Cross-frequency coupling: Psychophysics results from the Brazil QRI retreat

Posted on 13 May 2024 by Cube Flipper

Prior to the Brazil psychophysics retreat, Andrés’ friend Andrés Silva (El Capitán) developed a whole collection of psychophysics tools to experiment with. Two of these in particular demonstrated interesting results. Working together, they had discovered a couple of animated visual stimuli which appeared noticeably different while on psychedelics – which could provide supporting material for Andrés’ psychedelic thermodynamics framework – and so Andrés brought these along to the retreat.

In particular, we were interested in investigating how psychedelic-induced cross-frequency coupling might result in phenomena like symmetrical texture repetition and gestalt formation. For a discussion on why symmetry might be a stable attractor, I recommend Andrés’ conversation with Josie Kins of PsychonautWiki, which covers this topic, amongst many others:

In general, physical systems follow this general formula. When you have regions with a lot of stored energy in the form of stress, tension, or a lot of potential energy – or like electric potential – they will try to dissipate that. And they will do so as far as they possibly can, until they cannot dissipate it any more, and that usually will be an equilibrium state. Usually the equilibrium states will have features like symmetry, because when you have symmetry there’s no region which has any more stored energy than any other one. So that’s a stable attractor.

So what happens on a psychedelic, to a first approximation? One thing they do is activate internal sources of energy that energise your consciousness – very similar to a strobe. Neurophysiologically, there’s one account – I don’t know if this has been fully confirmed, but it was a good theory for a while – that the cortex functions as an inhibitory mechanism. What it’s trying to do is predict the next input, and whenever it can predict an input perfectly – you tune it out. In some sense you really only experience the things that were surprising.

And so, the cortex has this inhibitory effect on the thalamus – and the thalamus is kind of like this central hub where all of the sensory input gets aggregated. So the cortex is gating, it’s preventing the activation of the thalamus in every way it can – whenever it can anticipate what’s going to happen.

So James Kent – maybe you’ve heard of Psychedelic Information Theory? He has this article called The Control Interrupt Model of Psychedelic Action. So he has this idea that the cortex is an inhibitory mechanism. Imagine that it’s sending, like, a hundred signals per second to the thalamus, in order to inhibit sensory input. Now, something like LSD might block that inhibitory signal several times per second – so it’s actually inhibiting an inhibitory mechanism. As a consequence, the thalamus ends up propagating more energy, more information to the cortex. So the new homeostatic balance of energy is one where the cortex and the thalamus are more activated, because there’s a failure to inhibit several times per second.

Effectively, that ends up being something like an internal strobe in your brain, which prevents the inhibition of what you’ve just experienced – and this would be a very low level mechanism for tracer effects. Now, tracer effects will generate this build up of qualia, this build up of energy in your experience, and then there’s a lot of downstream effects that come from how your brain handles all that extra energy.

And that is where psychedelic thermodynamics comes into place – which is that there’s this extra energy which is trying to be dissipated – and in this theory, all of the crazy psychedelic effects are actually a result of that energy dissipation process. Like the symmetries that you see – are symmetries because the more symmetrical configurations are energy minima.

Armonia Natural Cuadricula

This stimulus was an animated grid-like texture which rotated slowly through a series of configurations – and its perceived rate of change was said to increase under the influence of psychedelics.

Armonia Natural Cuadricula

I tried it out during our first session, during which I took four grams of (weak) mushrooms. Sure enough, the effect was striking.

I’m not entirely sure that what I was observing should necessarily have been interpreted as an increased rate of change. It was more the case that the subtle evolution of the pattern was much more noticeable, as the lighter areas would now connect to one another in such a way that the shapes they made would propagate outside the foveal region of the visual field and across the entire canvas.

Additionally, as the stimulus had a chaotic element to it, as it rotated through different states completely different regions would couple with one another. Radically different harmonies would be amplified from moment to moment – making the effect all the more conspicuous.

It was not entirely unlike the mesmerising sensation of driving past a vineyard and watching as the trellises line up… eyes on the road! This had valence effects which were worth noting. As the pattern passed through a maximally harmonious nested 3×3 pattern, I felt a satisfying electric zing sensation pass throughout my body.

Later on, I attempted to generate a replication to demonstrate how this all looked:

Armonia Natural Cuadricula with the extrafoveal region blurred and enhanced. If you rest your eyes on the very center but study what happens in the periphery, this should be suggestive of the kind of thing I observed.

I am unsatisfied with this, so far as replication work goes – but I hope it gets the point across. I believe that a true replication of this phenomenon would involve writing a two-dimensional Fourier domain filter which is capable of transferring energy from the inharmonic to the harmonic frequency components.

Hypnagogic Quasicrystals

This stimulus was another animated texture, but composed from multiple layers of overlapping sine waves such that their interference patterns sporadically generate circular percepts. As I understood, as the psychedelic dose was increased, these percepts would couple together into larger and more complex gestalts.

Hypnagogic Quasicrystals, four layers

I found this effect was easily observable sober, but in the psychedelic state circles of different sizes would become visible, and these would couple into gestalts reaching far outside the foveal region – we observed many gestalts of various shapes, and gave them names like clouds, crystals, snakes, ouroboroi, octopi

It strikes me as important that the angles between the sine waves are such that the interference pattern circles don’t form an obvious grid or lattice. This seems to impede the typical symmetry propagation effect in a way which forces the development of gestalts.

Hypnagogic Quasicrystals, seven layers

When the number of layers is increased from four to seven, we begin to observe the formation a wide variety of quite interesting mandala gestalts. I find that this effect is quite strong even without psychedelics – and unlike the four layer stimulus, it fills the extent of the canvas.

My intuition is that the intensity of the symmetry propagation and gestalt formation effects might vary significantly from person to person. I’ve read reports from people who meditate observing symmetrical texture repetition in grass, but I’m sure there’s plenty of people who can observe this phenomenon without psychological or chemical assistance.

This is worth acknowledging! I’m not convinced that this psychedelic thermodynamics framework really needs to be oriented around psychedelics, specifically. It attempts to describe the dynamics which drive our subjective experience in general; and as such should really be called something like neural field thermodynamics or even phenomenal field thermodynamics.


Cross-frequency coupling

Both of these stimuli exhibit cross-frequency coupling – whereby oscillators that are near integer multiples of one other can interlock by adjusting their phases until they are in alignment with one another.

Around the time of the retreat, a friend of mine recommended I read a paper called The Devil’s Staircase (Bak, 1986). This paper provides a vivid illustration of this phenomenon:

In the 17th century the Dutch physicist Christian Huyghens observed that two clocks hanging back to back on the wall tend to synchronize their motion. This phenomenon is known as phase locking, frequency locking or resonance, and is generally present in dynamical systems with two competing frequencies. The two frequencies may arise dynamically within the system, as with Huyghens’s coupled clocks, or through the coupling of an oscillator to an external periodic force.

If some parameter is varied – the length of a pendulum or the frequency of the force that drives it, for instance – the system will pass through regimes that are phase locked and regimes that are not. When systems are phase locked the ratio between their frequencies is a rational number. For weak coupling the phase locked intervals are narrow, so that even if there is an infinity of intervals, the motion is quasiperiodic for most driving frequencies; that is, the ratio between the two frequencies is more likely to be irrational. When the coupling increases, the phase locked portions increase, and it becomes less likely that the motion is quasiperiodic. This is a unique situation, where it makes sense, despite experimental uncertainty, to ask whether a physical quantity is rational or irrational.

We shall see that if one plots the frequency of the oscillator against the frequency of the applied force the resulting curve may consist of an infinity of steps – the Devil’s staircase.

Dynamical-system staircases. The fractions are the ratios of competing frequencies that have locked to form the plateaus. a: Current-voltage characteristics of a niobium Josephson junction driven by a 295-GHz microwave current. The voltage is a measure of the frequency. b: Frequency of oscillations in a complex chemical reaction as a function of the reaction rate. c: Frequency of voltage oscillations in a superionic conductor, barium sodium niobate, driven by a direct current.

In the case of Armonia Natural Cuadricula, if we consider the horizontal and vertical stripes to be oscillators with distinguishing spatial phases and frequencies, I think that if one was to analyse those deeply they would find that three factors contribute to how strongly they couple to one another:

  • Absolute frequency: i.e. oscillators with high spatial frequencies don’t tend to contribute as much to the perceived global gestalt
  • Relative frequency: i.e. pairs of oscillators couple more strongly when their frequency ratio is simple, e.g. 1:1, 1:2, 1:3, 2:3 etc
  • Relative phase: i.e. pairs of oscillators couple more strongly when their phase offset is simple, e.g. 0, π, π/2, π/3, /3 etc

So a pleasing gestalt forms when you have a tidy network of these couplings such that the oscillators all mutually resonate with one another. As Armonia Natural Cuadricula rotates through a sequence of different configurations, we see these networks of resonance form and dissolve continuously.

Valence gradient descent

I find all of this quite reminiscent of earlier excursions into such territory. In a previous post, I described how DMT tends to increase the symmetry of three-dimensional objects volumetrically:

It thrives in an artificial environment, if sufficiently vibrant. Flat surfaces appear smoothed over, sometimes tiled with their own textures, while three dimensional objects conform to a global gestalt – as if aligned to a grid by an invisible carpenter with set square and ruler.

As I increase the dose, this normalisation process becomes more extreme, decimating geometry until the dimensions of objects begin to snap to small integer aspect ratios. Let’s say you apprehend a flatscreen television with an aspect ratio of 16:9 – perhaps it will adjust its shape to fit an aspect ratio of 2:1.

Small integer aspect ratios! Do I need to connect the dots?

Something I do hope we can demonstrate in future is how this class of phenomena are ultimately just examples of valence gradient descent. But that’s beyond the scope of this particular psychophysics report—