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30 October 2017

That Fucking Cat.

Most people have heard about Schrödinger's cat. Schrödinger was trying to disprove the so-called Copenhagen interpretation of quantum mechanics - the idea that until a particle is "observed" it is literally in all possible quantum states (i.e. spin, charge, mass, position, velocity, etc) at once. He thought this proposition was absurd so came up with this metaphor of the cat in the box.

We don't know what state the cat is in until we look, so the cat is both alive and dead. Which is clearly absurd where cats are concerned. But it might not be so absurd when we are thinking of, say, the "spin" states of sub-atomic particles. This is still the most popular interpretation of the wave equation, though slightly less than half of all physicists agree with it.

The real problem we get at the popular level is that people don't get that the "observer" is also a metaphor. They think consciousness must somehow be involved. But it isn't. No one ever directly observed anything at the nanometer scale - we are not equipped for it. "Observe" here means physically interact with. The wave function of the particle collapses whenever the particle physically interacts with another particle. And at the particle scale it means any time two matter particles (fermions) exchange a force particle (boson). No consciousness is involved or required.

In terms of the cat metaphor this means that the universe does know whether the cat is alive or dead, because the cat interacts with the matter around it—it has to be in contact with the floor of the box for example. Touching the box collapses the wave function of the cat and the cat is either alive or dead and not in superposition of all states (probably never is).

So the thought experiment does not work unless the cat is suspended in a perfect vacuum, in perfect darkness, isolated from all magnetic fields, and not subject to gravity (even from the box!). In other words it would have to be in another universe which consisted of the cat and only the cat, and which could not communicate with our universe in any way. In which case we'd never know the outcome of the experiment. The uncertainty is either permanent or non-existent.

In other words, in the end it's just a bad metaphor. Schrödinger decisively lost his argument with the Copenhagen crowd. They took this weak attempt to discredit them, and turned it into a powerful positive symbol of their approach. Ouch.

In fact in something on our scale - with (literally) millions of billions of trillions of particles in every gram of matter - the wave function is always collapsed because there is interaction going on all the time. People are always in one particular state at any time (though time flows incessantly).

If humans behaved like particles we would be diffracted every time we walked through a doorway. In other words we would emerge at a random angle every time. (I'm assuming we're sober, eh?).

If there were two doorways close together, as we approached  we would blur out, pass through both doorways simultaneously, interfere with ourselves, come back into focus moving at a random angle. I've staggered through some doorways in my time, but never two at once.

If people were like particles, when you did one forward-roll  (↻360°) you would end up upside-down, and would have to do another one to get right-way up.

If people were like particles we could only know where we are or where we were going, but not both at the same time.

If people were like particles, then having people watch you walk down the road would cause you to swerve.

Quantum doesn't work on our scale. There never was a cat. Consciousness has nothing to do with it. Most of us can safely ignore quantum and behave as if the world is classical because at our scale and in our frame of reference, basically, it is.  Or, to be more accurate, classical theories predict the behaviour of matter on scales of mass, length and energy we can actually experience, to a higher degree of accuracy and precision than we can currently measure.

Which is not to say that on very small scales it is not possible to have quantum effects. It is possible. Gravity is so weak you can ignore it on very small scales. If you cool everything down close to absolute zero, exclude electromagnetic fields, and tweak other conditions, you can see quantum effects up to the scale of some fairly large single molecules such as bucky-balls (C60H60). Beyond this, and much above absolute zero, quantum effects simply disappear.





















27 October 2017

Ancestors Fallacy

There's a cognitive mistake we make that needs a name but doesn't have one as far as I can tell. In the linked article about wolves the author starts out with an example from closer to home.


It's often assumed that because great apes knuckle-walk when on the ground, that we must have evolved from knuckle-walkers. We talk about "learning walking upright" to make the distinction clear. In fact we evolved from a common ancestor and that ancestor is likely to have been a brachiator - to have live mostly in the tree tops, like today's gibbons and (some) lemurs.

When a gibbon is on the ground it almost always walks on two legs. Using it's arms to stabilise itself. Youtube thinks this is very funny and has many videos of gibbons walking "like a human". It's not that they have "learned to walk like a human", that's just what they do on the ground. Note even the great apes adopt bipedalism when wading in water.

So there is a fallacy here. The fallacy tells us that the chimp is our closest genetic relative, so our ancestors must have been chimp-like (hiding in their somewhere is the assumption that chimps are "primitive" animals and that only humans evolve). But our ancestors were not chimp-like. Chimps, gorillas, and orangutans evolved knuckle walking, humans never did. Nor did gibbons.

The modern view of evolution is that all organisms currently alive have been evolving for exactly the same amount of time. So just because a bacteria looks archaic, does not mean that it is archaic. Everything currently alive is modern. Evolution doesn't stop for living things.

Chimps and humans have evolved for equal lengths of time. And neither of us is more like our common ancestor than the other.

This means that there are no "primitive" tribes. Hunter-gatherers living now are not necessarily representative of pre-historic humans unless we know the conditions they live in have not changed (and given the intervention of the last ice-age this is extremely unlikely).

Yes, humans arrived in Australia as long ago as 60,000 years before the present, but they constantly changed. The evolved literally hundreds of languages for instance.

In my field of study, modern schools of Buddhism, whether Theravāda or Tibetan or Zen are often seen are representative of some previous era. This is the same fallacy. All forms of Buddhism currently being practised are modern (though not all are modernist). No amount of social conservatism can prevent changes from accumulating over dozens of generations.

I'm not sure what to call this fallacy.

26 October 2017

Studying the Heart Sutra

As everyone knows by now, for the last 5 years I have specialised in studying the Heart Sutra. Apart from identifying several grammatical errors in the standard Sanskrit version, I've also made or substantially confirmed a couple of ground breaking discoveries about the text.
It is a curious thing about Western Buddhism that we privilege texts which we believe to have a Sanskrit "original". It is curious partly because Sanskrit did not come into popular use amongst Buddhists until about the 4th Century of the Common Era. Anything actually composed in Sanskrit, is quite late.

In fact, for well over 1000 years, the Heart Sutra was the most popular text in East Asia in it's Chinese version and probably few people were even aware that there even was a Sanskrit version. They might have understood that it notionally came from India, but the study of Sanskrit was never widespread outside of India and most people wouldn't have known any Sanskrit (much like now). Asians knew the Heart Sutra as the Xinjing and recited it in Chinese, or some approximation of the Chinese (in Korea, Japan, and Vietnam). The Tibetans had a Tibetan translation from about the 10th Century and used that exclusively (it also has errors in it!).

For a brief period in the 20th century, the Sanskrit text came to the fore. An old palm-leaf manuscript preserved in Japan was dusted off and became the primary focus of the study of the text. A number of very late Nepalese manuscripts were found. A couple of stone inscriptions from China were added. And from these Edward Conze constructed his edition. His version of the Sanskrit text (more like an original composition) became established in the minds of Westerners as the "original".
Then in 1992 Jan Nattier showed that the Sanskrit text is a translation from Chinese! The Heart Sutra was composed in China. This is quite a big deal for the most popular sacred text in the Buddhist world.

How have Buddhists reacted to the revelation that their most popular text was a fake, composed ~1100 years after the Buddha is supposed to have died? Mostly with denial or indifference. I'm still not sure whether the latter is admirable insouciance or something more dubious or insidious.

25 years after Nattier's amazing 90 page article (which I still consider the best example of academic writing in our field) there is still not much reaction - even when her idea is acknowledged, it is without any drama. The word apocryphon is sometimes used as a euphemism for "fake", but other than that no one seems bothered.

Nattier's article has had almost no impact on my own Buddhist Order. I suppose as a preeminent scholar of the text, I bear some of the responsibility for that, though I have written 32 essays on my blog which touch on aspects of the Heart Sutra. If anyone were really looking, they'd have found them.

Several people have lately encouraged me to teach on the Heart Sutra at the Cambridge Buddhist Centre. I think probably next year, but yes, I think that might be good.

19 October 2017

The Tyranny of Now*

Some people tell us that we can forget about the past and the future and just focus on now. And we do this then all our problems will disappear. I call bullshit. Screw Eckhart Tolle - I'm sure he's a nice guy, but he seems to oversimplify everything.

To begin with, this attitude assumes that if we don't think about our emotional baggage that it will stop having an impact. I don't know about you, but that's not how it works for me.

Leaving behind a lifetime of habit is a process, not an event. And that process may well take up the rest of our lives and remain incomplete when we die. Generally speaking we have to see that we are moving beyond one situation (past) and towards another (future) to stay motivated (now). 

So the past is useful because it is only in comparison to our memories that we have a sense of progress (or any change at all for that matter).

Similarly with the future. You are asked to set yourself adrift on the ocean with no destination and let the wind and currents take you where they will. But we know what this lack of purpose and direction looks like. It manifests as dissolution or in wasted, directionless lives. In one of my songs I sing about feeling like "a fish with no tail, eye's wide, no idea where I'm going". I don't sing it, but to me this is terrifying. This is Hamlet, watching helplessly as inevitability crushes him. Fuck that!

While it is certainly a good idea to focus on the task at hand, for many reasons one has to keep one foot in the past and an eye on the future. Tasks are more enjoyable if we are focused (now), but they are more meaningful if they take us toward a definite goal (future) and more satisfying if we have a sense of progress (past). And if that goal benefits the community then so much the better for us. When we contribute to something bigger than ourselves (society, basically) it is about the most meaningful thing we can do.

Most of the important things in life are complex and difficult and therefore require persistence over days, months, and years. Bigger goals cannot be achieved without a clear sense of direction or a sense of progress as one proceeds.

Without the future we have no sense of the meaning of our actions. Without the past we have no sense of progress. So whatever you do, do not lose sight of either.


~~oOo~~


*I took my title from a TED talk by Carol Dweck.

But I was also thinking about a Sanskrit phrase which translates as "future, past, and present buddhas" (atītānāgatapratyutpannā buddhāḥ). Chinese Buddhists routinely translated this as 三世諸佛 "all buddhas of the three times", a phrase which is never used in Sanskrit (with one exception). Then, when the Heart Sutra was translated back into Sanskrit, the phrase was literally rendered as "all buddhas of the three times" (tryadhvavyavasthitāḥ sarvabuddhāḥ) - this is the one exception. This is the smoking gun that tells us that the text could only have been composed in China. Expect a publication on this in due course.

18 October 2017

Passive Voice and Crime

This is a response to a Tweet that showed up in my Twitter stream a couple of days ago. We often speak about crime in the passive voice. And there's a thing about passive voice that will be clear to anyone who has learned Pali or Sanskrit - the passive voice has no subject. Which is why I prefer agent/patient to subject/object when discussing grammar.

In the active voice, a subject does an action to an object. In the passive voice an action is done by an agent to an patient. But we can and do use the passive voice without a subject, i.e. with just an action and a patient.

In terms of crime we can say things like:
"The woman was raped."
"A man was mugged."
"A child was run over."
"The official was bribed."
"The house was burgled"
This is a pretty common way of talking about crime. What's missing in all of these statement is the agent of the action: "... by a rapist", "... by a mugger", "... by the dangerous driver", "... by the developer", "... by a thief". And so on. Just because the verb is in the passive voice, does not mean that the action is not carried out by someone.

Similarly, there is a trend for people who have responsibility to skirt it by saying bullshit phrases like "mistakes were made". In which case we can always ask "By whom were the mistakes made?" Just because they shift to the passive voice, does not mean that we are forced to abandon the notion of a grammatical (and real) agent of the action.

Use of the passive voice without an agent is a problem to the extent that it shifts the conversational emphasis onto grammatical patient, i.e. the victim, the location, or the nature of the crime, while obscuring the agent of the action. Of course crimes happen to us, against our will, so the passive voice is designed for exactly these situations. But if we leave off the perpetrator of the crime, we may create an unfair situation.

Why? Because when we comprehend actions we typically understand them in terms of agents with motivations. And why is this? It's because the archetype for a willed action is our own experience of turning our head to say we've had enough milk. Or our first experience of grabbing something and pulling it closer. The archetypes in other words are our own willed actions.

So if we only mention the patient of the criminal action, then we leave a conceptual gap in which the victim (potentially) becomes the agent: i.e. we blame the victim. Someone has to make the action happen, and if the actual agent is out of the picture, then we look to the only other participant. Crime is emotive, and perhaps no crime more so than rape. If someone was raped, then yes, I think it is vital that we insist that it was an action carried out by someone.

In rape, resistance often makes things worse for example, because the assailant may become more violent and it both intensifies and prolongs the experience. Each case is different, but no woman ever wants to be raped, or "asks for it". That much has to be clear. And it ought to be clear in how we talk about it. But its not justice to hold a whole section of society to blame for the crimes of individuals. This is an important principle of our justice system: collective punishment is not just. I cannot be blamed or punished for crimes in which I am not explicitly involved in committing. I don't accept that just being a man makes me complicit in violence. I've been the victim of more violence than most people I know. Quite a bit of that was from women or girls, by the way.

With that said, I do want to continue to think more about the use of passive voice verbs in the way we speak of crimes generally. For example, with respect to the example of bribery, you may have thought, "hang on, the official who was bribed actively committed a crime by accepting the bribe." Yes, they did. The bribe was accepted by the official. Interesting, this is the passive voice, but in discussing bribery always seems to specify an agent. The verb is passive in this sentence, but it is clear who is doing what. So this makes it an interesting one to think about. For every crime there is a criminal.

It's important to specify the agent of the criminal action, especially in the case of groups who tend to be oppressed or disempowered. The story is not, to take a topical example, that some actor was raped, but that an actor was raped by Harvey Weinstein (allegedly). The criminal becomes the focus rather than the victim of the crime. Our justice system is skewed towards punishing perpetrators and so we have to identify them, or we consider that justice has not been served. A more restorative justice system would go about it differently and would require us to focus on the victims. 

A load of crime words are used in both the past active and past passive voice "he raped..." and "she was raped...". Similarly with murdered, robbed etc. We almost always talk about crimes in the past - unless we are in the process of being mugged or whatever.

Of course this is more difficult when the criminal is as yet unknown or as yet not proven guilty (as in Weinstein's case). But the thing about the passive voice is that it cries out to be qualified "by....". Which is why one amusing way to identify a verb in the passive voice is to see if following it with "by zombies" still makes sense. e.g.

  • The man was being pursued [by zombies]. Makes sense, verb is passive. 
  • The man pursued [by zombies] his dog. Doesn't make sense, verb is active. 

The person on twitter who inspired this little rant, was insistent that perpetrators should particularly be identified as men. To me this smacks of the old "all men a rapists" bullshit. A man might have raped a woman, and yes, it is usually a man, but actually the number of men who are rapists is pretty small. I have known many hundreds of men, and I know of one who was accused of rape. I'm not sure that anything is gained by emphasising the gender of criminals. In the case of violence, men are very much more likely to be the victims of violence than women are.

In any case, people sometimes say we should strive to eliminate the passive voice. When I looked at a few news headlines, I did not see much use of the passive voice. Many crime stories do use the active voice and of course are therefore forced to attribute the crime to someone. So maybe the prejudice against the passive voice is having an effect. In which case the original complaint might have overstated the problem.

On the other hand because we attribute crimes to someone, and are often lazy about the adverb allegedly, some people are splattered with guilt by association. The "no smoke without fire" fallacy. I have seen no evidence that anyone thinks that Weistein did not rape, molest, and pester women, though he has yet to be charged by the police, let alone appear in court to be judged. He is being tried in the media and punishment has already commenced.

On the other hand, when the police raided Cliff Richard's house, and tipped off the media so that they could film it, the man's reputation was severely damaged by the allegations. A crime was more or less deliberately attributed to him, when in fact, as far as anyone knows, he is innocent (false accusation is also a crime). Same with Paul Gambaccini, who was caught up in the same furore, but was always innocent. Accusations of child sex-abuse are extremely damaging, especially to someone who makes their living in the public eye. And that is balanced against the damage that sex-offenders cause if left unchecked (as they have been for decades in the entertainment industry).

So, even if we were to switch entirely to using the active voice, the way we talk and think about crime is not a simple matter. We usually have less than perfect knowledge and people are unreliable witnesses (both passively and actively).

There is nothing inherently wrong with the passive voice. Especially when things happen to us against our will, the passive voice is exactly what we need to express that directly. If someone punched me in the face we could look at it in different ways. If I wanted you to empathise with me and perhaps comfort me, I might say "I was punched in the face". The focus is on me. But if I want you to get angry I might say "Phil punched me in the face." Now I am directing your attention to Phil. If you report this to your friend you (unconsciously) make similar determinations, i.e. who is the focus? What emotion am I trying to elicit? Who is to blame? And so on. A good deal of subtly is available to us by adding extra words, stress, and facial expressions to the mix.



16 October 2017

Technological Frogs

The universe as we know it, began 13.7 billion years ago. The earth formed out of the solar disc about 4.5 billions years ago. The first definite evidence of life can be dated to about 3.5 billion years ago. Mammals evolved a bit over 200 millions years ago, and primates about 60 million years. Modern humans first appear between 300-200,000 years ago, they left Africa about 100,000 years ago, settled in Europe about 40,000 years ago (having bonked a few Neanderthals along the way).

Electricity was discovered in the 19th Century. The triode amplifier was invented in 1906. TV was invented in 1927. The first electronic computer was built using vacuum tubes or "valves" in 1943. The transistor in 1947. Integrated circuits combining multiple transistors was invented soon afterwards but were not mass produced until the early 1970s.

The first TV broadcast in New Zealand was in 1960. I was born in 1966. I remember the manual telephone exchange where you told the operator the number you wanted and they manually connected you. I remember the first time I saw colour television (ca. 1972), and the excitement of a second TV channel in 1975. I remember my older brother getting an electronic pocket calculator ca. 1976.

The first personal computer based on ICs was marketed in 1977 (just 40 years ago). You had to assemble the circuit board yourself!

I first saw a personal computer at school in 1980 and learned to program it in BASIC and Assembly Language (though I realised that I didn't really enjoy programming that much).

Computers double in power every 18 months or so (Moore's Law). So my current PC ought to be roughly 17 million times more powerful than those Apple II computers at Northcote College. But with, like, a billion times more RAM and a trillion times more external storage.

When I was born, a single channel black&white TV was the most advance consumer electronics device I knew. An adult could just about lift one on their own.

Now a computer is my TV, record player, clock, telephone, camera, video recorder, tape recorder, library, teacher, publisher, recording studio, translator, etc. And I can carry it around in my pocket.

I worry a bit that we're like the apocryphal frogs being slowly boiled alive and not noticing until it is too late. And I think it is too late already.

14 October 2017

Deliberative Democracy

"When a sample of citizens is brought together, divided into small groups, and, with the soft prodding moderator, made to discuss policy, good things happen. The participants in these discussions end up better informed, with more articulate positions but also a deeper understanding of other people's points of view." Mercier & Sperber. The Enigma of Reason, p.309-10.

Mindset

Last week on the radio, a BBC presenter interviewed Dr Carol Dweck. She was initially a child psychologist interested in why some kids succeed and why some fail (I'm leaving these undefined on purpose). She identified an important pattern that was predictive and found that it applied to adults as well.

She called the discovery "mindset". And it sounds deceptively simple. If you go at a problem with the mindset that you can learn then you will. It doesn't matter what the problem is, if you believe you'll make progress, then you will.

However, if you start with a fixed mindset that says you can't do it, then you won't learn, you won't make progress.

I sort of naturally have a growth mindset when it comes to certain things. I've taught myself to paint, play music, read Pāḷi and Chinese, and a bunch of other stuff, because it never occurs to me that I can't learn. I get interested and just work away at it. Nothing I've ever done was simple. I was never a natural at music for example. I sang incessantly as a kid, but so badly that my mum sent me to a singing teacher so that at least I would sing in tune (so she tells me). When I started playing the guitar nearly 40 years ago, I had no clue. I struggled with everything. I constantly made mistakes. But I just kept at it. I learned. I got better, slowly. It was hard. After 10 years I played pretty well. After 40 years I'm beginning to really understand the instrument. The learning never stops for me.

Now you may say that I have some kind of talent that perhaps you lack. But the research suggests that talent makes much less difference than we think. Mindset is is what makes the difference. Its the approach, that encompasses failure and is not destroyed by it, which makes the difference.

One of the upshots is that we should focus on process - an insight that keeps popping up. If you praise a kid, focus on what they tried, rather than what they achieved. Keep them excited about the process of learning rather the making praise contingent upon success. Ironically, if we make praise contingent upon success, then kids don't succeed as often. In fact they often give up.

How many times have we heard someone say "I'm no good at maths"? That is a mindset problem, not an inability to do maths. Actually, everyone can learn to do high-school maths - its just a matter of learning, and being convinced that learning is fun. If society or our teachers manage to suck the joy out of learning, this is not an indication that we are stupid. Yes?

And actually all along the way we fail. When you start playing the guitar or learning to drive or whatever, you fail every few seconds to start with. At the start, it's almost all failure. But you learn more from a failure than you do from a success; and if you learn then success starts to outweigh failure. If you are focused on *learning* then a failure is no big deal, because you learn more and actually enjoy it more. And with this mindset you succeed more often anyway.

A lot of people come to learn to meditate and the first time their mind wanders they say "I can't meditate" or "it's not for me". This is a fixed mindset. A growth mindset makes the mind wandering a fascinating learning exercise - you first of all realise that your mind simply wanders off without your permission(!), you start to understand why, you start to learn how to focus, and before long you are experiencing the incredible sensations of having a pinpoint focused mind. Then a whole new world can open up in which you use that pinpoint focus to examine your own mind. But only if you have a growth mindset, only if you approach it as something to learn, only if failure at first is not an obstacle to eventual success. Everyone can learn to meditate, with very few exceptions. Everyone would benefit from learning some basic meditation techniques, whether or not they want to take it further.

Learning goes on in a lively mind, it never stops. Every kid starts off with the lively mind. Staying lively has real benefits too. You are less likely to suffer dementia and other brain problems in later life. But you're also more likely to find meaning in what you do, because meaning emerges from being immersed in the process, not in achieving goals. Achieving a goal is a cadence, or punctuation point, in an ongoing process. And it is the process that really satisfies.

Very little else is satisfactory about my life and things have certainly not gotten any easier lately. But I'm still learning, still curious, still willing to take on new ideas and challenges. It's the process of learning that I love. It gets me out of bed each day and literally keeps me alive some days.

02 October 2017

Dunbar and Brain Size and Triratna

One of my colleagues wrote something, a little vague about the importance of the number 150 in human society, and since I have a long fascination with this, I thought I would write a brief introduction.


Dunbar and Brain Size

In 1992 Robin Dunbar published a paper in which he compared the average neo-cortex-to-brain-volume ratio in wild primates with the size of their social groups. There was a linear relationship which enabled him to predict that the average human social group would be 150.

Given that many of us live in cities with millions of people, what does this mean? It means that we use the most recently evolved parts of our brain to keep track of relationships - and to imagine how other people see the world, especially how they view their own relationships. This is an essential skill for a social mammal.

For example, all social mammals understand and operate a system of reciprocity. Sharing food, resources, grooming, guard-duty, or mates etc creates obligations for other group members. If I share with you, you have a social obligation to share with me. And vice versa. In apes and humans, we also keep track of obligations that are between third parties. I may share with you, knowing that you share with Devadatta and that way come into indirect relationship with Devadatta. Devadatta will probably notice that I share with you, and my reputation with him increases. Ans so on.

Humans can routinely track these abstractions into 4th and 5th order. Shakespeare could imagine how his audience would feel that Othello would feel about Cassio, after being convinced that Iago thinks that Desdemona loves Cassio; while we also know that Iago is lying. Shakespeare could imagine our tension as the story progresses. What if Iago is found out? What if he is not? This is part of what makes Shakespeare a great story teller.

Keeping track of these social obligations takes brain power. The more of our brain given over to keeping track of such things, the more relationships we can keep track of.


The Magic Number 

Dunbar predicted that on average the maximum number of relations humans could keep track of in this way would be about 150. And it turns out that the average community size in the New Guinea highlands, the units of Roman armies, and the average village size in the Domesday book (and a whole range of other measures) was .... 150.

But 150 is not the whole story. 150 is the size of an intimate community where everyone knows everyone's business. But we are usually involved in both smaller and larger groupings. If 150 is a tribe, the a tribe is usually made up from several clans of about 50 members. Clans comprise several families of about 15 members. Each person has approximately 5 intimates. These groupings may overlap. On the other hand tribes may be part of larger groupings, of 500, 1500, and 5000 and so on. The smaller the grouping, the more intimate and detailed, the knowledge; and contrarily the larger the grouping the less intimate and detailing the knowledge. The limits seem to go roughly in multiples of three, starting with 5 as the smallest.

What we expect is that, in a society of 150 people who live together, relying on each other, each will know all of the others, and who is friends and relations with whom. They will be intimately familiar with trists and disputes. And they will know who has what status under what circumstances.

In larger groupings there may be people we don't know. Larger tribal grouping may adopt symbols of membership with which to recognise other members. For example they may hang a strip of white cloth around their neck. They know that anyone who has one of these white strips is a member of the tribe. They can expect to have some basic values and interests in common, and thus are open to each other socially in ways they might not be with complete strangers. It may even be the case where the tribe mandates certain levels of hospitality are required. Some cultures require this even for strangers, when travellers are particularly vulnerable (as in the desert).

In larger groupings there are a number of ways of ensuring that every gets a say in how things are run. But let's face it, beyond 7 ± 2 everyone having a say is unrealistic. This is another magic number (aka Miller's Number) and relates to the capacity of our working memory. Groups bigger than ca 9, tend to schism into separate conversations, unless formal procedures apply.


Schism

With respect to schism, the 150 level is the limit of a sense of knowing everyone in a society living together on a daily basis. Much beyond it, and some of the people are going to start seemingly like relative outsiders. We don't know who they are friends with for example. This may explain why when humans meet who are part of a larger less intimate grouping, they often exchange information that establishes *who* they know. It's likely that some above average connectors know many more people, and across social networks. They are the glue that hold larger groupings together.

There is no absolute requirement to schism at any number. Schisms happen in small groups and large. But primates feel more comfortable with groups where they know the others. Being surrounded by strangers is often quite stressful for a social primate because they have none of the knowledge they need to know how to relate to everyone. On the other hand, being experts at empathy, primates pick up this info very quickly.

What tends to happen is that we are comfortable being relatively informal members of several larger groups, but prioritise our most intimate relationships and family.


The Order

The Order is complicated because most members of the Order are still enmeshed in other groups, particularly family. Even if there were only 150 of us, we don't live together as one community, relying on each other to survive. It is already a somewhat looser grouping than that, so the fact that it has crossed several thresholds (in total membership) is not a clear cut indicator of anything. Those who were around in the early days do tend to reminisce about how good it felt when you knew everyone. I would expect nothing less. But they all still had friends and family outside the movement too.

The Dunbar Number describes the dynamics in close knit societies living together. Beyond 150, such communities do tend to split into more manageable groups.However, it doesn't really say anything about the Order because we are not that kind of society.

Note that the more plugged into other groups we are, the fewer relationships we can track in the Order. And vice versa. Note also that pair-bonding makes no difference to Dunbar's numbers. Primates adopt a wide variety of lifestyles and these are secondary.


Conclusion

Dunbar's original article rapidly became a classic of anthropology and evolutionary psychology (the latter being Dunbar's main subject of interest). His predictions became known as Dunbar Numbers while he was comparatively young (he is still alive and working at Oxford University). If there was a Nobel for evolutionary psychology, he'd have won it for this discovery.

As a final caveat I would insist that Dunbar's numbers are theoretical averages, albeit with considerable empirical support. There will be a bell-curve on which individuals sit. Some will easily cope with 300 relations, some will barely cope with 50. There will always be outliers, but the existence of outliers does not alter the theory or the supporting empirical evidence of accuracy.

For further reading on the Dunbar Numbers and other concepts mentioned above, I very highly recommend "Human Evolution" by Robin Dunbar, published by Pelican in 2016. Aimed at a general readership, and highly readable, it nonetheless takes a cutting edge look at human evolution by incorporating Dunbar and his group's research on group sizes and theory of mind. Dunbar explains how we went from being general purpose apes, to highly specialised humans. How we solved the energy gap required by our big brains and big social groups through cooking, dance, laughter, and religion.