Mettannealing

A meditation technique that combines Neural Field Annealing principles with metta (loving-kindness) meditation.

Introduction

From 2015 to 2019, the paradigm of neural annealing was developed at QRI in a collaborative effort between Michael Edward Johnson and Andrés Gomez Emilsson, pulling from ideas such as the free energy principle, connectome-specific harmonic waves, psychedelic and meditation phenomenology, and more. This was crystallized in 2019 by Mike in a writeup on his blog(Johnson 2019). Neural annealing describes a core dynamic by which the brain pays down technical debt, making more robust and coherent predictive models for getting about in the world. In Mike’s words,

First, energy (neural excitation, e.g. Free Energy from prediction errors) builds up in the brain, either gradually or suddenly, collecting disproportionately in the brain’s natural eigenmodes;

This build-up of energy (rate of neural firing) crosses a metastability threshold and the brain enters a high-energy state, causing entropic disintegration (weakening previously ‘sticky’ attractors);

The brain’s neurons self-organize into new multi-scale equilibria (attractors), aka implicit assumptions about reality’s structure and value weightings, which given present information should generate lower levels of prediction error than previous models (this is implicitly both a resynchronization of internal predictive models with the environment, and a minimization of dissonance in connectome-specific harmonic waves);

The brain ‘cools’ (neural activity levels slowly return to normal), and parts of the new self-organized patterns remain and become part of the brain’s normal activity landscape;

The cycle repeats, as the brain’s models become outdated and prediction errors start to build up again.

Two years later in Healing Trauma with Neural Annealing(Gomez Emilsson 2021), some large implications of neural annealing were detailed and predictions made. The article relates neural annealing with REBUS and predictive processing more generally, proposing a duality between the phenomenal texture of experience and the computational state of the system.

Another key inference made was that the effects of psychedelics at the implementation level can be parsimoniously explained as modulation of the average synaptic path length, which naturally gives rise to some of the significant phenomenal effects.

By randomly adding connections to a network of coupled oscillators one first sees an emergent state of many competing patches of synchrony, and then, after a threshold is crossed, one starts seeing global synchrony emerge.

In particular, N,N-DMT seems to give rise to many competing clusters of coherence, while 5-MeO-DMT gives rise to global coherence, or in some unfortunate cases two incompatible coherent states competing with each other. As for the intentional and semantic content associated with such states, we find 5-MeO to be very low-information and therefore underfits reality while N,N is quite high-information and strongly overfits.

It was also mentioned that loving-kindness meditation, also referred to as metta, is an especially therapeutic practice when done regularly before and during a high energy experience. Here that energy comes from psychedelics, but in principle all energizers could work for this purpose.

It feels that metta practice over time anneals a consonant metronome which can become massively amplified during a psychedelic experience. In turn, a brightly shining metta metronome emits “healing waves of energy” within one’s world-simulation (I know how crazy this sounds!), which impact the contents of one’s subconscious in ways that reduces their internal dissonance.

Metta is described (approximately 6:45 - 13:30) by Rob Burbea as boundless, unconditional well-wishing(Burbea 2010). This is a deeply significant experience from many points of view, with a less frequently mentioned one being the direct computational benefits to the meditator. Because actions and thoughts are fundamentally motivated by how good or bad an experience feels, every part of a person’s mind can deeply synchronize with the wish to be well during metta practice. The qualities of boundlessness and unconditionality are crucial here, as these are what allow the understanding and feeling of metta to include all sensations that arise in your moment-to-moment experience and seep into your subconscious. The meditator then becomes more unified in mind and will because every part of their mind has a clear common ground to collaborate and coordinate from, but it’s also useful in other ways. Metta is an insight practice as well because it is simply true that all beings deeply wish to feel well, so practice results in more general predictive ability as the metta deepens. Experiences of the world and especially the agents in them become more parsimonious, yet retain or even gain vibrancy and detail. The more well-known emotional and interpersonal benefits of deeply embodying metta are left as an exercise to the reader.

The last ingredient in this cocktail of ideas is quite recent. At PhilaDelic 2023, a psychedelic science conference, Andrés presented an update to the paradigm of neural annealing(Gomez Emilsson 2023). That update was termed neural field annealing and describes the importance of field behavior for neural annealing. A field is characterized by smooth geometry and a wave equation; one example that was given in the presentation was a 40 hertz bodily vibratory wave. Here the wave equation would describe a simple 40 hertz sine wave in the sense of the body, and the smooth geometry means that sensations are locally continuous; there are no kinks, blockages, or shears preventing the smooth flow of energy. Fields are computationally significant because they transmit energy and information effectively due to their smooth geometry, and the wave equation of a field allows the coordination of complex changes in parallel without needing to centralize to a controller of some kind. Every point of sensation simply follows the wave equation locally, giving rise to global structure. Steven Lehar notes that wave behavior as a computational mechanism is extremely rich, allowing generation of quite complex patterns from simple input even in a case as basic as a Chladni plate (Lehar 1999).

“Chladni figures for a square steel plate (adapted from Waller 1961) demonstrates the fantastic variety of standing wave patterns that can arise from a simple resonating system. A square steel plate is clamped at its midpoint and sprinkled with sand. It is then set into vibration either by bowing with a violin bow, or by pressing dry ice against it. The resultant standing wave patterns are revealed by the sand, that collects at the nodes of the oscillation where the vibration is minimal.” (source)

There are also many desirable properties that harmonic resonance has for computation. He mentions rotation invariance in recognition and pattern completion, multistability between competing patterns, emergence of global coherence, and more(Lehar 1999). In his words,

… the resonance defines the topology, rather than the topography of the encoded forms. Resonances in connected systems, such as the engine and chassis of your car, have a natural tendency to synchronize or couple with each other so as to produce a single emergent oscillation which exhibits higher harmonics which are characteristic of each component resonator, embedded in a fundamental waveform that captures the resonance of the system as a whole.

This brings us to mettannealing, a meditation that uses the theoretical implications of neural field annealing to make more effective loving-kindness practice. Per neural annealing, increasing the energy and intensity of experience makes the mind more malleable, flattening attractor basins and weakening sticky priors; this is the sort of state that makes it easy to learn things and relax old habits. This is also what we intuitively notice to be the case, more intense experiences are often remembered better and often cause long-term changes in us. The idea is to use a clean, high-energy state to make the generation of metta easier and the learning of the practice faster. This isn’t just an effect from increased intensity though! The introduction of semantically neutral energy, in our case from breathing exercises, energizes the natural resonant modes of the mind. As mentioned earlier, it is a deep and natural wish of all beings to be well, so injecting semantically neutral energy causes natural generation of metta-like qualities. Additionally, Rob Burbea notes that when one personally has a strong sense of self and separation from the world or imagines that for others, love tends to be more jealous, conditional, and exclusive. However, when one engages with semantically neutral energy, metta more naturally arises, as feelings of love do not become trapped in a specific, complex, and intricate sense of self. Instead, they remain free to flow throughout the nervous system without blockages. QRI’s visiting scholars cohort volunteered to practice and refine mettannealing over the course of a few weeks. Similar to the memorization of graphlets and QRI’s series of guided meditations, our goals in engaging with this practice were to develop common knowledge and mastery of phenomenology.

Practice Instructions

The playlist practiced follows the simple formula of: (1) energize with semantically neutral energy, (2) direct energy to a “metta field”, and (3) cool slowly to anneal this desirable field behavior. While the playlist is a specific rendition of this general formula, one can envision many different implementations that are personalized for each individual’s needs and orientations. Below you find a discussion of the general formula illustrated with the specific playlist of Mettannealing that was used:

First, energize your experience however you wish. Possible choices are breathing exercises, physical exercise, really anything that causes high-energy experience. The energizer we used was a Wim Hof breathing exercise, ten minutes of intense focus on and work with the breath. This was a particularly nice energizer, as the regularity of breathing and instructions such as “make it circular” and “like a wave” establish a baseline of smooth geometry and wave-like behavior, which is quite pleasant and will be useful later.

Next, metta meditation. We typically used the second video in the playlist provided, it is a brief guided metta meditation. Rob Burbea’s talks on metta are also excellent, and I personally enjoyed them a great deal. If you do not want to listen while meditating, you can simply give attention to the genuine wish for yourself and others you know to be well, then gradually extend this wish at whatever pace works for you to encompass beings everywhere. As mentioned earlier, the qualities of boundlessness and unconditionality are crucial here. These qualities correspond to the wave equation of our field; the vibratory modes that we intend to energize are exactly those corresponding to unconditional and boundless loving-kindness, and because we have a lot of energy and a smooth field to start from, this is much easier to entrain than it is normally.

Finally, cooling. We listened to the Ratana Sutta, but personally I found that resting my mind with equanimity gave the best results. This is the natural feeling of peace and equilibrium that comes from realizing that all beings are the inheritors of their pasts, and that their well-being depends on their past actions. There’s also zero attraction or aversion to any being in this state, so you’re neither unconsciously getting pulled into or pushed away from any particular being, and as it generalizes to the mind, any particular mental event. You may also think of it as a practice of letting whatever happens happen, simply being aware and letting anything in your experience arise and pass on its own, without interfering with it or attempting to change it.

Phenomenology Reports

Ethan

Breathing

During the breathing, very strong and pleasant bodily vibrations started in my hands and feet especially, and the visual field seemed to sync with the breath. There were sometimes reaction-diffusion looking patterns across the visual field during the breath holds, though during the breathing the field was fairly uniform and clear, but vibrating and fluid. Quite obviously three-dimensional too.

Metta

Sometimes green-purple blobs moved in reaction-diffusion like patterns, but there was mostly subtle visual flicker that got smoother and finer as the meditation progressed. The emotional/bodily feel was quite smooth and soft, and oftentimes a memory would briefly pop up and I’d feel like having a perspective of loving-kindness on it healed or helped some bit of my consciousness. The loving-kindness synchronized with the vibration in my hands and feet from the breathing exercise, and those vibrations got much smoother as a result of that. There was a brief period once when the hand vibes were particularly strong where they started clicking as a unit and felt like they had a mind of their own, and waves of metta seemed to bounce between my hands, me, and the rest of my experience. Very pleasant.

Equanimity

Simply paying attention to the fact that anyone’s current well-being depends on their past actions is shockingly integrative and balancing/stabilizing. As the intensity dropped and the field smoothed out even more, there was a strong sense of the ability to accept anything, just as it is, without judging those sensations as attractive or aversive. There was also the sense of the past and future syncing up when I was paying attention to well-being as action-dependent, a reflective equilibrium started to become clear where the practice was demonstrating in real time that it was true that wellbeing is dependent on past actions, which made me feel more peaceful, which is further evidence, and so on. The metta remaining after this had a sense of durability and flexibility, like it was able to happen anywhere and anytime because it was aware of the causes of its existence, which are in the mind. One interesting note is that after getting up, my body feels significantly more responsive and light for a few minutes, with a little bit of the effect persisting throughout the day.

Riccardo

Breathing

Fast breathing shows patterns of small lights, flickering. Long breath hold shows slower transitions between lights/shadows. Short breath hold shows some patterns of thin lines of light traversing the visual fields, which seems like roots or blood capillaries.

Metta

Slow moving (wave-like) blobs in the visual field. Purplish, pink, gray colors. They increase in size and brightness as the meditation progresses. A general feeling of energy build up. Feeling as if the body is charging. More vibrating waves throughout the body, especially after gathering together a circle of people and starting to send mettā to them. Waves aren’t clearly directed from head to feet, but perhaps more as circles starting from the middle of the body (hearth?) and propagating in all directions. Waves feel extremely pleasant, ecstatic, full of joy and love.

Ratana Sutta

As the sutta ends I feel like I could keep going on forever because of the high valence of the stillness, but I also experienced twice exiting out of this very suddenly and with a gasp After the session, my body feels extremely energized with a soft and gentle charge.

After a few times doing mettannealing

Today I did it sitting in front of a window and it was very pleasant. Deep feeling of compassion and melting/deconstructing of both physical and mental structures. I also had the impression that waves and lights in the visual field were wider, slower and more smooth/stable as the practice progressed.

Carlos

The most eventful part of it, phenomenologically speaking, seemed to have been the first third focused on breathing. My experience very quickly acquired a certain pleasant ‘coldness’ or ‘mintiness’ to it, which was interesting, and felt more ‘energetic’ as well. During the 1.5-minute intervals where I stopped breathing, I felt an ‘emptying of myself’, and in a sense feeling more grounded (similar to what Riccardo experienced). I was somewhat tired when I started – but by the time I ended the Wim Hof breathing section, my tiredness had faded away. I’d say the breathing section served a useful purpose, as I might have fallen asleep during the other two thirds had I not done it (I did the breathing part with the eyes open). I had tried doing metta before, but I must admit doing it with a guided video was much easier and straightforward, as I didn’t have to expend energy coming up with the next being I should send metta to. Phenomenologically speaking, I felt ‘an infinite expanse’ at times, particularly when the cardinal directions were described. I heavily relied on my visual imagination during metta. Other than that, nothing visually interesting occurred, although that might change in following sessions. During the Ratana Sutta section, especially after spending time deliberately paying attention to the chanting, my mind ‘emptied’ and only the experience of hearing the chanting was left (important to note that my eyes were closed).

Generalized Mettannealing

As mentioned earlier, the core of mettannealing is to generate semantically neutral energy, direct that energy towards metta in order to learn the desired field behavior and smooth the texture of experience, then anneal with slow cooling to ensure that the state you’ve practiced is flexible and therefore generalizes nicely. Working with this core structure, there are a few key variables and activities that can be changed or added to alter the effects of mettannealing.

Cooling time

In analogy with annealing in metallurgy, after we have heated our material past the recrystallization temperature it must cool in order to allow the new microstructure to crystallize. Longer cooling time results in a more regular crystal lattice, while flash-cooling produces amorphous solids. For mettannealing and meditation more generally, the structure of experience when we have more time to cool is going to be more regular and pleasant than if we stop abruptly, and it will end up more flexible and ductile, allowing for better generalization out of distribution.

“Example illustrating the effect of cooling schedule on the performance of simulated annealing. The problem is to rearrange the pixels of an image so as to minimize a certain potential energy function, which causes similar colors to attract at short range and repel at a slightly larger distance. The elementary moves swap two adjacent pixels. These images were obtained with a fast cooling schedule (left) and a slow cooling schedule (right), producing results similar to amorphous and crystalline solids, respectively.” (source)

Temperature

In simulated annealing, having a high temperature to start means that we will first explore very large changes in state before narrowing our search as we cool. When we are looking for something novel or trying to get out of a rut in our practice, turning up the energy more than usual before the metta begins may be an efficient way to jump out of local minima before filling in the details. Also, as loving-kindness is a very natural state of our minds, having semantically-neutral energy accumulate disproportionately increases your chance of getting into such a state compared to other possible states.

Simulated Annealing (source)

Energizer

The energizer used seems to change the process and results. From personal experience, exercising beforehand seemed to give energy that was more durable but less clear than that given by the Wim Hof breathing exercise. In general, the texture of the energy you cultivate is likely to show up in the state you cultivate, so plan accordingly!

Pre-loading

Because smooth geometry is such an important part of desirable field behavior, it may be helpful to meditate on some smooth experiences before energizing so that when you get to the metta, you have already loaded beneficial aspects of the experience to some degree. Practicing metta a bit beforehand, even without the benefit of increased energy, may reveal “seed crystals” that you can use to cultivate metta more quickly after building energy.

Creating high-entropy alloys

In metallurgy, a high-entropy alloy is a material made of many, usually five or more, elements mixed together into an alloy. The crystal structure of these materials is often quite complicated, and due to combinatorial explosion, it is difficult to predict which high-entropy alloys have world-class properties beforehand. In experience, we have a similar problem, as we can mix different qualities like metta, equanimity, and compassion, and there are many possible ways for these qualities to harmonize depending on their relative proportions. Searching through this state-space efficiently may be possible by heating, mixing the qualities you want to to harmonize, cooling, then combing through the resultant experience for patches of regularity, which will be especially harmonious combinations of these qualities arising due to free energy minimization.

Atomic structure of a 5-metal alloy, clearly pretty complex, but it has nice properties! (source) (C.C BY 3.0)

Choosing your own Mettannealing

Keeping these possibilities in mind, we can build our own mettannealing practices just as we want them. We can choose what patterns to pre-load, what to energize the field of experience with and how much, characteristics of the metta field we intend to anneal, cooling time and content, and how we review and relax afterwards. Playing around with these options gives the opportunity to custom-make experiences that are deeply healing and simultaneously explore beautiful regions in the state-space of consciousness. That said, not all possible combinations will result in deeply fulfilling experiences. Jumping straight into high-powered energization, giving experience a quick splash of metta, cooling as fast as possible, then immediately trying to write code is probably not the sort of recipe that will allow the innermost facets of yourself to safely and smoothly enter deep harmony with the totality of your experience! Building a clean and simple foundation of metta from which to bootstrap more exotic states will be safer and more effective than jumping straight into the deep end. For long-term experimentation and practice, cultivation of the 7 factors of awakening in the context of neural field annealing will serve you well, allowing more precise control of relevant factors of experience and letting you stay in the zone more easily.

Acknowledgements

Many thanks to the other two 2023 visiting scholars, Riccardo Volpato and Carlos Quintero, for their insightful commentary on the phenomenology of mettannealing and conversations on the topics here more broadly! Additionally, thanks to Andrés Gómez Emilsson for feedback on my writing and helpful commentary on the mechanics of neural field annealing and Hunter Meyer for writing feedback and helping with characterization of the history behind these ideas

Tags

Meditation, Neural Annealing, Consciousness, Metta