The three marks of existence and the Fourier uncertainty principle

The three marks of existence is a Buddhist framework for understanding the nature of experience. It proposes that all conditioned phenomena exhibit the three characteristics of anicca, anattā, and dukkha – sometimes translated as impermanence, no-self, and dissatisfactoriness, respectively. The implication – if you are a sentient being who is reading this – is that apprehending and accepting these three properties is foundational for liberation from suffering.

The purpose of this post is to present an alternative formulation of these concepts using signal processing terminology, as proposed by my collaborator, Ethan Kuntz. I’ll start with a little background on the three marks, but if the reader would just like to read about Ethan’s framework, they can skip forward to the relevant section.

Anicca, anattā, and dukkha

Dharma nerds are notorious for sustaining intractable disagreements relating to the frameworks they use to model phenomena, and the matter of translation from Pāli dharma jargon into modern English only complicates the issue. The three marks are no exception. One well-regarded attempt to legibilise Pāli terminology is Romeo Stevens’ post (mis)Translating the Buddha, which includes a discussion of the terminology pertaining to the three marks. Along the way, he is careful to emphasise that these are statements about detectable mental events within the stream of physical sensation, and not statements about reality. An excerpt from Romeo’s post:

Dukkha is usually translated as suffering, which sort of works but misses important stuff. A more literal translation is ‘a difficult emptiness’. Approaches, even quite effective ones, for dealing with the suffering of life were already in existence at the time of the Buddha. Both schools that preached constant absorption into pleasurable meditative states, and schools that preached a doctrine and practice of ‘non-duality’. Both of these approaches survived, became mixed up with Buddhism, and today there are schools claiming to teach Buddhism which actually teach these methods. These methods do in fact decrease suffering, but they are only partial solutions. Both because they are reliant on maintenance of certain states and ways of being, and because while they deal with suffering caused by the immediate senses, you are still left with a more fundamental suffering related to feelings of emptiness or, dukkha’s other translation, ‘worthlessness’ and related feelings (nihilism etc. in the west). You’ve encountered this for yourself if you’ve experienced something cool during contemplative practice but then had a kind of ‘so-what?’ moment. The sense that this experience, while interesting and probably a temporary respite from your worries, hasn’t actually addressed the core problem. People especially have this coming back from retreat. If this were just considered on its own, without the teaching of the antidote, this might be called worthlessness, that it seems like things are never satisfying and thus nothing has any value.

Anicca is translated as ‘impermanence’ but this is off and it’s worth pointing out how this happened. In the 19th century when a lot of initial western translations of Hindu traditions was occurring, much of the translations of Buddhist texts were done by Sanskrit scholars. This is interesting because it was foreseen as a problem by the Buddha. There is a discourse where Sanskritists come to the Buddha and he specifically warns against conflating Pāli and Sanskrit terms as highly confusing (because there is a bunch of overlap in affixes and grammar)! He tells them not to translate the teachings into Sanskrit because it will lead to nothing but problems. In modern times we are saddled with exactly this having come to pass. The Pāli words for impermanence are adduwan or aniyata and the Buddha uses these terms elsewhere. This happened due to Sanskrit translators thinking that anicca was the same word as anitya, the Sanskrit word for impermanence. So what is an actual translation of anicca? Something more like our inability to maintain things as we like. This sounds philosophical, but there is a specific mental event it points to, namely the inverse: Nicca. And this gets at an extremely important point in how this stuff works. If suffering were truly just coming in from the outside in thousands of different forms (i.e. the way things seem on cursory inspection) then we wouldn’t have much hope of a single intervention helping us. Nor would we be confident in any such intervention since some new form of suffering can always show up. But if suffering is a result of something we’re doing, then if we can figure out how to stop doing that, the suffering stops. Which we can confirm for ourselves in moment to moment experience. So nicca is our tendency to believe that things could or should be maintained to our satisfaction. This is an identifiable mental event in how we reify an object or concept. Ignoring the very ephemeral nature of moment to moment experience in favor of only noticing those aspects which do occur as stable. Spotting it for yourself is very powerful. If this were just considered on its own without the teaching of the antidote it might be related to feelings of hopelessness. That there is no hope of maintaining the conditions that lead to things we like. Thus, the flow of positive and negative experiences are undependable, indefinite in duration, intensity, and frequency. That our hopes of forcing them to be stable with our mind will be in vain.

Anattā. Oh boy where to even begin? Like anicca, anattā was translated by Sanskritists as the same as the Sanskrit term anātman. A literal rendition of anātman is ‘no-soul’ but is also generally interpreted as ‘no-self’. This has probably lead more people astray than any other mistranslation. And again we have passages from the Buddha warning against this specific problem. People come to the Buddha to argue about self vs. no-self doctrines and he repeatedly says that if you hold a view of the self as existing then you are in error, and that if you hold a view of the self as not existing you are in error. The first major milestone on the Buddhist 4 path model is the release from having any particular view of the self because the whole point of the first milestone is that you’ve improved your understanding of the causal relations between mental events enough that you’ve seen that this distinction was predicated on a confused concept. Furthermore, if we were to take the translation of no-self as valid a bunch of discourses don’t even make grammatical or logical sense. Of course not making logical sense is considered a feature by mindlessness schools.

Like anicca, anattā is pointing to the inverse of a specific mental event, attā. Attā is a little hard to translate, we can translate it as more like a verb or more like a noun (Pāli is weird). If we see it more like a noun it might be translated as ‘essence’ and if we translate it like a verb it might be translated as ‘to take/have control/ownership of’. Together we have the notion that if something has a real immutable character or ‘essence’ to it that we understand, then we can really control it and that this control won’t be subject to change. Anattā is to point out the error in this way of seeing things. The point is to notice the mental event that represents objects or concept as though they could or should be inherently or essentially controllable/ownable. If this were to just be taken on its own without the teaching of the antidote it might be called helplessness, that things are without the possibility of being controlled. We use the mind to falsely pretend we are more in control than we are. This faculty of mind feels like one of those child’s car seats that has a fake steering wheel on it, made famous by The Simpsons opening credits. The mind either deludes itself by carefully moving the fake steering wheel in line with what it sees so that it can pretend it has control, or it strains itself throwing its weight ineffectually into cranking hard on the wheel when the car goes places it doesn’t like.

My interpretation is as follows:

• Anicca refers to how all phenomena lack inherent permanence; they might unavoidably come to arise or pass.
• Anattā refers to how all phenomena lack inherent essential qualities; those qualities which we might perceive as essential might change or stay the same. The self in no-self is confusing; the self as we commonly understand it is just one such phenomena, which also lacks essential qualities.
• Dukkha refers to the lack of inherent satisfactoriness in all phenomena.

Nicca, attā, and sukha

Romeo continues by reviewing why one might be motivated to understand these concepts:

Between dukkha, anicca, and anattā we already have a very important understanding. What the Buddha is saying is that by default our way of viewing the world is that things should or could have a stable, unchanging essence, by understanding that essence we can thus control things and thereby bring about conditions that leave us satiated and full. That the mind can make things stable, controllable, satisfying. That if we do this well enough we will no longer ‘go hungry’ for that which we can’t obtain. And that this way of viewing things unavoidably leads back to the suffering of emptiness, worthlessness, helplessness, hopelessness, because it was never aligned with how things actually work. That we never investigate how things actually work because to do so would force a confrontation with exactly these feelings that we were trying to avoid.

In short, that nicca, attā, and sukha (the opposite of dukkha) are maladaptive strategies. Not only do they not get us what we want but they maintain the conditions that lead us to keep using them. Instead of seeing that the whole strategy is broken we keep trying to do it more skillfully, making finer and finer carvings to try to only cut out the bits of things that are stable, controllable, satisfying. Rather than claims of truth about the universe, the claim that learning about these reduces fundamental ignorance is just a claim that we’re unaware that we’re already doing this.

Perhaps these concepts are better apprehended through their antonyms. In this context, nicca, attā, and sukha refer to the counterparts to the three characteristics – and the associated mental motions we might make while attempting to fixate or reify these characteristics. We might imagine that some particular phenomena will arise or pass, or change or stay the same – and by doing so, we might reduce our suffering locally or in the short term. However, if we learn to observe the inherent impermanence, inessence, and dissatisfactoriness in all phenomena, we then observe that these mental motions lead us to accrue the psychological equivalent of technical debt – which only leads to more suffering in the long run as our reifications become unmaintainable.

I’ll now hand over to Ethan, who offers the following interpretation of the three characteristics and their antonyms:

As a dharma nerd, I’d be remiss in not talking about how my model of the three characteristics relates to Romeo’s. Romeo takes them to be purely mental events – no claims about the external world required – and defines attā, sukha, and nicca as strictly maladaptive strategies. This is solid, but I think there’s more going on.

To distinguish my model from Romeo’s, I’ll use the (unfortunate) English translation pairs (impermanence/permanence, self/not-self, suffering/bliss) rather than the Pāli terms.

I like to think of the three characteristics as common and convergent mental motions for modeling three fundamental aspects of experience: time (impermanence/permanence), essentiality (self/not-self), and tension (suffering/bliss). If we take it as given that the external world seems to have three ubiquitous features – time as a relevant variable, natural categories/abstractions of varying salience, and pairs of action/reaction forces such as tension – then it follows that modeling these would be very important to the brain. Impermanence, not-self, and suffering are then something like the counterbalancing mental motions to permanence, self, and bliss. The three pairs allow the mind to span all three axes of time, essentiality, and tension.

In my model, none of these mental motions are inherently maladaptive strategies, but errors in handling and understanding them do happen. These modeling capabilities evolved for good reasons and serve important functions when used skillfully.

Alright. So, at the most reductive level we can get away with – what are these mental motions, and what exactly are these qualities of experience that we attempt to fixate?

Clenching and taṇhā

I suspected that my friend Matthew Leo did not realise that he was asking similar questions when he began writing his now-finished series of posts on clenching – but one thing he was interested in was how our motor systems respond to unpredictability. From his post, Harder: Better? Faster: Stronger? (2023):

How do we control the movements of our bodies?

One paper from 2019 asks a little more specifically: how do we change the way we reach with our arms, when outside forces interfere?

The authors set up a reaching experiment. Human volunteers sat at a desk with a display built into it, and reached across it while grabbing onto a robot arm. No, not like that prop in the lab in Terminator 2, but a rather more boring handle attached to a mechanical arm with sensors to measure the reaching path, and motors to disturb the reach with outside forces. The display showed visuals for the experiment, including position feedback: a cursor, which tracks the handle.

Imagine someone makes 100 reaches in a row, starting and ending at the same points, and returning to the starting point between one trial and the next. They are told before the session that their reaches should be straight. They are pretty good at reaching straight. But the annoying robot disturbs every single reach. It applies a constant leftward force to the handle. Initially, this bends the paths of the reaches to the left.

This kind of disturbance is consistent and predictable. Many past studies show that healthy volunteers and non-human primates will adapt and counteract a force like this after many trials, so that the path of their reaches returns to the straight shape it had before the force was added. Not so annoying, after all. Manageable.

If the disturbing force is suddenly omitted from the next trial, the reach bends in the opposite direction – in this case, rightward – instead of instantly becoming straight again. So the volunteers are still compensating, still predicting the force will be there. But over just a few more trials, their reaches become straight again.

What if the disturbing force only appears on a fraction – say, 20% – of trials, chosen at random? That’s not exactly predictable. Well… after a while the volunteer can tell they’re in a place where some trials are disturbed. But they can’t tell which ones until it happens. And then they hardly have time to switch their “opposing force” reaction on and off, since trials only last about a second. This is actually pretty annoying. And it would be unwise to use opposing-force on every trial, in this context. It’d help the 20%, but bend the other 80%.

Is some other strategy better, here?

The authors found that people “double down” on their movements. Their reach speed gets a bit faster – higher inertia. They respond more vigorously to changes in sensory feedback, such as shifts in the perceived position of their arm. And the muscles used for reaching all contract a bit harder.

This go-harder strategy isn’t a remedy for leftward disturbances in particular. Instead, go-harder reaches are slightly more robust to being altered by forces in any direction. Go-harder helps in case of 20% leftward disturbances, or 20% rightward, or a random mix of leftward, rightward, and something else (like a force field with curl) – in every case, go-harder won’t totally straighten, but will reduce the impact. And unlike opposing-force, go-harder doesn’t pointlessly bend the reach paths on trials where there is no disturbance.

Matthew was unfamiliar with any meditative literature at the time of writing, so I recommended that he read Romeo’s post. He later wrote a response, Who (mis)translates the (mis)translators? (2023). As he proposes, the mental motions related by Romeo are forms of clenching – or taṇhā, to use what we suspect is the appropriate Pāli term – attempts to increase our certainty around events that may be happening to us.

I think that myself and Matt would be in agreement that the increased clenching in the experiment is the result of pursuing nicca and attā – the participant is instructed to fixate the position of their arm in time and space, and responds to increased uncertainty by increasing muscle tension. Arguably, in this situation the increased tension is unavoidable – problems mainly arise when the patterns of clenching are superfluous in the first place, or are not released afterwards.

Ethan had the following to say with regards to relating taṇhā back to the three characteristics:

Taṇhā becomes particularly problematic when it fixates on any of these basic mental motions. Errors here are especially costly because these mental motions are foundational – they apply in some form to the fabrication of every experience. Romeo’s model does a great job detailing what happens when taṇhā causes one of these mental motions to get “stuck in the on position” due to taṇhā.

In my model, taṇhā can occur with any mental object or motion – not that mental motions and objects are fundamentally different. Critically, this includes the three pairs of mental motions for modeling time, essentiality, and tension. The maladaptive strategies that Romeo is talking about arise when taṇhā occurs with these mental motions. For instance, let’s say you are stabilizing something in mind, and taṇhā occurs on the mental motion of stabilization itself. Now, you will be auto-grasping for stability of something, feeling like “this should always be stable/unchanging”. This is what he calls nicca. Of course, this is not possible – everything is already in flux, so this “should” will be in tension with the way things are. Similar things happen for the other three characteristics and their counter-motions.

I’m willing to make the claim that similar dynamics play out at higher levels of cognition. We often use something like the psychological equivalent of muscle tension when attempting to fixate desirable states, and in the process of doing so we trade off grasping for certainty with something like increased psychological fragility. So, as Matthew asks, how can we unclench? To go further, perhaps we need to apprehend the three marks with maximal clarity.

Time, frequency, and uncertainty

The three marks are a foundational Buddhist teaching, and as such have been subject to much armchair analysis. They’re also a natural place to start when attempting to construct mathematical models of phenomenology. A couple of months ago, Ethan Kuntz was discussing some ideas with me regarding the mathematical structure of the three marks, when he proposed that the Fourier uncertainty principle could be a good fit for some aspects of the phenomenology. Later on, I said I’d help write this one up, so here we are.

The Fourier uncertainty principle – also known as the Gabor uncertainty principle – is analogous to the well-known Heisenberg uncertainty principle from quantum mechanics. This is often formulated as:

This relation states that the product of the uncertainties in position (Δx) and momentum (Δp) can never be smaller than half the reduced Planck constant (ħ). In other words, the more precisely we measure a particle’s position, the less precisely its momentum can be known – and vice versa.

Mathematically, this relationship follows from properties of the Fourier transform, and was used by Werner Heisenberg in 1927 to express the position-momentum uncertainty relation in quantum mechanics. In 1946, Dennis Gabor demonstrated that the same principle could be applied to signal theory and time-frequency analysis. It can be formulated as:

In this case, the relation states that the product of the temporal spread (Δt) and spectral spread (Δf) of a given signal can never be smaller than some unit value – in this case we use 1/4π, but this depends on which units and Fourier normalisation factors are used. This can be visualised in the following manner – from Foundations of Field Computation, Chapter 6: Gabor Representations, by Bruce MacLennan (2017):

Suppose we are trying to measure the frequency of a tone. Intuitively, the longer the sample we take, the more accurate will be our measurement, which suggests that the error in measuring the frequency, ∆f, is inversely related to the duration of the measurement, ∆t. How long must ∆t be in order to guarantee we can distinguish frequencies differing by ∆f?

So, given some signal t or f, how do we calculate its spread – its nominal duration Δt or nominal bandwidth Δf? We first calculate the area of its absolute value:

Then, if we overlay the product of the two spreads on the time-frequency domain, the relationship becomes clear:

Imagine squeezing this rectangle along one axis while stretching it along the other, all the while keeping the minimum area set by the uncertainty principle. Each one of these minimal rectangles contains one logon of information – Gabor’s term for the smallest quantum of information in time-frequency space.

While we’ve only spoken of time domain signals so far, the Fourier uncertainty principle can just as easily be applied to spatial domain signals – it’s just as valid to speak of frequencies over space as it is to speak of frequencies over time. As such, we should also consider the following space-frequency uncertainty relations:

From here onwards we’ll treat time domain and spatial domain properties of signals phenomena as somewhat interchangeable, or at least as exhibiting similar properties from the point of view of the uncertainty relations.

Alright – but how does this relate to the three marks? Let’s swap out the variables in the uncertainty relations:

We believe that the concepts of anicca and anattā relate to spatiotemporal and spectral properties of phenomena, respectively. As such, we expect that their behaviour should respect the Fourier uncertainty principle.

Anicca refers to the mental motion of acknowledging impermanence, which describes how phenomena arise and pass – both in time and space. To provide a concrete example, I think the participants in the reaching experiment are resisting anicca when they clench their arms to maintain a certain position in space.

Anattā refers to inessence, which describes how the qualities of phenomena change over time – and arguably, said qualities can be apprehended by their spectral characteristics. It would make sense to do so, given that frequency domain representations are good at representing the qualities of signals which remain invariant with respect to space and time. Perhaps when the panda doesn’t notice that the grimacing is not actually essential to the operation of breaking the bamboo, he’s actually resisting anattā?

Dukkha refers to dissatisfactoriness, which relates to the fundamental tension inherent in all phenomena – the minimum uncertainty that cannot be eliminated. The inequality states that this tension has a lower bound – you cannot reduce the product of spatiotemporal and spectral uncertainties below a certain threshold. All phenomsena require at least this quantum of tension in order to exist at all – but it’s also possible to massively overshoot this lower bound by clenching against uncertainty rather than accepting it.

We propose that a time-frequency domain model may provide a clearer lens through which to apprehend the three marks. This framing might be intuitive for signal theory enthusiasts, but we recognize that not everyone might find it obvious how to dissect subjective phenomena into their spatiotemporal and spectral characteristics.

In my previous post, I included some transcripts from a recent conversation I had with the meditation teacher Wystan Bryant-Scott. During that conversation, I also introduced Wystan to Ethan’s framework. I include further transcripts here in order to illustrate what this kind of vibe domain analysis looks like in practice.

Dukkha, dissatisfactoriness, and uncertainty

When one perceives with wisdom that all conditioned things are unsatisfactory, then one turns away from suffering. This is the path of purification.

— Dhammapada 278

We started the conversation by reviewing Ethan’s framework, and I brought out pen and paper so that I could draw the time-frequency uncertainty relation for Wystan. Wystan himself has invested a lot of time cleaning up the amount of dukkha he experiences, and so he had some opinions to share about the nature of suffering:

Cube Flipper: So, for starters, we have anicca, anattā and dukkha, which off the top of my head are impermanence, and I like saying no fixed essences, and then unsatisfactoriness or suffering or what have you – then if we fill in the blanks, anicca times anattā is equal to dukkha…

Wystan: For the phenomenal field to interact with itself effectively there’s like a minimum viable fabrication and reification that it has to perform in order to actually have sensorimotor function. We usually do a lot more than is necessary, and that causes a lot of stress.

Cube Flipper: So what this suggests is that anicca is all about trying to fix a signal in time or in space or what have you – and anattā is like the same thing but in the frequency domain.

Wystan: The phenomenal field has this property where if one part of it grasps or fixates another… it’s a bad time. Feels real bad man. And fabrication in general – compared to less fabrication, it just feels worse, generally – but there’s a kind of drive for novelty. If an awake human nervous system were just going for total individual suffering minimization, then you’d see people throughout history just spend the maximum amount of time in cessation. That’s not what happens.

Cube Flipper: So the gist of it is that there’s a minimum amount of both of these things you need for fabrication, but you can also massively exceed that bound by doing unskilful things.

Wystan: Correct. And everyone does that almost all the time. And thus, much more dukkha than the base – the base, like, stress required for a fabricated but dereified and still functional visual field is like, so negligible that it’s fine.

Cube Flipper: For sure, the visual field doesn’t require much clinging, that’s the impression I get – but somatic sensations can go fucking haywire.

Wystan: Generally, but even that can be cleaned up to a great extent.

Anattā, inessence, and spectral uncertainty

I thought it would be illustrative to find some concrete examples of phenomena with specific spectral qualities, where recognising anattā makes them more pleasant to deal with:

Cube Flipper: So anattā might be something like – like a really high level example of something I would think of as being in the frequency domain is, like, say you have someone who habitually builds very complicated models of people and how they behave – very reified, very essentialised models – and if someone then behaves in a way which is contrary to those models it could be quite unsettling for them. But you can imagine scaling that all the way from very high level—

Wystan: To very low level.

Cube Flipper: Like an example might be – I’m pedalling my bike, and I expect my pedals to feel the same every time they go around, but maybe I experience just a tiny amount of friction, so it’s random each time even though I’m expecting a regular oscillation.

Wystan: Funny thing—

Cube Flipper: Squeaky wheel. I know Daniel Ingram’s got that analogy.

Wystan: That’s a good one.

I was thinking back to when I was a young teenager. I never really understood why people were expected to think and behave consistently across time – or at least, I never understood why I was expected to behave like this. Personally, I was prone to erratic behaviour, but I didn’t understand where this came from – so I tried to avoid holding myself to such standards, even when this chafed with the expectations of others. I also assumed that others were the same way, and that their own behavioural patterns were just as unpredictable to them as mine were to me.

In my third year of high school, I took a class in statistics, and fell in love with the Gaussian curve. I promptly realised that human minds are clearly stochastic processes and to treat them with empathy is to model them as such. Perhaps this is obvious? In any case, this realisation was incredibly helpful to my teenage self and how I related to myself and other people.

Presumably the way we construct models of one another is by observing invariants in each others’ behavioural patterns. Perhaps it’s also reasonable to assume that in order to recognise these patterns we are looking qualities which remain constant across time. Could we be using something akin to a Fourier transform but applied to the space of behavioural patterns? Do we sometimes then try to essentialise those spectral representations in order to make it easier to model each other?

I take issue with the way anattā gets translated as no-self. I think the term self is loaded with strong connotations – I much prefer the less loaded term inessence. I wanted to ask what Wystan what he thought about this, and he had a technical answer:

Cube Flipper: So anattā always gets translated as no-self—

Wystan: It’s technically not-self. An- is the negative prefix, it means not. So an-attā is not-self.

Cube Flipper: And attā is being translated as self, here, but it could mean, like, any object might have a “self”?

Wystan: Right. And it is used that way. In later tradition, the term that’s used is svabhāva. Which is usually translated awkwardly as own-being or essence or intrinsic being or inherent existence. But sva- is like self-own, and bhāva is being. Emptiness is like, okay, what are phenomena – including people – empty of? And what they’re empty of is svabava. That’s the technical term.

Wystan: So – there’s the twofold emptiness, or the corollary twofold grasping – there’s grasping at phenomena and there’s grasping at self, and these are mutually reinforcing. So there’s like the perceiving of the essence of an agent, a subject, a do-er, a knower, a be-er, a perceiver, that’s one bundle of reification – but in a mutually dependent and reinforcing way. Then there’s, well, this has an essence—

Wystan taps the table

Cube Flipper: Cars have essences.

Wystan: People, ideologies.

Cube Flipper: Energy drinks have an essence. If they changed the flavour of my favourite energy drink, I’d be very—

Wystan: This later term that came into much more favour in much later Buddhist traditions, emptiness – it’s just a more general term for self-lessness with regards to the essences of things. Including persons.

Anicca, impermanence, and spatiotemporal uncertainty

By comparison, I think anicca is a less abstract term – it’s pretty easy to find examples of the desire for temporal certainty or control over starting, stabilizing, or stopping phenomena in time or space.

Cube Flipper: I want to zoom in on anicca, here. It feels like there’s two really obvious categories of anicca that people might notice – desiring something to persist, and desiring something to go away.

Wystan: Correct, yeah. It’s the same mistake.

Cube Flipper: The low-level, daft example I always want to bring up is cooking. I watch a friend of mine who experiences a lot of clinging in the kitchen. Classic example is, he cracks an egg, gets egg white on his fingers, and I watch the way that he holds his hands until he can wash them – and I want to say, you actually can just keep cooking—

Wystan: With a little bit of egg on your hands.

Cube Flipper: —and you can put your attention on the egg on your hands, and not ignore it – until you get a spare moment to wash your fingers. But I still do this.

How can we put observing anicca into practice? How can we respond skilfully to unpleasant stimuli that we might otherwise wish would go away? We discussed some options:

Wystan: Well, there’s several strategies, right – one thing, this goes for pain or any other sensation, you can zoom in, and weight it more, and get really clear about the sensations, and get clear on how you’re resisting those sensations, and then find relief that way. Or you can go really broad and diffuse, and then any irritation or resistance is kind of downweighted, because it’s occupying a very small portion of the whole field. Two strategies.

Cube Flipper: Do you have any recommended low-level meditation practices that might help someone attend to anicca and anattā in this manner?

Wystan: Standard vipassanā is really good for anicca. You can practice that – most people find it easiest to start with the somatic field, to try to get as high resolution of sensation in the somatic field and deliberately homing in on subtler and subtler, finer and finer, more rapid…

Cube Flipper: I think most of it for me is just figuring out and noticing ways that I’m, like, twisting my body in response to something – and it’s quite tricky, because often the twisting, or the cringing, is spatially localised quite far away from the sensation itself.

Wystan: Often, yes. For that, attempting to maintain global body awareness as often as possible, that works.

Cube Flipper: Something I’ve got quite good at over the years is, if there’s a loud noise, like a car backfiring – like, I’m friends with noise sensitive people, so I can watch what happens to their bodies when a car backfires.

Wystan: It’s like a ripple, and then a clench—

Cube Flipper: With me – I mean, I’m the kind of person who likes noise music, so – I’m well enough attuned that if a loud noise happens, my attention just snaps on to it straight away, there’s no flinching away. But if it’s sufficiently loud, and I’m a bit anxious or a bit stoned – I will notice an actual longitudinal wave pass through my body – and it doesn’t feel like there’s any muscle movement attached to it, it’s purely subjective – snap – like that, really fast. It’s pretty unpleasant, but it would be a lot more unpleasant if I flinched.

Wystan: In a Zen context, there’s often a lot of sharp sounds punctuating different parts of the training schedule. There’s these woodblocks that announce the different periods that are clapped together. It’s quite a sharp sound, it’s like a sharp—

Wystan claps his hands together

Wystan: —and you can tell what someone’s state of samadhi is based on any movements that they make in response to that.

All phenomena are impermanent – even excessively long infodump posts. This seems like a great time to wrap up this piece. Clack!

Open questions

What do you think of this model? Perhaps if you disagree that it’s a fit for the three marks, we do believe it says something important about our subjective experience and the nature of suffering. There’s a lot more we could explore, and once again I wrap up a post with a fair number of loose threads which could be expanded upon. The following are some of the open questions I’ll be continuing to think about:

Are we using the term dukkha correctly, here?

I’m not a Buddhist, and most of my understanding of Buddhism comes from cultural osmosis from the Buddhists around me – so I feel somewhat out of my lane trying to write about these things. Still, I’ve noticed that dukkha as it is discussed in the context of the three marks seems different to my previous understanding of dukkha as a reactive, secondary phenomenon, something we do to ourselves largely by accident.

Ethan recommended looking into the two arrows. From the Salla Sutta:

When touched with a feeling of pain, the uninstructed run-of-the-mill person sorrows, grieves, & laments, beats his breast, becomes distraught. So he feels two pains, physical & mental. Just as if they were to shoot a man with an arrow and, right afterward, were to shoot him with another one, so that he would feel the pains of two arrows; in the same way, when touched with a feeling of pain, the uninstructed run-of-the-mill person sorrows, grieves, & laments, beats his breast, becomes distraught. So he feels two pains, physical & mental.

There are two types of dukkha in this ontology:

• The first arrow – raw, unavoidable suffering inherent to experiences themselves. This would include any necessary dukkha up to the minimum lower bound.
• The second arrow – additional suffering that we create ourselves through reactive mental patterns. This would include any unnecessary dukkha surpassing the minimum lower bound.

My updated understanding is that the dukkha of the three marks refers to both arrows, whereas my previous understanding was that dukkha referred only to the second arrow.

Is the proposed mapping the only valid way of mapping the three marks onto the uncertainty principle?

Throughout our discusssions, Ethan has been careful to remind me how the proposed mapping – of anicca onto temporal spread and anatta onto spectral spread – might be only one of several valid mappings from the three characteristics into signal processing terminology:

There are other reasonable mappings between the three characteristics and the terms in the uncertainty principle. A classic analogy for dukkha is a squeaky wheel or misaligned axle. Following this analogy, we might map spectral spread to dukkha – as spectral uncertainty will lead to a mismatch between prediction and expectation – a “bumpy ride” kind of issue. Then we have anicca, which still maps straightforwardly to temporal spread. Lastly, anattā would map to the product of the spectral and temporal spreads. This is the sense in which no phenomenon can be said to have intrinsic being or essence; it would be quite odd to claim: “This thing definitely has intrinsic, absolute existence, but we are fundamentally limited in how much we can know about it. It’s a good platonic object, sir.”

There are other mappings too, with varying ease of justification and intuitive reasonableness. It’s an open question in my mind to characterize all of the mappings and under what conditions each are reasonable. The brain is a signal processor of some sort and clearly uses a lot of wave-based computation, so it must contend with the Fourier uncertainty principle in various ways. At the same time, the three characteristics seem like deep ways of looking at the world, and they have worked quite well historically for liberation from suffering – so they also seem like things that the brain must care about a lot. Given that, investigating the interaction of the uncertainty principle and the three characteristics likely yields quite important insights.

What physical units are most appropriate for quantifying the three marks?

When working with the Gabor uncertainty principle, Δt is measured in seconds, while Δf is measured in hertz. Therefore, Δt Δf is dimensionless – the units cancel out:

In quantum mechanics, where we use the Heisenberg uncertainty principle, Δx Δp has units of Joule-seconds or action:

However, Ethan tells me that the entropic uncertainty principle could be more appropriate than either of these. In which case, the units used throughout would be bits or nats of information. I hope to see him develop this further.

Can dukkha be reformulated in predictive processing terms?

I have explained the predictive processing model previously:

In the predictive processing model, the brain has two interlocking information processing streams running in opposite directions – a sensory stream, and a prediction stream. At each layer, from low-level sensory processing all the way up to high-level world modelling, the difference between sensory information and predictions about sensory information is calculated and passed up to the next layer as a prediction error.

What if we assume that the only information which makes it into conscious awareness is that which doesn’t match the predictions made – the prediction error?

The free energy principle is a related theory, in which biological systems are understood to be minimising variational free energy. If this is implemented in such a way that free energy is used to represent prediction error, and all experience is constructed from prediction error, is prediction error then equivalent to dukkha? This would make sense – when an organism successfully minimises its own suffering, it would simultaneously be minimising prediction error or free energy in accordance with these theories.

Does experience have an equivalent of a sampling window?

When taking the Fourier transform in practice, we generally divide our time-series signal into shorter segments, and then perform the Fourier transform on those – this is known as the short-time Fourier transform. Is our consciousness doing something similar, and if so, how would this affect conscious experience?

There’s an argument from phenomenology to be made that conscious experience is divided into separate consciousness frames – which some people estimate to have refresh rate of approximately 40 Hz. Kenneth Shinozuka describes the phenomenology in Shinzen Young’s 10-Step Model for Experiencing the Eternal Now (2021):

I noticed that my entire visual field was flickering at a high frequency while my eyes were open. It seemed like my visual field had arranged itself into a series of uniformly distributed Gabor patches that were fading in and out very quickly. I have yet to perceive the wavy essence of mental imagery or mental talk, though.

If our brains perform a Fourier transform once per consciousness frame, this would impose a limit to the accuracy with which we could measure the frequency domain qualities of sensory signals. This sounds like the kind of thing we could construct psychophysics experiments to test.

Brad Caldwell believes that the way ketamine bunches up action potentials could result in consciousness frames being more observable. Personally, this squares with my experience – ketamine can make me feel like I’m running at a much slower clock rate. Correspondingly, this makes me feel like I can then introspect on subjective experience with much greater precision.

Why do some people find it intuitive that objects and people have “vibes”?

I gather the impression that people think in a wide variety of different ways, so I can’t assume that someone will relate to the use of signal processing terminology to discuss for process of modelling objects or people.

A friend of mine – a talented software developer who has even worked on space probes – once told me a story about the time he took LSD at a regional Burning Man event. In his own words, he had an abrupt realisation that he’d spent his entire life modelling people using if-else expressions. Under the influence of LSD, he somehow managed to switch his GPU on.

What do we think happened there? Did he suddenly discover how to pay attention to the vibes he uses for reifying models of people? Would this open up a more efficient way of thinking?

Why does acceptance of one of the three marks all the way lead to a cessation state?

A cessation is a state accessible by some experienced meditators where the entirety of subjective experience blinks out for a moment. I discussed these extensively with Wystan in my previous post. Daniel Ingram claims that there are three types of cessation, each of which is accessed via one of the three doors, which describe contemplative practices relating to the three marks. From Mastering the Core Teachings of the Buddha, Chapter 31: The Three Doors:

Each of the doors turns on its head something about attraction, aversion, and ignorance, and finally gets to do the skillful thing that they were unskillfully trying to accomplish. Attraction wants to plunge into and stay with the pleasant parts of reality, to merge with them, and the no-self door actually does this. Aversion wants to get away from the unpleasant parts of reality, and the suffering door actually does this. Ignorance is a tough case, as it wants to detune from reality and do something else, and the impermanence door actually does this.

It’s actually a little more complicated than this – each type of cessation might include aspects of one of the other two characteristics. Cessations happen incredibly fast, so he is careful to emphasise how these claims are based on extensive experimentation:

The strength of our concentration practice and the recent continuity of practice will also help determine how clear these experiences are. I had to go through them hundreds of times with an eye to exactly how they presented before I could write a chapter such as this one.

Relating this back to Ethan’s framework, I’m quite curious as to why acceptance of spatiotemporal or spectral uncertainty all the way might result in a cessation state. I suspect that answering this question may well lead us to understanding something quite important about consciousness itself.