¸¸¸.·´ ¯ `·.¸¸¸ The Bump on a Curve, Notepad 

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 philosophy called 'biomimicry'.   This  'notepad'  offers a method anyone can learn for building original new understanding of the eventful systems of their own world, what's happening around them, built by and for teaching one's thoughts to mimic the evolutionary life-cycles of natural systems)

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

a) Natural Systems - Where Are They!

Well, in case the title isn't a clue,... natural systems are *in* every 'bump on a curve', all those pesky phenomena that come and go by a series of local developments, say,...like you and me.   That's where they are.  Now the work is to turn that into a new kind of window on the universe.   It's making it into a useful clue to what's going on around you, noticing little details you were not previously asking about, discovering the true magic of nature in every one of them.   What you find is that local creative processes are required for every cause, as well as for lots of things that are quite 'unnecessary'.   You find that 'necessity' isn't enough, because necessity takes creativity too.  

b) Learning to point

What you also find is that when two people learn to 'point' to independent natural systems, they no longer need to agree on how they're defined to talk about the same thing!!  It may not simplify human communication until we develop a little skill, but replacing human 'agreements & definitions' for things by learning to point to the things themselves, represents a major simplification for dealing with a real world.  Referring to real things, rather that guessing what other people mean by what they say,  has the benefit of letting us trust that everyone has a valid alternate point of view on them. 

 
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).

e) Chapter I. |  by +, +, +, +,...etc.
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. 
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 
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.
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.
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