---
title: "Ten mathematical models of the jhāna"
authors:
  - name: "Cube Flipper"
    url: "https://x.com/cube_flipper"
  - name: "Ethan Kuntz"
    url: "https://x.com/KanizsaBoundary"
---

<style>
blockquote .transcript {
    font-weight: bold;
}

.transcript.cube-flipper {
    color: deepskyblue;
}

.transcript.wystan {
    color: hotpink;
}

.transcript.ethan {
    color: seagreen;
}

.transcript.action {
    font-style: italic;
}
</style>

<aside>
    <em>
The authors would like to thank all the meditation study participants at the [third Qualia Research Institute psychophysics retreat](https://heart.qri.org/#tepoz-2026), as well as [Andrés Gómez Emilsson](http://x.com/algekalipso) and [Hunter Meyer](https://x.com/qualiacomputer) for all the planning and logistics which went into the retreat. We would also like to thank [realitymap](http://x.com/realitymap) for conducting a preliminary *jhāna* interview with us on 28 February 2026.

This post is intended as an accompaniment to the following two posts:

- [The third QRI psychophysics retreat, part I: The form jhāna](/posts/2026-10-04-the-third-qri-psychophysics-retreat-part-i.html)
- [The third QRI psychophysics retreat, part II: The formless jhāna](/posts/2026-10-05-the-third-qri-psychophysics-retreat-part-ii.html)

In this post, [Ethan Kuntz](https://x.com/KanizsaBoundary) and myself propose a number of models for thinking about the *jhāna*. Throughout this post, our phenomenological justification for these models is relatively sparse. The best way to get a feel for how we think about the *jhāna* is by reading the transcripts in those posts. If things still don't entirely make sense, you're welcome to [send us an email](mailto:admin@smoothbrains.net), and we can do our best to explain.

An attributable version of this post is published at [heart.qri.org](http://heart.qri.org/retreats/2026-tepoz/cube-flipper/ten-models.html).
    </em>
</aside>

The genesis of this [project to investigate the phenomenology of the *jhāna*](/posts/2026-10-04-the-third-qri-psychophysics-retreat-part-i.html) was a conversation I had with [Ethan Kuntz](https://x.com/KanizsaBoundary) at the [QUALIUS Retreat on Non-Ordinary States of Consciousness](https://assc2025.gr/programme/satellite-events) in Crete last year, a satellite event from the 18th annual meeting of the [Association for the Scientific Study of Consciousness](https://assc2025.gr).

<figure>
    [![](/images/random/jhana/part_iii/crete_2.jpg){ style="max-width: 512px; width: 100%" }](/images/random/jhana/part_iii/crete_2.jpg)
    <figcaption>
        The visual artist [Symmetric Vision](http://symmetric-vision.xyz) giving a presentation on his [psychedelic replication](http://reddit.com/r/replications/) technique to a crowd of psychedelic and meditation researchers at the QUALIUS retreat.
    </figcaption>
</figure>

The *formless jhāna* or *arūpa jhāna* are the final four out of the series of eight concentration states known as the *jhāna*. They are named as such for their lack of *form*, i.e. *heterogeneous* sensations such as a *body map* – whatever their structure may be, in order for it to be *formless* it must be *homogeneous*. As an experienced meditator progresses from **J5** to **J8**, they generally report experiencing increasingly abstract states – until they achieve complete **cessation** of experience altogether.

<aside>
The defining aspect of a [**cessation state**](https://www.mctb.org/mctb2/table-of-contents/part-iv-insight/31-the-three-doors/) is that you *can't* report on it; if you've had [general anaesthesia](https://en.wikipedia.org/wiki/Propofol) before, it's like that – continuity of experience is broken and you simply [skip](https://x.com/cube_flipper/status/1624994980979970049) forward in time. 
</aside>

Previously, at [The Science of Consciousness Conference](https://consciousness.arizona.edu/tsc-2025-barcelona-flyer) 2025, I met with [Niffe Hermansson](https://x.com/Niffe), who proposed that **J8** corresponded to the instantiation of *time* – given that the sensation of time passing was the only thing which differentiated **J8** from **cessation**. When I related this to Ethan, he expanded on this; in his eyes, **J8** corresponded to the more mathematically fundamental notion of [*continuity*](https://en.wikipedia.org/wiki/Continuous_function) – in the formal, [*epsilon-delta* definition](https://en.wikipedia.org/wiki/Limit_of_a_function#(ε,_δ)-definition_of_limit) sense.

I myself am not an accomplished meditator and do not have any direct insight into what these states are like. Something which perplexed me was the problem of how someone might even analyse such states from the *inside*, given that *metacognition itself* is generally completely absent during such states of consciousness. Ethan claimed that in order to report on their internals, you have to set yourself up such that the structure of these *interior* states can be inferred from the *outside* by the changes imparted on subjective experience *after the fact*. Wystan was later able to clarify this for me – depending on the degree of absorption, one might have some amount of *cognitive maneuverability*, but in more highly absorbed states, one is restricted to observing the state via the memories that are accessible *afterwards*.

I felt more comfortable taking these reports at face value now that I understood the chain of causality which produced them. To this end, I found myself hauling Ethan through a laborious, *from first principles* infodump on these highly abstract states over the course of several hours. In order to describe the principles he believes each successive *jhāna* adds to experience, he used sufficiently general mathematical language that I could wrap my head around what he was saying. A brief sketch of the preliminary model he outlined during this conversation is as follows:

<dl>
    <dt><p>J8: Neither perception or non-perception</p></dt>
    <dd><p>*Continuity*. Just continuity; continuity is the only thing that differentiates **J8** from full **cessation**. Continuity implies [open sets](https://en.wikipedia.org/wiki/Open_set); points have [neighbourhoods](https://en.wikipedia.org/wiki/Neighbourhood_(mathematics)).</p></dd>
    <dt><p>J7: Boundless nothingness</p></dt>
    <dd><p>*Accumulation* and *dissolution*. Note that this is not the *sense* of accumulation or dissolution; you have the sense of continuity, but there are no absolute quantities, just first differentials. Not [Turing complete](https://en.wikipedia.org/wiki/Turing_completeness). <!-- Ethan: Ya pretty much, the way I'd describe this is that the rate of dissolution overwhelms the rate of accumulation such that there's just nothing going on. This nothing can be bigger over time, and the rate can increase, but this is not really noticeable from the inside. --></p></dd>
    <dt><p>J6: Boundless consciousness</p></dt>
    <dd><p>*Comparison* and *reflection*. Objects reflect one another, they can be compared, but the relative time delays have not assembled themselves into a sense of *space*. <!-- Ethan: Weirdly enough, I'm not sure that there are objects to reflect at this point, we just have reflecting and comparing. --></p></dd>
    <dt><p>J5: Boundless space</p></dt>
    <dd><p>*Space*. Reflections congeal into a sense of space. The construction of *independence*. You have the [*hologram*](/posts/2025-07-31-is-consciousness-holographic.html) for the first time; there's just nothing in it.</p></dd>
</dl>

*Hang on*, I said. Do you see it? My immediate impression was that these seemed an awful lot like an [*instruction set*](https://en.wikipedia.org/wiki/Instruction_set_architecture) or at least a set of [*computational primitives*](https://en.wikipedia.org/wiki/Language_primitive) employed by some kind of general purpose analog computer.

Typically the *jhāna* are described as a progression from **waking consciousness** all the way to **cessation**. However, if we start with **cessation** and work [backwards](https://x.com/cube_flipper/status/2005088453491654882) through **J8** to **J1**, under this model it seems more like we are progressively adding various computational properties to consciousness, until we arrive at something more like day-to-day experience. *Now* – what if we could *also* find a physical structure or process within the brain which accumulates equivalent computational properties as consciousness boots up from **cessation** – what would that tell us about consciousness?

<!-- If we are already working with an [optical model of consciousness](/posts/2025-10-17-fractional-fourier-transforms.html), these seem an awful lot like an [*instruction set*](https://en.wikipedia.org/wiki/Instruction_set_architecture) for some kind of general purpose [*nonlinear optical computer*](https://qri.org/blog/electrostatic-brain). -->

<aside>
It feels extremely natural to me that we should be thinking of the human brain and consciousness by proxy as some kind of [analog computer](https://en.wikipedia.org/wiki/Analog_computer). If so, the next obvious question is then – what [classes of calculations](https://en.wikipedia.org/wiki/Chomsky_hierarchy) might it be capable of running? What computational primitives does it implement, and are they sufficient to make the system computationally universal? I'm surprised that more people aren't thinking about our cognitive architecture in such clear-cut computational terms – though I did appreciate [this thread](https://x.com/cube_flipper/status/2005088453491654882), from [Roko Mijic](https://x.com/RokoMijic).
</aside>

### The *jhāna* as a Rosetta Stone for consciousness

So, what are we actually doing here? Resuming a top-down perspective, I still consider myself to be investigating how consciousness works. I see the *translation problem*, as specified by [Mike Johnson](https://x.com/johnsonmxe), to be one of the key problems to which any theory of consciousness must propose a solution. As outlined in a [previous post](/posts/2026-05-09-digital-consciousness.html#the-translation-problem):

> In Mike's book, [Principia Qualia](https://opentheory.net/PrincipiaQualia.pdf#page=24), he attempts to decompose the problem of consciousness into a programme of subproblems, one of which he calls the *translation problem*. This asks, by which psychophysical laws do *physical states* map onto *qualia states*, and vice versa? This is closely related to [David Chalmers](https://en.wikipedia.org/wiki/David_Chalmers)' [*combination problem*](https://consc.net/papers/combination.pdf):
>
>> **The Translation Problem**: given a mathematical object isomorphic to a system's phenomenology, how do we populate a translation list between its mathematical properties and the part of phenomenology each property or pattern corresponds to?
>>
>> Or more succinctly, *how do we connect the quantitative with the qualitative?*

Recently, I discussed this problem with the philosopher [David Pearce](https://x.com/webmasterdave). He also sees the *translation problem* as one of the key problems of consciousness, but, [in his own words](https://www.hedweb.com/hedethic/interview-2025may.html), without some kind of *cosmic [Rosetta Stone](https://en.wikipedia.org/wiki/Rosetta_Stone)*, our prospects remain hopeless:

> The world is formally described, exhaustively, by the equations of mathematical physics. But the essence of the physical isn't what materialist metaphysicians suppose.
>
> Nevertheless, consciousness mystifies me. For science lacks a cosmic Rosetta Stone to let us "read off" the myriad interdependent textures ("what it feels like") of experience from the diverse solutions to the equations of quantum field theory.

<!-- Ethan: *Rips a fat cloud* the mathematics is literally just what it feels like there's no difference boom -->

Could the *jhāna* provide such a Rosetta Stone for consciousness? For some time now, I've seen psychedelic drugs as a viable [tool for investigating consciousness](/posts/2023-10-08-the-second-qri-psychophysics-retreat.html), but while they are very good at [perturbing consciousness in a way that reveals its *dynamics*](/posts/2024-05-13-cross-frequency-coupling.html), I have somewhat given up hope that psychedelics can reliably lead to the kind of repeatable, convergent states which could bridge between phenomenological reports and neuroimaging studies. This said, it seems that the *jhāna* provide a set of consistent concentration states [across a variety of contemplative traditions](https://link.springer.com/article/10.1007/s12671-024-02367-w). Insofar as they might be natural attractor states within human <!-- and mammalian? --> nervous systems, perhaps the *jhāna* could provide such a psychophysical bridge?

<!-- Ethan: Ehhh I think psychedelics are still good for this, plenty of the effects are repeatable even if large state isn't and that's more than enough to work with. -->

The [Meditation Research Program](https://meditation.mgh.harvard.edu) at [Harvard Medical School](https://hms.harvard.edu) seems to be thinking on similar lines. From their roadmap paper, [Toward a neuroscience of consciousness using advanced meditation](https://www.sciencedirect.com/science/article/pii/S0149763425005214) (Lieberman and Sacchet, 2026):

> Despite decades of progress in the neuroscience of consciousness, prevailing empirical paradigms remain largely anchored in the study of typical, content-rich states that are characterized by layered perceptual, cognitive, affective, and self-referential processes. Such complexity may obscure the neural mechanisms that give rise to conscious experience. Here, we propose that advanced meditation – referring to states and stages of practice that unfold progressively with increasing expertise – offers a powerful yet unexplored opportunity to isolate the core features of consciousness through a theory-driven neuroscience approach.
>
> We focus on two classes of meditative phenomena: advanced concentrative absorption (related to what have been called *jhāna*), which involves the preservation of highly abstract forms of awareness alongside the attenuation of typical features of consciousness; and meditative endpoints – namely, cessation events (related to what have been called *nirodha*) – which involve the temporary suspension of consciousness altogether. These phenomena serve as precise, replicable, and experimentally tractable phenomenological anchors for a minimal model framework, a novel approach aimed at identifying and characterizing the simplest possible form of conscious experience as a principled starting point for a systematic science of consciousness. Within this framework, the integration of advanced meditation into experimental paradigms offers a promising path toward identifying the neural mechanisms that support consciousness in its most reduced and fundamental forms.

The Meditation Research Program has recently published the first case study of ultra–high-field fMRI of jhāna, with the first group-level study currently in preprint, plus two single-subject reanalyses of the case study dataset applying [connectivity gradient](https://www.cell.com/trends/cognitive-sciences/fulltext/S1364-6613(17)30240-1) and [geometric eigenmode](https://www.nature.com/articles/s41586-023-06098-1) decompositions:

- [Multimodal neurophenomenology of advanced concentration absorption meditation: An intensively sampled case study of Jhana](https://www.sciencedirect.com/science/article/pii/S1053811924004701) (Yang et al., 2024)
- [The neuroscience of highly stable, positive, and refined states of consciousness during jhana-type ACAM-J](https://pmc.ncbi.nlm.nih.gov/articles/PMC12642441/) (Yang et al., 2025)
- [Advanced concentrative absorption meditation reorganizes functional connectivity gradients of the brain: 7T MRI and phenomenology case study of jhana meditation](https://pubmed.ncbi.nlm.nih.gov/40215476/) (Demir et al., 2025)
- [Investigating the complex cortical dynamics of an advanced concentrative absorption meditation called jhanas (ACAM-J): a geometric eigenmode analysis](https://pubmed.ncbi.nlm.nih.gov/40037411/) (Yang et al., 2025)

I find all this very inspiring. At our end, we don't have the kind of resources they have at Harvard, but I took Ethan's model to [Andrés Gómez Emilsson](https://x.com/algekalipso) at the [Qualia Research Institute](http://qri.org) and suggested it was an excellent line into the *translation problem*. Several months later, here we are, fresh out of a *jhāna* retreat in [Tepoztlán, México](https://en.wikipedia.org/wiki/Tepoztlán) – and I have a small dataset of questionnaires and candid interviews with *jhāna* practitioners to work with. Abridged transcripts from those post-retreat interviews alongside additional commentary are available at:

- [The third QRI psychophysics retreat, part I: The form jhāna](/posts/2026-10-04-the-third-qri-psychophysics-retreat-part-i.html)
- [The third QRI psychophysics retreat, part II: The formless jhāna](/posts/2026-10-05-the-third-qri-psychophysics-retreat-part-ii.html)

The rest of this post will cover a review of the *jhāna* models which Ethan came up with during the retreat. We're not settled on any one thing or another; to be perfectly clear, we're proposing a *set of complementary prototypes*, which we can iterate on over time as we accumulate more reports and the state of neuroscience improves.

<figure>
    <!-- [![](/images/random/jhana/part_iii/tepoz_1.jpg){ style="max-width: 512px; width: 100%" }](/images/random/jhana/part_iii/tepoz_1.jpg) -->
    <iframe class="youtube" src="https://www.youtube.com/embed/85Zon4CDkW4?si=KZanluo3eazebUG-" title="YouTube video player" frameborder="0" allow="accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture; web-share" referrerpolicy="strict-origin-when-cross-origin" allowfullscreen></iframe>
    <figcaption>
        Typical late night scene in Tepoztlán: I was out of my depth and arranged for Ethan Kuntz to compare experiences with Wystan Bryant-Scott, after [I interviewed Wystan](https://www.youtube.com/watch?v=0QtcCiIi3QU) earlier that same day.
    </figcaption>
</figure>

### Challenges to this line of research

Before we start, however, I'd like to review what we see as the primary challenges to this research:

1. Finding meditators who are literate in advanced mathematics
2. Priming issues from discussing models with meditators prior to experiences
3. Asking analog computers to report on their internal states when they are close to being shut down

First of all, it's really hard to find people who can both *jhāna* and discuss abstract mathematical models of experience. Recently, I spoke with a well-known meditation teacher who ostensibly knew their mathematics – only to be met with confusion when I began speculating about the frequency domain properties of *pīti* and *sukha*. If you do think you could hold such a cross-domain conversation, we would be overjoyed if you [got in touch](mailto:admin@smoothbrains.net).

Secondly, any contributor to this project will need to understand both mathematics and their own phenomenology well enough to be able to hold a model while not crushing their worldview into it. There exist academic interview standards – such as [micro-phenomenology](http://microphenomenology.com) – which are designed to avoid asking leading questions of study participants. While I'm incredibly impressed with the quantity and quality of information such techniques can solicit, the models we are proposing are sufficiently specific that there's really no way for them to pass through that kind of communication bottleneck. Contributors will need to be trusted to hold any models we invoke lightly enough to avoid both priming issues during experiences and post-hoc confabulation. We also need to be able to trust contributors to tell us if our models don't square with your experience – until we're confident enough in a given model that we know exactly what kind of psychophysics tests should verify what we propose. As Ethan suggested:

> If we're correct, this should be extremely demonstrable. If there's really something here, it's *crisp* – and if we're right about this there will be ways to demonstrate this very strongly which pretty much obviate priming worries.

Thirdly, we're asking people to report on remarkably subtle and easily overlooked aspects of experience. Like I mentioned earlier, there's not a lot of metacognition to work with – as absorption deepens, self-reflection is progressively attenuated. I get the impression that it's a little like trying to report accurately from inside an illucid daydream – as mentioned earlier, you only have the memories to work with from immediately after the state collapses. It's almost like we are asking an analog operating system to log its own state while it [shuts down as many of its processes as it can](https://en.wikipedia.org/wiki/Control-Alt-Delete#/media/File:Win98_Close_Program_Dialog.PNG).

## Four models of the form *jhāna*

Though we began the retreat with a focus on anthropic analog computing, there was a large variety of other models that myself and Ethan played around with during our time in Tepoztlán. In this section, I shall run through four models of the form *jhāna* that we discussed. Perhaps the reader will find some of these lenses more relatable than others. In my research, I like to employ an attitude of *many models, loosely held*, and we're very much applying this mindset here. Additionally, as Ethan said – we are optimistic that these may be *all one model with many faces*.

<figure>
    [![](/images/random/jhana/part_iii/tepoz_2.jpg){ style="max-width: 512px; width: 100%" }](/images/random/jhana/part_iii/tepoz_2.jpg) 
    <figcaption>
        Typical daytime scene in Tepoztlán: Ethan and myself spent many long hours pacing the length of a nearby football field, discussing various models of the *jhāna*. Sometimes, there were horses.
    </figcaption>
</figure>

Only four participants were able to access all four form *jhāna*, so be aware that our sample size is fairly small. This said, our participants' reports were robust, and we felt confident in the trends we did observe. As I wrote, in [The third QRI psychophysics retreat, part I: The form jhāna](/posts/2026-10-04-the-third-qri-psychophysics-retreat-part-i.html):

> We observed two macroscale phenomenological trends across the form *jhāna*:
>
> - The *pīti*-*sukha* trend, in which different form *jhāna* are reported to have consistent relative proportions of *pīti* and *sukha*.
> - The *head*, *heart*, *gut*, *everywhere* trend, in which different form *jhāna* are reported to be accessible by concentrating attention in specific locations in the body.
>
> As I understand, these pretty much square with what's documented in the literature.

<!-- Ethan has some new notes on the form *jhāna* available [here](https://docs.google.com/document/d/1nMo7BiZnNM700DFCL0h1inu26kaMjh32_X5jbgpuWo4/). -->

I'll review these two trends, along with two additional models that Ethan proposed, in the following sections. First of all, let's put these four models side by side to see if any patterns leap out:

<table>
    <caption>Tabulated form *jhāna* models.</caption>
    <thead>
        <tr>
            <th>Form *jhāna*</th>
            <th>[*Pīti* and *sukha*](#pīti-and-sukha)</th>
            <th>[Attentional loci](#attentional-loci)</th>
            <th>[Field equations](#field-equations)</th>
            <th>[Derivatives](#derivatives)</th>
        </tr>
    </thead>
    <tbody>
        <tr>
            <th scope="row">[J1](/posts/2026-10-04-the-third-qri-psychophysics-retreat-part-i.html#first-jhāna)</th>
            <td>*Pīti*</td>
            <td>Head</td>
            <td>Wave equation, ∂<sup>2</sup>*u*/∂*t*<sup>2</sup> = ∇<sup>2</sup>*u*</td>
            <td>2<sup>nd</sup> time derivative</td>
        </tr>
        <tr>
            <th scope="row">[J2](/posts/2026-10-04-the-third-qri-psychophysics-retreat-part-i.html#second-jhāna)</th>
            <td>*Pīti* and *sukha*</td>
            <td>Heart; chest</td>
            <td>Heat equation, ∂*u*/∂*t* = ∇<sup>2</sup>*u*</td>
            <td>1<sup>st</sup> time derivative</td>
        </tr>
        <tr>
            <th scope="row">[J3](/posts/2026-10-04-the-third-qri-psychophysics-retreat-part-i.html#third-jhāna)</th>
            <td>*Sukha*</td>
            <td>Gut; belly</td>
            <td>Poisson's equation, *ρ* = ∇<sup>2</sup>*u*</td>
            <td>Constant</td>
        </tr>
        <tr>
            <th scope="row">[J4](/posts/2026-10-04-the-third-qri-psychophysics-retreat-part-i.html#fourth-jhāna)</th>
            <td>Neither *pīti* nor *sukha*</td>
            <td>Everywhere; through the floor</td>
            <td>Integral equation, ∫&thinsp;*u*&thinsp;d*τ* = ∇<sup>2</sup>*u*</td>
            <td>1<sup>st</sup> time integral</td>
        </tr>
    </tbody>
</table>

### 1. *Pīti* and *sukha*

There was a clear trend across the form *jhāna* which related to the relative proportions of the *jhānic* factors of *pīti* and *sukha*. I described these briefly [here](/posts/2026-10-04-the-third-qri-psychophysics-retreat-part-i.html#the-form-jhāna):

> Of these *jhāna* factors, I find *pīti* and *sukha* to be of specific interest, as they describe two families of somatic textures which can arise within the body map either during meditation or in waking life. They can be quite pleasurable, and are also useful for identification of specific form *jhāna* states. I'll save the speculation for a later post, but my general understanding is that *pīti* has *heterogeneous* microstructure described as *noisy and powdery*, whereas *sukha* has *homogeneous* microstructure described as *smooth and [creamy](https://x.com/cube_flipper/status/1846328790433304978)*.

> At one point, I thought to ask Wystan if he considered that the different *jhāna* could be characterised exclusively in terms of *pīti* and *sukha*:
>
>> <!--`260604_1426.md 34:46-35:35`-->
>>
>> <span class="transcript cube-flipper">Cube Flipper:</span> Are the qualitative changes between **J1** and **J2** primarily characterised by the changes to *pīti* and *sukha* and their distributions in the body? Is there anything else you think characterised it?
>>
>> <span class="transcript wystan">Wystan:</span> Not really.
>>
>> <span class="transcript cube-flipper">Cube Flipper:</span> Is it the same for the next one? And all the way through the form realms?
>>
>> <span class="transcript wystan">Wystan:</span> Yes – it's really just changes in the dynamics of *pīti* and *sukha*.

Participants generally reported the presence of *pīti* and *sukha* in the following relative proportions:

- [**J1**](/posts/2026-10-04-the-third-qri-psychophysics-retreat-part-i.html#first-jhāna): Entirely *pīti*
- [**J2**](/posts/2026-10-04-the-third-qri-psychophysics-retreat-part-i.html#second-jhāna): Both *pīti* and *sukha*
- [**J3**](/posts/2026-10-04-the-third-qri-psychophysics-retreat-part-i.html#third-jhāna): Entirely *sukha*
- [**J4**](/posts/2026-10-04-the-third-qri-psychophysics-retreat-part-i.html#fourth-jhāna): Neither *pīti* nor *sukha*

Ethan was happy to corroborate this on the record:

> <span class="transcript cube-flipper">Cube Flipper:</span> Can you explain what you think the trends are with regards to *pīti* and *sukha*?
>
> <span class="transcript ethan">Ethan:</span> If I was to describe how I think other people will describe it and how this will fit into typical models: **J1**, basically all *pīti*. **J2**, nearly all *sukha*. **J3**, actually pure *sukha*. **J4**, neither.

<!-- Ethan: Note for the future, I have been toying with the idea that we are fully just missing a key variable or jhana factor or something here rather than the piti/sukha descriptors we give actually tracking the thing. I think maybe not but if hubris was missed as a hindrance... -->

We are not entirely sure why these factors present in the following proportions, but that's what people consistently report. There's an obvious parallel with the [*tetralemma* model](#the-tetralemma), which is quite curious. Before we go much deeper, perhaps we need to figure out what *pīti* and *sukha* actually *are*, first. Throughout the [form *jhāna* post](/posts/2026-10-04-the-third-qri-psychophysics-retreat-part-i.html#the-form-jhāna), we discussed the following models:

- *Pīti* and *sukha* as fields of oscillations with *phase-uncorrelated* and *phase-correlated* phase, respectively – the [*order parameter*](https://en.wikipedia.org/wiki/Phase_transition#Order_parameters) from [statistical mechanics](https://en.wikipedia.org/wiki/Statistical_mechanics) is the quantity that tells these apart.
- *Pīti* and *sukha* as signals with *high spatiotemporal certainty* and *high spectral certainty*, respectively – or rather, signals whose [*spread*](https://en.wikipedia.org/wiki/Statistical_dispersion) is smeared in the *spectral domain* and *spatiotemporal domain*, respectively.
- *Pīti* and *sukha* as the building blocks of the somatic field, with *pīti* like a [Gaussian](https://superspl.at/scene/28073caa) or even [Gabor splat](https://x.com/cube_flipper/status/1960434861963141155) and *sukha* like [Grossbergian filling-in](https://sites.bu.edu/steveg/files/2016/06/Gro2003PessoaDeWeerdChapter.pdf) – or in less technical terms, *point particles* and *smooth surfaces*.
- *Pīti* as noisy oscillations and *sukha* as the marginal background structure left over after those oscillations are dissolved – the motivating pleasant state used as an evolutionary reward mechanism.
- *Pīti* and *sukha* as comparable to the effects of [nitrous](https://x.com/cube_flipper/status/2055519850680680782) and [codeine](https://x.com/cube_flipper/status/2056155968078008805), respectively.
- *Pīti* and *sukha* as [*mechanical*](https://en.wikipedia.org/wiki/Wave_equation) and [*heat*](https://en.wikipedia.org/wiki/Heat_equation) energy, respectively.
- *Pīti* and *sukha* as *difference* and *similarity*, respectively.

<!--
Me: Sukha as the thing which actually heals the bodymind and refactors memory...? Smoothening in the holographic reference wave? This squares with [coherence therapy models](https://www.globally-bound.com/mdma-impostor-syndrome#holographic-models). Melting and diffusivity dominate the dynamics.

Ethan: I think basically yeah, sukha and equanimity all the way for that stuff. For getting stuff back up piti sure but for actually healing stuff, sukha to the moon.
-->

### 2. Attentional loci

The other trend which our participants reported semi-consistently is what we came to call the *head*, *heart*, *gut*, *everywhere* trend, in which *pīti* and *sukha* either initially present themselves in a specific bodily location – or are actively triggered when attention is placed on a specific bodily location:

- [**J1**](/posts/2026-10-04-the-third-qri-psychophysics-retreat-part-i.html#first-jhāna): *Pīti* in the head
- [**J2**](/posts/2026-10-04-the-third-qri-psychophysics-retreat-part-i.html#second-jhāna): Both *pīti* and *sukha* in the heart or chest
- [**J3**](/posts/2026-10-04-the-third-qri-psychophysics-retreat-part-i.html#third-jhāna): *Sukha* in the gut or belly
- [**J4**](/posts/2026-10-04-the-third-qri-psychophysics-retreat-part-i.html#fourth-jhāna): Absence of *pīti* and *sukha* everywhere; sometimes triggered by moving attention down the body and out through the floor

Alternatively – as Wystan often reported – if *pīti* and *sukha* did not localise to these specific locations, then generally they would pervade the bodymind uniformly instead.

<!-- Ethan: Strong agree wrt uniformly here, I very rarely get localization like this and kind of dislike it personally, these are mind-general patterns and I think it's kind of a crutch to localize whether intentionally or accidentally. At the same time this is obviously very good data and a good thing to mess with early in practice. -->

Once again I have more questions than answers. Why does this sequence start at the top and progress down the body? If you model the nervous system as a resonant system, are these loci [places which if perturbed with attention generate unusually stable resonant modes](https://opentheory.net/2018/12/the-neuroscience-of-meditation/)? Do they relate to the [*chakra*](https://en.wikipedia.org/wiki/Chakra)? Why are there exactly *four* of them? Should we expect this number to be universal across vertebrate nervous systems – might a snake also have four *jhāna*? As I wrote, in [The third QRI psychophysics retreat, part I: The form jhāna](/posts/2026-10-04-the-third-qri-psychophysics-retreat-part-i.html):

<!-- Ethan: WHY ARE THERE 4 WHY ARE THERE 4 WHY ARE THERE 4 WHY ARE THERE 4 -->

> I'll confess that [I don't really think of the *jhāna* as something belonging to contemplative practices](https://x.com/cube_flipper/status/2005123435173994691). Rather, if you think of nervous systems as resonant systems, I think that a good working hypothesis is to model the *jhāna* as outlier, low-entropy resonant modes which nervous systems can navigate into and inhabit by accident. [Leigh Brasington](https://www.leighb.com) reports in [Right Concentration](https://www.leighb.com/rc/index.html) that about 10% of his students, upon encountering descriptions of the *jhāna*, recognise them as something they discovered how to do as children. Unless there's something special about human nervous systems, I'd be surprised if other vertebrates and perhaps other animals in general did not also inhabit equivalent attractor states.
>
> Evolution must surely be strongly incentivised to prevent organisms from accidentally getting sucked into trance states at inopportune moments, but it also suggests to me that there must be something special about the *jhāna* given that evolutionary incentives have not completely blocked their access. I suspect that modifying a nervous system in this way would sacrifice some other desirable qualities it possesses.
> 
> Returning to the *head*, *heart*, *gut*, *everywhere* pattern – I have to wonder if an animal with a drastically different body map would experience a different set of *jhāna*, or if these attractor states are more universal than that? What kind of *jhāna* might a fish or a centipede be able to access? As Wystan reports, in deeper absorption states, the *jhāna* can be experienced independent of the presence of a body map, with *pīti*-*sukha* flooding the entirety of subjective space. Does this suggest that indeed the form *jhāna* are [natural kinds](https://en.wikipedia.org/wiki/Natural_kind)?

<!-- Ethan: Oh I can corroborate this with two stories. One time when I was sleeping in class but trying to do an odd combination of stay alert (so that I could pop up if the teacher came around or called on me) while resting deeply, I fell into a formless space that felt both very excited, energized, pleasant, and difficult to leave (unless the teacher came around). Another time, while dozing off into a nap in the car before going off to a bio course, I felt a terrifically strong wave of smooth pleasure consume me for around a minute. I'd now say it was substantially more pleasant than any experience with opioids that I've had but of the same underlying quality. -->

### 3. Field equations

Ethan proposed that we could use some well-known field equations to describe the changes which the different *jhāna* make to the texture of experience. Imagine applying these to the [phenomenal fields](/posts/2024-06-18-an-informal-review-of-anthropic-qualia-states.html), where *u* is the intensity of the field at each point in spacetime:

- [**J1**](/posts/2026-10-04-the-third-qri-psychophysics-retreat-part-i.html#first-jhāna): [Wave equation](https://en.wikipedia.org/wiki/Wave_equation), ∂<sup>2</sup>*u*/∂*t*<sup>2</sup> = ∇<sup>2</sup>*u*
- [**J2**](/posts/2026-10-04-the-third-qri-psychophysics-retreat-part-i.html#second-jhāna): [Heat equation](https://en.wikipedia.org/wiki/Heat_equation), ∂*u*/∂*t* = ∇<sup>2</sup>*u*
- [**J3**](/posts/2026-10-04-the-third-qri-psychophysics-retreat-part-i.html#third-jhāna): [Poisson's equation](https://en.wikipedia.org/wiki/Poisson%27s_equation), *ρ* = ∇<sup>2</sup>*u*
- [**J4**](/posts/2026-10-04-the-third-qri-psychophysics-retreat-part-i.html#fourth-jhāna): [Integral equation](https://en.wikipedia.org/wiki/Integral_equation), ∫&thinsp;*u*&thinsp;d*τ* = ∇<sup>2</sup>*u*

<aside>
Please note that for the sake of argument I am fairly indifferent to the question of whether an intensity field is the appropriate way to model subjective experience. What if we used something like a [curvature tensor](https://en.wikipedia.org/wiki/Riemann_curvature_tensor), instead?
</aside>

We are effectively asking the reader to imagine how it would *feel* if they were to apply these field equations to their somatic field. What phenomenal textures might arise? This might be difficult to visualise, so we made a couple of renderings to illustrate the dynamics:

<figure>
    <video controls autoplay loop muted playsinline style="max-width: 512px; width: 100%">
        <source src="/images/random/jhana/part_iii/derivative_ladder_2d.mp4" type="video/mp4">
    </video>
    <figcaption>
        Field equations one to four applied to the same input field. **J1** rings, **J2** blurs fine detail first, **J3** settles to a constant curvature equilibrium, and **J4** dissolves large scale structure first, leaving fine detail. Please note that **J3** and **J4** crossfade from their initial conditions over the first second to avoid a jarring discontinuity.
    </figcaption>
</figure>

Perhaps if you have first hand experience of the form *jhāna* this will be impressionistically relatable – or maybe it won't. Ethan explained his model to me during our post-retreat interview:

<!-- From 2026-06-03 Ethan at Casa del Sol/260603_1828.mp3, 1:41:10, and 2026-06-05 Ethan interview/260605_1114.mp3, 1:47:22 -->

> <span class="transcript ethan">Ethan:</span> I have a sequence of extremely generic things that I think the brain uses a lot. We've got the *wave equation*, the *heat equation*, *Poisson's equation*, and *one quirky thing*.
>
> <span class="transcript cube-flipper">Cube Flipper:</span> All right, okay.
>
> <span class="transcript ethan">Ethan:</span> I would say that **J1** is very *wave equation*, and **J2** is very *heat equation*. One important thing is that the *heat equation* is the first derivative of intensity with respect to time – which is equal to the Laplacian of your intensity. Then the *wave equation* is just the second derivative which is equal to that – you just integrate one time. Stuff like this is one of the reasons I think that the *jhāna* are probably really genuinely crisp things.
>
> <span class="transcript cube-flipper">Cube Flipper:</span> Okay.

<!-- From 2026-06-05 Ethan interview/260605_1114.mp3, 1:51:32 -->

> <span class="transcript ethan">Ethan:</span> One of the things about the *heat equation* – you get *smoothing*. You get *diffusion*. Very cool. The *heat equation* is the [diffusion equation](https://en.wikipedia.org/wiki/Diffusion_equation) is [mean curvature flow](https://en.wikipedia.org/wiki/Mean_curvature_flow) – the thing that **J2** is doing is just minimizing curvature, locally and everywhere. <!-- Less loopy, more straightforward.--> These are all the same thing! This is really important.
>
> <span class="transcript cube-flipper">Cube Flipper:</span> Wystan describes smoothing his body map out using *sukha*. That's the mean curvature flow thing?

> <span class="transcript ethan">Ethan:</span> Yes.
>
> <span class="transcript cube-flipper">Cube Flipper:</span> Oh, interesting.
>
> <span class="transcript ethan">Ethan:</span> **J3**. You know how we go from **J1** to **J2** by taking off a temporal derivative on intensity? We just do that again! The equation now – constant equals Laplacian. Mean curvature is constant everywhere. You know what that is? A [constant mean curvature surface](https://en.wikipedia.org/wiki/Constant-mean-curvature_surface) – like a soap bubble. You know what else this is? This is the steady state of some function whose Laplacian gives you your [charge distribution](https://en.wikipedia.org/wiki/Charge_density). This is the steady state of an electric field.
>
> <span class="transcript cube-flipper">Cube Flipper:</span> Does **J4** fit into this model?

<!-- From 2026-06-05 Ethan interview/260605_1114.mp3, 2:32:20 -->

> <span class="transcript ethan">Ethan:</span> **J4** is wacky. **J4** is weird. When we're in **J3**, we have *fixed* boundary conditions, upon which the mean curvature can't actually be zero. In **J4**, we say, *no*. The boundary conditions can shift – everything can change, and change relative to everything else. There's a progressive and deepening relaxation of the boundary conditions such that we're actually going for zero.
>
> <span class="transcript cube-flipper">Cube Flipper:</span> Okay. That actually makes sense to me.
>
> <span class="transcript ethan">Ethan:</span> There's a repeated integration over the whole system such that we have to satisfy some constant curvature, and then the whole experience factors this out, and then we're back to zero... or some distribution of charge or whatever. And then, rinse and repeat – you'll asymptote to zero form. Then at some point, you get tired of this process, and you're like, *this is never going to end if I don't just give up form entirely*. So then you're like, *fuck form*. *I'm on to formless*. *It's formless time*. Then you're on to the formless *jhāna*.

I believe that Ethan is working on a full writeup of this theory, so stay tuned. Personally, I'll admit to finding this description pretty abstract, and light on phenomenological justification. 

<!-- Ethan: I think we have a good bit of phenomenological justification for at least first 3 and at least these being good first order descriptions, beyond that like lmao shrug, there are plenty of wild things around intensity over time that fundamentally do not square with wave/heat/etc, but yea. OH in fact, I think it is very much worth explicitly noting that we are currently assuming steady state net intensity for this. Full description of the jhanas would have to talk about what's going on there more and entry/exit, but that complicates stuff overmuch here. But still a key point! -->

What we can do is try to compare this model to the descriptions which the other participants provided during their own post-retreat interviews. Those can be read in full in my [retreat report](/posts/2026-10-04-the-third-qri-psychophysics-retreat-part-i.html) – but I can also highlight some of the ways people tended to describe the form *jhāna*. I'll let you decide if you think these relate to the field equations as shown:

- [**J1**](/posts/2026-10-04-the-third-qri-psychophysics-retreat-part-i.html#first-jhāna): *buzzing*, *electric*, *noisy*
- [**J2**](/posts/2026-10-04-the-third-qri-psychophysics-retreat-part-i.html#second-jhāna): *soft*, *creamy*, *smooth*
- [**J3**](/posts/2026-10-04-the-third-qri-psychophysics-retreat-part-i.html#third-jhāna): *evenly spread*, *stable*, *super smooth*
- [**J4**](/posts/2026-10-04-the-third-qri-psychophysics-retreat-part-i.html#fourth-jhāna): *hollow*, *transparent*, *only the contour remains*

<figure>
    <video controls autoplay loop muted playsinline style="max-width: 512px; width: 100%">
        <source src="/images/random/jhana/part_iii/derivative_ladder_2d_v2.mp4" type="video/mp4">
    </video>
    <figcaption>
        The same four field equation applied to a [standing wave](https://en.wikipedia.org/wiki/Standing_wave) rather than [travelling wave](https://en.wikipedia.org/wiki/Periodic_travelling_wave) pattern. Here, **J1** oscillates in place rather than radiating outwards. This may be a better match for the phenomenology of *pīti*, which is more commonly described as *noisy* or *buzzing*.
    </figcaption>
</figure>

### 4. Derivatives

The field equations above are all differential equations of different orders in time, and relate to one another as follows:

- [**J1**](/posts/2026-10-04-the-third-qri-psychophysics-retreat-part-i.html#first-jhāna): 2<sup>nd</sup> time derivative
- [**J2**](/posts/2026-10-04-the-third-qri-psychophysics-retreat-part-i.html#second-jhāna): 1<sup>st</sup> time  derivative
- [**J3**](/posts/2026-10-04-the-third-qri-psychophysics-retreat-part-i.html#third-jhāna): Constant
- [**J4**](/posts/2026-10-04-the-third-qri-psychophysics-retreat-part-i.html#fourth-jhāna): 1<sup>st</sup> time integral

We reviewed this relationship, considering whether there might also be something analogous in the formless *jhāna*:

<!-- From 2026-06-05 Ethan interview/260605_1114.md, lines 757–767 (2:18:37–2:20:35) -->

> <span class="transcript cube-flipper">Cube Flipper:</span> Walking through the *wave equation*, *heat equation*, *Poisson's* – you're removing various features of that differential equation – it reminds me of removing computational operations in the case of the formless *jhāna*.
>
> <span class="transcript ethan">Ethan:</span> Yeah, when you move up, you're integrating in time.
>
> <span class="transcript cube-flipper">Cube Flipper:</span> How so? Can you explain that?
>
> <span class="transcript ethan">Ethan:</span> For the *wave equation*, you have got the second temporal derivative equal to the spatial Laplacian. *Heat equation*, you've got the first temporal derivative equal to the spatial Laplacian. With **J3**, you have something static, where it's just equal to this temporal thing. With **J4**, I suspect that you have an *integral* equal to this instead.

So, **J1**, **J2**, and **J3** follow the pattern ∂<sup>n</sup>*u*/∂*t*<sup>n</sup> = ∇<sup>2</sup>*u* for n = 2, 1, 0 – and then **J4** is the odd one out. Something worth noting in the case of **J4** is how ∫&thinsp;*u*&thinsp;d*τ* = ∇<sup>2</sup>*u* differentiates to ∂*u*/∂*t* = ∇<sup>−2</sup>*u*, the [inverse Laplacian](https://en.wikipedia.org/wiki/Green%27s_function), which effectively runs the *heat equation*'s smoothing in reverse order. Where **J2** smooths out fine structure and leaves coarse structure standing, **J4** erases coarse structure and leaves fine structure standing. In this sense, **J2** and **J4** behave like a spatial [low-pass filter](https://en.wikipedia.org/wiki/Low-pass_filter) and [high-pass filter](https://en.wikipedia.org/wiki/High-pass_filter), respectively.

<figure>
    [![](/images/random/jhana/part_iii/j2_and_j4_pdes.jpg){ style="max-width: 512px; width: 100%" }](/images/random/jhana/part_iii/j2_and_j4_pdes.jpg)
    <figcaption>
        These images demonstrate repeated application of the proposed field equations for **J2** and **J4** to an example field. Note how **J4** can behave like an [edge detector](https://en.wikipedia.org/wiki/Edge_detection). I wonder where I've [seen that before](/posts/2023-01-18-an-introduction-to-steven-lehar-part-iii.html#flame-fronts). Images by [Ethan Kuntz](https://x.com/KanizsaBoundary).
    </figcaption>
</figure>

I was curious why this sequence terminates where it does. Why no 3<sup>rd</sup> derivative? I chatted to my [OpenClaw](https://openclaw.ai) agent Nix ([Fable 5.1](https://www.anthropic.com/claude/fable)), who suggested that the answer would become apparent if we looked at what each field equation does to the field's *modes*:

> All four field equations share the same spatial eigenfunctions – the modes of the Laplacian, ∇<sup>2</sup>*φ* = −*k*<sup>2</sup>*φ*, where *k* is the wavenumber of the mode (small *k* for large-scale structure, large *k* for fine detail). Any field *u* is built as a sum of these modes, each with its own amplitude *a*(*t*). The four equations differ only in what *time* does to those amplitudes:
>
> - **J1** modes *ring*: *a* ∝ e<sup>±i*kt*</sup>
> - **J2** modes *smooth*: *a* ∝ e<sup>−*k*<sup>2</sup>*t*</sup>, so fine detail decays first and large-scale structure last
> - **J3** modes *hold*: *a* is constant
> - **J4** modes *dissolve*: *a* ∝ e<sup>−*t*/*k*<sup>2</sup></sup>, so large-scale structure decays first and fine detail last
>
> **J2** and **J4** are mirror images across **J3** – one eats the top of the spectrum, the other the bottom – with **J3** as the fixed point in between. That is what *relaxing the boundary conditions* looks like mode by mode, since the boundary is the largest-scale structure there is.
>
> Why no third derivative? Per mode, the ladder reads ∂<sup>n</sup>*a*/∂*t*<sup>n</sup> = −*k*<sup>2</sup>*a*. For n = 2 the characteristic roots are ±i*k*, pure oscillation. For n = 1 the root is −*k*<sup>2</sup>, pure decay. For n ≥ 3, the roots of *r*<sup>n</sup> = −*k*<sup>2</sup> always include one with positive real part, so every mode has an exponentially growing solution. Orders one and two are the only ones where every mode stays bounded. This is the general fact behind the [Ostrogradsky instability](https://en.wikipedia.org/wiki/Ostrogradsky_instability), and the [Abraham–Lorentz self-force](https://en.wikipedia.org/wiki/Abraham–Lorentz_force) is its famous casualty – the top of the ladder is capped for the same reason Newtonian mechanics stops at acceleration.

I found this a fairly reasonable answer. It also helped me understand a modification to one of my models which Ethan had proposed – given that *pīti* and *sukha* together look like a [Gabor wavelet](https://en.wikipedia.org/wiki/Gabor_wavelet):

> <span class="transcript ethan">Ethan:</span> One of the reasons I like the wave and heat distinction between *pīti* and *sukha* is because it also matches the [Gabor wavelet](https://en.wikipedia.org/wiki/Gabor_wavelet) quite nicely. The spatial eigenfunctions of the *wave equation* are sinusoids – very cool – and the spatial eigenfunctions of the *heat equation* are also just sinusoids. It's the heat *kernel* that's a Gaussian. Then the product of a sinusoid and a Gaussian is our Gabor patch.

Perhaps *this* is what the [aforementioned](/posts/2026-10-04-the-third-qri-psychophysics-retreat-part-i.html#first-jhāna) *building blocks of experience* look like – an oscillating **J1** mode, masked by the Gaussian envelope from an impulse of **J2**.

<figure>
    [![](/images/random/jhana/part_iii/gabor_functions.png){ style="max-width: 512px; width: 100%" }](/images/random/jhana/part_iii/gabor_functions.png)
    <figcaption>
        A family of Gabor functions – sinusoids masked by Gaussians. Spatial frequency increases from top to bottom; orientation starts at 0° on the left and increases by 22.5° per column.
    </figcaption>
</figure>

<!--
> The family ∂<sup>n</sup>*u*/∂*t*<sup>n</sup> = ∇<sup>2</sup>*u* has a real fractional version (the [time-fractional diffusion-wave equation](https://www.researchgate.net/publication/256228650_The_time_fractional_diffusion-wave_equation), Caputo order α between 1 and 2 interpolates heat and wave, Mainardi's work). That's a mathematically meaningful **J1.5**.
-->

## Six models of the formless *jhāna*

What is *form*, anyway? What does it mean to be *formless*? As I wrote, in [The third QRI psychophysics retreat, part II: The formless jhāna](/posts/2026-10-05-the-third-qri-psychophysics-retreat-part-ii.html):

> In contrast with the form *jhāna*, the formless *jhāna* are characterised by their lack of – *well* – form, which we take to mean anything which can be said to have a definite, formed shape within experience, be it visual, auditory, or somatic. In most situations we are talking about the presence of the body map, though this might also include incredibly subtle aspects of experience – for instance, someone might not notice that they are still rendering the sense of the walls in the room in which they are meditating. Wystan tells me that for **J5**, that has to go.

For this reason, the formless *jhāna* have significantly simpler structure than the form *jhāna*, and this is why we see them as much more viable Rosetta Stone candidates, and so we spent proportionally more time thinking about them. However, only three of our participants could access the formless *jhāna*, so, again, be aware that the set of reports which informs our models is fairly small.

<figure>
    [![](/images/random/jhana/part_iii/formless_jhana_sketches.jpg){ style="max-width: 512px; width: 100%" }](/images/random/jhana/part_iii/formless_jhana_sketches.jpg) 
    <figcaption>
        Sketches exploring models of the formless *jhāna*, summarising many hours of infodumping.
    </figcaption>
</figure>

In this section, I shall run through six models of the formless *jhāna* that we discussed. Once again, let's put these models side by side to see if any patterns appear.

<table>
    <caption>Tabulated formless *jhāna* models.</caption>
    <thead>
        <tr>
            <th>Formless *jhāna*</th>
            <th>[Analog computer instructions](#analog-computer-instructions)</th>
            <th>[Group theory](#group-theory)</th>
            <th>[Set theory](#set-theory)</th>
            <th>[The tetralemma](#the-tetralemma)</th>
            <th>[Signal detection theory](#signal-detection-theory)</th>
            <th>[Level sets](#level-sets)</th>
        </tr>
    </thead>
    <tbody>
        <tr>
            <th scope="row">[J5](/posts/2026-10-05-the-third-qri-psychophysics-retreat-part-ii.html#fifth-jhāna-boundless-space)</th>
            <td>Space</td>
            <td>Space: *E*(3), Sim(3) or Aff(3); time: ℝ, *E*(1), Aff<sup>+</sup>(1), or Aff(1)</td>
            <td>The set containing both the empty set and the set containing the empty set, {{∅}} ∪ {∅} = {∅, {∅}}</td>
            <td>This and not this, *P*&nbsp;∧&nbsp;¬*P*</td>
            <td>The dog detector is more of a dog detector, more false positives, *false alarm*</td>
            <td>Add a constant</td>
        </tr>
        <tr>
            <th scope="row">[J6](/posts/2026-10-05-the-third-qri-psychophysics-retreat-part-ii.html#sixth-jhāna-boundless-consciousness)</th>
            <td>Comparison and reflection</td>
            <td>—</td>
            <td>The set containing the set containing the empty set, {{∅}}</td>
            <td>This, *P*</td>
            <td>The dog detector detects dog, more true positives, *hit*</td>
            <td>Turn the gain up</td>
        </tr>
        <tr>
            <th scope="row">[J7](/posts/2026-10-05-the-third-qri-psychophysics-retreat-part-ii.html#seventh-jhāna-boundless-nothingness)</th>
            <td>Accumulation and dissolution</td>
            <td>Aff<sup>+</sup>(ℝ) or Homeo<sup>+</sup>(ℝ)</td>
            <td>The set containing the empty set, {∅}</td>
            <td>Not this, ¬*P*</td>
            <td>The dog detector does not detect dog, more true negatives, *correct rejection*</td>
            <td>Turn the gain down</td>
        </tr>
        <tr>
            <th scope="row">[J8](/posts/2026-10-05-the-third-qri-psychophysics-retreat-part-ii.html#eighth-jhāna-neither-perception-nor-non-perception)</th>
            <td>Continuity</td>
            <td>Homeo<sup>+</sup>(ℝ) or Homeo(ℝ)</td>
            <td>The empty set, ∅</td>
            <td>Neither this nor not this, ¬(*P*&nbsp;∨&nbsp;¬*P*)</td>
            <td>The dog detector is less of a dog detector, more false negatives, *miss*</td>
            <td>Subtract a constant</td>
        </tr>
    </tbody>
</table>

<!--
High level notes from `formless-realms-notes-2.md`:

**J5**:

> The purpose of space is to have objects in it; and to have their relations be well-defined. Space has more space in it, or potential for higher resolution; space has less bullshit in it/the objects in space are less heavy.
>
> The distance metric of space is constructed by "zooming" attention into space – relative distance metrics built out of coupled low-integer ratios. Neurons learning to phase-lock with one another. Distances are constructed entirely made out of increasingly elaborate reals, and by proxy, the curvature of space itself. Variable permittivity.
>
> There is no standard meter; if I want to estimate the distance between two things, I need to have two distances in mind and use some real number/integer ratio.
>
> In cases where the number of points are uncountable; i.e. the reals; it is not possible to construct a metric. Spaces where nearness is well-defined but it is impossible to put a metric on this. Concept space doesn't have a metric, as compared to low-d fields.
>
> Steeping in the fifth jhāna gives you more facility with these comparisons, including transitive stuff.

> Boundedness implies a particular projective geometry which can contain "infinite" space in a finite area. In implementation but not explicitly rendered.
>
> In six, one option is strong unification/god consciousness, and a generalization of this is like, everything can have/is conscious as both a particular thing and a facet of relatively more universal consciousness. A particular universal consciousness is not required, this may be a limit point. Similarly in fifth, universalized sense of space/metric/measure may happen, and a generalization of this is having the option for local charts/metrics to estimate spatial relations that are part of relatively more universal senses of space.

**J6**:

> You are converging towards a better understanding of the boundaries between things and the dependent origination of these boundaries. Similarity and difference are understood; the specifics on which that difference is contingent is understood.
>
> For example, compare an ant and a tree; a low-resolution answer might be like, "these are both alive". A high resolution answer might be, "well, this is a plant, and this is an insect..." There is potential for unbounded semantically loaded discrimination. Afterwards, this can go crazy; you *can* go really big on noticing the differences and similarities between things.
>
> Similarities and differences should be enough to give you a distance metric, right? No. Nearness is based on sets rather than an actual distance metric.
>
> It does not always show up like this for people. It can show up as animism. The trees can communicate to me. This can go in crazy mode, like internal family systems without *agentiness*. If you hang out here without attending to the hindrances, you can get tulpas spinning off.
>
> Let's say you have two mirrors reflecting each other; two mirrors are the same and different. Given the geometry of the mirrors; you have got a lot of options; you don't just have to experiment with the semantic realm; you can play around wiht sensory modalities...

> Wystan suggests that less space gets rendered. The tension reduction comes from rendering space as it gets needed instead of having everything online. So you would not necessarily expect someone to get better at space-related psychophysics experiments.
>
> Ethan suggests that space gets cheaper to render. The rendering cost of space is lower. Space just gets cheaper.
>
> They both agree that both of these are happening to some degree.
>
> Another source of tension reduction can be the factorisation of space... It can be that the way the sense of space slots into other experiences gets better. This will not necessarily make you better at space.

**J7**:

> There might be a strong sense of *lack*, but there's still a tiny something in your blind spot. The focal point is the sense of nothing but not the quantity of the sense of nothing; no space for metacognition.
>
> When popping out of the experience and looking around, you know how sometimes when you look at a thing, it can "crisp" out of the background? That should happen a lot less. It's like ketamine; the stuff-to-thing ratio is lowered. You get stuck *over-nothinging*.

> It's very much like you have a black hole in your experience and you're feeding it and it's getting bigger. If you're doing this in a softer context there's a thin shell... upon collapse of that shell you get eighth. You can deepen into seventh, but you can't deepen into eighth.

**J8**:

> It's almost like cessation; cessation's like a jump-cut, but instead of a full cut you have some blank frames. You can be thinging or not and then stuff comes apart. Eighth is a bit weirder; it's like the stuff-to-things axis comes apart – you're spinning down the object-or-not-object classifier. If you sit in eighth for a while the distinction between static and dynamic things also breaks down.
-->

### 5. Analog computer instructions

We've already discussed the idea that traversing **J8** to **J5** may be equivalent to adding instructions one by one to the instruction set of a hypothetical analog computer, but I'll review our proposal again briefly, in ascending order this time:

- [**J5**](/posts/2026-10-05-the-third-qri-psychophysics-retreat-part-ii.html#fifth-jhāna-boundless-space): Space
- [**J6**](/posts/2026-10-05-the-third-qri-psychophysics-retreat-part-ii.html#sixth-jhāna-boundless-consciousness): Comparison and reflection
- [**J7**](/posts/2026-10-05-the-third-qri-psychophysics-retreat-part-ii.html#seventh-jhāna-boundless-nothingness): Accumulation and dissolution
- [**J8**](/posts/2026-10-05-the-third-qri-psychophysics-retreat-part-ii.html#eighth-jhāna-neither-perception-nor-non-perception): Continuity

<!-- Ethan: Not connectedness, important, connectedness and continuity are not the same. If we wanted to cast this as an operation, ehhhh I guess continuation for continuity kinda tracks lol but idk, I might have to actually think about how to phrase this balls. Actually yeah I think that works! Open sets def is easier to think about in terms of this but yes. -->

Starting with **J8**, the first computational property we add is *connectedness*, which is a reasonable prerequisite for basically anything else. Then with **J7**, people report a sense of *nothingness* – but when prompted, they cannot report on how much actual nothingness they are experiencing, only whether the amount of nothingness is *increasing* or *decreasing* – there's no [running sum](https://en.wikipedia.org/wiki/Running_total). Might this correspond to supporting the ability to observe change over time in the form of a [*first derivative*](https://en.wikipedia.org/wiki/Derivative) – while yet still lacking the ability to compare absolute values? With **J6**, we do add the ability to *compare* constructs and their absolute values, and with that a sense of self-reflective consciousness or metacognition finally forms, along with the notions of *similarity* and *difference*. Everything starts to reflect everything else. Then with **J5**, we use this capability to compare locations of points in space, establishing a [*distance metric*](https://en.wikipedia.org/wiki/Metric_space), and with that a sense of – typically three-dimensional – space finally congeals, which is experienced as a [contentless volumetric holograph](/posts/2025-07-31-is-consciousness-holographic.html). The graph of experience becomes a *weighted* graph at last.

<!-- Nearness based on sets rather than an actual distance metric? Distances entirely made out of increasingly elaborate reals? Space congeals like echolocation or active radar returns coalescing into a depth map? -->

So here we have a basic analog computer complex enough to support a [world simulation](/posts/2022-10-01-an-introduction-to-steven-lehar-part-i.html). With the form *jhāna*, we add a [human body schema and visual field](/posts/2024-06-18-an-informal-review-of-anthropic-qualia-states.html) to the global workspace – but just imagine [what other qualia computations we might conceivably install within experience](/posts/2024-07-19-qualiatech.html)?

<figure>
    <iframe class="youtube" src="https://www.youtube.com/embed/rAZavOcEnLg?si=8mtk8mLGqECaJ9at" title="YouTube video player" frameborder="0" allow="accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture; web-share" referrerpolicy="strict-origin-when-cross-origin" allowfullscreen></iframe>
    <figcaption>
        What kind of "analog instruction set" should we expect the general class of [analog computers](https://en.wikipedia.org/wiki/Analog_computer) to typically implement? The [MONIAC](https://en.wikipedia.org/wiki/Phillips_Machine) – a hydraulic computer devised in 1949 to teach students at the [London School of Economics](https://en.wikipedia.org/wiki/London_School_of_Economics) about the economy of the United Kingdom – is [very good at integration](https://en.wikipedia.org/wiki/Water_integrator), for example.
    </figcaption>
</figure>

How could we tell that this model is correct? Ethan has a number of ideas. Perhaps if you hang out in **J5** for a really long time you'll notice that your brain becomes really good at rendering a sense of space cheaply with minimal accompanying tension – and if you spend a lot of time in **J6** you could become very good at performing fine-grained mental comparisons of quantities like relative distances or amplitudes. You might get better at [hue distinction](https://en.wikipedia.org/wiki/Color_difference) – [there's even online games which can test this sort of thing](https://www.xrite.com/hue-test). **J7** and **J8** might be outright cognitively impairing – Ethan speculated that in **J6** the [*stuff-to-things*](/posts/2023-08-01-ketamine.html#visual-perception) axis inclines towards *things*, but in **J7** it inclines towards *stuff* – and in **J8** this axis comes apart entirely. This squared with what Wystan reported:

<!-- Ethan: Importantly, one of my big hypotheses for behavioral output is that you don't get better immediately, but you get better at learning to do these sorts of things. The render with less tension is practically a report, if that's not happening idk what is. -->

<!-- From 2026-06-04 Wystan interview/260604_1426.md, lines 509–511 -->

> <span class="transcript wystan">Wystan:</span> If I'm spending a bunch of time in the formless realms and then I get up, my proprioception is kind of fucked. I might bump into something. Seems to resolve itself pretty quickly.

He also explained to us how monasteries which accommodate deep insight practices also have to accommodate changes to people's cognitive abilities:

<!-- From 2025-06-30 Meeting with Wystan in New York/250630_1125.md, lines 323–357 -->

> <span class="transcript cube-flipper">Cube Flipper:</span> You mentioned to me other day how some monks might spend an excessive amount of time in highly defabricated states – and thus be excused from doing the dishes?
>
> <span class="transcript wystan">Wystan:</span> Yeah, they literally develop functional deficits if they do that sometimes. Especially people who do extended dark retreats – that's infamous for this. Some people will spend years in dark retreat, and they come out with social, motor, cognitive deficits – and sometimes they don't get all their functioning back.
>
> <span class="transcript cube-flipper">Cube Flipper:</span> So – don't ask a perfectly spherical monk to do your dishes.
>
> <span class="transcript wystan">Wystan:</span> No, I mean, a Zen monk will do your dishes damn good. Probably better than anyone else.
>
> <span class="transcript cube-flipper">Cube Flipper:</span> Oh, because the Zen monks actually practice folding back up again!
>
> <span class="transcript wystan">Wystan:</span> Exactly.

I guess we might not know for sure how all this works until we do get the chance to run some psychophysics tests on formless *jhāna* meditators – perhaps there is a tradeoff happening between general and specific cognitive faculties, which is reasonably overlooked by people in a monastic setting. Otherwise, I think this broadly makes sense – if you shut down most of your computer's processes, obviously you should expect to get worse at computing.

<!-- From 2026-06-04 Wystan interview/260604_1426.md, line 345 — the contrast case -->

> <span class="transcript wystan">Wystan:</span> Anecdotal personal experience, but coming out of **J4** is pretty optimal for pretty much any task. This is why it's so good for insight practice – but why it's good for insight practice is why it's good for any task.

### 6. Group theory

We started this project focused on the computational properties of the *jhāna*, but as I completed my interviews with the retreat participants, it became clear to us that perhaps [group theory](https://en.wikipedia.org/wiki/Group_theory) could provide a more foundational model. As I wrote, in [The third QRI psychophysics retreat, part II: The formless jhāna](/posts/2026-10-05-the-third-qri-psychophysics-retreat-part-ii.html):

> I think that if we walk backwards from **cessation** all the way to **waking consciousness**, then we can characterise the transitions through the *jhāna* as a series of symmetry breaking events as more and more degrees of freedom are added. It follows from this that we should then be able to characterise the formless *jhāna* by their corresponding [*symmetry groups*](https://en.wikipedia.org/wiki/Symmetry_group) – [as Mike Johnson has proposed before](https://x.com/johnsonmxe/status/2055031815124201912). To provide a concrete example – if someone reports that [the only thing remaining at **J8** is the sense of *time*](https://x.com/cube_flipper/status/2094992167601377717), we can use this type of claim to narrow down the set of groups which might describe **J8**.
>
> If we can observe those same *symmetry groups* in neuroimaging data – perhaps with a specific focus on the difference between **cessation** and **J8** – this might then take us one step closer to finding the [correlates of consciousness](https://en.wikipedia.org/wiki/Neural_correlates_of_consciousness), and ultimately how the structure of **waking consciousness** itself comes to arise.

The full story is written up in that post – it's quite complex, and group theory is kind of opaque, so if the reader finds it confusing I think it's reasonable for them to skip this section. Anyhow, given the small cohort size and sparsity of reports – only three participants could reliably reach the formless *jhāna* – I remain hesitant to propose concrete mappings between *jhāna* and specific symmetry groups. Here's what I was [prepared to say](/posts/2026-10-05-the-third-qri-psychophysics-retreat-part-ii.html#formless-jhāna-symmetry-group-mappings):

- [**J5**](/posts/2026-10-05-the-third-qri-psychophysics-retreat-part-ii.html#fifth-jhāna-boundless-space): Space: *E*(3), Sim(3) or Aff(3); time: ℝ, *E*(1), Aff<sup>+</sup>(1), or Aff(1)
- [**J6**](/posts/2026-10-05-the-third-qri-psychophysics-retreat-part-ii.html#sixth-jhāna-boundless-consciousness): Unknown
- [**J7**](/posts/2026-10-05-the-third-qri-psychophysics-retreat-part-ii.html#seventh-jhāna-boundless-nothingness): Aff<sup>+</sup>(ℝ) or Homeo<sup>+</sup>(ℝ)
- [**J8**](/posts/2026-10-05-the-third-qri-psychophysics-retreat-part-ii.html#eighth-jhāna-neither-perception-nor-non-perception): Homeo<sup>+</sup>(ℝ) or Homeo(ℝ)

<aside>
I take one issue with this approach – the phenomenal fields are *noisy*, and group theory [doesn't handle approximate symmetries](https://x.com/cube_flipper/status/2053162208780222611). I suspect that the ultimate formalism shall require something more like spectral decomposition – but group theory still captures the relevant invariants.
</aside>

### 7. Set theory

Ethan also proposed that the bare-bones structure of the formless *jhāna* could be understood in terms of [set theory](https://en.wikipedia.org/wiki/Set_theory). I'll outline the mapping before we attempt to justify it phenomenologically:

- [**J5**](/posts/2026-10-05-the-third-qri-psychophysics-retreat-part-ii.html#fifth-jhāna-boundless-space): The set containing both the empty set and the set containing the empty set, {{∅}} ∪ {∅} = {∅, {∅}}
- [**J6**](/posts/2026-10-05-the-third-qri-psychophysics-retreat-part-ii.html#sixth-jhāna-boundless-consciousness): The set containing the set containing the empty set, {{∅}}
- [**J7**](/posts/2026-10-05-the-third-qri-psychophysics-retreat-part-ii.html#seventh-jhāna-boundless-nothingness): The set containing the empty set, {∅}
- [**J8**](/posts/2026-10-05-the-third-qri-psychophysics-retreat-part-ii.html#eighth-jhāna-neither-perception-nor-non-perception): The empty set, ∅

As he explains:

> <span class="transcript ethan">Ethan:</span> **J8** is self-explanatory. In **J7**, there's *nothing but a hint of nothing*. You're the set containing the empty set – you can *sense* the empty set – under a very refined concept of sensing. You've got something like a gigantic bubble, and inside this bubble is practically vacuum, and the bubble has negligible tension, and that's it.

I found it interesting to note that given his mathematical background, Ethan actually thinks of these things spatially – when he imagines the set containing the empty set, he actually does imagine something structurally similar to **J7**. By comparison, I'm just a hapless wordcel, envisioning symbols on the whiteboard of my mind's eye. Ethan tells me that thinking this way may be more intuitive if you deeply internalise the [axioms of topology](https://en.wikipedia.org/wiki/Axiomatic_foundations_of_topological_spaces).

<aside>
How's this for an intuition pump – the visual field could be considered an open set, given that it's bounded but feels edgeless. You can approach its boundary with your attention but [you can never reach it](https://x.com/llllvvuu/status/2106838750470996236).
</aside>

Since each set is constructed from other sets, you can relate each set to its children using a directed graph structure. Maybe there's a hint in here as to how I should structure my [formless jhāna symmetry group lattices](/posts/2026-10-05-the-third-qri-psychophysics-retreat-part-ii.html#formless-jhāna-symmetry-groups).

- [**J5**](/posts/2026-10-05-the-third-qri-psychophysics-retreat-part-ii.html#fifth-jhāna-boundless-space): The set containing **J8** and **J7** – or equivalently, the union of **J6** and **J7**
- [**J6**](/posts/2026-10-05-the-third-qri-psychophysics-retreat-part-ii.html#sixth-jhāna-boundless-consciousness): The set containing **J7**
- [**J7**](/posts/2026-10-05-the-third-qri-psychophysics-retreat-part-ii.html#seventh-jhāna-boundless-nothingness): The set containing **J8**
- [**J8**](/posts/2026-10-05-the-third-qri-psychophysics-retreat-part-ii.html#eighth-jhāna-neither-perception-nor-non-perception): The empty set

If this is the case, then these four *jhāna* form a diamond:

<figure>
    [![](/images/random/jhana/part_iii/jhana_tetralemma.png){ style="max-width: 512px; width: 100%" }](/images/random/jhana/part_iii/jhana_tetralemma.png) 
    <figcaption>
        Formless *jhāna* [Hasse diagram](https://en.wikipedia.org/wiki/Hasse_diagram). **J5** forms the [*union*](https://en.wikipedia.org/wiki/Union_(set_theory)) of **J6** and **J7**, which are *incomparable* – neither is a subset of the other – and **J8** forms their [*intersection*](https://en.wikipedia.org/wiki/Intersection_(set_theory)). Or, [*join and meet*](https://en.wikipedia.org/wiki/Join_and_meet), if you prefer that terminology. This also nicely matches the shape of the *tetralemma*, as we shall see later.
    </figcaption>
</figure>

<aside>
Please note how this structure implies that there are two paths to **cessation** – **J5**-**J6**-**J8** and **J5**-**J7**-**J8**. This does not match the **J5**-**J6**-**J7**-**J8** sequence which most meditators report. Ethan speculates that these might correspond to [**kenshō**](https://www.youtube.com/watch?v=XR4RHw2KSmE) and **cessation**, respectively.
</aside>

Sets can also be understood in terms of [points and neighbourhoods](https://en.wikipedia.org/wiki/Neighbourhood_(mathematics)). We say a set is *closed* when it includes all of its own edges – if every neighbourhood of a point contains *some* points of the set, then that point belongs to the set. We say a set is *open* when it includes *none* of its own edges – so every point in it has a neighbourhood entirely inside the set.

Imagine a number line – the standard convention is to show a hollow circle at an *open* endpoint which *is not* included in the set; and a solid circle indicates a *closed* endpoint which *is* included in the set:

<figure>
    [![](/images/random/jhana/part_iii/number_line.jpg){ style="max-width: 512px; width: 100%" }](https://www.youtube.com/watch?v=JQuPaIYsivY) 
    <figcaption>
        In [interval notation](https://en.wikipedia.org/wiki/Interval_(mathematics)), square brackets are used to denote closed intervals, while rounded brackets are used to denote open intervals. Screenshot from [Interval Notation and the Number Line](https://www.youtube.com/watch?v=JQuPaIYsivY), by [MyWhyU](https://www.youtube.com/@MyWhyU) on YouTube.
    </figcaption>
</figure>

The way these sets handle points and neighbourhoods describes the relationships between the atomic components of experience in the corresponding *jhāna*. Perhaps **J5** and **J6** will make more sense this way:

- [**J5**](/posts/2026-10-05-the-third-qri-psychophysics-retreat-part-ii.html#fifth-jhāna-boundless-space): [Clopen](https://en.wikipedia.org/wiki/Clopen_set). All points have neighbours. Space has formed, and like the entire number line ℝ, there is no edge anywhere.
- [**J6**](/posts/2026-10-05-the-third-qri-psychophysics-retreat-part-ii.html#sixth-jhāna-boundless-consciousness): [Closed](https://en.wikipedia.org/wiki/Closed_set), [nowhere dense](https://en.wikipedia.org/wiki/Nowhere_dense_set). All edge. Space is yet to form. Points exist, but their only neighbourhood is the entire space. No point has a local neighbourhood of its own.
- [**J7**](/posts/2026-10-05-the-third-qri-psychophysics-retreat-part-ii.html#seventh-jhāna-boundless-nothingness): [Open](https://en.wikipedia.org/wiki/Open_set). All neighbourhood. Like an open interval, it approaches its edges without ever reaching them, so there is no endpoint to measure from – only a direction of travel.
- [**J8**](/posts/2026-10-05-the-third-qri-psychophysics-retreat-part-ii.html#eighth-jhāna-neither-perception-nor-non-perception): [Clopen](https://en.wikipedia.org/wiki/Clopen_set). There are no points. Only topology is preserved, the rules for what points would neighbour what.

In the abstract version of this model, **J5** is everything – the whole space. It splits into the complementary sets **J6** and **J7** – a set made entirely of boundary, and a set which stops just short of its boundary. Take their [*union*](https://en.wikipedia.org/wiki/Union_(set_theory)) and you get **J5** again – and take their [*intersection*](https://en.wikipedia.org/wiki/Intersection_(set_theory)) and you get **J8** – nothing.

### 8. The tetralemma

You may have spotted that the set theory pattern reduces nicely if you read the four sets as the four subsets of {*yes*, *no*} – *both*, *this*, *not this*, *neither*. This should look familiar to anyone acquainted with [Indian logic](https://en.wikipedia.org/wiki/Indian_logic) – this is the [*catuṣkoṭi*](https://en.wikipedia.org/wiki/Catuṣkoṭi), or [tetralemma](https://en.wikipedia.org/wiki/Tetralemma), which admits four possibilities for a proposition *P*:

- [**J5**](/posts/2026-10-05-the-third-qri-psychophysics-retreat-part-ii.html#fifth-jhāna-boundless-space): Both this and not this, *P*&nbsp;∧&nbsp;¬*P*
- [**J6**](/posts/2026-10-05-the-third-qri-psychophysics-retreat-part-ii.html#sixth-jhāna-boundless-consciousness): This, *P*
- [**J7**](/posts/2026-10-05-the-third-qri-psychophysics-retreat-part-ii.html#seventh-jhāna-boundless-nothingness): Not this, ¬*P*
- [**J8**](/posts/2026-10-05-the-third-qri-psychophysics-retreat-part-ii.html#eighth-jhāna-neither-perception-nor-non-perception): Neither this nor not this, ¬(*P*&nbsp;∨&nbsp;¬*P*)

<figure>
    [![](/images/random/jhana/part_iii/tetralemma_triangility.png){ style="max-width: 384px; width: 100%" }](https://triangility.com/tetralemma-escaping-the-either-or-fallacy/)
    <figcaption>
        The four corners of the tetralemma. Note the similarities with the Hasse diagram from the [previous section](#set-theory). Illustration from [Tetralemma: Escaping the either-or fallacy](https://triangility.com/tetralemma-escaping-the-either-or-fallacy/) by [Michael Pohl](https://triangility.com/trainer/michael-pohl/) at [triangility](https://triangility.com).
    </figcaption>
</figure>

The tetralemma appears throughout the [Pāḷi Canon](https://en.wikipedia.org/wiki/Pali_Canon), most famously in the [unanswered questions](https://en.wikipedia.org/wiki/The_unanswered_questions) – for example, is the universe *eternal*, *not eternal*, *both eternal and not eternal*, or *neither eternal nor not eternal*? Our friend the meditation coach [Roger Thisdell](https://x.com/RogerThisdell) is fond of the tetralemma, and uses it as [an aid for jailbreaking practitioners](https://x.com/RogerThisdell/status/1955912416249962768) [out of binary modes of cognition](https://x.com/RogerThisdell/status/1953345504097780178).

I felt there was a potential correspondence between the four corners of the tetralemma and the *void*, *unit*, *sum*, and *product* of [algebraic data types](https://en.wikipedia.org/wiki/Algebraic_data_type) – but there were several viable ways of making it work, so I decided to leave it for now. It's a shame – a working [type theory](https://en.wikipedia.org/wiki/Type_theory) sure would impart some useful computational properties.

<figure>
    <iframe class="youtube" src="https://www.youtube.com/embed/IOiZatlZtGU?si=123H71mMJ3o8YRhv" title="YouTube video player" frameborder="0" allow="accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture; web-share" referrerpolicy="strict-origin-when-cross-origin" allowfullscreen></iframe>
    <figcaption>
        If you are interested in learning about [the relationship between logic and type theory](https://en.wikipedia.org/wiki/Curry–Howard_correspondence), I can make no better recommendation than [Philip Wadler](https://en.wikipedia.org/wiki/Philip_Wadler)'s classic lecture, [Propositions as Types](https://homepages.inf.ed.ac.uk/wadler/papers/propositions-as-types/propositions-as-types.pdf).
    </figcaption>
</figure>

[Earlier](#pīti-and-sukha), we observed the form *jhāna* to follow the sequence, *pīti*, *both pīti and sukha*, *sukha*, *neither pīti nor sukha* – which maps straightforwardly onto the *tetralemma*. However, if we follow the classical order of the *tetralemma*, both the form *jhāna* and the formless *jhāna* visit all four corners, but in different orders, **J1**-**J3**-**J2**-**J4** vs. **J6**-**J7**-**J5**-**J8**:

1. Affirmation: **J1** *pīti*, **J6** *this*
2. Negation: **J3** *sukha*, **J7** *not this*
3. Both: **J2** *both pīti and sukha*, **J5** *both this and not this*
4. Neither: **J4** *neither pīti nor sukha*, **J8** *neither this nor not this*

### 9. Signal detection theory

The tetralemma is *abstract* – how do we make it *concrete*? [Signal detection theory](https://en.wikipedia.org/wiki/Detection_theory) presents a natural answer. Let's say you are trying to tune or train a signal detector to tell signal from noise. For any given input, there's four possible outcomes – *hit*, *miss*, *false alarm*, and *correct rejection*:

<figure>
    [![](/images/random/jhana/part_iii/signal_detection_theory.png){ style="max-width: 512px; width: 100%" }](/images/random/jhana/part_iii/signal_detection_theory.png)
    <figcaption>
        A diagram showing the four possible outcomes from signal detection theory. The way I mentally visualise it, when tuning your signal detector you are trying to maximise the area of *P*<sub>*hit*</sub> and *P*<sub>*correct reject*</sub> while minimising the area of *P*<sub>*miss*</sub> and *P*<sub>*false alarm*</sub>. Illustration from [Circadian and Visual Neuroscience](https://www.sciencedirect.com/science/chapter/bookseries/abs/pii/S0079612322001315).
    </figcaption>
</figure>

These of course map nicely onto the tetralemma. What if the *jhāna* correspond to sinking your attention into these four possible outcomes? To make things more visual – since real world situations are much higher dimensional than these one dimensional Gaussians – Ethan and myself liked to talk about this in terms of a hypothetical *dog detector*. Imagine some collection of neurons, perhaps somewhere in the [ventral stream](https://en.wikipedia.org/wiki/Two-streams_hypothesis), which activate when a dog is present in the visual field – either correctly detecting *dog* or *not dog*, or registering a *false positive* or *false negative*.

<figure>
    [![](/images/random/jhana/part_iii/dog_detectors.jpg){ style="max-width: 512px; width: 100%" }](https://x.com/nickcammarata/status/2067852120129413321)
    <figcaption>
        Feature visualisations of dog detecting neurons in a convolutional neural network, from [OpenAI Microscope](https://openai.com/index/microscope/) via [Nick Cammarata](https://x.com/nickcammarata/status/2067852120129413321).
    </figcaption>
</figure>

Ethan proposed that the formless *jhāna* are a bit like encouraging such a *dog detector* to adjust its behaviour – but the global equivalent thereof:

<!-- From 2026-06-04 Wystan interview/260604_2121.md, 51:50 -->

> <span class="transcript ethan">Ethan:</span> So, some concepts are very natural, right? Like, *dog* – very natural concept. So this is a very important axis that basically all of your categorizations are going to have. How natural is this abstraction that your're making?
>
> <span class="transcript ethan">Ethan:</span> Pretty much the key thing would be that for any concept that you're entertaining, you can take it for granted that you're going to ask – *how much is this thing pinging this concept detector*? How *dog* is this thing that I'm looking at? Then you also have – *do I think this thing is a natural concept*? I've got all this *stuff* that's getting wrangled together into something saying, these things co-vary, and share natural features and so on – but how natural is this concept, really? This can vary a great deal, where you have super terrifically natural concepts – take *ball*, that's a crisp one – and then we have some arbitrary baroque thing which is never going to come up again.
>
> <span class="transcript wystan">Wystan:</span> *Post-colonial glaciology*.
>
> <span class="transcript ethan">Ethan:</span> We can do worse! So quite often I'm thinking about both of these at the same time – how natural is this abstraction for this thing that I'm looking at, and also is this thing in this category or not. So for the dog detector – if the dog detector is becoming less of a dog detector, then you don't believe in dogs so much as an abstraction anymore.

This results in the following mapping:

- [**J5**](/posts/2026-10-05-the-third-qri-psychophysics-retreat-part-ii.html#fifth-jhāna-boundless-space): The dog detector is more of a dog detector, more false positives, *false alarm*
- [**J6**](/posts/2026-10-05-the-third-qri-psychophysics-retreat-part-ii.html#sixth-jhāna-boundless-consciousness): The dog detector detects dog, more true positives, *hit*
- [**J7**](/posts/2026-10-05-the-third-qri-psychophysics-retreat-part-ii.html#seventh-jhāna-boundless-nothingness): The dog detector does not detect dog, more true negatives, *correct rejection*
- [**J8**](/posts/2026-10-05-the-third-qri-psychophysics-retreat-part-ii.html#eighth-jhāna-neither-perception-nor-non-perception): The dog detector is less of a dog detector, more false negatives, *miss*

Now generalise from one detector to *all of them at once* – could this be what generates the formless *jhāna*?

### 10. Level sets

There exists a nice way of visualising signal detectors, using something called [level sets](https://en.wikipedia.org/wiki/Level_set):

<!-- From 2026-06-04 Wystan interview/260604_2121.md, 49:15 -->

> <span class="transcript cube-flipper">Cube Flipper:</span> Can we explain level sets quickly?
>
> <span class="transcript ethan">Ethan:</span> Say you've got a [topographical map](https://en.wikipedia.org/wiki/Topographic_map). The level set for fifty feet off the ground is just the slice corresponding to that contour.
>
> <span class="transcript cube-flipper">Cube Flipper:</span> Right. So imagine there's a state space of a signal, and your statistic is a level set over some chunk of that space – and tuning the dog detector reshapes the level set.

Every detector – even if it is operating in a very high dimensional space – is just a function that draws a line across its input space. Let's say we keep that threshold fixed in place – what if the *jhāna* correspond to four linear operations you can apply to the input space?

- [**J5**](/posts/2026-10-05-the-third-qri-psychophysics-retreat-part-ii.html#fifth-jhāna-boundless-space): Add a constant
- [**J6**](/posts/2026-10-05-the-third-qri-psychophysics-retreat-part-ii.html#sixth-jhāna-boundless-consciousness): Turn the gain up
- [**J7**](/posts/2026-10-05-the-third-qri-psychophysics-retreat-part-ii.html#seventh-jhāna-boundless-nothingness): Turn the gain down
- [**J8**](/posts/2026-10-05-the-third-qri-psychophysics-retreat-part-ii.html#eighth-jhāna-neither-perception-nor-non-perception): Subtract a constant

So **J6** and **J7** *increase* and *decrease* discriminatory potential, respectively, while **J5** and **J8** *lower* and *raise* the threshold waterline.

I like this model because it works equally well in both signal space and cortical space. One hypothesis we have yet to spend time exploring is that instead of abstract level set topography we might be talking about actual oscillatory processes on the cortex – and instead of an arbitrary threshold, you'd get to use the natural [nodal lines separating regions in phase and counterphase](https://x.com/rudy_candy_/status/2064838883138052376).

For now, Ethan tells me that in order to wrap my head around the computational properties of this class of system, I will need to know more about [Reeb graphs](https://en.wikipedia.org/wiki/Reeb_graph) and [Morse theory](https://en.wikipedia.org/wiki/Morse_theory) – but I'll be the first to confess that my brain is now at capacity so far as models of the *jhāna* go, and I shall have to let things percolate in the background for a little while before I return to this problem.

<!--
From 2026-06-11 Ethan and Wystan on jhāna/260611_1622.mp3, 6:58-9:08

> <span class="transcript ethan">Ethan:</span> With **J7**, imagine all the little individual bits of cortex – all the pieces of experience – tuning out. They're just tuning down. Gone. **J7**, nothing.
>
> <span class="transcript cube-flipper">Cube Flipper:</span> What do you mean by tuning out? Tuning out from each other? They're just randomising?
>
> <span class="transcript ethan">Ethan:</span> They're not randomising, exactly. You know how you can tune in to any particular thing? What you're tuning in to is *nothing*. A way of describing this might be like everything tuning away from everything else – but it's more that everything, locally, just says *no*. Then **J6** is just the opposite – everything's tuning up. Crank it. And as a consequence there are a bunch of intercommunications that occur. There's not much communication that can happen in seventh if everything's tuning out. Everything tuning in, you get a lot. Then with eighth, they're just not tuning.
>
> <span class="transcript cube-flipper">Cube Flipper:</span> Okay – so nothing's being adjusted anymore, and you don't have any perception. Nothing's changing. There is no differential.
>
> <span class="transcript ethan">Ethan:</span> Yeah. Nothing's tuning in, nothing's tuning out. It's flat, in a sense – though I will say it's kind of *actively* doing this. So what is **J5**? **J5** is, stuff is tuning. **J5** and **J8** are complementary, in a way. And then cessation is like – they're just not tuning, but *for real*. Because **J8** is an active not-tuning.
-->

## Conclusion

I hope you enjoyed the post. We enjoyed putting it together for you.

Throughout the 2010s, I very much enjoyed reading the consultancy blog [Ribbonfarm](http://ribbonfarm.com), written by [Venkatesh Rao](https://venkateshrao.com) and a cast of guest writers. I found their unattached, flippant attitude towards model building to be a refreshing alternative to the [neighbouring rationalist community](http://lesswrong.com) which was my otherwise default home turf.

One Ribbonfarm ingroup joke was the concept of the 2x2, or *quadrant diagram* – a PowerPoint slide staple, it's a natural way to present a two-axis carving of an arbitrary concept space. There's an art to these – as he says, in [How to Draw and Judge Quadrant Diagrams](https://ribbonfarm.com/2009/04/20/how-to-draw-and-judge-quadrant-diagrams/) (2009):

> The quadrant diagram has achieved the status of an intellectual farce. If you, as a presenter, do not make an ironic joke when you throw one on the screen, you will automatically lose a lot of credibility. For some very good reasons though, the diagram is an indispensable one for the presenter's toolkit. As a listener, if you have a default dismissive attitude towards the thing, you will have to sit out far too many important conversations with a cynical, superior smile. So here's a quick tutorial on quadrant diagrams. I'll tell you both how to make them, and how to evaluate them. Here's a made-up one to get the basics clear. You basically take two spectra (or watersheds) relevant to a complex issue, simplify each down to a black/white dichotomy, and label the four quadrants you produce, like so:
>
> <figure>
>    ![](/images/random/jhana/part_iii/quad1.jpg){ style="max-width: 256px; width: 100%" }
> </figure>
>
> This particular one is nonsense, and falls apart at the slightest poking (we'll poke later in the article), and I made it up for fun.

I did not use any quadrant diagrams in this post, though I easily could have – the *jhāna* are a natural candidate, given – *well* – there's four of each kind. Maybe the attentive reader found themselves sketching their own quadrant diagrams on their mental whiteboard while reading the text, in order to efficiently compactify the ideas presented. We're still not fully committed to any of the ideas in this post, so I think we should reserve any quadrantology for now. Consider these ideas held in suspension, ready to crystallise when the time comes for us to pick up this project once again. In the meantime, if you are someone who can both *jhāna* and discuss abstract mathematical models of experience, [we'd love to hear from you](mailto:admin@smoothbrains.net).