Boys Playing Tag
Tonight I watched four little boys playing tag in a small area outside a restaurant while their parents were waiting for their table. They were, I'd guess, 8-12 or 13, and neatly orderable by height. The tallest and the two smallest looked and were dressed most alike, so it may have been three brothers and one friend. (But really maybe not, as we'll see.) The second tallest was noticeably "huskier" than the other three; I'll call him 2, and the others 1, 3 and 4 -- again, by height.
So here's what happens: every time 2 is "it", he goes after 4, the smallest. 4 often ends up going after 2, in part probably as payback, and in part because he's the closest target, having just tagged him, though he would go after the others as well. There were so many "tag-backs" I wondered if they were going to create a rule to stop it. 1 sometimes followed the action around and even, at least once in my hearing, exhorted 2 to go after someone else. 3 was barely in the game at all, mostly watching from the sidelines.
One result of this is that 4 is getting the most play, most often being chased and most often chasing because he's most often "it". He also never gets much of a break.
My observation was this: someone, 4, is singled out, and someone, 2, is doing the singling out, and his behavior is changing the game for everybody. 1 noticed this and tried to encourage the more inclusive chaos a game of tag usually is. 2 did not appear to be interested. (Quite possible 2 and 4 were brothers and this is typical pre-teen big brother behavior.) 3, as I said, was almost entirely sidelined from play and either didn't care or didn't have the confidence of 1 (the tallest) to do anything about it, or didn't want to invite being singled out by 2.
I'm not sure what to make of it. I'm tempted to say that 2, by being intent only on winning, and thus always going after the smallest boy, wrecked the game, at least as far as 1 and 3 were concerned, and possibly 4, though as I said 4 was at least playing a lot and he seemed okay with the challenge. I would assume 2's behavior would be different if he saw it as group fooling-around, an activity better the more everyone's involved, rather than as a competition. I don't want to poo-poo competition as such, though -- that would be pretty silly. And when I was a kid, and there were a couple dozen of us playing tag during recess, it was pretty chaotic and everyone was involved, so some of this is down to the circumstances.
What we don't see here -- but maybe saw in my schoolyard, I'm not sure -- is everyone competing, everyone trying to win, and that evening out in such a way that everyone's playing and having fun. You got something noticeably different here.
It feels like there's a political analogy here -- something about how democratic or even market practices can fail to produce the expected or desired social result, but I'm not sure there's an analogy for being "it", for having temporary control of the game and the direction it takes. Still, it's suggestive.
ADDED: Should have clarified that when 2 was "it" he would ignore 1 and 3, even if they were right next to him, and always chase 4. You could see that as a sub-optimal strategy, but on the other hand, he wasted no energy on the boys he might not catch.
So here's what happens: every time 2 is "it", he goes after 4, the smallest. 4 often ends up going after 2, in part probably as payback, and in part because he's the closest target, having just tagged him, though he would go after the others as well. There were so many "tag-backs" I wondered if they were going to create a rule to stop it. 1 sometimes followed the action around and even, at least once in my hearing, exhorted 2 to go after someone else. 3 was barely in the game at all, mostly watching from the sidelines.
One result of this is that 4 is getting the most play, most often being chased and most often chasing because he's most often "it". He also never gets much of a break.
My observation was this: someone, 4, is singled out, and someone, 2, is doing the singling out, and his behavior is changing the game for everybody. 1 noticed this and tried to encourage the more inclusive chaos a game of tag usually is. 2 did not appear to be interested. (Quite possible 2 and 4 were brothers and this is typical pre-teen big brother behavior.) 3, as I said, was almost entirely sidelined from play and either didn't care or didn't have the confidence of 1 (the tallest) to do anything about it, or didn't want to invite being singled out by 2.
I'm not sure what to make of it. I'm tempted to say that 2, by being intent only on winning, and thus always going after the smallest boy, wrecked the game, at least as far as 1 and 3 were concerned, and possibly 4, though as I said 4 was at least playing a lot and he seemed okay with the challenge. I would assume 2's behavior would be different if he saw it as group fooling-around, an activity better the more everyone's involved, rather than as a competition. I don't want to poo-poo competition as such, though -- that would be pretty silly. And when I was a kid, and there were a couple dozen of us playing tag during recess, it was pretty chaotic and everyone was involved, so some of this is down to the circumstances.
What we don't see here -- but maybe saw in my schoolyard, I'm not sure -- is everyone competing, everyone trying to win, and that evening out in such a way that everyone's playing and having fun. You got something noticeably different here.
It feels like there's a political analogy here -- something about how democratic or even market practices can fail to produce the expected or desired social result, but I'm not sure there's an analogy for being "it", for having temporary control of the game and the direction it takes. Still, it's suggestive.
ADDED: Should have clarified that when 2 was "it" he would ignore 1 and 3, even if they were right next to him, and always chase 4. You could see that as a sub-optimal strategy, but on the other hand, he wasted no energy on the boys he might not catch.
Comments (43)
It's social-ethical behaviour; so, analogous to many (if not most, or all) instances of social group dynamics (e.g., a philosophy forum). Or, consider it to be more generally applicable to game theory.
Yes. It seems to have something to do with this 10% finding referenced in Wikipedia's article about tipping points.
"The shift from Newtonian determinism to statistical science is what makes a
physics of society possible." - Philip Ball (Critical Mass, 2004). In this book, Ball reveals how human social group behaviour appears to be predictable to the extent that it conforms to power-law probability (Pareto) distributions.
What particularly interested me here was how this intransigent behavior changed the game for everyone. We've all had experiences like this, I should think, an argument someone is unwilling to let go spoiling a conversation among friends, that sort of thing.
You could describe this as one game being turned into another by the choices and actions of one participant. What's curious is what happens if that actor is intransigent: if the original game requires, or at least if it was intended to involve, everyone, including this actor, that's off the table; other options are playing a similar game that doesn't involve him (just expel or confine this actor and carry on) or agreeing to play by this one actor's rules.
So it is with the RPI simulation of a social network's marketplace of ideas -- a small group that never adjusts gets its way.
I also found it suggestive that the specific mechanism in this case was one minority, not to put too fine a point on it, singling out a more vulnerable minority. The others respond by watching from the sidelines or trying to coach or coax the one changing the game to quit it. But their options are severely constrained; the game has changed.
BTW, I just finished Nate Silver's book, in which power-law distributions play a leading role. I'll check out Ball, and thanks for the reference!
Thanks for the clarification.
Inasmuch as the game of tag you described is a display of aggression (specifically, dominance) by an individual, the situation bears greater resemblance to an instance of the bystander effect than it does to the effect of a minority opinion. Others may be aware of more relevant research.
Here's another stab at this ...
Quoting Srap Tasmaner
There are games of coordination (the sort of thing that Lewis takes as the basis of convention) and games of competition, and a game can be purely one or the other or mixed, as in the prisoner's dilemma.
Quoting Srap Tasmaner
I might be way off here, but it seemed to me that democracy and free markets are sometimes viewed as systems of competition that somehow provide a solution to the coordination problem of living together as a society.
My example doesn't address that directly -- here, I think most of the boys treat the game as mixed, both coordination and competition. What's curious is that the one who treats the game as pure competition changes the game for everyone.
Presumably the same would be true for someone who treated it as pure coordination. I guess he would let himself be tagged rather than running? If you're playing a game with someone who isn't even trying to win, that ruins the game too.
If anything, my perhaps faulty memory of playing tag as a kid (described in the second quote) supports the market idea, that somehow competition can solve a coordination problem. But I don't have a clear view of the mechanism there. I wonder too if, in those games of tag I played as a kid, we didn't treat them as mixed rather than purely competitive, at least by avoiding the singling-out behavior in my example. I think my friends and I would have disapproved of someone going after the slowest kid in class every time he was "it".
I agree.
I think each boy decides what type of game it is, and how they will play it, before the game even begins.
I think any game which doesn't have rules that are enforced becomes a dominance conflict. Spoiler: psychopathy always wins a dominance conflict.
I don't really see any of this as a game in terms of it being a fair contest where there can be a meaningful winner. It's really just social interaction where kids are learning to interact with one another. If one turns out a bully, he'll be ostracized and he'll learn that sort of behavior will limit his social interaction. It's like watching puppies rolling around on the floor. Let them play and figure out what they can get away with as long as none are too aggressive where they're doing harm.
Good point. But, if a learning game, then not applicable to political economy?
I have a similar reaction to Hanover but from a different angle: that the tag-example is oddly individualistic. It would only start applying to political economy if alliances, whether overt or not, began. If Hanover's bully were subtle they wouldn't get ostracized - they would get allies - and the game would enter social psychology.
How is the tag example oddly individualistic?
If the problem is presented in terms of game theory, isn't it applicable to many types of behaviour (including those addressed by social psychology, political science, economics, etc.)? Does the problem become irrelevant to one discipline when the terms of another discipline are substituted?
So, if the tag example is a mixed motive game (i.e., a conflict problem) where convention is ignored by one player, the other players will also disregard convention (Bicchieri). Further, if the other players adopt a form of reciprocal altruism (e.g., a tit for tat strategy) toward the deviant group member, cooperation ensues (Axelrod).
Suggested initial response to the bully: all players repeatedly tag the bully.
Caveat: isolation is the only viable solution for psychopathy.
1 thought they were all playing 'tag'. 2 was actually playing 'get 4', a quite different game.
Similarly, a cricketer who misses hits in order to lose a match and get a reward from a betting syndicate is apparently playing cricket but is actually playing 'beat the punters'.
It's true, I would need to go back to square one with individualistic game theory, to criticise its relevance to another discipline. I just thought quickly in answering, from the heart. I don't know enough about game theory to talk in its terms. I know 'cooperative game theory' is regarded as something of a poor man's game theory, but I don't understand why: as you can see, my instinct is to examine alliances to explain behaviour. But I speak from ignorance, not of tag (!), but of your model.
As I tried to emphasize, what really jumped out at me was how the choices of a minority change the game for everyone. There are various ways they can respond, but now we're talking about something else. The game doesn't perfectly absorb their different approaches. -- In a sense it does, and they can go on playing obliviously, but the percentage each boy is It shifts noticeably. -- That made me wonder about social theories that ignore not just the different strategies participants might adopt, but the effect this can have on the game as a whole. If a minority can force a game to be one thing rather than another, that's an issue in a lot of areas.
For instance, I think I have a sort of Rortian faith in democratic practice being conducive to finding truth, in the perhaps very long run, in everything from Science to internet fora. I recently found myself saying, elsewhere on this forum, that we need to be mindful both of the philosophical import of our words and their effect on the health of the forum. I think I have some idea why now.
I should really do some research I guess, but it also seems likely to me that the issue is really whether the strategies participants in the game adopt are in sync to some degree. As I said, someone not even trying to win can also ruin a game. The best result would seem to come from everyone having a similar mix of competition and cooperation in their choices.
This is what I had in mind: there are theories that expect cooperation to be emergent from competition.
Excellent point.
Quoting Srap Tasmaner
My systems science perspective sees competition and cooperation as the complementary local and global poles of social organisation. So while cooperation is emergent, competition would be so as well. Each needs the other to be able to definitely distance itself from the other. There is an inner drive to bifurcate towards one or the other state. Which seems disruptive as a dynamic. And yet also, hierarchical stability is achieved overall because cooperation is generalised constraint, competition is generalised degrees of freedom. There is a balance when the overall cooperation is forming the "right kind" of locally competitive behaviour. That is the kind of competition that is (re)constructing the higher level general constraints.
So a "fair" tag game has the implicit rule that individual interactions are randomly targeted. They should approach a normal distribution. One individual then flipping the other way - deterministically targeting one interaction - is going naked competition and that breaks the general rule.
In a big enough game of tag, there would be room to be a cheater like this and get away with it. You could target the easy to get kids as a group, or target one particular kid while also throwing in enough exceptions to look reasonably random to the rest. But your small sample size means that the distance between chasing fairly and chasing unfairly doesn't offer much room except to completely flip state from cooperative to competitive mode.
The emergence of strong cooperation in social groups is about the removal of the opportunities to cheat like this. An anthropologist noted that a tribe shared evenly all the food it gathered. Until they put up their tent and found individuals wanting to take the opportunity to hide food with the outsiders' help.
So it is a tricky thing. But consider how you are viewing tag as a lesson in social fairness. You want it to be a competitive game without winners. Players should cooperate to randomise the outcome to the degree that it is simply an accident who comes out top. And as parents of kids, that seems like a great lesson in life. Pure cooperation at work. Kids like it to. It is natural to enjoy being part of a crowd having fun and where winning isn't really the thing.
But then as we get older, then games become serious. Now there are meant to be winners. And so targeting the weaknesses of opponents is no longer unfair by the rules. You do need a much tighter game structure. Lines on the ground, enforced turn taking, all kinds of rules to create equality of opportunity. But while the cooperative structure of the game is thus made completely explicit - the chaos of tag becomes the order of Wimbledon centre court - so also the competitive element becomes sharply focused. The whole point becomes that it ends with a winner and a loser.
So as I said, social organisation is about this natural dynamic of competition and cooperation. Each is emergent from the other as each can only measure itself in terms of its dialectical "other". And this dynamic is vague in a game of kid's tag. Only parents standing outside would start to form the sharp rule that interactions ought to be self-consciously random. For kids, the chaos itself would be more the point - the chance to be inside a moment of learning how sociality works.
But then mature adult games are this kind of chaotic learning stage becoming clearly polarised. We form concepts of social equality and social order, as well as the matching concepts of individual striving and acceptable degrees of social cheating. How to be acceptably competitive is also something that clearly emerges for us.
How this relates to powerlaws or scalefree network models is then another story. A further complication. Enough to say that it is the difference between a steady-state system and an expanding one. A dynamical system that is static or not growing has an equilibrium balance that conforms to a normal distribution. One that is growing freely will conform to a powerlaw distribution.
So "global fairness" looks quite different in the two regimes statistically. It has a mean in one, and no mean in the other.
This is the reason why we are conflicted by the 1% and current social inequality. Why should an individual like Bill Gates be worth more than many nations? In a static world economy, wealth ought to be normally distributed. In an accelerating world, then wealth will naturally tend to a powerlaw distribution. That becomes the new random outcome. The bigger question is whether exponential growth is possible for long in a resource-limited world. But there you go.
I wondered about this, but my guess was what mattered was the percentage. 25% is clearly enough, but my guess is that a much smaller percentage of the population could effect this kind of change. They wouldn't even need to conspire if there was an objective way the choose a target.
Not being you, I hadn't thought in terms of constraint and freedom, though it makes obvious sense.
Again, take notice of the background thought here. There are two views. Either we try to engineer the system like a machine, or we recognise the power of self-organisation based on a probabilistic view of nature.
So as I say, probability theory sees two kinds of natural attractors when it comes to "fair" outcomes, fairness being really another word for globally random and unbiased.
This is one of my favourite papers on the issue - https://stevefrank.org/reprints-pdf/09JEBmaxent.pdf
Should Bill Gates be taxed to bring him back within normal distribution bounds of wealth? Or is his wealth in fact fair because we want to create a social world that is exponentially growing and not stuck in a steady-state equilibrium in terms of consumption?
Fairness or randomness or cooperation are themselves globally emergent outcomes that can be polarised by two general settings when it comes to thermodynamical balance, or emergent natural patterns.
Quoting Srap Tasmaner
In probability theory, there are always fluctuations. The question is whether the system itself is at a tipping point where the perturbation makes a difference. In a perfectly poised system, like the weather, a butterfly wing flap can be the difference. In a severely constrained system, it would take something huge - bigger than itself - to smash things apart. You can kick the mountain and it won't fall. It would take an asteroid, or millennia of eroding rain drops, to do that. But an avalanche could just "give way" because of the tiniest vibration.
But again, your tag game seems too small a sample size to really show any emergent dynamics like this. You just have a kid taking it into his head to win in the easiest fashion. And you as an outsider see that as being against the rule of winning in tag being random. You want this tiny sample size to replicate your ideal of social dynamics where everyone has something they can win at, and so - as the corollary -
nobody wins at everything.
But is your tag game a good model from which to extrapolate? It has unnatural features like that it is a closed system - only these four kids are playing. If there were a large pool of kids and behaviour was observed over time, then more dynamical and self-organising conclusions could be drawn.
In a realistic game of tag - as nature plays it - would this one kid switch the system? Even in your tag game, the two others are just left out. They don't change their strategy. The smallest kid is the only other one who feels forced into joining in the mutual strategy switch. Wait a little longer, and doesn't the smallest kid get fed up and walk away?
So you are illustrating the breaking of a system, not the gestation of a new self-balancing state of system organisation. There just is no organisation unless it has a self-perpetuating balance of competition vs cooperation. There is a sort of cooperativity between your 2 and 4 for a while. But it seems one that must soon break down - 4 walks off - rather than being the new stable state with mutual benefits.
This particular game was just a jumping off point, and I don't expect to draw any conclusions from it.
This is interesting:
Quoting apokrisis
I think we all know this. But then the paradigm shift is seeing that it is a natural, probabilistic and self-organising thing. It is a mutuality or dichotomy that emerges through "pure statistics". That is why the new wave of system modelling - based on complexity and thermodynamical thinking - offers the right analytic tools.
And then the other paradigm surprise is that the statistical models themselves are polarised. We get Gaussian vs Powerlaw systems as the two limiting cases of natural probabilistic systems.
A few years back, Nassim Nicholas Taleb had a best-seller, The Black Swan, that expressed his surprise that the modern social world had become a case of Extremistan vs Mediocristan - http://kmci.org/alllifeisproblemsolving/archives/black-swan-ideas-mediocristan-extremistan-and-randomness/
Likewise there was an explosion of popular talk about fat-tail distributions.
But it was a surprise that anybody could be surprised. Once we started to get the computer power to handle non-linear calculations from the 1970s, an abundance of "emergent constraint" mathematical models poured out of science. Fractals, scalefree networks, etc.
So it offers a metaphysically-general shift in frame. We have got used to thinking of reality as a deterministic Newtonian clockwork. But actually it is all about emergent self-organising probability - the organicist or natural philosophy view.
That then is how I would analyse your example of a misplayed game of tag. You were seeking to extract some example of how a few strong actors might tip a much larger dynamical social order into a new regime - effect a phase transition. A modern probability based metaphysics makes that a right approach. It is a good starting intuition.
But then also - the point I made - this particular game could just be a breakdown in self-organisation. The lesson might be more about what now counts as unnatural about the situation described - like the short-run view of the system you were taking, and its very small number of possible interactions.
Yes, that's where I'm headed.
(BTW, I'm reading Life's Ratchet now on your recommendation. Good stuff.)
The largest and most complex type of human social group is the stratified society, which is composed of nested complex systems (e.g., political, economic, legal, etc.).
In society formation, culture (the collective mindset and consequent products of a human social group) emerges spontaneously from the resolution of dominance and territorial conflicts (Sherif & Sherif).
Cultures develop over time. Changes in mindset/convention have cascading effects on nested systems, transforming society. Sudden and/or dramatic changes in mindset/convention can cause societal breakdown.
What type of predictions can be expected of complex system modelling with regard to cultural development in stratified societies?
Well stratification or nested hierarchical organisation is itself predicted by Barabási's scalefree networks. The emergent powerlaw statistics of airports will be a familiar example. Eg: http://www.pnas.org/content/104/39/15224.full.pdf
And now Bejan's Constructal Theory is pushing explicitly into social modelling. This marks a shift from purely statistical models to thermodynamical ones. Introductory chapt here:
http://www.springer.com/la/book/9780387476803
In general, hierarchy theory, which has been going strong since the 1970s, does explain hierarchical organisation in emergent terms. But that was more heuristic explanation and not mathematically developed models. Now the general mathematical models are arriving, as in the above.
You seem to be asking about cultural trends in particular. I would say that remains at the heuristic stage of argument. If you could pinpoint some trend of interest, that might jog my memory on relevant mathematical strength modelling.
But one obvious trend explained is how modern life is polarised by the contrasting pulls of specialisation and generalisation. We are both more homogenous and more diverse at the same time because we all get exposed to Trump/Kardashians/Bieber as our universal shared culture, and yet also the same social media lets us dive into the most obscure interests shared by a few.
Fifty years ago, everyone was clustered on a middle ground because TV had just a few channels. And homes, a single device. Now the internet has created a scalefree sociocultural environment. Going viral is now a thing - an emergent behaviour that is perfectly familiar.
I guess my particular slant here is then making the connection between emergence/hierarchy theory and Peircean, or even Hegelian, semiosis and dialectics.
So Peirce makes the logical and metaphysical point that all emergence must be grounded in Firstness or Vagueness - a state of pure potential or pure symmetry.
Then there is a symmetry-breaking or dichotomisation. One becomes two, as in dialectical thesis and antithesis. You get complementary bounds emerging - as in canonically, the local and global scales that are the basis of a triadic hierarchical organisation. See Stan Salthe on his basic triadic system in his classic, Evolving Hierarchical Systems.
So the emergent model is the Peircean one of an unbroken potential that breaks and separates in opposite directions, and having done that, becomes stratified because the two tendencies thus created get mixed - go to statistical equilibrium - across all available scales.
And it is very easy to read this into current world affairs. For instance, we have had 30 years of economic globalisation. And the natural response to that is a new call for economic localisation.
This is being read as a pendulum swing in politics. We went one way, now we must go the other. But really, political attention should be focused on the systems fact that an economic agenda predicated on liberated growth is going to go strongly in both these directions anyway. That is predictable. What will vanish from the system is the middle ground. Or rather, any proper mean or average scale of economic action.
So it is not either/or, but both - and both being expressed across all available scales of organisation. And we can then measure a "fully stratified" hierarchical organisation in terms of its approach to this powerlaw ideal of having no actual mean.
A non-growth system would be characterised by approaching the Gaussian limit of a precisely specified mean. A free-growth system does the opposite. And understanding this is pretty important if you want to have a sensible political conversation about the emergence of radical wealth inequality, or the "surprising" disappearance of the middle class.
So for instance when mass communication was limited to a small number of broadcast media, TV, local radio, local newspapers, then you expect a Gaussian distribution in people's knowledge of current events, sports, entertainment: most would have moderate levels of knowledge, and very few little or lots. Right so far?
Once communication channels start proliferating, we see power-law distributions instead, right? In the past, lots of people knew at least a little about the Brooklyn Dodgers, few knew nothing, and few knew a lot. Nowadays, there could be some artist that a small number of people know tons about, but almost everyone knows almost nothing.
Am I getting this right?
That's it. The popular account of all this has been the talk about fat-tail distributions, or seven degrees of separation - http://www.nytimes.com/2009/02/08/magazine/08wwln-safire-t.html?mcubz=1
Or as I mentioned, Taleb's Black Swan. Or "disintermediation" - https://en.wikipedia.org/wiki/Disintermediation
So everyone is picking up on what is happening with the internet and now social media. People are inventing terminology left, right and centre.
That makes it rather hard to see that this is not just about the web. It is an absolutely generic self-organisational story.
Again, that Franks' article is excellent in identifying the fact that we are talking of two contrasting probabilistic regimes in nature - where before people thought there was only really the one, the good old bell curve. Now we are seeing that powerlaw (or log/log) statistics are not some kind of weird exception, but the other natural limit.
Instead of trying to assimilate all structure to Gaussian outcomes. we should expect nature to be fractal, scalefree, hierarchical, exhibit fluctuations over all scales, simply because of emergent probability.
Powerlaw behaviour is in fact more normal or basic as it is less constrained. It is the first stage of order that you get because "free growth", or dissipative structure, is the simplest form of emergent organisation. It takes the addition of limits on growth to then start to get Gaussian closed system behaviour where fixed limits force the system towards a single-scale mean.
Metaphysically, this is revolutionary. The Second Law of Thermodynamics would no longer be fundamental as it describes an already closed world in which entropy has an average. The lid has been put on the pot, as it were. Instead, you need a modified law - one based on dissipative structure, or Prigogine's "far from equilibrium" systems - that starts with powerlaw behaviour.
So Gaussian probability - the central limit theorem - was worked out first. But it is the more constrained statistical situation. We are now working out the models of statistics with the least possible constraints. And so while powerlaw behaviour seems weird and exceptional, it is really the more generic case in nature.
Even the Wikipedia's article is staggering in the number and range of examples.
http://www.gaianxaos.com/pdf/dynamics/zeeman-catastrophe_theory.pdf
You can see it covers abrupt changes of state in stockmarkets or rage/fear responses in dogs. So it gets at the kind of dynamics you raised in the OP.
I was really terribly bored by what I was studying in class. It was so reductionist. Catastrophe theory was an almost mystical blast of something utterly different.
But it was like a solitary trumpet call. At least given that one just did not have access to the "whole world of academia" back in those days. If your prof didn't know about it, you were hardly going to find out.
Then 10 years later, it all came spilling out of the closet as deterministic chaos theory, fractals, complexity theory, far from equillibrium thermodynamics, etc. Everyone was talking about it. And the spreading continues.
I'm glad you are checking out Life's Ratchet. To me, that is another such trumpet blast when it comes to establishing the physical basis of biosemiosis.
Powerlaw stuff is all about sorting out the story of self-organising material dynamics. Semiosis is then the follow-on issue of how life and mind can constrain that dynamics in entropically fruitful fashion using information.
And biophysics is identifying how this informational trick is something that "must happen" emergently at a particular nanoscale of being - the "edge of chaos" or transition zone which is the quasi-classical scale of atomic behaviour.
Such a beautiful and satisfying story.
It would be a useful public policy tool to have a model which predicts the optimal number and type (age range, religion, academic and professional qualifications, ethnicity, sexual orientation, family and marriage status, etc.) of immigrants that should be permitted to enter a country, based on its sustainable assimilative capacity in terms of:
1) Labour force needs.
2) Social welfare demographics.
3) Social institution budgets.
4) Tolerance for diversity.
5) Land development costs.
In view of the existence of natural limits on resource availability and economic growth, shouldn't all social systems be engineered (i.e., not be permitted to fluctuate naturally in the interest of social stability), and all public policy modelling be Gaussian?
Most nations want unbounded growth. It would be a major change to switch to a steady state ambition as things stand. Even if natural environmental constraints say we should.
So for immigration, what globalisation has produced is worker mobilty. The smart choice - if you can manage it as a nation - is to try and import the creative educated elite on a permanent basis, and then take advantage of imported cheap labour - Philipino construction workers, Mexican fruit pickers - on temporary labour visas.
Of course - going in the other direction - you want to export all your polluting and slave wage jobs to the developing nations. They can run the extractive industries and call centres. You only have to import temporary workers to be the nannies, the care home staff, the dairy workers.
So the true immigration picture does look dictated by an economic growth agenda. Then within that might come the discussion whether the desired balance of social stability/social creativity is best served by assimilationist vs multicultural migrant policies.
I agree. Of course, most are aware that the global economy is currently experiencing an engineered "prosperity" which will be subjected to a natural correction. In that event, steady state ambition may become much more appealing.
I'm still trying to understand the connection between unchecked growth and power-law distributions, when my youngest comes up and tells me the Minecraft mod we installed last night keeps crashing. We're used to this, because anyone can make a Minecraft mod, and the vast majority of them are never maintained and updated; only a very small number are of very high quality, popular enough to attract other developers, etc. It's another power-law distribution driven by the low barrier to entry of modding, yes?
In the case of minecraft mods, mods can be freely added to the pool and freely selected from the pool. So popularity of any mod will have a powerlaw distribution in that you have two contrasting actions freely continuing. And then the frequency with which any mod is both added and selected is simply "an accident".
The model treats the choice as a fluctuation that can have any size (there is no mean). But also there is a constant power expressed over every scale. So you should expect a fat tail of a lot of mods with very few takers, and then also a few mods which almost everyone adopts.
But there's still some feedback in more popular mods (songs, movies, etc) becoming more well known and more often selected.
How do we represent that evolutionary mechanism?
So it seems you want to track the deterministic train of particular events in the minecraft scenario. One mod was really good. A lot of others just stank. The outcome over time would be explained in terms of the individual merit of each mod.
But that defeats the point of a probabilistic analysis. The surprise - to the determinist - is that all that locally true stuff is still irrelevant in the largest view where we are inquiring into the fundamental set up of the system. The same global patterns emerge across all kinds of systems for the same general global reasons. The deterministic detail is irrelevant as it doesn't make a difference. What creates the pattern is the simple thing of two free actions orthogonally aligned.
Again, read Franks. The Gaussian~powerlaw dichotomy works just the same whether we are talking about a host of independent deterministic variables, or random variables. If you step back far enough - if the ensemble size is a large number - then what seems like an essential metaphysical distinction (random vs determined) becomes just a statistical blur. Now we are just talking about the nature of the global constraints. Are they the set up for a closed Gaussian single scale system, or an open powerlaw multi-scale system?
Local determinism - like some objective judgement that a mod either stinks or works, hence the "feedback" that determines its popularity - just drops out of the picture. It makes no difference to the answer. What we are now talking about is the limits on indeterminism itself. Randomness at a global systems level turns out itself to be constrained to fall between the two bounds described by normal and powerlaw distributions.
Folk like to talk about chaos. But chaos turned out to be just powerlaw behaviour. Mess or entropy has its top upper limit.
Which then leads to the next question of what lies beyond messy? Again, back to Peirce, the answer becomes vagueness or firstness or Apeiron. Or rather, vagueness is the ground from which maximum mess and maximum order co-arise as the dichotomisation of an ultimate unformed potential.
Sorry -- what was this again?
Quoting apokrisis
But to know this is to know something about the domain, isn't it? To have some idea of the mechanisms at work. How else can you really know whether two variables, say, are independent of one another?
For instance, natural selection provides an explanation for why you might find alleles of some gene distributed in power-law fashion: most mutations were fatal or marginally contributed to survival or reproductive success; an allele that gave any relative advantage wins, and wins big.
(Nate Silver repeatedly makes the point, in his book, that models based on a solid understanding of the domain outperform purely numerical analysis.)
I don't get your objection. If you observe a powerlaw statistics, then that is when you should suspect this free othogonality to be at work. And the very fact we are so accustomed to mapping the world like this - with an x and y axis which models reality in terms of two variables - should tell you a lot.
And as I say, the alternative is that the correct interpretation might be that it ought to be a Gaussian plot - normal/normal axes rather than log/log. You can of course then have log/normal distributions as a mixed outcome.
So it is curve fitting. You have some bunch of dots that mark the location of an observable in terms of two orthogonal or independent variables - whatever labels make sense for your x and y axis. Then either you can draw a good straight line through the middle of them if the relationship is fixed and linear using normal/normal scaling (just counting up 1, 2, 3... on both axes), or you find that the relationship is a flat line plot only when you uses axes that count up in orders of magnitude (so 1, 10, 100...).
Both gaussian and powerlaw distributions presume two independent variables. The question then is whether the axes need to be linear or exponential counting when it comes to the making the resulting equilibrium balance a simple flat line.
Back in the real world, yes one might need extra knowledge about the domain as more complicated stuff will usually be going on. Your independent variables might in fact not be so independent.
But my point - and Franks's point - is that domain issues wash out at the grand metaphysically general scale.
This is the truth we can derive from the maths of hierarchy theory - Stan Salthe I have already mentioned too. At a large enough scale of observation, the local and global bounds of a system are far enough apart that any coordination - any determistic connections - become so fine-grained as drop out of the picture.
It is the law of large numbers. Eventually local differences cease to matter as you zoom out far enough. All that domain detail becomes just a blur of statistical sameness. You can now see a system in terms of its general characteristics - like whether it is closed and single scale Gaussian, or open and multi scale fractal or powerlaw.
Thanks for the reference.
I suppose I'm not in any hurry to get to metaphysics -- there are domains I'm actually interested in.
Quoting apokrisis
Right, and this is where Silver argues that domain knowledge can help you avoid overfitting (modeling the noise), but at the sort of granularity you're talking about this can't be much of an issue.
Quoting apokrisis
Absolutely -- I expressed myself poorly. But my thought was something like this, that when you see, for instance, how alleles are distributed, then you go look for a mechanism that would produce such a distribution. If you can't find one, then you could reasonably wonder whether you've properly represented the data. (And then there's spurious correlation.)
I'm just confused about whether you're telling me to quit taking that second mechanism-seeking step, or whether it's just that you're talking metaphysics and I'm usually not.
Thanks for putting up with my questions here! A whole lot of this is new to me.
Sure. I get that you want to get going with real world modelling. That is where correlations between variables start to mess up attempts to model in terms of assuming independent variables.
But my response to that is you have to start with the clean basic models. You have to have a (metaphysically general) foundation which sorts out what you even mean by independent or random. And as I say, it is a huge thing to discover that the statistical world is larger than just the central limit theorem. It is indeed really huge to realise that powerlaw statistics is the more general natural case (as being a system with the fewest actual constraints).
So you have to establish the baseline that legitimates any modelling. And then you can start building back in the kind of sophistication that starts to deal rigorously with messy domains with possible internal correlations you might want to talk about.
Systems with correlations or coordination dynamics have been a big deal for statistical mechanics for a good 50 years. That is what phase transition models are all about. Remember your interest in the logistic functon or S-curve - the reason why transitions can be sudden as global correlations suddenly kick in? Rene Thom's Catastrophe Theory? Spontaneous symmetry breaking? Autocatalytic networks? Ising models? There's a thousand variations of statistical mechanical models that start with a clean baseline of "no interactions", and then find ways to model the realistic emergence of those interactions or collective behaviour.
Take the Ising model - the story of a bar magnet. When it is hot, all the iron atoms jiggle and don't line up. All their magnetic fields are aligned in a non-interacting fashion. But cool the metal and it hits a point where the thermal jiggling gets suddenly overtaken by the potential local attractions. Correlation goes from zero to infinite in a flash. Voila. The bar has a fixed global magnetic field in which all individual variety is completely constrained.
Its the usual story. Modelling has to break the world apart to put it back together. You have to work out the baseline simplicity before you can hope to model the real world complexity.
So it is not about quitting your second mechanism step. My point is that statistical mechanics - at its fundamental level - has only been able to move forward with a new era of thermodynamically-inspired models (ones that deal with coordination or constraint-making as itself emergent within a system) by realising that Gaussian statistics are the special case, not the general one.
For me, I agree, this has metaphysical import. I like to think what it means about existence itself.
You might be just interested in baseball statistics or whatever Nate Silver has in mind as some particular domain. And fair enough.
That makes tons of sense. Thanks, apo!