On a personal note, the first aha! moment for me was reading a 1976 SciAm article on Rene Thom's Catastrophe Theory as a biology undergrad.

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.

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. — apokrisis

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?

Surely whether you want unbounded growth or a steady state is what would determine whether you decide to engineer for a powerlaw or Gaussian situation.

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.

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. — apokrisis

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?

A powerlaw distribution is a log/log plot. So the result of exponential growth or uninhibited development in two contrasting or dichotomous directions.

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?

Models simplify. They shed information. A plot of a frequency distribution is a snapshot of the state of affairs that has developed over time. It is not a plot of how that state of affairs developed. That is the bit that the plot treats as accidental or contingent - information that is ignorable and can be shed.

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.

Again, read Franks. — apokrisis

Sorry -- what was this again?

What creates the pattern is the simple thing of two free actions orthogonally aligned. — 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.)

Franks - https://stevefrank.org/reprints-pdf/09JEBmaxent.pdf

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.

But my point - and Franks's point - is that domain issues wash out at the grand metaphysically general scale. — apokrisis

Thanks for the reference.

I suppose I'm not in any hurry to get to metaphysics -- there are domains I'm actually interested in.

So it is curve fitting. — 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.

If you observe a powerlaw statistics, then that is when you should suspect this free othogonality to be at work. — 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.

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. — Srap Tasmaner

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!