I’m building a VR technodelic-style game/experience and I need a name!

Music visualizers work by turning sound into a visual experience. Dancing, especially in certain styles, works by turning sound into a kin[esth]etic experience. Here’s a diagram:

Fig 1. music visualization (top arrow) and dancing (bottom arrow)

My idea is to chain these processes, using computer vision and pose estimation, like this:

Fig 2. music visualization via dancing and computer vision

I’m doing this in virtual reality, and I have a working prototype that proves the concept. What should it be called so I can rename my files and launch a Discord?

What Color Are Your Vowels?

One of the most exciting trends in technology is the ability to hook up our sensory and motor systems in splendid new ways. One example is Soundself, a virtual reality “technodelic” that puts you into an audiovisual feedback loop with your own voice. Soundself promised to turn your voice into a psychedelic experience, and I wrote a review explaining my experience with it and why I don’t think it quite lived up to the promise.

In this post I introduce a little demo I made that I call “What Color Are Your Vowels?”, and my hope is that it can illustrate what I think is possible with technodelics. Without further ado, you can try the demo out here. I have only tested it on MacOS (Safari/Chrome/Firefox), Windows 10 (Internet Explorer/Firefox), and iOS (Safari) so no promises it’ll work elsewhere. You start by sustaining three vowels and capturing the background noise level (works better with total silence though) for calibration, and then you’re free to make any other sounds you want and see what color they make.

How it Works

The color space that humans see is three-dimensional because humans have three types of cones in our retinas. If you fix brightness, however, then color space is two dimensional, and you can call it chromaticity space.

Fig 1. Chromaticity space is two dimensional because it fits on an XY plane (Wikipedia)

The dimensionality of vowel space has more caveats, but it’s more-or-less two dimensional, corresponding acoustically to the two frequencies of the first and second formants in the frequency spectrum and anatomically to the two directions of where high-to-low and back-to-front the tongue is.

Fig 2. Vowel space is also two-dimensional (Wikipedia)

What I do with my demo is overlay these two space, mapping each point in vowel space to a point in chromaticity space.

Fig 3. Two 2D spaces, superimposed

It took me ~15 hours and ~200 lines of Javascript to make this demo. This is the kind of thing that I wanted from Soundself. Take my voice, do some linguistically-aware processing, and turn it into compelling visuals that represent it faithfully even in the radically different medium. To do this well you need to have some idea of the parameters that are generated in speech (formants, aspiration, sibilation, rhoticity, etc), some of the parameters that are used in sound visualizers (symmetry, repetition, color, shape, motion, etc) and an artistic flourish in mapping the former set of parameters to the latter set of parameters. There is a lot of potential here to make something truly splendid!

[Footnote] A slightly more technical “How it Works”: I record frequency spectra for your /u/ /a/ and /i/ phonemes, and then take the dot-product of future spectra with those recordings for the R, G, and B levels, respectively. Feel free to dive into the source code, also on my GitHub.

SoundSelf Technodelic Review

After weeks of anticipation in the midst of quarantine-fueled boredom, SoundSelf finally released today. SoundSelf pioneers the self-styled “technodelic” genre of games, and is the first to launch to a wide public audience. Technodelics harness the power of technology to create integrated experiences at the crossroads of psychedelics, meditation, song, dance, and music visualization. They are highly atypical “games”, as they do not have strategy or narrative, but for the most part they can be run on the same gaming platforms, virtual reality in particular. SoundSelf harnesses your microphone, speakers, and display to create a meditative tunnel of light and splendor that echoes your own ahs and oms into a session like you’ve never experienced before.

SoundSelf should receive praise for planting a tall flag in the technodelic turf. I must, say, however, that I was not blown away. I’ve been following technodelics for a year or two now and virtual reality for over a decade, so I’ve been itching to get my hands on those new experiences that I know are possible. What I want is to close the sensorimotor loop of my head, larynx, shoulders, knees, and toes on the one hand and my visual and auditory fields on the other. I want rich feedback between playful fluctuations of voice or step and color, flicker, timbre, beat, and fractals. I want to sing my way through the Mandelbrot Set and dance a virtual sun over a scintillating Dalí horizon. What I want is clearly much more than I could ever have expected SoundSelf to deliver today, but I was hoping for maybe 10% of it.

SoundSelf is essentially a meditation enhancer. Many of the features and constraints (like the smooth-spoken tutorial every time you launch it that you can’t turn off and the 3D perspective that resets whenever you move your head too far) are clearly built in to accommodate that one use-case. There is only one tunnel you can go through. You can’t modulate or change the gain on how your voice affects the visuals. You can barely tell what your voice is doing to the visuals unless you run careful and flow-destroying experiments lasting minutes at a time (I want to hum “ee” instead of “oo” and see something change—I’m not sure what, maybe a triangle turn colors—before I take my next breath). You can’t change the echo interval. You can’t change the music. If what you want is to lie back and be somewhat passively and mindlessly entertained, SoundSelf will work for you, but what I wanted was a vocal technodelic: nimble and pulsating audiovisuals responding to my every formant, susurration, yodel, and yawn.

Do I recommend SoundSelf? I definitely recommend putting technodelics on your radar, and SoundSelf is currently the best way to do that, and there’s no way to know what they’re about without experiencing them yourself. The creators are eager and energetic, so I have faith that they will continue to expand the experience, but keep your expectations tempered, and take it for what it is: a first impression on the debut of an entirely new art form. Throw in a few dollars with a friend and try it out, it’s definitely worth the cost of a theater ticket.

Dimensionality in the Annealing Metaphor

(~960 words)

The concept of annealing has escaped the materials science context where it originated. In the material context, it is straightforward to see how the characteristics of physical space might constrain annealing. For example, the 3-dimensional “kissing number” (with a value of 12) constrains the number of neighbors a 3-dimensional atom can have and thereby the possibility of movement, diffusion, and change within a 3-dimensional material. If the kissing number was greater than 12, a given annealing treatment regime would be more effective. The kissing number is merely one measure of the abundance and profile of interatomic associations in a material—associations which carry stress-energy, and which stress-energy is reduced in annealing via the shifting of those associations. In many systems, among them metals, societies, brains, each “atom” or basic unit has a number of associations, which in turn have their own associations, and the shape of the association network can be reckoned as living in a space with a certain dimensionality and geometry. Analyzing such spaces helps to enrich the annealing metaphor, pinpointing similarities and contrasts with material annealing in its 3-dimensional Euclidean space.

Let’s start where annealing began. A piece of metal essentially never has pure crystal structure throughout. On the one hand, the casting process usually proceeds in an uneven way, with multiple centers of solid crystalline order (“nucleation sites”) growing inside the molten metal as the entire piece solidifies, leaving irregular “grain boundaries” between the multiple “grains” that grew. Metal pieces that solidify quickly have many small grains, and pieces that solidify slowly have few but large grains. On the other hand, nothing is perfect, and even a mostly pure crystalline grain will have “point defects” like a vacancy where there should be an atom, or an interstitial atom wedged where there should be none. In a perfect FCC or HCP metal crystal, every atom would have 12 neighbors (following the 3-dimensional kissing number), but in any actual piece of metal, however, many atoms will not have 12, and their vacant or interstitial neighbors present opportunities. Metals anneal when vacancies and interstitial atoms march through the material (often along grain boundaries), readjusting grains to relieve stress or even creating entirely new grains within.

Annealing is well known to be affected by the preexisting abundance of point defects and grain boundaries and the treatment temperature, but the theoretical angle to armchair about here is how different dimensionalities (and kissing numbers) would affect annealing. Given an abundance of point defects (say, 0.1% of lattice sites being irregular), how many of these any given atom has as a neighbor will depend on the kissing number. If this number is very small, then any atom will rarely have a defective neighbor, but if this number is very large, then any atom likely may. The more atoms with defective neighbors, the more possibilities for vacancy or interstitial diffusion, and the greater efficiency at minimizing stress. So the hypothesis is that increasing the dimensionality of a metal makes it easier to anneal. Unfortunately, our Universe furnishes us with zero tools to change the dimensionality of the space that metals are in, so this must remain a hypothesis.

Instead of a metal, one can imagine a society where every individual has 12 friends. Or instead of 12, maybe 6, or perhaps just 2. These three numbers are the kissing numbers in 3, 2, and 1 dimensions, respectively, and they are totally conceivable even for real humans in our ordinary World, albeit rather drearily. The point is that human society, which it ostensibly embedded in the 3-dimensional World, can have a structure that belongs to a different dimensionality. If everyone had 24 friends, then human society would be effectively 4-dimensional. These numbers are of course totally crude, but there is an actual fact of the matter as to how humans are associated in society. I have spoken to f people in the past week, paid g people in the past month, touched h people in the past year. If we had an appropriate dataset, it would be possible to reconstruct the effective dimensionalities of human societies, down to their local fluctuations across communities and time. The dimensionality of urban areas is certainly higher, for instance, than the dimensionality of rural areas.

Some societies are easier to anneal than others. Many people have too many associations or too few for their local social lattice, but in societies with high dimensionality, it is easy for people to diffuse and find their balance. Because of the parallel association of dimensionality and “heat” in annealing, to heat a society is to increase the number of interpersonal associations, and to decrease interpersonal associations (as in pandemic lock-downs) is to cool it.

The hallmark of brains is that neural tissue is not populated by oval-ish cells like everywhere else in the body, but instead by extraordinarily spindly cells that branch and reach and associate directly with myriads of other neurons, clearly many more than 12 of them. Axons and dendrites are the transcendence of neurons in neural tissue beyond the 3-dimensional kissing number. The brain is 3-dimensional but its neural network is not. The exact mechanism of annealing in brain is unknown but it certainly involves neurons changing which other neurons they are connected to and how strongly, and because of neural tissue’s higher-than-3-dimensionality, it is uniquely capable of doing so among all human tissues.

There are many more systems whose dimensionality and annealing properties could be analyzed. The fundamental picture is that, despite the 3-dimensionality of space in our Universe, systems inside of it can adopt effective dimensionalities that are quite different via various mechanisms, and because there is a keen relationship between spatial associations and annealing, annealing in these systems will vary in methodical ways from annealing in materials.

Remultiplication: a term for compositional analysis

(~360 words)

In my study of compositionality, I’ve found a rather blatant pattern that lacks a word-handle. When things come together to compose something larger, the things are extremely often similar or even identical things. I call this pattern remultiplication: the coincidence of similar entities in a composition, especially on the same level within the composition’s partonomy and often when every single one of the partonomic siblings on that level are involved.

Remultiplication is everywhere. From my vantage point writing this, I can observe the remultiplication of strings on a guitar, the remultiplication of pixels on a display, of keys on a keyboard, of fingers on my hand, threads in a shirt, legs in a table, panes in a window, leaves on a branch. This can even happen with words: “salad-salad” in English, “wiki-wiki” in Hawaiian (“very fast”), or “rikrikrik” in Molikese. In linguistics, such a doubling or a tripling of elements is called “reduplication” or “retriplication,” respectively, and I find “remultiplication” to be the natural generalization of that concept to quantities beyond three and entities beyond words.

There are often very different reasons for remultiplication. The remultiplication of planets in a star system happened by them coalescing simultaneously out of a gas cloud. The remultiplication of cells in a body happened when one cell started dividing and the daughter cells stuck together. The remultiplication of bricks in a wall happened because a bricklayer iteratively put them there. The remultiplication of distributaries in a river delta happened because of iterated sediment deposition and channel switching. Regardless of the mechanism, there is a recurring compositional theme in all of these, and I call that remultiplication.

Figure 1. The remultiplication of stamina in a flower and of flowers on an inflorescence in Acacia dealbata.
(photo credit: me)

Remultiplication and fractals

“Fractal” is another term used for entities with internal similarity. Whereas remultiplication is concerned with similarity on one level of a partonomy, fractals also exhibit similarity across different scales and thus up and down the levels in a partonomy. It is possible for there to be up- and down-scale self-similarity without remultiplication, such as in a logarithmic spiral, whose zoomed-in center is self-similar to the zoomed-out whole.

Metatopes: a novel and simple mathematical construct for statistical ontology

(~400 words)


A metatope is a mathematical object constructed by a layering of spaces. For any space in a metatope, points can be plotted in it. These points in the space correspond to either (1) datapoints from a dataset with a commensurate dimensionality as that space or (2) spaces that contain either (1) or (2) (potentially ad infinitum).

A directed graph can be constructed from any metatope. The spaces within the metatope map to nodes and the connections from a space to the spaces plotted within it map to the vertices. A “highest space” can generally be identified, and that is the root of the metatope’s graph. The degree of a metatope is the maximum distance in the directed graph starting from the root. The degree counts the number of layerings in the metatope: a metatope of degree-0 is just a normal space, and its graph is just a solitary node with no vertices. If there is a root space in the metatope and all the other spaces connect upwards to exactly 1 space, then the graph of the metatope is a rooted tree.

For instance, consider a dataset of faces, both normal and cyclopean, parameterized by a robust set of features such as interocular distance, nose length, cheekbone position, etc. All the normal faces can be plotted in one space, and all the cyclopean faces can be plotted in one space, but these two spaces are incommensurate because there are several dimensions that are not shared (most saliently from the list above: interocular distance). Both spaces, however, can enter as points in a higher-level space that would have one dimension called “number of eyes.” This would be a degree-1 metatope, and its graph would have two nodes connecting upwards to the root node, for a total of three nodes.

Note that the structure of any metatope depends entirely on the relevant set of datasets (actual or theoretical) and the reckonings made in how to combine them, and that multiple metatopes can often be combined into one metatope.


My motivation is to develop a mathematical construct similar to the mere space that can be applied rigorously even when dimensionalities are incommensurate. I have often encountered conversations where “the space of x’s” is tossed around even when the x’s obviously or probably differ in the number of dimensions from one x to another x, such as “the space of conscious experiences.” I hope that the construct operates as an intuition pump and leads to interesting insights, from myself or others.

Symmetric vs Asymmetric, Free vs Bound Othermindfulness

(~700 words)

The practice of othermindfulness comes in various flavors, but generally as I have described it I have emphasized one specific form of it: symmetric, free othermindfulness. These descriptions of mine have centered on othermindfulness as a practice connecting you to someone in a similar state of mind (hence symmetric), and an arbitrary someone at that and not a specific person in particular (hence free). I’d like to describe the other forms of othermindfulness that can be found when the properties of symmetry and boundedness are allowed to be different.


A symmetric othermindful experience happens—just to recap—when a person having an experience chooses to share it othermindfully with someone else having a similar experience and someone else having such a similar experience reciprocates with the same intention. An asymmetric othermindful experience happens when a person having an experience shares it with someone else having a different experience and someone else having that different experience shares it back in turn with the person having a different experience. Symmetric othermindfulness is generally easier to engage in because empathy is more readily available for people who feel the same things, but asymmetric othermindfulness can be more rewarding.

If I am joyful and content and I engage symmetrically, then in my othermindful engagement I will connect with someone else who is also joyful and content, and we can enjoy our positivity together. If I am joyful and content and I engage asymmetrically, then I can connect with someone who is suffering or dejected, and they will know that I am joyful and content because they have chosen an asymmetric engagement also, and together we can find balance between our energies.

Symmetric othermindfulness accentuates and communifies what one already feels by providing a companion feeling the same thing. Asymmetric othermindfulness, on the other hand, allows someone to tap into a different state of mind. Someone suffering can find a commiserator with symmetric othermindfulness, but they can instead find someone with abundant, brimming-over positivity with asymmetric othermindfulness. One of my first applications of othermindfulness was in shuttling positive energy from my good days to my bad days during a depressive episode, and I couldn’t have done that without asymmetric othermindfulness.


Othermindful experiences can vary depending on whether the participants desire to connect specifically with each other. When I was connecting with myself between my good and bad days as I mentioned above, for instance, I was connecting very specifically with myself. That is bound othermindfulness, because the experience is bound to that specific person. Bound othermindfulness also occurs when two people regularly think about each other and know that they do so. Indeed, it is the ordinary state of two people in love, and it is the essence of reciprocated limerence. Bound othermindfulness can also be transient. It often occurs in the few hours or days after sharing the idea of othermindfulness with a new person; both may have othermindful experiences with each other as long as the conversation remains fresh in memory.

Free othermindfulness is the more radical version, and it is the one that as far as I can tell is the true conceptual innovation. Free othermindfulness expects no specific person to reciprocate the othermindful experience, instead relying—essentially on faith—that someone somewhere reciprocates. It relies on no set expectations or plans, merely harvesting the law of large numbers and the magnitude of the human (or sentient) race(s) to ensure its reality.


Symmetric, bound othermindfulness: two people who know (about) each other, (othermindfully) sharing each other’s similar experiences, such as two people who are in love.

Symmetric, free othermindfulness: two people who don’t know about each other, sharing each other’s similar experiences, such as two random suffering people on Earth giving each other empathy.

Asymmetric, bound othermindfulness: two people who know (about) each other who are not having the same experiences but desire to (othermindfully) connect, such as the friend who promises to send good thoughts and vibes to another.

Asymmetric, free othermindfulness: two people who don’t know about each other, sharing their different experiences with each other, perhaps entirely altruistically.

Praxis for Open Individualism

(~1500 words)

Philosophical analysis is necessary but insufficient. Often when engaging with interesting philosophical perspectives, the only drive is to understand, dissect, compare and contrast. If the primary vehicle for philosophical encounter is words on a page, the straightforward philosophical participation is to muse and write new words on new pages. There’s nothing wrong with that; my words would not be here without such a drive. There is, however, a well-known complement to the mind’s remapping of read words into written words that engages the mind in something other than mere verbal transformation. Aside from the digestion and regurgitation of theory, there is the embodiment and the practical living of theoretical precepts, which is called praxis.

Open Individual (OI) is the theoretical perspective on personal identity that holds a single experiencer as the subject of all experiences. The single experiencer in OI is seeing through my eyes right now and saw through them yesterday, but it is also seeing and saw through your eyes and everyone else’s too at all times. Open Individualism contrasts with Closed Individualism, the more conventional view in Western philosophy that holds a distinct experiencer for every body, remaining stable throughout each body’s life, and it contrasts with Empty Individualism, which holds a distinct experiencer for every experience, tearing apart even all of the back-to-back experiences in single bodies that CI would bind together.

That’s a short introduction to Open, Closed, and Empty Individualism—probably way too short for the reader that has never encountered them before (if that’s you, here is a good resource). My goal, however, is not to develop more theory about them, but to imagine what a praxis or praxes of OI might look like. Praxis can be described abstractly, but it is better to derive it concretely. Thus I trace my imagination through a specific example that I’ve cultivated for several years. I don’t doubt that this is but one example among many. Still, I haven’t searched the space of OI praxis particularly thoroughly, so I can’t be certain of that certainty. My mission is thus both to expound my example of OI praxis and to demonstrate a process for how other examples might be found.

Before I begin with my own example of praxis for OI, I can identify one recurring soundbite that might also be an example, but which on closer inspection I do not believe is particularly compelling. The claim often (if not generally) surfaces in presentations of OI that if Open Individualism were a widespread belief, then human society would express much more compassion and empathy. Certainly this is a likely consequence. A shift in perspective about the connectedness of our minds with those of others would likely lead to a shift in altruistic vs selfish behaviors. To adopt such a futuristic possibility about human society as a praxis, however, would involve its immediate politicization and its shoehorning into a social movement. Such a praxis would be little more than ordinary human organizational behavior with an extraordinary goal notwithstanding: to spread a message about the nature of who we are. Adopting such a praxis may certainly be noble, but to do so in an exclusive way would be to ignore OI qua OI and its fascinating and unique contributions distinct in kind from all different beliefs that would also induce compassion and empathy at scale.

Open Individualism makes some radical claims about our relationships with each other and our relationships with our experiences. These claims may not be “true” in a way that permits empirical or technological advantages over Closed and Empty Individualism, but they do offer a framework for constructing new thoughts and identifying new connections. Most importantly, that framework may allow us to see alignments between conceptualities and deliberate behaviors that are the very substance of praxis. We can consider ordinary activities and then cast them into the extraordinary framework of OI and see what kind of hopes and motivations come out.

One activity that seems to be extremely common among humans is talking with oneself, and it is the basis of the example I will use. In particular when it is done with the movement of no muscles, we all have the experience of engaging, silently and effortlessly, with each of our own self as an audience. Often it’s just a brief monologue, sometimes a more intense dialogue. What happens if we consider such talking with oneself in the context of Open Individualism? Well, if we’re all just one experiencer, then the ability to talk with oneself silently and effortlessly would include the ability for anyone to do so with all the other pseudo-I’s elsewhere and elsewhen. Obviously this isn’t a deduced claim about the nature of OI (else it would be immediately disproved!), but instead more of an aspiration—a child’s gleeful dream sprouting after Open Individualism is sown on the fertile ground of their imagination. When the goal is praxis, what follows after a gleeful dream is not a return to rigor and a proof or disproof, but a creative pursuit of the dream—a good faith attempt to reconcile the dream with the theory in a way that motivates behavior.

So let’s try to reconcile this dream resulting from the collision of Open Individualism and talking with oneself. A hallmark of OI is that it understands the relationship one has with oneself at different times to be substantially similar to the relationship one has with others. Thus OI can inspire us, as a first step, to think about talking with oneself as an activity temporally displaced across experiences in one body. Usually we think about talking with oneself as something that can be packaged up into a short, self-contained episode happening at a specific time, but we can imagine what it would be like for one to talk to oneself in the past or the future. I could bury a letter to myself in a time capsule or upload myself speaking to myself to YouTube, but let’s stay with the silent and effortless motif suggested earlier. Silently and effortlessly talking to myself with temporal displacement would require me to start an intentional dialogue with myself that I would set down and then continue later after a period of time doing other things. I can think to myself “I hope you’re doing well :)” while imagining myself later thinking “Why yes, thank you, I’m doing well :)” and then later remember myself thinking “I hope you’re doing well :)” while thinking to myself “Why yes, thank you, I’m doing well :).”

This is nothing particularly revolutionary yet. Open Individualism, however, encourages us to analogize the temporally-displaced relationship with oneself with one’s relationships with others. I can think “I hope you’re doing well :)” and someone else can think “Why yes, thank you, I’m doing well :).” A problem arises here. The reason I am capable of enacting both sides of the dialogue as illustrated beforehand is that I have memory that connects my temporally displaced selves. Unfortunately, I have no such shared memory with others. Is memory actually necessary for this feat, though? This is the junction where the dream is most a dream. Memory is sufficient, evidently, because it’s responsible in at least that one case. Responsible for what? Responsible for two instances of the cosmic experiencer engaging silently and effortlessly with each other. Are there other media that can accomplish the same bridging as an individual memory can? Are media strictly necessary at all?

Telepathy makes an entrance. Unfortunately, telepathy does not appear to be a real phenomenon. Telepathy is disproved by the impossibility of causally disconnected information transfer. But information transfer is not the specific praxis we seek; we seek mindful engagement: silent and effortless talking. Telepathy lies disproved, but such engagement is, conceptually, something different. People accurately anticipating and responding to each other’s silent and effortless talking does not have to be telepathic. Perhaps they conferred on what to anticipate beforehand, or perhaps the anticipated is so quotidian that it is likely to spontaneously happen among a set of individuals practicing half-dialogues. The former is a medium leveraging memory, but instead of one memory it is two memories joined at a prior conversation. The latter is no medium at all. Both allow disconnected people to engage in silent and effortless talking; both are the cosmic experiencer communing with itself.

We have hit upon engaging in half-dialogues as a praxis for Open Individualism by building from talking with oneself. It is inspired by what Open Individualism has to say about the commonalities among the relationships between entities that experience, and then it enters back in as something whose practice makes those relationships more tangible and manifest. I’ve elsewhere called this Othermindfulness, and I consider it a praxis for OI. There is more work that can be done to take other activities and cast them into the framework of OI in order to get other or more developed praxes. I hope that you’re inspired to do so, and I hope that you’re also inspired to practice half-dialogues, but if not I hope that you’re at least more familiar with the ways in which others live the principles of Open Individualism.

Market Utilitarianism

(~1900 words)


Two classic versions of utilitarianism are average and total utilitarianism. They are classic, but they have well-known problems. Both have rather simple formulations. They begin with a reckoning of utilities across the population of individuals, and contend with a simple, linear aggregation of those utilities: average utilitarianism takes the mean of utilities and total utilitarianism takes the sum. I propose an intermediate, nonlinear version of utilitarianism, predicated on the local population of utility-experiencers in their abstract statistical space(s). When optimized, this formulation of utilitarianism recapitulates certain properties of a marketplace. I will show how “market utilitarianism” resolves issues with both average and total utilitarianism, though it introduces issues of its own, and I will consider some theoretical ramifications it leads to.

1. Definition

Given a number of individuals experiencing utility, average and total utilitarianism can be given simple mathematical expressions:

Total utilitarianism:

(1) U_T = \sum_i u_i

Average utilitarianism:

(2) U_A = \frac{\sum_i u_i}{N} = \sum_i \frac{u_i}{N}

Where U_T is aggregate total utility, u_i is the intrinsic utility experienced by individual i, U_A is aggregate average utility, and N is the total number of individuals, and \sum_i is of course the summation for all individuals of the subsequent expression.

In market utilitarianism, the contribution of an individual’s utility to aggregate utility is attenuated by the existence of similar individuals, in proportion to the quantity of similar individuals. Market utilitarianism creates a rift between intrinsic utility as experienced by the individual and extrinsic utility as recognized by the aggregator, a quantity which relates inversely to the abundance of similar individuals for any individual. Market utilitarianism can thus be expressed:

(3) U_M = \sum_i E(u_i)

Where U_M is aggregate market utility and E(u_i) is the utility of individual i as possibly attenuated by others extrinsically. E(u_i) \simeq u_i when individual i has no similar matches and E(u_i) \simeq 0 when i has indefinitely many. More precisely:

(4) E(u_i) = \frac{u_i}{L_{S, P}(u_i)}

Where L_{S, P}(u_i) is the local population of individuals in the statistical space S around individual i, as defined by some nearest neighbor or local population parameterization P. L_{S, P}(u_i) can never be less than 1 because an individual is always near itself, and it can never be more than the total sum of individuals, N, identified previously. Putting it all together:

(5) U_M = \sum_i E(u_i) = \sum_i \frac{u_i}{L_{S, P}(u_i)} \quad 1 \leq {L_{S, P}(u_i)} \leq N

Thus market utilitarianism is intermediate between total and average:

(6) U_T \geq U_M \geq U_A because \sum_i \frac{u_i}{1} \geq \sum_i{\frac{u_i}{L_{S, P}(u_i)}} \geq \sum_i{\frac{u_i}{N}}

The denominator L_{S, P}(u_i)  of the extrinsic function depends on both the choice of statistical space (one example for S could be Blau space) and the choice of local population parameterization (one example for P could be a count of individuals falling within a similarity hypersphere centered at i in S with some radius r, with r = 0 equivalent to total utilitarianism [given no two things being exactly identical] and r = \infty equivalent to average utilitarianism). S is somewhat arbitrary and often a subspace of a richer space, but P should attribute monotonically decreasing importance to less similar individuals (and which individuals are similar or dissimilar obviously depends on the choice of S).

2. Behavior of the optimum

What is important about aggregate utility is the optimum that it achieves under the range of possible conditions. These conditions relate both to the set of individuals in a population of utility-experiencers and to the intrinsic utilities that each individual in the population experiences. This optimum prescribes the appropriate behavior—a choice or policy—assuming a prescriptive understanding of utilitarianism.

Let’s assume until further notice that the population is fixed at some size with some specific list of individuals. Then total and average utilitarianism will always experience an optimum of aggregate utility together. The reason is that total and average utilitarianism both aggregate all individual intrinsic utilities linearly (and without additive inversing, i.e. multiplication by -1, which is a linear operation but one that flips the maxima and minima). Thus, total and average utilitarianism always prescribe the same behavior (again: given a fixed population).

Market utilitarianism aggregates non-linearly, however, so the optimum of its aggregate utility will not necessarily co-occur with that of total and average utilitarianism. In particular, the same amount of intrinsic utility will contribute more to aggregate utility if spread among individuals in a sparsely populated region of the statistical space, such that relative to the optimum for total and average utilitarianism, intrinsic utility can be sacrificed among common individuals to provide it to more unique individuals. The conclusion here is that even though aggregate market utility is intermediate between aggregate total or aggregate average utility, its optimum is less similar to either of those than they are to each other (again: given a fixed population).

Let’s remove the assumption of a fixed population. This is where total and average utilitarianism both break, leading to absurd prescriptions for behavior. If the population can be adjusted, then the optimum for total utility occurs when every last individual exists who experiences net positive utility, even if barely non-miserable, and the optimum for average utility occurs when no individual exists except the one experiencing the most utility. This result is discussed in the literature on the mere addition paradox.

The optimum for market utilitarianism on the other hand is influenced by an important statistical fact: the more individuals that exist, the more likely any individual will have similar matches (and this is true for any S and P). Thus, aggregate market utility does not increase past a certain point of diversity saturation (dependent on the footprint of P) because any new individual added is statistically likely to be similar to any other. Conversely, the optimum for aggregate market utility occurs at more individuals than the optimum for aggregate average utility, because any additional individual is statistically likely to be unique in that regime.

3. The absurdity of market utilitarianism, with a caveat

In market utilitarianism, aggregate utility can be changed without changing the number of utility-experiencers nor any of their experienced utilities. It can be increased merely by making the experiencers different from one another. This seems intuitively like an absurd result. It seems like individuals should be treated directly equally and not indirectly through terms regarding who else they’re similar to.

Note, however, an extremely keen analogy with the behavior of the job market. The job market apportions utility to individuals in the form of monetary compensation. This compensation depends on their ability to perform a set of duties, but also on the abundance of other individuals that can perform the same duties, i.e. similar individuals, analogously to market utilitarianism. Job market compensation can be fit to the model of market utilitarianism by finding the appropriately parameterized space of skillsets and other job-related characteristics S (with an unfitted, out-of-the-box P), that is shaped such that an equal distribution of intrinsic utilities across individuals yields larger extrinsic utilities in sparsely populated regions as densely populated regions.

With market utilitarianism as a model, the job market can thus be understood to “see” human variation in a very specific way. Humans can in turn see with similar eyes in their choices to increase their own utility/compensation, and they will behave in such ways as to migrate the population from dense regions to sparse regions in the relevant space. If market utilitarianism is absurd, then the job market deserves intense scrutiny, along with the economic system built upon it. In the other direction, if the extant economic system is not held to be absurd, then market utilitarianism shouldn’t be considered particularly absurd either.

4. Utility-experiencer space vs experience space

Individuals experience utility, and individuals vary in their experiences of utility, with varying degrees of similarity between pairs of individuals. This fact presents a conundrum to market utilitarianism; if the space for individual variation chosen is the one-dimensional space of their experienced utility, absurd consequences quickly follow. Utility is but one measure of an experience, closely related to if not synonymous with valence. That and the other measures of experiences, all of them ostensibly qualia, together construct a space of experiences that utility-experiencers populate that is separate from the space that captures their “external” characteristics, even if they are highly correlated in some or perhaps even most domains (such as with the frequencies of incident light on the retina and perceived color or biological sex and felt gender).

Market utility can be computed in both utility-experiencer space or experience space. The latter might make more sense with the utility/valence dimension removed, but that still leaves behind rich structure. The correlations between the two spaces entail that a lot of the activity in one will be reflected in the other. Again, these are but two of endless possibilities for the choice of space, but they highlight some odd properties that market utilitarianism can exhibit.

5. Towards a reverse-engineering of the Universe’s actual objective function

Given the history of the Universe as data, there are many quantities predicated on this data or specific subsets of it that have increased or decreased mostly monotonically over time. Some are well-established constructs like entropy or Gibbs free energy or various other thermodynamic permutations. I’m interested in the realm of high-level compositions where utility-experiencers live, and so I ask what constructs predicated on that subset of data—the subset referencing high-level compositions—are actually being maximized in the Universe? Note that this question is emphatically not about quantities that subsystems may be maximizing each on their own, such as biological species maximizing their fitness, but about the aggregate. Are these constructs generally aligned with each other or totally scattered (especially modulo Occam’s Razor)? Is there any sense in which a moral compass of the Universe’s own can be detected on the basis of the constructs and quantities it maximizes?

Finally, I’d like to reflect on the role of utility/valence as a significant player in the development of compositions. As I have noted elsewhere, there are more levels of compositionality in the biological and cultural ecologies on Earth than have been observed in the rest of the Universe as a whole. Utility/valence has been organized into the psychologies of some life forms in a specific way, most importantly in the process of individuation and the separations between utility-experiencers. The properties of that space of experiences (and the distributions within it which can only be defined after a process of individuation)—along with its associations and correlations with the space of externals—drive much of the evolution of compositions, and essentially all of it within the human economy. Humans have the additional ability to share their experiences either by communication or faithful and intentional re-creations. If such experiences would be traded on a market, then the full exploration of the space of experiences would be incentivized. How would such an economic arrangement, especially if widespread, align with the Universe’s high-level compositional “moral compass”?