On Hierarchy and Value

Footnotes to Peterson


Humor Theory
The Ugliness of Beauty
Postural Anesthesia
Oxytocin and the Vortex of Love
On Suffering
What is Anger
Notes from on the Ground

An essay on Hierarchy might start with what it is not: Oneness. Oneness has a relationship with beauty; indeed, this was excised from my essay on beauty, because it was taking over. Hierarchy has a habit of doing that. Let's instead keep it in its own box, so we can have our own choice about it.


Consider then, oneness, or at least, to begin with, fewerness, also known as simplicity. Mathematical simplicity seems to be considered beautiful. If you're struggling with a million equations that lead nowhere then meaningful simplicity is a relief and thus perhaps beautiful. Oneness as between social and emotional categories, certainly, can be fraught with error and confusion, but can also sometimes be quite useful and wise. See my notes on inner surrender and the central prayer of Judaism, which references oneness.)

But if I ask for salt and citing the ideal of oneness you give me pepper, you would seem to need a little talking to. On the other hand merger of distinctions is not always bad.

My PhD adviser Mark Liberman taught me that the discovery that two or more things thought to be different are actually instances of the same thing, is a great day in science. His teaching can be seen as a celebration of oneness. This is Ockham's Razor, Chomsky's Minimalism, Kolmogorov's Complexity, Shannon's Minimum Entropy, the path of science, the goal of thought: insight as simplicity. At least some of the noise can be reduced to signal. This is all good.

Oneness in Marx and Peterson

A couple other examples will draw in both ends of the philosophical and ideological spectrum to the same good place.

Karl Marx merged, made one of, human nature, human action, and the human ideal in his basic philosophy, aiming to an ideal society of creative, self-actualized workmanship. Obviously to the contrary, taking each pair of these: First, part of human nature is non-action, stillness and rest. Second, humanity's ideals also include plenty of inactivity at end of day or week, not to mention transcendent stillness: more non-action. And third, plenty of human action is not ideal, do I need to exemplify? Yet generalizations need not be perfect to be useful, and Marx's merger remains a guide for the communist utopia of the future, asserting that humans be provided with (2) action or work corresponding to their (1) actual nature and which also represents (3) their ideal. Who would really argue? Not even Marx-haters. If your ideal is what you naturally do, that would seem to be a low energy system state. Notice that an inclusive free market of interesting and socially constructive labor would seem to satisfy Marx's requirements, without exactly requiring a Leninist/Stalinist revolution on the way.

Similarly that popular anti-Marxist, Jordan Peterson, merges things that seem quite different: hierarchies of dominance, admiration, and skill or competence, along with the biology of human emotion. Thus at the societal level, the interpersonal level, the individual level, the emotional level, a metric of value enables all to live peaceably together despite differences. Socially, it enables any connected two or few to compete constructively with one another (more as an information gathering exercise than as a mutual killing opportunity), to establish fair and mutually accepted hierarchical relationships, then to engage as constructive competitors, as friends, as practice partners, or as teacher and student, and to do so in a way that maximizes peace, personal development, competence, and respectful connection. At the individual level a metric of value helps one to prioritize one's actions in life. And at the emotional level it helps us to know how we are doing in order to know how we are to feel about things and about ourselves.

If the same idea shows up at all these levels, if it exists in the biological response to evolutionarily ancient hormonal factors, and it also organizes survival-enhancing work, interpersonal relationships, and society in general, then first maybe it would seem to be actually a true idea, and second, we can thereby understand how those complexities evolved, how they combined in a way advantageous to the species, and third, we can see how they support the life of each individual, including ourselves.

Is this a message only for boys, to therefore get up and go, to develop your skills and competences, to climb your own most appealing hierarchies in order to find a place in society and to refine your values and your knowledge? No, not only for boys. Even the most feminine of anti-competitive, nurturing homebodies has a definite metric of value and a deep, intent, even constant focus on the monitoring of one's group, and making sure that its needs are met. This may be elaborated to a high level of competence, and it generates a admiration and value hierarchy that may be simple and of only a few levels, but nevertheless is definitive and society-structuring. It establishes fair and accepted hierarchical relationships like Grandmother to Mother to Child.

Has Peterson in this way asserted the same merger of nature, action, and ideal, that Marx did? Human nature according to Peterson is to participate in dominance hierarchies, which is nothing else but to have an ideal and put it into action. Human nature, human action, human ideal, wasn't that Marx's philosophy? It appears friend Peterson is actually Marxist in basic philosophy. LOL!

From dominance hierarchies to admiration hierarchies.


So as Jordan Peterson is famous for remarking, the seratonin-mediated social dominance hierarchy system has been structuring the shared living arrangements of larger groups of animals as far back on the evolutionary tree as lobsters. One speculates, Could even plants use some similiarly effective communication mechanism to mediate group survival, since population spread even of plants seems to require some shared negotiation of resource sharing and what tree might have to die in order to let the other reach the sun. My essay, Populating, wonders if an old growth forest of well-spaced mature trees had to arise from what looks like a negotiation, or at least a mutual adaptation, of that type. That is, there certainly exist population pressures within the species, and mechanisms at various levels have evolved, and successful evolved species must successfully have established, ways of surviving with those pressures.

If competition to the death detracts from the success even of the winner, then a species would benefit by losers stepping down a little sooner. Suicide of a smaller tree in the shadow of a larger tree for the benefit of the forest, like apoptosis, the programmed cell death of a much simpler cell in an environment of its fellows which collectively benefit from its death, seems like an evolutionary strategy about equal to the intelligence of cells or perhaps of trees, rooted immoveably in their surrounding environment. Even the pruning of neural interconnections at a subcellular level, and mutual inhibition among neurons at polycellular level, as well as apoptosis or programmed cell death, all have this logic where better group functioning results if sacrifices are made of individual members. So we see that death is certainly an option, to manage group success for the benefit, somehow, of at least some survivors.

In whole animal species on the other hand, we see a solution that is more sophisticated: the dominance hierarchy. The prototypical dominance hierarchy says, Let's fight! And the winner will be the dominant one, perhaps because I'm bigger, or perhaps I'm just more willing to put it on the line, as Hegel himself in 1807 wrote in Phänomenologie des Geistes, the Phenomenology of the Spirit, a popular vision of (psycho)history based on the Master and the Slave, long before the discovery of serotonin. Now that I'm dominant, you can hunch over and walk around subordinate, and I'll stand up taller and walk around dominant, but I won't kill you even though, as our fight just proved, I could. (Later when the competition is about production rather than fighting, Hegel's Slave becomes master of the unproductive, now incompetent Master.)

Dogs at play provide a fountain of examples: once dominance is established, and the non-dominant submits whether by feet in air, or presenting a neck which could be bitten, or as with puppies piddling on the floor, the dominant dog typically immediately ceases serious attacks. The purpose of domination supercedes and obviates killing.

Yes, the basic point of the dominance hierarchy is compassion and inclusion: it actually to provide more of us a way to live and let live. If A doesn't have to kill B, or B, the smaller "tree" in our species community, doesn't have to die, nor kill itelf, then both can live, and then probably our community will have more offspring who are more survivable. Yes, even in environments of population pressure, even if we can get away, being more mobile than trees or cells or dendrites and we can spread across the landscape far and wide, because eventually we will overpopulate our island or continent or ecosystem and be forced to face each other and then again through the serotonin mediated system which governs humans and lobsters quite analogously, we will be saved from murder or suicide by the dominance hierarchy system. THAT is compassionate, inclusiveness, compared with the true alternative.

And liking it

An advantage that might upholster the bare dominance hierarchy, for a species which performs better when happier, might be if its non-dominant members held admiration for the higher-ups. It's not just that they beat me up and beat me down, but that they are admirable in some sense, so that I can admire them and construct an affiliation of my self with them. Even if I'm not as good as they are, still I share their values, their valuation of the metric on this particular hierarchy, we both affiliate self with the skill, the characteristic, the ability, the quality, the metric of being higher on this particular hierarchy. Sharing values, plus admiration, lets losers not just survive but live happily. We can honor the big bully, tell stories about how big and how much a great bully he is, wish we might grow up to be equally big and to equally successfully bully others, or if we're old now, we can remember how big was our bullying when we were young and strong enough and smart enough to bully others. (I've always wanted to read The Courtier by Castiglione, which was on my Western Civ reading list but I never cracked open.)

What's perhaps most surprising about this self-deceptive, self-detrimental game is how people seem to actually sign up for it and engage in it seriously. It's not really pretty, exactly, but it does let us all survive, which is the point. In a species where even the non-dominant members can contribute to the survival of others, the let-live aspect of dominance hierarchy structured society is optimal.

Even the mere fact of being admired, itself, would seem to dramatically reduce the bloodthirstiness of the dominant. Doesn't your anxiety level fall a lot when you find out you are admired? There are two correlated behaviors, the submission of the non-dominant, and the mercy of the dominant. Are both the result of serotonin? I think so.

Considering all this, that the alternative to dominance hierarchy is death, for the losers individually, and at the species level a population of isolates, that is, members that exert no population pressure on one another, maybe we should be glad for dominance hierarchies.


Humans of course have lots of dominance hierarchies. We are capable of a wide range of skills and achievements, and of admiring an even wider range. Perhaps this is due to raw intelligence, or perhaps to its application as social intelligence.

I read recently that Neanderthal groups supposedly maxed out at 50, while human groups maxed out at 150 in early-human evolutionary times. A proliferation of dominance hierarchies is one way to allow more conspecifics to live together without killing each other. Not that we are far from killing each other; recall the result of the Mutiny on the Bounty, where the 16 mutineers sailed first to Tahiti for wives, then to Pitcairn Island to live out their idyllic tropical island lives, with the result that when the survivors were finally discovered 24 years later, there was only one single man left alive. The dominance hierarchy system had failed, except in preserving the women and children, and the men had all killed one another until only hardly any were left. This is our species in the wild. We are beastlier than beasts.

But if we have a society that can at least get off the island to reduce the social pressures a bit, then we can also develop a variety of skills that we can all appreciate. The best of warriors can appreciate the best of swordsmiths, for example, and so that both may survive in a more complex society together. Although combat is surely the prototypical, primary, the Ur dominance hierarchy, even prior to (if correlated with) hunting, the multiplicity of things humans do has itself spawned a multiplicity of things humans can do better and worse, and thus a multiplicity of hierarchies.

Or is it just conformist passivity?

My theory on the larger human groups has wavered. The argument above suggests that greater social intelligence, along with greater variety of metrics of value on which to base dominance or admiration hierarchies, allows and supports larger groups.

My recent, simpler view was quite different, that the stupidity and passivity of the crowd leads to the success of larger groups. If everyone falls into line beneath the biggest bully, then the group can indeed be bigger.

I'm sorry I lost my photo of an electronic traffic sign that I took three or four years ago on the 405 passing Kirkland heading toward Bellevue, Seattle, and Redmond, which are incidentally among the centers of innovation in the world, in which three lanes of tightly packed and nearly parked vehicles on the freeway stared unresponsively (unblinkingly? unmovingly) at a great blinking sign saying "Accident in right lanes, use the carpool/toll lanes for free", and I was the only one I could see moving to the left. Up and down, I could see, say 50 cars, in the zone that I could personally see, which certainly faced the choice I made, but did nothing. So call it a random sample in which, <2% of people are actually eyes-open and willing to change behavior based on changed circumstances.

Anyone that thinks social change is possible will have to come to grips with this fact and the principle it exemplifies: We are, more or less, as a species, blind stupid followers, moles in our holes, unable to look around and find an obviously superior alternative path, unable to not follow the herd, unable to think or be awake or open at all. Good luck thinking otherwise.

Most people who want to make changes therefore disguise their innovation in the guise of tradition. Thus strict constructionism as a legal theory, fundamentalist literalism as an approach to interpretation of selected scriptures, et cetera. Novelty wrapped in pretended traditionality is the path to widespread social acceptance.

So maybe the theory of stupid masses makes for larger human communities, but I'd still like to believe that multiplicity of value hierarchies leads to specialization into skill hierarchies and thereby into high functioning larger communities. But probably the truth includes both, so that we do get, one the one hand, a blacksmith and a carpenter, a monk, some stonemasons and a traveling merchant amongst our masses of farmers and herders, each admired and admiring within their trade and tolerated and supported within the wider society, but yet on the other hand we also get everyone keeping their heads down and otherwise sucking up to the murderous, truly frightening, killer-dominant, local military nobility. Our conformity and submissiveness is perhaps not less a mass-survival instinct than our (correlated) variation in temperament, skills, and values.

Hierarchy Geometry

This section is a bit of a pointless reverie, so feel free to skip forward anytime you like, to the next, unless you like math for its own sake.

So mathematically, what do hierarchies look like?

Apparently chicken groups sort into dominance hierarchies, the "pecking order", which break up when there are more than 30 chickens, because the sorting is so finely graded and chickens will keep fighting their near-equals. Since farmers want all the chickens to survive to become meat, they can't tolerate groups with any unsortable pair, so they should keep the groups under 30, is the principle I infer. That would be called a full sort. And if you need a full sort, that leads to smaller groups than if dominance just needs to keep the weak, stupid, or passive down, when they being down at shared levels won't themselves kill each other.

If, then, you just need to sort into definite levels, then instead of an ordering you get a branching or tree structure, where the branching factor can be greater than one (an ordering is a degenerate tree, with branching factor one). The dominant one at a higher level can dominate that branching factor number of less-dominant ones at the next level down.

The branching factor number was 10 for Genghis Khan's armies, organized on the decimal system: each military command unit included ten of the next smaller down level of units. Britain dominated India for generations with an enormous branching factor, what was it? Tens of thousands versus hundreds of millions?

The branching factor, and the number of levels, are parameters of a society.

Ping Pong as an example

Once upon a time I fell in love with spin. Can you even imagine 5' chord to tangent, describing the curve between your touch point and mine? Amazing. So yes, I became a pingpong freak and by now I've also spent many years coaching it, so I know enough to be dangerous talking about it.

So I tell people who come in, Don't worry that you just got hammered by the oldest creakiest old man or the thimble-sized little girl over there, even though you thought you were the best player you yourself ever met in your life. Pingpong is a highly highly stratified sport, and size and age don't make as much of a difference as in other sports. We have a rating system borrowed from the chess rating system, where everyone gets some rating or other, the average of club players is supposed to be 1500, and if you beat someone your level you both get your rating adjusted by 8 points, and if you're 200 points apart and it's an upset, you get a 50 point adjustment, or 2 points change if it's not an upset. Over time this results in players spreading out across the rating scale system and after not many years it turns out there are players legitimately rated maybe as low as 300, and others above 3300, after Ma Lin and the Chinese, and Joo Se Hyuk and the Koreans, came to the US Open and blew the top off our highest recorded levels.

Bear with me a bit longer. The thing is, if you make a graph of upsets by rating difference, obviously the upsets get fewer if the rating difference gets bigger. Let me report a result from a graph I once made with this data: it showed that at 100 points rating difference, the histogram showed a 12.5% frequency of upset. That's 1/8. If you're 100 points apart, you'll have an upset only once in eight times. I'm willing to call that a distinct level: you can play someone 100 points higher and they'll beat you seven out of eight times, yeah, they're a different level. (Since (3300-300)/100 = 30, we have about 30 levels in pingpong. Just like the chickens.)

And yes, outcomes are highly predictable, surprises are few, even with everybody doing their best. But it's worse than that. Consider, if the levels were independent, what 3 levels might mean: (1/8) * (1/8) * (1/8) = 1/512. This is relevant because most people coming into the pingpong club are 800 or below, and most people in the pingpong club are 1100 or above, which means 300 points apart, which, under a model with independent levels, suggests that the probability of an upset, when a newby comes in and wins might be (1/8)^3 = 1/512. You see what I mean? No chance.

And yes, quite often people do come in, get hammered, even though they, being about 800 in rating, are 200 points above their sister or their Mom or the next best player they ever encountered at home or at school or ever in their life and they never met anyone close to their level, and they STILL have 1/512 chance of winning at the pingpong club against the worst player in the house. It's quite a shock, and a lot of people can't get over it; they walk out a bit quickly, trying to forget, or thinking, this sport is definitely not for me. Unless there's a friendly encouraging voice near the door watching for the disoriented bully boys, saying, No, it's just that we have 30 levels! So calm down and enjoy the process of learning, you will be able to do it, eventually. That was my job.

Skill induces admiration

And even the modern generation of brittle kids who in their own minds have to be Olympic caliber already or they'll cry or leave, even these kids immediately orient positively with emotional admiration and close mental attention toward the skill of the teacher when you serve a few right past them or demonstrate by pointing some direction and give them a spin that they can't help by hit in the pre-indicated direction. They immediately discover they WANT to learn this and you HAVE something to teach them and they suddenly transform into eager students. Skill immediately grabs everyone and ranks them in the hierarchy, immediately makes them accept their position in it, immediately gives them a high degree of admiration for people higher in the hierarchy, that admiration is constituted by a desire to emulate, a high degree of attentive focus on the behavior of the model, and a commitment to carrying out emulating behaviors. See? Metrics of value organize society, organize effort, organize emotion, organize, organize. Everyone falls enthusiastically right in line, puts their shoulders to the same wheel, does their best, feels great or terrible about their progress or lack thereof and praises and blames others for their progress or lack thereof, and it becomes a little social universe of its own, and this is the kind of universe humans specialize in. Maybe this paragraph should have been written in the previous section. It could have been written by Jordan Peterson, no doubt, except for the pingpong part.

Okay, the point of that is that pingpong players may have 30 levels just like chickens, and actually the analogy goes farther than we might like because we actually prefer to fight others that are about at our level (so perhaps humans are more socially functional than chickens). But we don't have to make a complete sort in order for the social hierarchy to apply, to provide an orientation towards value or merit, to give us positive emotion connected to fitting in somewhere and climbing up the skill hierarchy over time. Humans find learning meaningful, particularly if it is learning a skill that is the sorting metric on a valued hierarchy. Self-identification plays its role, we all share that valuation metric in valuing others, we also accept that valuation metric in valuing ourselves, and we accept our own position in the hierarchy as measured by that metric. Dopaminergic pleasure comes with climbing up the hierarchy. Yes. Peterson's logic certainly applies.


Both the branching factor, and the number of levels, are parameters of a hierarchically organized society. Levels?

So one of Genghis Khan's decimal-organized armies of 100,000 had 5 levels of management. The US Army has seven nominal levels: general, colonel, captain, lieutenant, sergeant, corporal, private, but each of those has its own various sub-levels. The Catholic Church with pope, cardinal, archbishop, bishop, priest, deacon, layperson seems to have about seven levels.

Small geometric descriptions handle plenty of social complexity. A branching factor of only ten, with a number of levels equal to only 10, specifies a hierarchical system more than big enough to encompass our entire world population of less than 10^10 = 10 Billion humans, assuming it is tree structured, that is, Genghis Khan style, without overlapping subordinates. (Did you notice that base and exponent are the same as branching factor and depth? Is it general? Numbers are so convenient!) On the other hand a lattice structure like the US pingpong rating system, where each level might dominate or be dominated by levels with something like the same number of players, and with free association within and across levels unlike a command hierarchy, can still have the complexity of 30 levels, way more than the Catholic church and Genghis Khan's army stacked on top of each other, even within the tiny population of pingpong lovers that go to tournaments. For that matter, 30 chickens which you might order delivered in a box in the springtime, already might comprise such a lattice.

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Copyright © 2000-2020, Thomas C. Veatch. All rights reserved.
Modified: June 12, 2020.