¸¸¸.·´ ¯ `·.¸¸¸ A Bump on a Curve Notepad, a Users Guide

 Methods for closely observing the Transformative Chapters in the great narrative of life

exploding increase

exploding decrease

tapering increase

tapering decrease

When you see one of these dynamic shapes of changing scale over time, (nature's main shapes of irreversible change), you know the changing scale is being caused by some system in the process of changing organization, and that organized process of changing organization...  is where to look for more and more of the whole story.
 

Beginning Research Projects:        1) First Attempt         2) At the Office

Advanced Design Projects:    1) Development Impacts    2) Creative Bureaucracy   3) Reducing Poverty

There's a somewhat popular design idea called 'biomimicry'.  
This  'notepad'  offers a way to understand how natural systems develop and take care of themselves in nature, using a learning method that mimics nature's own way of developing systems of relationships.     It's a method of using a simple general model and let it grow in design and detail from your observations of the eventful systems that are part of your experience.    It produces a kind of behavioral "map" used like a navigator would, for referring back to the eventful systems that were the "territory" your information to build the map came from.   It's a learning and observation tool.    It's mainly for teaching one's thoughts to mimic the evolutionary changes of nature, to understand world of complex systems in which we are immersed.

What's there to look for?  - useful first principles of system change

Make believe that you are in a vehicle, born there, and didn’t realize it needed to be steered or could be, and you find yourself part of the first generation of humans to realize that. With there being no established method for doing it, no one else can tell you how. What would you do?

The first thing is to familiarize yourself with all the parts you had just taken for granted before, like all the amazingly common complex things that take care of themselves and never needed tending before. We need to look at them with fresh eyes, as if we were new born and dropped unexpectedly into a new environment. As you survey the parts of nature that naturally take care of themselves, the climates large and small, biological cells and conversation networks, the organisms and species, the natural and human economies, you find some curious common features.

One is that all kinds of self-managing systems, animate and inanimate, use energy somewhat like economies do, collecting, transforming and distributing resources and energy using a complex multi-stage process. They’re a family of individual organizations.

You also find that things that take care of themselves have individual life cycles, and that those life cycles all begin and end with developmental processes, for creating and completing themselves. They don’t always determine their own limits or their own outcomes, but they always determine their own paths of development within their limits, and so develop unique features. Developmental processes work by building on themselves, accumulative change in which all parts of the developing process are changing at once. It operates without central or external control, like fire, climate, technology or politics.

A different kind of science is needed to understand them, because one thing they generally don’t have is any consistent categories for comparing the things that are unique about them. We just can’t compare our economy’s experience today to that of any other ever before.

The most useful “first principles” of system change start with recognizing how periods of “self-organizing development” generally start. It is with combining some kind of seed pattern and seed source of energy. That seed pattern become’s the nascent system’s “killer app”, how it uses it’s “fossil fuel” seed of energy to start multiplying. The combination sets off the “runaway process” of multiplying “auto-catalytic” change, leading to a point where the change process changes.

That event at the end of growth may be dramatic as when a mammal ends it’s explosive growth in the womb and is born. For convection systems, like for the column of warm air in a cumulus cloud, the end of it’s acceleration is at the top of the column when it becomes turbulent and billows out at the top of the cloud. There are lots of other individually different ways for runaway development processes to end in transforming the system that started with them. That one-two punch, growth and change, produces a “punctuated equilibrium” of change in form brought about by a regular developmental process.

The strangest of all things about growth processes may be that they work at all. They grow by inventing increasingly complex designs without a plan, without experimentation or trial and error. Isn’t that an amazing trick?! Somehow uncontrolled processes can achieve things that controlled ones never could. They don’t have any way of having foresight, but in many ways act as if they did. Like the explosions of creativity that come with emerging technologies, growth systems are magnets for new things to fit, exposing threads of opportunity in their environments that are often previously unobservable and inconceivable.

From a deterministic view, contagions of creative design like that can only be predicted by making up rules in hindsight, and are generally too complex to individually describe. The real secret to how they work is by linking complementary opposites, like readers and books, wheels and axels, meat and fire, organisms and niche’s, investment and profit, with the resulting contagion propagating to the exhaustion of its environment’s potential for synergy from those complementary links.

People never really needed to explain how growth systems worked before, only to have some notion whether they would or not. When they “worked” they often worked like crazy, sometimes too crazy, with little way to tell the difference. No science ever saw a way to understand them as emergent creative processes with surprising ends before, either. Now we need to, and find the “first principles” that have eluded us so far. The growth system for our civilization has already progressed well into its change of form at the end of its growth, and is visibly causing massive disruption in critical things that once took care of themselves.

So our growth system, anyway, is clearly NOT taking care of ITS self. As a culture we don’t appear to know the first thing about it though. What is actually happening to us is that we are being caught off guard by this change of form of our growth system beginning without our noticing. Our whole society, its languages and laws, rules and institutions, expectations and value systems, developed and solidified a couple centuries ago with the modern age. All that developed around a culture and model of continual runaway growth. That worked fairly well for most of that time, as if it could continue forever.

In the early period of economic growth each path of opportunity exposed even greater ones, up until about 1950. At that time the pattern of ever multiplying opportunity started to smoothly switch to one of multiplying difficulties. That we still haven’t noticed is the greatest and most dangerous problem facing us. As the natural response to our increasing investment in growth reversed, we kept applying the strategy that gave us ever greater freedom before. It has produced mounting costs, complications and conflicts instead.

The longer we wait now, the more unaffordable it will become to respond to them later. As we wake up to this it may indeed seem like being a newborn dropped into an alien environment. It is indeed a situation that very different from what our culture taught us to expect.

So as you explore and organize your maps of what to look for in this new territory of ours, it’s maintaining the open questions you find and keeping yourself from really closing them, that will save you from the most dangerous pitfall of common reasoning. It’s better to have questions become richer questions, giving you a choice today and a deeper awareness of relationships for tomorrow. Without open questions it’s easy to let the subject turn to one’s own internal self-constructed world view, disconnected from what other people are referring to, leaving us to mostly just talk to ourselves.

What can connect us in the end is only the individual systems of the external world that constitute our common physical reality and of which we all naturally remain largely ignorant.

Short Entries  #a ,  #b,  #c,  #d,  #e,  the model

a) Natural Systems - Where Are They?

Well, in case the page title isn't a clue,... natural systems are *in* every 'bump on a curve', in the process of what's happening.  They're in all the many kinds of 'phenomena' that come and go development, like the lives of people, or storms or cultural or economic changes.    The work is locate their boundaries and explore them as their own little universe of self-related processes,  as a new kind of window on the eventfulness of change around you.   The main distinction is just becoming better able to tell what changes are beginning and what are ending, learning to notice what's going on around you, noticing little details that you could use to change the whole process of events.   It's not just discovering fascinating new layers of magic in nature, but also learning the moves and becoming a better dance partner with the many other living partners you share your environment with.   Part of what you find is that local creative processes are part of every cause.   The "deterministic" rules of cause and effect do help when working with, things that seem highly predictable.   They are the other kind of "notepad" for what's happening.   The two kinds can work together.    You find that 'necessity' often isn't enough, because necessity always takes possibility too.  

Why then don't we see them?

3/18/09 Well, I've been wondering for a long time why the flows of change are so hard for people to see, and do think there's some kind of "fixed world illusion" to contend with.   There's a list of reasons why we don't update our information regularly and so miss the flows of change because of that.    It's a little speculative, but another detail caught my attention recently, that even when repeated changes in "normal" are quite dramatic, people often only have to "sleep on it" to readjust and see even very short lived situations as if they were permanent and a brand new permanent "normal".  

Nearly every pundit and media source from 2007 to the present has radically changed their stories about the economic collapse nearly every week... for example, always seeming very comfortable with the "ever present" finality of their quickly changing stories.    It's like there's a "reset button" that they all keep using, that hides the facts of accelerating change.

I've been wondering about what that has to do with sleep.   Could it be that the way the mind digests information collected during a waking day is similar to how your computer loads new software updates when you shut it down to reboot?  Could both need to operate with a fixed system that is regularly updated when turned off?   Sleep might clear the memory and refresh the world image.   Perhaps relieving the conscious mind of continual complex rethinking accounts for our not noticing how our own world is changing.   That would be a very efficient design concept, having brain's that refresh their model of life every night and give you an fresh but changeless new "snapshot" copy every day, an ever changing "blank page".   If you live in a stable world it's only a minor defect that the strategy would arrange our awareness as always of a fixed world, moving you through life one fixed frame at a time, that you would not need to consciously account for.   That sort of defines the "fixed world illusion", as well as the common experience of life in a changing world as an "ever present".    So as I said,... it's speculative, but something like that does seem to make it hard to see the dramatic flows of complex change occurring in our life circumstances, which are quite clearly visible in the data but not perception.   Change has been measurably multiplying in speed and complexity, quite dramatically for decades, and not appearing to change our daily life experience of time at all.  

Somehow our minds seem to erase the increments of change, and their accumulating effects, so we miss how changes of scale in environmental relationships precipitate changes in kind.    If that integration is what is normally done for us while we are unconscious in sleep, and sleep is then when we are conscious of change and its reprogramming of the world, what is needed to become more aware is something like a way of "sleeping on the evidence" while awake, watching change without fixing it as a permanent state, a kind of "walking meditation" to let the questions develop without loosing them in answers.

b) Learning to point

The alive and kicking system individuals that people can learn to 'point' to as sharing our common environment are the circles of relationships that display themselves by acting together.   They're the actively changing networks of relationships that have always been the main subject of human interest, but we have needed to make up our own separate stories about.    Our stories of change tend to be accurate descriptions, but elements of the stories have not worked well for understanding cause and effect.    Systems have distributed processes and individually learning parts, so wherever you look most of the action is somewhere else, every 'cause' leads to multiple effects and the effects change each time.  Looking for linear sequences of causes mostly just leads in a wandering tangle of circles, until you notice that the circles, as wholes, have progressive increments of change.   Then, looking for the circle in which the increments develop may begin to offer something much more concrete and useful for watching progressions of change in and environmental relationships for.  Remember, it's not your own meanings for the parts of a system that it is aware of, and that the things of nature themselves operate as they do with none of our meanings at all.  It's their languages you're looking for a hint about, a chance to step into another organism's way of relating to its universe.  It's actually hard to separate the things we see from the meanings we give them.   You can keep track of the difference a little by noting that the physical things themselves generally have more discoverable features than we can make meanings for.

When two people learn to 'point' to independent natural systems, they no longer need to agree on how they're defined because physical things define themselves, so people have a chance of referring to and talking about the exact same thing!    (well hopefully)    It may not simplify communication until you develop a little skill, but at least attempting to point to different features of the same physical things represents a major advance in dealing with a real world.    Much of the time in conversation people are all talking about their own self-made world of cultural values, and often unaware that that is what others are doing as well.   Trying to refer to changing networks of relationships as real things, that share the common wilderness of the physical world with us, has the benefit of letting us then explore the same common subject with each other's views in mind.   Otherwise the tendency is for everyone to pass judgment without quite understanding what each other person is referring to!

c) The main distinction

The main distinction is between variation in degree that is 'elastic' and 'regular' 'fluctuation', and the kind that represents things that permanently come and go, 'independent events'.   We're not talking about the information that something has happened, but the natural physical process.  Information does not have these shapes, only natural process.   'Regular fluctuations'  directly reflect their own past and continually repeat by rippling out over and over in their futures and may have no clear boundary in time or space.

Independent events are localized and their processes come and go.  Their changes in degree represent a sequence of permanent developmental changes.    They're actually two aspects of all natural systems, like different views of the same thing.   If you see one gain a lot of insight by finding the perspective that lets you see its 'other half'.   Everything that happens has both aspects of change, repeating cycles and permanent developments.   

This story is about looking at both together as part of a continual process of change, understanding how cycles come and go, and how things that come and go are built from cycles.   All living things, and lots more, make their first appearance with compound growth from almost nothing, then mature, have a bit of sustained freedom for a while and then decline and vanish.   Animals display the continual swings that take them along  the 'wheel of change' in having a continual heart beat and constant breathing, for example.  In following these 'wheels of change' you can discover how the wheel itself permanently comes and goes, that rhythms are found within whole events.   To understand either one needs to understand both.   Though we sort of know the trick to it, it stills fools us all the time.  These connections are mostly invisible to us for a special reason.   They're inside, inside the things that we observe from the outside.   That gives much of nature an organizational appearance like that of Swiss cheese, i.e. full of holes, with all the real happening somehow going on where we see nothing at all.   This is about digging in the holes and finding lots and lots of cool stuff.

One of the little things that helps shed light on what's inside nature's 'dark holes' is finding that cycles are not circles, but have accumulative effects that change the cycle itself on each turn.   It's a matter of nature doing "almost the same thing", over and over, but we tend to fudge the small accumulating differences as making a circle.   It's a large error.   The little proportional changes we commonly overlook do actually 'exponentially' change relationships within the cycle and with its world.   When we let our minds take the little shortcut of considering cycles as "exactly the same thing" it's taking a kind of wishful thinking shortcut.    We'd like to imagine the designs of nature as 'fixed',  but that also hides a great deal of natures true design.

d) A Calculus for the very young in heart

I mean 'young in heart' here as being fascinated by and delighted with just the accelerations of the world around around you, in the way kids in their peak learning years from 6 to 12 are delighted with discovering physical accelerations in particular.   Learning to ride a bike or swing high on a swing is HUGE entertainment for them.   It also marks a period of time when the anticipation of something about to go Zoom! is perhaps even more fun that the event itself.    When little hints for something about to happen are skillfully used by a teacher, or a puppeteer, or even a friend teasing you playfully with their confidences, affections or even worms.   Anticipations alone can cause explosions of anxiety, delight.   With ghost stories the thrilling anticipation of something about to happen is a manipulation of real fear, permitted as an experiment in a secure setting,   Physiologically it's all about learning the tiny cues available to be read in the shapes of change, the basic subject of calculus.   When it's done right the foreshadowing of events is perceived in the tiny signals of approaching dramatic change, messages about the acceleration of accelerations of accelerations, 'gotcha'.     If you tell the story, or hint at the prize in a lifeless manner, allowing the signals to be obvious, or disconnected, leaving out the strategic silences when the audience anticipation would grow, well, all that's produced is a big disappointment even if the ghost or tickle that finally appears is just the same.

Dramatic events ARE dramatic not only because they 'blow up' but more because you're aware of their 'sneaking up' first.  In navigating the real world as adults we use this kind of learning from childhood games for reading 'the score' all manner of grown up games in very complex ways sometimes.   This is about taking that same set of basic interests and skills, and using them to help read a new level of organization in the ordinary events of the world around us.    The normal course of natural system events initially follows a course of accelerating acceleration, that starts very innocently, perhaps providing ample time to respond, but then smoothly develops to 'jumping' out at you as a big surprise, even if you were in on the secret all along.  What you're reading during the anticipation period is the beginning story of all stories, that gentle quickening in the rhythm of small things that signals great change.    What you're reading with your gut level feelings of anxiety and excitement are it's 'derivatives' the deep levels of ultimate explosiveness in smooth processes of progressive change.   The thing that scientists have yet to quite recognize, and most people at least understand intuitively, is that patterns of acceleration in events tell you a great deal about what they are about and where they're headed.   The idea here is to recognize these patterns more consciously, with experience to better understand the real difference between the signs of beginning and ending, of stability or instability, of whether things are cyclic, or  happening near bye, sensed only from echoes, the trends indicate reversible and irreversible change.    Those are important things to know!

But,... if it so happens that you don't really feel anticipation on a gut level, and aren't really interested in what details of events legitimate those feelings, well then, maybe you just won't find natural systems as easy to start learning that way.   Maybe your way would be to start from the logic of how near-living things evidently have to work, and as you pattern recognition develops work backward to enlarging your intuitive and emotional experience of them.   Wherever you start there are lots of avenues to explore.   It inevitably gets personal, though, because by 'natural systems' we're also talking about, are more or less, whatever it is that gives that magic combination of continuity and animation to our lives.  

One scientific detail needs to be mentioned.   In order to consider the shapes of change you need a consistent way to 'value' or 'measure' their changes.  If your own way of valuing things is moving around, the changes you see are not of the thing you're valuing.   How to make consistent value judgments or measures is an art in itself, so just take it for granted at first.   What you're looking for in the language of accelerations is when things pick up or ease off in their successive changes and what those things are connected to.  When events are 'picking up' in a way that is itself picking up, what you're recognizing are different levels of intensity within that process of change, that's reading the derivatives.   We have names for the easy ones, the zero derivative 'size', the first derivative 'speed', and the second derivative 'acceleration'.    The 'higher derivatives', beginning with the rate of increase of acceleration, are what I referred to as the 'intensity' of acceleration.   Because accurately reading the direction of events is a very legitimate survival skill, in which we've been trained for millions of years actually, you may find that learning about this 'very complicated stuff' is really not very complicated at all sometimes.

I think most natural gut feelings or physiological reactions to acceleration are directly reading at least the 3rd, 4th or higher derivatives, ones that our conscious minds have real difficulty picking out.    So the idea here is that you'll be able to help inform your conscious mind about what these things mean in the world around you by becoming more consciously aware of your your easy and natural gut feelings for them.    When looking at graphs, like those below, you can use the gaps between your fingers as a kind of shutter to move over the curve, and think about the 'roller coaster' feelings stimulated by watching the bits of the curve in the gaps between your fingers.    The following paragraphs describe some technical aspects of each of the classic irreversible chapters in the whole individual story of natural system events, the classic beginning middle and end progressions.  Reading these cartoons says relatively little but what you're looking for in real individual events, and the more interesting shapes they'll have and from which one can read a great deal more information about them than you might guess.  Here's a popup of the diagrams for reference: if you'd like.   Oh,... I almost forgot, the trick.   The trick is to read *through* the curves of real events to understand the real behavioral loops of the natural process behind them.   Looking *at* the curves of events will show you little or nothing at all until you are asking specialized questions about mathematical and statistical properties of the data points.   To learn to read change in the world, you look through the changing shapes of its curves and interior connectedness of the evolving networks they represent the continuous behavior of (1).

"Chapters" of a whole event (Full version)

1.Building up (i, 2. Building down, 3. Maintaining, 4. Breaking up, 5. Breaking down

 Chapter I. |  by +, +, +, +,...etc.
Building Up - Interior networks elaborate,
Uniform distribution of connectedness
Expansion free of limits
Increasing Faster and Faster - Speed, 1st and higher accelerations, positive
Growth or Emergence - persistent positive feedback, what's behind it is:
Irreversible process of elaborating a starting interior design, expanding explosively without any hint of its limits.

Chapter II. | by +, -, -, -, -,... etc. 
Building Down - Interior networks  refine (or destabilize)
Inverse sq. distribution of connectedness
Expansion responding to limits
Increasing Slower and Slower - Speed positive, 1st and higher accelerations negative
Climax or Stabilization or Integration or Becoming - persistent negative feedback, what's behind it is:
An irreversible process of refining, stabilizing and adapting to fit surrounding networks, (or alternately, destabilizing in turbulence).  The end of growth and the beginning of climax for living things generally occurs at their time of birth, when a seed ends its first sprout, what would normally be considered the beginning of their lives.

Chapter III. by +, -, +, -, +,... etc, & opposite 
Maintaining - Adaptation, maintenance, 'homeostasis'
Connections into other networks expand
Integrating with environments
Stable and Fluctuating - Speed, 1st and higher accelerations alternating signs
Homeostasis or Stability or Maturity - alternating positive and negative feedback, what's behind it is:
Sustainable relationships in which divergences tend to be corrected, cybernetic control, self correction

Chapter IV. | by -, +, +, +, +,... etc.
Breaking up - Network disintegrates
Unknown statistical features...
Internal & external connections break
Decreasing Faster and Faster - Speed negative, 1st and higher accelerations positive
Faltering or Collapse or Failure - persistent positive feedback, what's behind it is:
The increasingly rapid disintegration of the system of self-correcting systems.

Chapter V. | by -, -, -, -, -, ... etc.
Breaking down  - Network decays
Unknown statistical features
By-products retain some evolved links, 'compost'
Decreasing Slower and Slower - Speed, 1st and higher accelerations negative
Fading or Decay- persistent negative feedback, what's behind it is:
The lingering of separately sustainable parts, having lost the overall organizing principle of the whole

f) Why they've been mostly invisible to us

natural systems....the forms under the sheets

It used to be that science thought nature followed formulas, and now it seems we're making progress in understanding the actual physical processes.   Broad classes of events can be usefully represented with statistical models, but on examination, individual events all occur by individual evolutionary processes.   The discussion of how they work is called either 'systems theory', 'complexity', or just 'physical process'.  They seem to be what animate all events and their dominant characteristic is of many layers of fairly disorganized organization, thus the term 'complexity'.   I refer to the reliable principles that can be deduced, and the rigorous methodologies for exploring and displaying them as the 'physics of happening'.   The big jump is to understand that any representation of events are going to be lacking, and that any valid way to describe them has to include referring to the things themselves directly.   That uses an approximate explanation to help direct attention away from explanations, toward the real things we're trying to explain.   For the sciences that switch is very new and uncomfortable.   This short conversational discussion is both a 'notepad' itself, and design for how anyone can construct their own 'notepad' for recording complex system observations, thinking first about it as a 'mental notepad'.

The type of physical event of most interest here is things that begin and end, and have some period of stability in-between.   That's a highly selective filter that helps identify physical things that exist as individuals and develop and animate original networks of relationships.   There are also lots of other kinds of physical processes, that don't exist as individuals.   Frequently they're just echoes of other distant or past events, most simply categorized as 'pressure flows' or 'waves', that fit the 'chain of events' model of causation.   Lots of these are what science has been most successful in describing with formulas.   That's not the subject here though.     Complex natural systems are neither 'top-down' nor 'bottom up' kinds of organization, but have organizational development and resilience 'through and through', and how extremely common they are in ordinary events. 

What makes complex self-organizing events possible to find, and provides links to exploring how they work, is that they all follow the same evolutionary sequence of changes over time ¸¸¸¸.·´ ¯ `·.¸¸¸¸.   This 'defines' what a system is by pointing to them, not as a set of connections to other words.   One of the things that makes them difficult to discuss, requiring some groping around, is that natural systems are sort of a new discovery that's complicated and unfamiliar.  Our language just don't have shared words for many parts of it.    Building new words for things that have always been around but we never really thought about before is a big part of the task.   What you'll find is that we live in a world chock full of complex systems, and because they've been around as long as we have that a lot of our traditional thinking, issues, story lines, jokes, values, etc. reflect a sound awareness of natural complex systems.   In many cases our natural language displays a very sophisticated but unintentional 'complex systems thinking'.  Natural language (as opposed to formal definitions) will be found highly useful as you begin to put things into place.   There are many ways to enter into the subject, but the most available, rigorous and reliable is that complex systems come from growth, and that growth, curiously, is an exceedingly intricate process of accumulating organizational development without any apparent cause.  It develops on its own, every instance as a separate and independent event!

The 'mistake' science has been making is describing all natural behavior as following 'rules'.  People follow and find rules useful, not nature which entirely uses complex physical processes.  Taking the 'rule idea' too far efficiently hides from view all the things of nature that are continually changing their rules and definable only by pointing.   That turns out to be most things that directly matter to people, and why for most people it seems that science is irrelevant.    Recognizing that any 'bump on a curve' (1) generally identifies and links observation to evolutionary systems in operation, provides a method of pointing to the individual animating parts of our world that matter.   A first example is a trace of the word use of 'sustainability' in the NY Times over the past 10 years.  In this record you see something beginning, and you can see the complexity of what's going on inside.  That's where you start.   Of course, you have to watch out that one 'bump on a curve' doesn't really represent an overlay of many unrelated things, or maybe just a fluctuation in a process with no evidence of beginning or end, and follow other basic rules of observation.  It's very hard to see the beginning and end of a ripple in a pond, for example.   Science has used ripples as a teaching example of  natural systems in steady state.  What systems thinking is more helpful for are the things traditional science has had trouble with, things that are are changing and not in steady state, and the things things science has been most successful with tend to be the hardest to use for studying evolving processes.     Yes, these cautions do rule out considering a great many kinds of 'bumps on a curve', but just from your beginning learning process, not from the whole picture.  

Start with singular events in something you're immersed in, know well and care about:  the steps of beginning and ending a community activity or plan, preparations that swell climax and fade away like for the 'big game' at your school, or your family or community celebration of the holidays, a fad at the office or among your gang of friends, the experience of finding new loves either a lover or a life's work, the sadness and personal growth of break-ups and disappointments.   These all follow nature's design process, starting from some seed, developing a wider and wider involvement of things and then typically stabilizing and refining a new domain of relationships which has some duration of stability before coming apart in some way, dieing down and fading away.    To follow them you try to define some consistent quality or measure and trace how that quality or measure changes, noting when the trend displays flowing shapes in time and when those shapes change direction.  

The magic of the holidays is maybe the best sort of thing to watch.   We know it's going to happen, but we just can't make it happen without going through the whole process, and it always seems to involve the inclusion of strangers and unexpected absences, the whole range of life's issues in a sprawling design process involving many players where you know what's going to happen, and that it'll come to a head, but is hard to feel for real until it does.  The curves of excitement or expectation you sketch do not describe what is producing those measures.   What they do is help point to what is doing it out in the world, and to when and how those connections branch out and return through a network.   What you tend to find are patterns of broken connections that are more 'discovered' than 'compelled', an opportunistic world of distributed and 'decentralized' physical events involving wide varieties of informal hierarchies of unnamed and unnamable things.   It helps expose a common mystery, providing some keys for making a puzzle of the parts you care to explore.  Then having developed basic skills you can read the growth and climax of other things.   You might not expect to learn about the great events of history, say the 600 year exploding growth of modern man, or the mysterious appearance of terrorism, from watching small scale growth and evolution events in personal experience, but they're they all have major similar in their fundamental evolutionary processes.

In the NY Times yesterday (3/3/07) Krugman mentioned that: "The truth is that efforts to pin the stock decline on any particular piece of news are a waste of time".  Of course, he's referring to the huge amount of time professionals have been spending doing just that!   This seems to me to be another of the good ways to begin to notice where natural systems are involved in our lives, when you notice people offering complete nonsense to explain what's happening, but it largely remains uncontested.     Take politics for example...  Oh well, I'll resist the temptation to rant, but really, when people claim all sorts of ridiculous theories of cause and effect that no one else seems able to contest, it's a sign of something bigger going on that all are at a loss to comprehend, and where someone may be abusing the opportunity to deceive us.   If you switch from asking whether you agree or not, to a learning mode of thinking, improbable explanations offer a good sign of where progressing loops of natural systems may be active, and a good reason to widen the scope of your questioning.

The formal approach starts with learning to recognize growth and decay curves in some measure of events.  Why growth and decay?  Because that's what things begin and end with.   What it tells you, say the growth of the insurgency in Iraq, or unexpected progressive change in one's own personal relationships, or in the physical properties of the material you're working on your work bench, is that there's something happening 'on its own'.   That autonomous 'happening' is invariably a self-connecting loop of relationships that is multiplying, essentially a living thing with an interior world of its own.   I remember watching the multiplication of the Iraqi insurgency, and feeling very helpless in being unable to point out what was happening, in the face of the incomprehensible theories of causation that were being bandied about and supported almost entirely by misplaced fear.   The insurgency was the tiniest thing at first, evidenced by independent local 'defenders' irrationally walking out in the open and taking pot shots at the huge columns of the US army streaming bye.   Our soldiers shot them down and laughed, but these insignificant irritations slowly but methodically multiplied.  That pattern tagged it as a cultural event, misguided if you like, but of a widely distributed organic self-defense response to an alien presence.   That the insurgency grew to the point where it was then taken over by various gangs of manipulators with nefarious intent hides the fact that those gangs didn't produce the groundswell of rejection in the first place, we did.    To me, the initial evidence of growth in the insurgency was the sign we should immediately surrender, ask to speak to their leaders, and tell these indigenous defenders that they were the very people we came to liberate... but no, we carried through with trying to impose our own organization plan on a different kind of society, treating anyone who objected as the enemy.   Now the killing in defense of sacred  honor on all sides is in an endless rut and an almost unsurpassable example of a complex systems disaster of huge proportions.   There are others brewing too.

The specific method for first identifying where complex systems are located and then how they work starts with learning when you can treat a series of dots as a curve [¸¸¸¸.·´ ¯ `·.¸¸¸¸], and then where that curve changes direction.  In the first phase of complex system evolution there is explosive growth, and the issues relate more to elaborating the original 'idea' and 'connection' that the expanding new loop of relationships represents.   In the second phase the progression of change reverses, turning its responses and 'attention' to the future, making successively smaller steps toward completing its form and fitting in with it's world.  The tough insight to develop is that the switch from start-up elaboration to stabilization and refinement can be either internal or external to the system, either the system's own internal 'choice' or an imposition.    Our traditional language is really not quite equipped to deal with this, the idea that anything in the world but humans makes choices, but the evidence is really there when you begin to look.    You can say it's because of evolution rejecting all other forms of life, perhaps, but all living things turn off their own explosive growth from the inside, long before they exhaust their resources or their multiplying burdens induce the collapse of their own structures or environments.   Seeds stop exponential growth when they have their first two leaves, an embryo gives up its explosive development at or near birth.   All living things switch off their exponential growth at the beginning of their lives.    Living things don't stop growing because their skin gets too tight and their organs strangle.   That's the kind of thing you'd see if growth was always limited by pressing its physical limits, always 'maximized'.   Living things don't actually maximize their growth relative to their external limits.  They're 'smarter' than that.   The fact is that how growth is maximized in living systems is with respect to a comfortable freedom from external limits, giving them resilience, independence and stability.   What signals living growth systems to climax when they still have freedom to develop is another question, but how we'll find them is by tracing the links from the places and moments in time where we see it happening, the inflection points in their growth.    The inflection points, like the origins and ends of growth, are times when nothing at all seems to be changing, except the entire way the system is changing.   The major causes of change in complex systems are always quite invisible.

The best way to begin thinking about what sort of thing the autonomous choices of complex systems might be is to reflect on the spontaneous choices of the same type that we make every day.    In lots of ways we work to get things to build and multiply, then pick a time called 'enough' to switch and get them to stabilize and refine.   Then we support them until it's time to let them fall apart again, scattering their parts into the same kind of mysterious soil from which they first came.   Systems design is just farming, with a little extra creativity.    The key observation, though, is 'enough'.   It's a recognition that successful growth itself is a multiplication of instabilities and inherently requires that those instabilities be brought back into balance or to go out of control.   Nature's secret of creativity is also dangerous. 

A struggle to get things going, and then picking a point called 'enough' certainly describes both my easy and difficult struggles to get out of bed every morning.   It's that kick-start routine, most often beginning with a denial of wakefulness and then staggering around till I've had a cup of coffee and, after a moment's pause, am ready to engage with the world again, having aimed at the particular level of intensity needed for the day I envision ahead.    Another every-day example is in throwing a party. Once people have arrived, some time is spent pumping it up to make it fun, with say, a little provocative behavior and alcohol.   The purpose is creating an elevated sustainable state of enjoyment.   It's not for multiplying the excitement of risky behavior to the point of humiliating or injuring people, destroying the fun and the reputations of everyone involved.  Those are different choice points on the exact same path, separated by the marker called 'enough'.   People who can't have fun without ever more dangerous approaches to the edge of doing harm,... usually regret it.    In a family business the power to multiply profits by growing the business is usually taken to the point of comfortably serving their original market, letting them turn back to their original purposes, living a good life, helping their kids get started and paying for their retirement.   In all these common daily transformations there are recognizable creative flows and turning points at which there are changes in kind.

So, when you see multiplying trends it's a sign of multiplying things, developing on their own, creatively out of control.   Forget all the hooey that draws on your fear that someone else is magically powerful and 'controlling' events.  The eventfulness of nature comes from 'living' natural conspiracies.  They're mostly only dangerous where we ignore them.    Connecting the dots, yourself, is the critical step.  Though, as I said above, we actually know a lot more about this subject than we first think, it takes some baby steps first.   The first two steps, to then be repeated over and over as you slowly expand your technique, is first recognizing series of dots that represent flowing shapes of change, and then looking for the progressing loops of relationships that connect them.   Most things, say the approach of change in your personal or business life, are wonderfully productive to understand on a deeper level, but don't push to conclusions.   First be satisfied by expanding their mystery.    Noticing that a series of dots is a flow with signs of multiplying progression, perhaps bending toward  a crisis of change, means envisioning a complex systems as a curve [¸¸¸.·´¯ `·.¸¸¸] , and thinking about it's progressive physical loops connecting the dots perpendicular to the page.     That mental map of flows in time and loops in space is itself a notepad in that it gives you a map of future discoveries and a way to organize their relationships..