Order/Chaos Relativity and Complex Systems

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GeoComplex
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Order/Chaos Relativity and Complex Systems

Post by GeoComplex »

Hey everybody, I'm new, I'm a geologist and I have some fascinating questions about complex systems to ask the ERE group.

Do you guys remember in Jacob’s ERE book in section 5.1.2 where he states “You can never do just one thing!”? I am trying to figure out why that statement seems to be the case at all levels of reality (bear with me). The question I am asking myself is why does our society divide systems into simple orderly ones (has structure, is predictable, is deterministic, is linear) and complex chaotic ones (has randomness, is unpredictable, is nonlinear, maybe self-organizing or adaptive)? I speculate that the universe doesn't distinguish between the two things, and you can't have one without the other! They are possibly relativistic equivalents, and an analogy would be energy and matter (E=mc2) or spacetime! There seems to be order from chaos and chaos from order, going up and down the scales (smaller to bigger and bigger to smaller) of both physical reality and social reality (economy), if you think about it. This idea I am trying to get at probably explains why even though we know so much detail about the physical sciences and social sciences, and even with the large amount of data on the internet, our society is still struggling with so many inter-related problems like climate change, fossil fuel depletion, social stratification, etc. Every "simple" or "rational" solution that we come up with to solve a seemingly "isolated" problem generates unending unintended consequences (problems) that need more solutions as Jacob explained in the ERE book! The problem is that many in our society ignore that everything is interconnected and complex. Consequently, the philosophy of Early Retirement Extreme is by far the best “solution” I have seen to all these societal problems, because it is so open-ended, flexible, and adaptable on an individual level! Great work Jacob!

Let's call this theory that I am thinking about the law of conservation of complexity or alternatively the theory of order/chaos relativity! I'm reading a book about the science of complex systems and computation and it turns out that all these scientists and philosophers studying complexity can't decide on an "objective" definition of complexity. I guess that situation must be the definition of complexity itself! I define complexity as a bunch of things that are all interconnected and interacting with each other in chaotic fashion (complex system). By that definition, the science of complexity is itself a complex social system, with all the different scientists and philosophers each with complex personalities (and biases) studying complexity! Complexity is conserved! To me, this law states that at all scales of the universe both physical and social (economy) there exists complexity!

What about the "physical" universe? Well, virtually every physical scientist tries to "isolate" a system in order to "fully" understand it “objectively”.... but, humans have to keep in mind that the universe doesn't seem to make a distinction between systems, because isn't it everything in the universe interconnected in some way? I think that complexity is conserved over all of scales of reality (quantum to atomic to molecular to organisms to ecosystems to Earth to galaxies...), but only when you “isolate” a system from all the other systems (e.g. one molecule or one plant) does it looks like it is simple to understand, has order, and is predictable! It seems from the literature that the crazy quantum mechanics complexity statistically cancels out at the atomic and molecular scale but that complexity is replaced by molecular complexity in chemical reactions which then seems to cancel out at the organism scale but that previous molecular complexity is replaced by ecological and evolutionary complexity at the organism scale and so on. Regarding social systems, the economy might be something that’s complex at all scales because one of its basic units is an unpredictable human! I think the possible law of conservation of complexity, the theory of evolution, the law of conservation of mass/energy, the second law of thermodynamics, and Howard Odum's Maximum Power Principle might all be related in some unifying law... I mean, why can so many analogies be made between seemingly “isolated” systems in widely different disciplines (economics, ecology, physics etc.) and at all different scales? Why is energy so important for the growth and maintenance of all complex systems like chemical reactions, organisms, ecosystems, and civilizations?

Instead of the conservation of complexity maybe we could say that complexity (chaos) and simplicity (order) are relativistically equivalent through energy and call it the law of conservation of chaos/order? I say relativistic, because maybe deciding whether a system is simple and orderly or is complex/chaotic is totally dependent upon how you observe the system (isolate it)? Maybe the distinction is totally dependent upon the scale of your system (your frame of reference). Order from chaos and chaos from order. All in all though, I'm not sure how to rigorously define simplicity, order, chaos and complexity.

Anyway, as I think about all this, it shows to me personally that the ERE strategy for living is even more awesome than I originally thought then when I first read the book a few months ago. Be flexible, be adaptable, be a generalist, because it’s all interconnected. Our society could definitely use more generalists who see the big picture!

What do you guys think, am I way off? Could anybody point me in the direction of more info? Maybe books by IIya Prigogine?

Dragline
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Re: Order/Chaos Relativity and Complex Systems

Post by Dragline »

I'm not sure there is any way to prove or disprove a connection between ordered and chaotic systems in the Popperian sense. But its an interesting conjecture.

I agree that most things that "matter" a lot are in the chaotic or complex world -- what Taleb calls "Extremistan," including such things as weather, earthquakes, financial markets and the distribution of wealth. They are power-law distributed. Trivilialities, like the height of humans, are distributed on normal (Gaussian) functions (so-called "Mediocristan"). I think that is as good a definition as any. But it doesn't lead to any obvious connectedness. It's just a convenient descriptive terminology telling you what it is relatively easy to predict and what is not.

Apparently (according to the head of communications at CERN), most of the universe is made up of stuff we can't see and can't really describe very well that we have labelled "dark matter" and "dark energy" for convenience: https://www.youtube.com/watch?v=HneiEA1B8ks Which has led to lots and lots of conjectures and hypotheses.

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Re: Order/Chaos Relativity and Complex Systems

Post by jacob »

I don't think or know of any principle of the conservation of complexity.

The way I see the universe is that everything is generally connected. In the physical sense by forces. In the human sense by laws, conventions, and agreements.

These connections can be strong or weak.

The connections can be first order, second order (a connection to a connection), etc.

Humans try to model or explain the world. They have various tools for that. Hard sciences try to understand connections by setting up an experiment that isolates one connection from most others. Reductionism. Mathematically speaking, analysis is the tool used in this case. Engineers mostly think in this way: "How can I reduce the degrees of freedom/the number of uncontrolled connections in my widget by as much as possible. Engineering is the deliberate process of eliminating connections until something can be understood well enough to be controlled. Humanly created widgets that behave unexpectedly is an example of poor engineering. Engineering is only capable of understanding simple things. The most complicated widget known to man only has a few dozen degrees of freedom.

For situations where there are too many connections, we might be lucky that the mostly cancel each other out. The mathematical tool for this is statistics. This is how we can describe a gas in terms of overall factors of the statistical distribution and relate those to things like pressure and temperature. Economists try to do the same with the economy trying to summarize it in terms of GDP and interest rate. Macroeconomics is a good example of trying to use the wrong tool because human action can not be summarized in two numbers because human interactions are substantially more complex that the interaction of gas particles.

We have in our tool box two successful tools.

Analysis which deals with few particles and few interactions. From this comes engineering and a lot of hard science.

Statistics which deals with many many particles and few interactions. From this comes thermodynamics, actuarial science, but also ironic jokes like macroeconomic theory and associated bad ideas like central planning.

There are a bunch of new tools coming up which are still very much in their infancy. They haven't been that successful compared to the previous two.

"Big data" which deals with many many particles and slight more than just a few interactions. From this comes netflix recommendations, directed marketing, and NSA spying. It's a somewhat more sophisticated form of statistics.

"Network theory" which deals with more than just a few particles but many interactions. From this comes facebook, epidemic understanding, etc.

"Chaos theory" which deals with situations whose ultimate behaviour is highly sensitive to initial precision. From this comes ... a dose of computational/predictive humility.

"Complexity" is just a word we use when the situation described exceeds and falls between the cracks of our current tools. I do not think complexity is an inherent feature of the system.---Sure I can devise some criteria for describing if/when a situation falls between the cracks, but that doesn't mean---to me---that it's complex but simply that my tools are inadequate. What may be complex to a stupid person is not necessarily complex to a smarter person. In some areas we're all stupid. However, the chance of the average person encountering an unknown-known (at the top of Mount Stupid) is much larger than the smart person being troubled by a known-unknown because we, humans, deliberately try to arrange our matters such that we control these unknowns by either eliminating them or avoiding them as much as possible. This leaves the unknown-unknowns which are the bane of conceited smart people. These are the black swans.

I mostly blame the two successful tools for this conceit. Both of them ignore connections which are clearly visible (to anyone who actually bothers to look) in the name of tractability. People are deliberately being lazy in order to make precise statements when they should be focusing on accuracy or simply admitting that "we just don't know".

For example, many people, including yours truly, saw the credit crisis coming at least a year in advance. I even wrote about this on the blog in spring 2008. Yet most people and indeed most professionals missed this because they ignored important connections in order to get an easy answer from their statistical models. Many in this latter group still insist that because their simple math models couldn't and can't predict such non-statistical behaviour, "nobody" can.

The human brain is interestingly enough capable of understanding levels of complexity that our simple tools (analysis, statistics, big data, and network theory) can not understand. Again, this does not deter many from insisting that if something can't be demonstrated statistically to exist, it does not exist. Statistically speaking, they're committing a type II error (failing to detect what's present). Alternatively, scientists often tend to believe that if we don't understand the underlying "physics" we can't engineer a product. Yet this happens all the time. Inventors often come up workable widgets than science only explains in retrospect. Breaking the sound barrier for one.

To summarize, the point "that you can never do just one thing" is the recognition that any action probably has more connections to other things and actions than is generally realized by the usual/current analytical or statistical ways of thinking about things.

For books, I'd suggest reading Weinberg's book on systems theory.

GeoComplex
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Re: Order/Chaos Relativity and Complex Systems

Post by GeoComplex »

Thanks for all the info guys. Jacob or Dragline, are you guys familiar with Kurt Godel's Incompleteness theorem? Didn't Godel prove in 1931 that mathematics can never be both complete and consistent? So maybe it is impossible to prove a connection between an ordered or chaotic system? The reason I bring this up is because I guess all this mathematics and computation that scientists are doing to try to explain everything may be making the "big picture" more confusing, while at the same time making "smaller pictures" much more understandable in a mathematical sense? I guess the new tools of Big Data, Network Theory, Chaos Theory, etc. may help with the "big picture" at some point. By big picture I mean the global economy coupled to the problems of peak oil, peak gas, peak coal, climate change, ecosystem destruction, technological development, etc. I see technological development as a possible problem (could be a solution as well) because of the law of conservation of matter, if 7 billion people want high-tech "stuff" it has to come from the crust somewhere as engineers re-arrange the matter into widgets to sell to consumers...

I guess what I am most interested in the study of complex systems is the role of energy, matter, entropy and "time". Isn't an implication of the laws of thermodynamics that everything must be connected to each other energy-wise as well as force-wise? I mean, for example, is it correct to state that the supernova's that created the matter for the solar system don't "affect" us today because they no longer "exist" in a "time" sense? I don't think that statement is correct because aren't these supernovas, in a sense, embodied in everything around us including ourselves (we are all made of star-dust)? Wouldn't that be a "strong" connection or "tightly" coupled? Isn't everything that is occurring at this moment possible because of those supernova's and the Big Bang? If time is relative, then maybe is it better to think of the "past" as a series of cascading energy-matter-entropy transformations that make "the future" possible?

I mean, we say that the Big Bang happened 13.7 billion years ago, but isn't time relative? Is it wrong to state that the "big bang" still exists, in a sense, embodied in every particle, atom, molecule, rock, organism, planet, star, galaxy, and all the electromagnetic radiation and spacetime in-between? How do physicists decide to make a distinction that the big bang happened a certain amount of time ago?

I see this in the human economy too. Every single transaction and widget is connected not only with $$$ but also because of the mining industry and the energy industry among other things. I don't know, maybe I am nuts?

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Re: Order/Chaos Relativity and Complex Systems

Post by jacob »

GeoComplex wrote:... are you guys familiar with Kurt Godel's Incompleteness theorem? Didn't Godel prove in 1931 that mathematics can never be both complete and consistent? So maybe it is impossible to prove a connection between an ordered or chaotic system?
An axiomatic system can not be complete and consistent at the same time. Other systems can, so this has no implications for science which doesn't work on logical axiomatic principles but on the scientific method. In science math is only used to unequivocally and often quantitatively express theories that were developed in unaxiomatic ways.

Science is not a positivist expression of math similar to how positivism is a rather inadequate filter in terms of language. I can express ideas to you in a language that's not grammatically correct and yet you'll still understand me, e.g. "I can haz hamburger?" English is grammatically incomplete in the sense that it can't express this statement, yet for this example you understand both the question and the underlying sentiment. Indeed this sentence while being grammatically incorrect is even more expressive than grammatical English.
GeoComplex wrote:I guess the new tools of Big Data, Network Theory, Chaos Theory, etc. may help with the "big picture" at some point. By big picture I mean the global economy coupled to the problems of peak oil, peak gas, peak coal, climate change, ecosystem destruction, technological development, etc.
All such tools help to describe and think about problems. Big Data etc. allows us to think about problems in new ways. The new tools are certainly better than mathematical analysis or statistics in terms of describing complex systems (many agents, many degrees of freedom) but they are far from sufficient. Some of them have an edge over humans when it comes to many data points but humans have a very strong edge when it comes to making connections between disparate things. A person's intelligence is very much correlated to how many separate connections the brain can hold simultaneously. A moron (or whatever the pc word is these days) can make 2 or 3 simultaneous value-adding connections, e.g. (bus early, too far, not gonna make it). A genius can make 7-9 such connections and thus grasp far more complicated things. An average person can make 4-7 connections. However, considering how many possible connections there are in the world (thousands, millions, ...) we're wholly inadequate. Furthermore, even very "smart" computer systems are about as intelligent as the average person in the connection sense. They're only edge is that they're faster and more precise (humans are notoriously slow and imprecise) And they're built by the most intelligent humans.
GeoComplex wrote:I see technological development as a possible problem (could be a solution as well) because of the law of conservation of matter, if 7 billion people want high-tech "stuff" it has to come from the crust somewhere as engineers re-arrange the matter into widgets to sell to consumers...
Matter is not the shortage. The concentration of free energy is. Free energy is the capacity to do work. Given our limits in intelligence, every advance in humanity has come from finding a source of more concentrated free energy. There are very few inventions in the history of humanity that has increased our collective intelligence: writing (preservation of knowledge/communication), scientific method (systematic investigation), religion (organized social control), money/capitalism (distributed trust), ... and sometimes these inventions has come at the cost of a decrease in individual intelligence.
GeoComplex wrote: I guess what I am most interested in the study of complex systems is the role of energy, matter, entropy and "time". Isn't an implication of the laws of thermodynamics that everything must be connected to each other energy-wise as well as force-wise?


No. This rabbit hole goes deep but the first thing should be to understand what energy and entropy actually is. They are just convenient concepts. Energy is a quantity you can calculate mathematically based on the positioning of the matter in the system. This quantity is conserved. A more abstract way to think about it would be that energy is invariant to translation in time (similar to how momentum is invariant under rotation). This seems to be a universal property of certain systems.

Similarly entropy refers to the number of combinations in which we observe a system in 1 state (because we ignore the details) compared to the total available number of combinations. For example, there are 6! ways to arrange 6 numbers. There's only one way to arrange them like 1-2-3-4-5-6. There are 5! ways to arrange them if we only consider whether the first number is a 1. Hence, the entropy of that is something like 5!/6!. The use of logarithms in entropy calculations are just to make multiplications additive. It's each to think of entropy in terms of "some quantity called entropy that adds" but what's really going on under the hood is multiplicative combinatorics in system-state space that multiplies. "Entropy" is but another convenient quantity, like energy, that doesn't really exist (you can put neither energy nor entroyp in my hand) but is a convenient mental model.
GeoComplex wrote: I mean, for example, is it correct to state that the supernova's that created the matter for the solar system don't "affect" us today because they no longer "exist" in a "time" sense?


That's correct. Nobody who does any physics, engineering, finance, politics, etc. has any equations or modelling or understanding that accounts for nucleosynthesis, galactic chemical evolution, and the origins of the solar system. It is certainly true that all composition of matter and all the ratios you see around us (why is must of the universe made of hydrogen and helium) and why is there so much carbon, nitrogen, oxygen, silicon, aluminum, and iron on the planet and not e.g. boron, sulfur, scandium, and galium? That's mostly because of specific nuclear resonance levels and reaction paths. However, while these nuclear levels affect deep philosophical question like the anthropic principle, they are irrelevant in the consideration of how a steam engine works or why trees grow.
GeoComplex wrote: I don't think that statement is correct because aren't these supernovas, in a sense, embodied in everything around us including ourselves (we are all made of star-dust)? Wouldn't that be a "strong" connection or "tightly" coupled? Isn't everything that is occurring at this moment possible because of those supernova's and the Big Bang?
Nuclear reaction physics, supernovaes, and interstellar mixing are strong connections if you try to understand nucleosynthesis (why the isotopes we see appear in the concentrations they do). But it's a non-existent connection for practically all other models in the world. In other words, the connection is very interesting to about "5"(*) people in the world (I used to be one of these people) but utterly irrelevant to anyone else.

(*) For this area, it's more like 500 people out of 7,200,000,000 people.
GeoComplex wrote: If time is relative, then maybe is it better to think of the "past" as a series of cascading energy-matter-entropy transformations that make "the future" possible?
What do you mean by "time is relative". Do you understand precisely what this statement means in a relativistic sense? The technical definition is far less "sexy" than the "philosophical" cooption.
GeoComplex wrote: I mean, we say that the Big Bang happened 13.7 billion years ago, but isn't time relative? Is it wrong to state that the "big bang" still exists, in a sense, embodied in every particle, atom, molecule, rock, organism, planet, star, galaxy, and all the electromagnetic radiation and spacetime in-between? How do physicists decide to make a distinction that the big bang happened a certain amount of time ago?
We mean that if a clock locally at rest in space time residing with where we are now that showed t=0 at BB would show 13.7 billion years now. In practical terms, we observe the increasing redshift as increasingly more distant galaxies and quasars and conclude that the universe is expanding. If we extrapolate backwards, everything must have come together at one point 13.7 billion years ago (or whatever the accurate count is these days).
GeoComplex wrote: I see this in the human economy too. Every single transaction and widget is connected not only with $$$ but also because of the mining industry and the energy industry among other things. I don't know, maybe I am nuts?
A little ;-) ... I think I've take a somewhat more practical approach to understanding things. Think of a Taylor expansion. For many functions e.g. cosin(x) they have an infinite number of terms. Suppose we didn't know the function but only the terms.
You're thinking about all those terms. I'm only thinking about the leading terms to whatever precision I require. A large part of the physics education is learning what's relevant to solve a given problem and what's not. Where can we simplify and where can we not simplify?

GeoComplex
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Re: Order/Chaos Relativity and Complex Systems

Post by GeoComplex »

Wow, thanks for answering all the questions, Jacob! I was getting confused by the notion of cause and effect, relativity, energy/matter and spacetime, but I am not a physicist, I just read the pop science books. Oh yeah, I guess I was trying to think about too many connections to things. I think I will stick to my day job (groundwater modeling), as it is much simpler to grasp, haha! I think what is really worrying me is that the fact that few economists include any materials or energy in their models. I think this is a big problem, as they are in their own little "universe" where everything makes sense according to their mathematical models that do not include physical reality!

Dragline
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Re: Order/Chaos Relativity and Complex Systems

Post by Dragline »

Yeah, jacob pretty much cleared that jeopardy category.

All models have limitations, whether they be in economics or another social science, the hard sciences or philosophical or religious ones. It's always a good practice to understand (1) what a model was designed to explain; and (2) what are the underlying assumptions that make the model work in its particular domain. Many models are misapplied in a willy-nilly fashion on the internet and arrive at erroneous conclusions, because these questions are assumed away.

If you are interested in models that cross from the physical science domain into economics, have a look at the works of this person: http://en.wikipedia.org/wiki/Nicholas_Georgescu-Roegen

If you are interesting in how to apply different models across disciplines, consider this website, which is based on the advice of Charlie Munger to apply multiple models to any question about predicting the future to see if more than one model arrives at the same answer: http://www.thinkmentalmodels.com/ Also Google Charlie Munger and "big ideas" for more like that.

I have a personal affinity for the entropy model as practical advice for how to approach life in general -- i.e., left to their own devices, most things tend to decay or otherwise become disordered if some effort or energy is not applied to keep them in order. If you don't actively use your muscles, mind, etc., they tend to atrophy or rot like an engine that rusts, a garden that becomes full of weeds when not tended, or a kitchen that becomes infested with germs or cockroaches when not kept clean. If you don't put any energy into a relationship, it will probably fail, too. The corollary to this is that it is really not really possible to devise a perfect anything, whether it be a financial plan, marriage, etc. in a "set it and forget it" fashion. Thus, its not really worth the effort to perfect anything, because it won't stay that way. Just decide for yourself what is "good enough" and be prepared to apply some energy to whatever it is periodically to keep it at that level.

"Pin your ear to the wisdom post
Pin your eye to the line
Never let the weeds get higher
than the garden
Always keep a sapphire in your mind
Always keep a diamond in your mind"

-- T. Waits, "Get Behind the Mule"

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Re: Order/Chaos Relativity and Complex Systems

Post by jacob »

Pop science books are kinda dangerous to the mind. They provide way more confidence than actual insight. I try avoid them for that reason. However, freshman/101 level books should by construction be understandable by HS graduates so I prefer those.

Connecting energy and economics was popular in the 1970s when the world was believed to be running out of energy. Aside from Roegen, Vacla Smil is another good source for this. The keyword is thermo-economics. A lot of the ideas of the 1970s are resurfacing, as predicted.

PS: DW wrote her phd on groundwater modelling. I'd be interested in knowing what you do more specifically.

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Re: Order/Chaos Relativity and Complex Systems

Post by GeoComplex »

Hey Jacob, that's awesome! I am working on my master's thesis on the effect of mine excavations on groundwater levels... I use the theory of poroelasticity: the hydromechanical coupling between water and the rock. In the early history of groundwater science, most geologists completely ignored the fact the water and rock changed together when devising the well-known well hydraulic equations. The development of poroelasticity theory is what made me think of coupling between everything on Earth and maybe the whole universe, which lead to the post above on complexity. I wrote a whole essay earlier, but decided to delete it, it was very long winded. I guess it all boiled down to this question: is it possible that matter and dark matter and energy and dark energy are coupled together? And that the universe might be static? This cosmologist thinks the universe is increasing in mass and universe could be static: http://phys.org/news/2013-08-cosmologist-universe.html. The reason I ask is I think Howard Odum's ideas about embodied energy, self organization, and evolution at all scales might be correct at different scales of the universe.

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Re: Order/Chaos Relativity and Complex Systems

Post by GeoComplex »

Never mind about the questions, I am poring through a physics forum and realizing I am way off!

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Re: Order/Chaos Relativity and Complex Systems

Post by jacob »

This is what I mean about popsci books being dangerous to the mind :-D

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Re: Order/Chaos Relativity and Complex Systems

Post by GeoComplex »

:lol: , yeah, I've definitely learned my lesson. I am going to try and steer clear of those now. I guess the only physics I truly understand is rock/fluid mechanics (stress, strain, hydraulics, earthquakes, etc), and the basics from physics 101. Everything else is pretty confusing to me. I would like to learn a lot more about thermodynamics after I finish my thesis, though.

Dragline, thanks for the link to the info on mental models, I will check that out.

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