00, followed by Q&A]

ELI5 “The Hyperbolic Geometry of DMT Experiences”

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I wrote the following in response to a comment on the r/RationalPsychonaut subreddit about this DMT article I wrote some time ago. The comment in question was: “Can somebody eli5 [explain like I am 5 years old] this for me?” So here is my attempt (more like “eli12”, but anyways):

In order to explain the core idea of the article I need to convey the main takeaways of the following four things:

  1. Differential geometry,
  2. How it relates to symmetry,
  3. How it applies to experience, and
  4. How the effects of DMT turn out to be explained (in part) by changes in the curvature of one’s experience of space (what we call “phenomenal space”).

1) Differential Geometry

If you are an ant on a ball, it may seem like you live on a “flat surface”. However, let’s imagine you do the following: You advance one centimeter in one direction, you turn 90 degrees and walk another centimeter, turn 90 degrees again and advance yet another centimeter. Logically, you just “traced three edges of a square” so you cannot be in the same place from which you departed. But let’s says that you somehow do happen to arrive at the same place. What happened? Well, it turns out the world in which you are walking is not quite flat! It’s very flat from your point of view, but overall it is a sphere! So you ARE able to walk along a triangle that happens to have three 90 degree corners.

That’s what we call a “positively curved space”. There the angles of triangles add up to more than 180 degrees. In flat spaces they add up to 180. And in “negatively curved spaces” (i.e. “negative Gaussian curvature” as talked about in the article) they add up to less than 180 degrees.

oct

Eight 90-degree triangles on the surface of a sphere

So let’s go back to the ant again. Now imagine that you are walking on some surface that, again, looks flat from your restricted point of view. You walk one centimeter, then turn 90 degrees, then walk another, turn 90 degrees, etc. for a total of, say, 5 times. And somehow you arrive at the same point! So now you traced a pentagon with 90 degree corners. How is that possible? The answer is that you are now in a “negatively curved space”, a kind of surface that in mathematics is called “hyperbolic”. Of course it sounds impossible that this could happen in real life. But the truth is that there are many hyperbolic surfaces that you can encounter in your daily life. Just to give an example, kale is a highly hyperbolic 2D surface (“H2” for short). It’s crumbly and very curved. So an ant might actually be able to walk along a regular pentagon with 90-degree corners if it’s walking on kale (cf. Too Many Triangles).

kale

An ant walking on kale may infer that the world is an H2 space.

In brief, hyperbolic geometry is the study of spaces that have this quality of negative curvature. Now, how is this related to symmetry?

2) How it relates to symmetry

As mentioned, on the surface of a sphere you can find triangles with 90 degree corners. In fact, you can partition the surface of a sphere into 8 regular triangles, each with 90 degree corners. Now, there are also other ways of partitioning the surface of a sphere with regular shapes (“regular” in the sense that every edge has the same length, and every corner has the same angle). But the number of ways to do it is not infinite. After all, there’s only a handful of regular polyhedra (which, when “inflated”, are equivalent to the ways of partitioning the surface of a sphere in regular ways).

Weinberg-1-102711_jpg_630x171_crop_q85

If you instead want to partition a plane in a regular way with geometric shapes, you don’t have many options. You can partition it using triangles, squares, and hexagons. And in all of those cases, the angles on each of the vertices will add up to 360 degrees (e.g. six triangles, four squares, or thee corners of hexagons meeting at a point). I won’t get into Wallpaper groups, but suffice it to say that there are also a limited number of ways of breaking down a flat surface using symmetry elements (such as reflections, rotations, etc.).

tiling2

Regular tilings of 2D flat space

Hyperbolic 2D surfaces can be partitioned in regular ways in an infinite number of ways! This is because we no longer have the constraints imposed by flat (or spherical) geometries where the angles of shapes must add up to a certain number of degrees. As mentioned, in hyperbolic surfaces the corners of triangles add up to less than 180 degrees, so you can fit more than 6 corners of equilateral triangles at one point (and depending on the curvature of the space, you can fit up to an infinite number of them). Likewise, you can tessellate the entire hyperbolic plane with heptagons.

61b801a08a7ef2780e96e0a574b82136

Hyperbolic tiling: Each of the heptagons is just as big (i.e. this is a projection of the real thing)

On the flip side, if you see a regular partitioning of a surface, you can infer what its curvature is! For example, if you see that a surface is entirely covered with heptagons, three on each of the corners, you can be sure that you are seeing a hyperbolic surface. And if you see a surface covered with triangles such that there are only four triangles on each joint, then you know you are seeing a spherical surface. So if you train yourself to notice and count these properties in regular patterns, you will indirectly also be able to determine whether the patterns inhabit a spherical, flat, or hyperbolic space!

3) How it applies to experience

How does this apply to experience? Well, in sober states of consciousness one is usually restricted to seeing and imagining spherical and flat surfaces (and their corresponding symmetric partitions). One can of course look at a piece of kale and think “wow, that’s a hyperbolic surface” but what is impossible to do is to see it “as if it were flat”. One can only see hyperbolic surfaces as projections (i.e. where we make regular shapes look irregular so that they can fit on a flat surface) or we end up contorting the surface in a crumbly fashion in order to fit it in our flat experiential space. (Note: even sober phenomenal space happens to be based on projective geometry; but let’s not go there for now.)

4) DMT: Hyperbolizing Phenomenal Space

In psychedelic states it is common to experience whatever one looks at (or, with more stunning effects, whatever one hallucinates in a sensorially-deprived environment such as a flotation tank) as slowly becoming more and more symmetric. Symmetrical patterns are attractors in psychedelia. It’s common for people to describe their acid experiences as “a kaleidoscope of colors and meaning”. We should not be too quick to dismiss these descriptions as purely metaphorical. As you can see from the article Algorithmic Reduction of Psychedelic States as well as PsychonautWiki’s Symmetrical Texture Repetition, LSD and other psychedelics do in fact “symmetrify” the textures you experience!

8697209364_91f2ab133e_h

What gravel might look like on 150 mics of LSD (Source)

As it turns out, this symmetrification process (what we call “lowering the symmetry detection/propagation threshold”) does allow one to experience any of the possible ways of breaking down spherical and flat surfaces in regular ways (in addition to also enabling the experience of any wallpaper group!). Thus the surfaces of the objects one hallucinates on LSD (specially for Closed Eyes Visuals), are usually carpeted with patterns that have either spherical or flat symmetries (e.g. seeing honeycombs, square grids, regular triangulations, etc.; or seeing dodecahedra, cubes, etc.).

wade_symmetry_best_blank_2

17 wallpaper symmetry groups

Only on very high doses of classic psychedelics does one start to experience objects that have hyperbolic curvature. And this is where DMT becomes very relevant. Vaping it is one of the most efficient ways of achieving “unworldly levels of psychedelia”:

On DMT the “symmetry detection threshold” is reduced to such an extent that any surface you look at very quickly gets super-saturated with regular patterns. Since (for reasons we don’t understand) our brain tries to incorporate whatever shape you hallucinate into the scene as part of the scene, the result of seeing too many triangles (or heptagons, or whatever) is that your brain will “push them into the surfaces” and, in effect, turn those surfaces into hyperbolic spaces.HeptagonsIndrasPearls

Yet another part of your brain (or system of consciousness, whatever it turns out to be) recognizes that “wait, this is waaaay too curved somehow, let me try to shape it into something that could actually exist in my universe”. Hence, in practice, if you take between 10 and 20 mg of DMT, the hyperbolic surfaces you see will become bent and contorted (similar to the pictures you find in the article) just so that they can be “embedded” (a term that roughly means “to fit some object into a space without distorting its properties too much”) into your experience of the space around you.

But then there’s a critical point at which this is no longer possible: Even the most contorted embeddings of the hyperbolic surfaces you experience cannot fit any longer in your normal experience of space on doses above 20 mg, so your mind has no other choice but to change the curvature of the 3D space around you! Thus when you go from “very high on DMT” to “super high on DMT” it feels like you are traveling to an entirely new dimension, where the objects you experience do not fit any longer into the normal world of human experience. They exist in H3 (hyperbolic 3D space). And this is in part why it is so extremely difficult to convey the subjective quality of these experiences. One needs to invoke mathematical notions that are unfamiliar to most people; and even then, when they do understand the math, the raw feeling of changing the damn geometry of your experience is still a lot weirder than you could ever anticipate.

hexagon_sphere_plane_hyp_032

Anybody else want to play hyperbolic soccer? Humans vs. Entities, the match of the eon!

Note: The original article goes into more depth

Now that you understand the gist of the original article, I encourage you to take a closer look at it, as it includes content that I didn’t touch in this ELI5 (or 12) summary. It provides a granular description of the 6 levels of DMT experience (Threshold, Chrysanthemum, Magic Eye, Waiting Room, Breakthrough, and Amnesia), many pictures to illustrate the various levels as well as the particular emergent geometries, and a theoretical discussion of the various algorithmic reductions that might explain how the hyperbolization of phenomenal space takes place based on combining a series of simpler effects together.

Qualia Computing at Consciousness Hacking (June 7th 2017)

I am delighted to announce that I will be presenting at Consciousness Hacking in San Francisco on 2017/6/7 (YMD notation).

Consciousness Hacking (CoHack) is an extremely awesome community that blends a genuine interest in benevolence, scientific rationality, experiential spirituality, self-experimentation, and holistic wellbeing together with an unceasing focus on consciousness. Truth be told, CohHack is one of the reasons why I love living in the Bay Area.

Here are the relevant event links: Eventbrite, FacebookMeetup.

And the event description:


What would happen if a bliss technology capable of inducing a constant MDMA-like state of consciousness with no negative side effects were available? What makes an experience good or bad? Is happiness a spiritual trick, or is spirituality a happiness trick?

At this month’s speaker presentation, Consciousness Hacking invites Data Science Engineer, Andrés Gómez Emilsson to discuss current research, including his own, concerning the measurement of bliss, how blissful brain states can be induced, and what implications this may have on quality of life and our relationship with the world around us.

Emilsson’s research aims to create a mathematical theory of the pleasure-pain axis that can take information about a person’s brain at a given point in time and return the approximate (or even true) level of happiness and suffering for that person. Emilsson will explore two dimensions that have been studied in affective neuroscience for decades:

  • Arousal: how much energy and activation a given emotion has
  • Valence: the “feel good or feel bad” dimension of emotion

If the purpose of life is to feel happy and to make others happy, then figuring out how valence is implemented in the brain may take us a long way in that direction. Current approaches to valence, while helpful, usually don’t address the core of the problem (ie. usually just measuring the symptoms of pleasure such as the neurotransmitters that trigger it, brain regions, positive reinforcement, etc. rather than getting at the experience of pleasure itself).

A real science of valence would not only be able to integrate and explain why the things people report as pleasurable are pleasant, it would also make a precise, empirically falsifiable hypothesis about whether arbitrary brain states will feel good or bad. This is what Emilsson aims to do.

You will take away:

  • An understanding about the current scientific consensus on the nature of happiness in the brain, and why it is incomplete
  • A philosophical case for both the feasibility and desirability of a world devoid of intense suffering
  • A new candidate mathematical formula that can be used to predict the psychological wellbeing of a brain at a given point in time
  • An argument for why bliss technology that puts us in a constant MDMA-like state of consciousness with no negative side effects is likely to become available within the next two to five decades
  • The opportunity to network with other people who are serious about figuring out the meaning of life through introspection and neuroscience

About our speaker:

Andrés Gómez Emilsson was born in México City in 1990. From an early age, he developed an interest in philosophy, mathematics, and science, leading him to compete nationally and internationally in Math and Science Olympiads. At 16, his main interest was mathematics, but after an unexpected “mystical experience”, he turned his attention to consciousness and the philosophical problems that it poses. He studied Symbolic Systems with an Artificial Intelligence concentration at Stanford, and later finished a masters in Computational Psychology at the same university. During his time at Stanford he co-founded the Stanford Transhumanist Association and became good friends with transhumanist philosopher David Pearce, taking on the flag of the Hedonistic Imperative (HI). In order to pursue the long-term goals of HI, his current primary intellectual interest is to reverse-engineer the functional, biochemical and/or quantum signatures of pure bliss.

He is currently working at a Natural Language Processing company in San Francisco, creating quantitative measures of employee happiness, productivity, and ethics at companies, with the long-term intent of creating a consciousness research institute that’s also a great place to work for (i.e. one in which employees are happy, productive, and ethical). In his free time he develops psychophysical tools to study the computational properties of consciousness.

Schedule:

6:30: Check in, snacks

6:45: Structured schmoozing

6:55: Event intro and meditation

7:00: Andrés Gómez Emilsson

7:50: Break

8:00: Break-out Sessions (small group discussion)

9:00: Break-out Recap

9:15: Closing meditation

About our venue:

ECO-SYSTM is a dynamic community of creative professionals, startups, and freelancers, founded on the idea that entertainment, creativity and business can come together to offer a truly unique work experience for Bay Area professionals. Check out membership plans here: http://eco-systm.com/


 

Hedonium

Desiring that the universe be turned into Hedonium is the straightforward implication of realizing that everything wants to become music.

The problem is… the world-simulations instantiated by our brains are really good at hiding from us the what-it-is-likeness of peak experiences. Like Buddhist enlightenment, language can only serve as a pointer to the real deal. So how do we use it to point to Hedonium? Here is a list of experiences, concepts and dynamics that (personally) give me at least a sort of intuition pump for what Hedonium might be like. Just remember that it is way beyond any of this:

Positive-sum games, rainbow light, a lover’s everlasting promise of loyalty, hyperbolic harmonics, non-epiphenomenal bliss, life as a game, fractals, children’s laughter, dreamless sleep, the enlightenment of emptiness, loving-kindness directed towards all sentient beings of past, present, and future, temperate wind caressing branches and leaves of trees in a rainforest, perfectly round spheres, visions of a giant ying-yang representing the cosmic balance of energies, Ricci flowtranspersonal experiences, hugging a friend on MDMA, believing in a loving God, paraconsistent logic-transcending Nirvana, the silent conspiracy of essences, eating a meal with every flavor and aroma found in the quantum state-space of qualia, Enya (Caribbean Blue, Orinoco Flow), seeing all the grains of sand in the world at once, funny jokes made of jokes made of jokes made of jokes…, LSD on the beach, becoming lighter-than-air and flying like a balloon, topological non-orientable chocolate-filled cookies, invisible vibrations of love, the source of all existence infinitely reflecting itself in the mirror of self-awareness, super-symmetric experiences, Whitney bottles, Jhana bliss, existential wonder, fully grasping a texture, proving Fermat’s Last theorem, knowing why there is something rather than nothing, having a benevolent social super-intelligence as a friend, a birthday party with all your dead friends, knowing that your family wants the best for you, a vegan Christmas eve, petting your loving dog, the magic you believed in as a kid, being thanked for saving the life of a stranger, Effective Altruism, crying over the beauty and innocence of pandas, letting your parents know that you love them, learning about plant biology, tracing Fibonacci spirals, comprehending cross-validation (the statistical technique that makes statistics worth learning), reading The Hedonistic Imperative by David Pearce, finding someone who can truly understand you, realizing you can give up your addictions, being set free from prison, Time Crystals, figuring out Open Individualism, G/P-spot orgasm, the qualia of existential purpose and meaning, inventing a graph clustering algorithm, rapture, obtaining a new sense, learning to program in Python, empty space without limit extending in all directions, self-aware nothingness, living in the present moment, non-geometric paradoxical universes, impossible colors, the mantra of Avalokiteshvara, clarity of mind, being satisfied with merely being, experiencing vibrating space groups in one’s visual field, toroidal harmonics, Gabriel’s Oboe by Ennio Morricone, having a traditional dinner prepared by your loving grandmother, thinking about existence at its very core: being as apart from essence and presence, interpreting pop songs by replacing the “you” with an Open Individualist eternal self, finding the perfect middle point between female and male energies in a cosmic orgasm of selfless love, and so on.

The Binding Problem

[Our] subjective conscious experience exhibits a unitary and integrated nature that seems fundamentally at odds with the fragmented architecture identified neurophysiologically, an issue which has come to be known as the binding problem. For the objects of perception appear to us not as an assembly of independent features, as might be suggested by a feature based representation, but as an integrated whole, with every component feature appearing in experience in the proper spatial relation to every other feature. This binding occurs across the visual modalities of color, motion, form, and stereoscopic depth, and a similar integration also occurs across the perceptual modalities of vision, hearing, and touch. The question is what kind of neurophysiological explanation could possibly offer a satisfactory account of the phenomenon of binding in perception?
One solution is to propose explicit binding connections, i.e. neurons connected across visual or sensory modalities, whose state of activation encodes the fact that the areas that they connect are currently bound in subjective experience. However this solution merely compounds the problem, for it represents two distinct entities as bound together by adding a third distinct entity. It is a declarative solution, i.e. the binding between elements is supposedly achieved by attaching a label to them that declares that those elements are now bound, instead of actually binding them in some meaningful way.
Von der Malsburg proposes that perceptual binding between cortical neurons is signalled by way of synchronous spiking, the temporal correlation hypothesis (von der Malsburg & Schneider 1986). This concept has found considerable neurophysiological support (Eckhorn et al. 1988, Engel et al. 1990, 1991a, 1991b, Gray et al. 1989, 1990, 1992, Gray & Singer 1989, Stryker 1989). However although these findings are suggestive of some significant computational function in the brain, the temporal correlation hypothesis as proposed, is little different from the binding label solution, the only difference being that the label is defined by a new channel of communication, i.e. by way of synchrony. In information theoretic terms, this is no different than saying that connected neurons posses two separate channels of communication, one to transmit feature detection, and the other to transmit binding information. The fact that one of these channels uses a synchrony code instead of a rate code sheds no light on the essence of the binding problem. Furthermore, as Shadlen & Movshon (1999) observe, the temporal binding hypothesis is not a theory about how binding is computed, but only how binding is signaled, a solution that leaves the most difficult aspect of the problem unresolved.
I propose that the only meaningful solution to the binding problem must involve a real binding, as implied by the metaphorical name. A glue that is supposed to bind two objects together would be most unsatisfactory if it merely labeled the objects as bound. The significant function of glue is to ensure that a force applied to one of the bound objects will automatically act on the other one also, to ensure that the bound objects move together through the world even when one, or both of them are being acted on by forces. In the context of visual perception, this suggests that the perceptual information represented in cortical maps must be coupled to each other with bi-directional functional connections in such a way that perceptual relations detected in one map due to one visual modality will have an immediate effect on the other maps that encode other visual modalities. The one-directional axonal transmission inherent in the concept of the neuron doctrine appears inconsistent with the immediate bi-directional relation required for perceptual binding. Even the feedback pathways between cortical areas are problematic for this function due to the time delay inherent in the concept of spike train integration across the chemical synapse, which would seem to limit the reciprocal coupling between cortical areas to those within a small number of synaptic connections. The time delays across the chemical synapse would seem to preclude the kind of integration apparent in the binding of perception and consciousness across all sensory modalities, which suggests that the entire cortex is functionally coupled to act as a single integrated unit.
— Section 5 of “Harmonic Resonance Theory: An Alternative to the ‘Neuron Doctrine’ Paradigm of Neurocomputation to Address Gestalt properties of perception” by Steven Lehar

The Hyperbolic Geometry of DMT Experiences: Symmetries, Sheets, and Saddled Scenes

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

Friends, right here and now, one quantum away, there is raging a universe of active intelligence that is transhuman, hyperdimensional, and extremely alien.

—Terence McKenna

The Geometry of DMT States

This is an essay on the phenomenology of DMT. The analysis here presented predominantly uses algorithmic, geometric and information-theoretic frameworks, which distinguishes it from purely phenomenological, symbolic, neuroscientific or spiritual accounts. We do not claim to know what ultimately implements the effects here described (i.e. in light of the substrate problem of consciousness), but the analysis does not need to go there in order to have explanatory power. We posit that one can account for a wide array of (apparently diverse) phenomena present on DMT-induced states of consciousness by describing the overall changes in the geometry of one’s 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 measurements of distances we experience on DMT (coming from the relationships between the phenomenal objects one experiences in that state) has an overall geometry that can accurately be described as hyperbolic (or hyperbolic-like). In other words, our inner 3D1T world grows larger than is possible to fit in an experiential field with 3D Euclidean phenomenal space (i.e. an experience of dimension R2.5 representing an R3 scene). This results in phenomenal spaces, surfaces, and objects acquiring a mean negative curvature. Of note is that even though DMT produces this effect in the most consistent and intense way, the effect is also present in states of consciousness induced by tryptamines and to a lesser extent in those induced by all other psychedelics.

Conceptual Framework: Algorithmic Reduction

We will use the reduction framework originally proposed in the article Algorithmic 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 people’s phenomenology in DMT states. We do not claim “the substrate of consciousness” is becoming hyperbolic in any literal sense (though we do not discard that possibility). Rather, we interpret the hyperbolic curvature that experience acquires while on DMT as an emergent effect of a series of more general mechanism of action that can work together to change the geometry of a mind. These same mechanisms of action govern the dynamics of other psychedelic experiences; it is the proportion and intensity of the various “basic” effects that lead to the different outcomes observed. In other words, the hyperbolization of phenomenal space may not be a fundamental effect of DMT, but rather, it may be an emergent effect of more simple effects combined (not unlike how our seemingly smooth macroscopic space-time emerges from the jittery yet fundamental interactions that happen in a microscopic high-dimensional quantum foam).

In particular, we will discuss three candidate models for a more fundamental algorithmic reduction: (1) the synergistic effect of control interruption and symmetry detection resulting in a change of the metric of phenomenal space (analogously to how one can measure the geometry of hyperbolic graph embeddings), (2) the mind as a dynamic system with energy sources, sinks and invariants, in which curvature stores potential energy, and (3) a change in the underlying curvature of the micro-structure of consciousness. These models are not mutually-exclusive, and they may turn out to be compatible. More on this later.

What is Hyperbolic Geometry?

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

The picture to the left shows a representation of a “saddle” surface. In geometry, saddle surfaces are 2-dimensional hyperbolic spaces (also called “hyperbolic planes” or H2). For a surface to have “constant curvature” it must look the same at every point. In other words, for a saddle to be a geometric saddle, every point in it must be a “saddle point” (i.e. a point with negative curvature). As you can see, saddles have the property that the angles of a triangle found in them add up to less than 180 degrees (compare that to surfaces with positive curvature such as the 2-sphere, in which the angles of a triangle add up to more than 180 degrees). Generalizing this to higher dimensions, the middle image above shows a cube in H3 (i.e. a hyperbolic space of three dimensions). This cube, since it is in hyperbolic space, has thin edges and pointy corners. More generally, the corners of a polyhedra (and polytopes) will be more pointy in Hn than they are in Rn. This is why you can see in the right image a dodecahedron with right-angled corners, which in this case can tile H3 (cf. Not Knot). Such a thing- people of the past might say- is an insult to the imagination. Times are changing, though, and hyperbolic geometry is now an acceptable subject of conversation.

An important property of hyperbolic spaces is the way in which the area of a circle (or the n-dimensional volume of a hypersphere) increases as a function of its radius. In 2D Euclidean space the area grows quadratically with the radius. But on H2, the area grows exponentially as a function of the radius! As you may imagine, it is easy to get lost in hyperbolic 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 avoid getting burned or freezing to death you would have to place your planet within a very narrow distance range from the center star. Most of what you do in hyperbolic space either stays as local news or is quickly dissipated in an ever-expanding environment.

We Can Only Remember What We Can Reconstruct

We cannot experience H2 or H3 manifolds under normal circumstances, but we can at least represent some aspects of them through partial embeddings (i.e. instantiations as subsets of other spaces 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 embed H2 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 difficulty turns out to be crucial for understanding why DMT experiences are so hard to remember. In order to remember the experience you need to create a faithful and memorable 3D Euclidean embedding of it. Thus, if one happens to experience a hyperbolic object and wants to remember as much of it as possible, one will have to think strategically about how to fold, crunch and deform such object so that it can be fit in compact Euclidean representations.

What about DMT suggests hyperbolic geometry?

Why should we believe that phenomenal space on DMT (and to a lesser extent on other psychedelics) becomes hyperbolic-like?  We will argue that the features people use to describe their trips as well as concrete mathematical observations of such features point directly to hyperbolic geometry. Here is a list of such features (arranged from least to most suggestive… you know, for dramatic effect):

  1. Perception of far-out travel (as we said, small movements in hyperbolic space lead to huge changes in the scene).
  2. Feelings of becoming big (you can fit a lot more inside a circle of radius r in hyperbolic space).
  3. The space experienced is often depicted as “more real and more dense than normal”.
  4. The use of terms like “mind-expanding” and “warping” to describe the effects of the drug are very common.
  5. People describing it as “a different kind of space” and frequently using the word “hyperspace” to talk about it.
  6. Difficulty integrating/remembering the objects and scenes experienced (e.g. “they were too alien to recall”).
  7. Constant movement/acceleration and change of perspectives which are often described as “unfolding scenes and expanding patterns” (cf. the chrysanthemum, jitterbox).
  8. Continuous change of the scene’s context through escape routes: A door that leads to a labyrinth that leads to branching underground tunnels that lead to mirror rooms that lead to endless windows, and the one you take leading you to a temple with thirty seven gates which lead you to a kale salad world etc. (example).
  9. 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!”)
  10. Reported similarity with fractals.
  11. 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.
  12. 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 DMT*).
  13. PSIS-like experiences 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).
  14. Psychedelic replication pictures usually include features that can be interpreted as hyperbolic objects embedded in Euclidean 3D.
  15. People describe “incredibly advanced mechanisms” and “impossible objects” that cannot be represented in our usual reality (e.g. Terence Mckenna’s self-dribbling basketballs).
  16. At least one mathematician has stated that what one experiences on DMT cannot be translated into Euclidian geometry (unlike what one experiences on LSD).
  17. 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 6 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 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.)

(1) 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.”

SONY DSC

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 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.

(2) 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.

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 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 is one of my all-times favorite).

In Algorithmic Reduction of Psychedelic States 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 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, top middle, the rest were made with this service):

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 (i.e. statistical texture), 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 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…

(3) 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 hand-shake between bottom-up perception and top-down modeling.

In everyday conditions one solves the 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-occluduing 3D1T depth maps)
  3. Extremelly lowered information copying threshold.

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-Sheets

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 extremelly lowered information 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 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.

katoite-hydrogarnet

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 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).

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). 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 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).

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. 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 applied to the qualia patterns on the Magic Eye level. This concentrated hyperbolic synesthetic texture is what becomes the walls of the Waiting Room…

(4) 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: The curvature 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”.

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 Wating Room 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…

(5) 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.

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.

(6) Amnesia Level

Unlike 5-MeO-DMT, “normal DMT” experiences are not typically so mind-warping that 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 difficulty 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, 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. 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:

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.

DMT Space Expansion

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

DMT entities come in many forms, and their 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.

  1. 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.
  2. 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.
  3. 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.
  4. 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 immediatly obvious.
  5. 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) 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.
  6. 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 are obliterated and replaced by the feeling of becoming an all-encompassing entity. “Union with God” and “Samadhi” 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, 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:

(1) Control Interruption + Symmetry detection = Change in Metric

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

  1. Control Interruption (which amounts to a “longer half-life for all qualia”)
  2. Drifting (“breathing walls, eyes moving from their normal place, waving sensations”)
  3. Enhanced Pattern Recognition (pareidolia, cf. Getting Closed to Digital LSD)
  4. 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 together with extremelly 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 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).

(2) 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) appropriate ways of modulating the amount of energy present in different modules of one’s mind. That is, we have many programs that work as energy 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 and finding 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 one’s 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 one’s mind so that (1) energy freely passes from one form into another, and (2) energy floods the entire system. Let’s talk about energy sources and sinks.

Energy Sources and Sinks

In this algorithmic reduction DMT increases the amount of consciousness in one’s mind by virtue of impairing our normal energy sinks while increasing the throughput of its energy sources. This may frequently manifests as phenomenal spaces becoming hyperbolic in the mathematical-geometric sense of increasing its negative curvature as 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 recognition functions as an energy sink.

The Hamiltonian of a World-sheet

The total energy in one’s 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 one’s 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. One’s 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-sheet you will come up 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 the information content and the experiential intensity of DMT experiences.

helicatenoid

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.

Under normal circumstances the curvature of one’s world-sheet is, as far as I can tell, arousal-dependent. Have you noticed how when you feel tired you are more likely to defocus your visual experience? You are tired late at night and you are trying to watch a movie, but bringing the scene in focus is too much of an effort so you defocus for a little bit (still listening to the dialogue). What did you do that for? In the framework here proposed, you did that to diminish the energy it takes you to sustain a curved world-sheet with a lot of information. Doing so may be aesthetically pleasing and rewarding when fully awake or excited, but when tired the returns on doing the focusing are not great given how much effort it needs and the fact that the dialogue is more essential for the plot anyway.

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

Bayesian Energy Sinks

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 understanding expected things. In the presence of new information that one cannot easily integrate, however, one’s 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 to generate a mental model that works out a likely model of what we are experiencing we tend to remain in an over-active state.

This general principle applies to the world-sheet. One of the predominant ways in which a world-sheet reduces 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 seem desperate 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 don’t 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 of consciousness! New varieties of bliss! Music of the angels! OMG! Laughter till infinity and more- shared across the galaxy- in a hyperbolic transpersonal delight! It’s like LSD and N2O! Wow!

Forgive me, it is my first day. Let’s 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 spiral out of control. This explains in part the non-linear relationship between experienced intensity and DMT dose.

Like all aspects of one’s consciousness, the negative curvature 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” and embedding 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 intense the “folding” property of attention will be. Thus, for different dosages one reaches different homeostatic levels of overall curvature in one’s phenomenal space. Since attention does not stop at any point during a DMT trip (it keeps being bright and intense all throughout) there isn’t really any rest period to sit 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 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 deliberatively create) stable phenomenal objects whose structure can survive the warping effect of attention.

(3) 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 (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. 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 Möbius 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.

Generalizing hyperbolization to non-spatial experiential fields

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.

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 complement of the knot (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 DMT trip by creating a stabilizing 4D hyperbolic manifold in four easy steps:

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 extremelly 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 (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 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 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.


*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. Damn, don’t stare at a cauliflower while high on DMT if you ever intend to eat one again.

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 subredit. 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:

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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. That’s 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.: Example on world-sheet bending:

Below you can find two gifs that illustrate the behavior of a world-sheet on a 5mg vs. 20mg dose. The speed at which you are adding curvature to it increases so much that the shapes and objects keep shifting to accommodate it all.

(Source of super-trippy symmetric hyperbolic manifold representations: http://newearthlovelight.tumblr.com/post/70053311720)