Post on 28-Dec-2015
Spring School in Complexity Science
Introduction toComplexity Science
Complexity: Scale and Connectivity
Seth Bullock, 2006
Conceptual Landscape
In this lecture we will explore two things:
some of the conceptual diversity running through the complexity literature
some key issues for understanding how complexity can be applied across domains
Seth Bullock, 2006
Defining Complexity
It is widely acknowledged that "complexity" is:poorly definedmultiply definedCan mean:challenginginterestingcomplicatedor just large
Seth Bullock, 2006
Definitions
A plethora of attempted definitions (36+!).
Approaches to defining complexity: computational vs. statistical structural vs. functional sequential, hierarchical, etc.
Particular definitions include: algorithmic c. Kolomogorov c. minimum description length effective measure c., effective c., physical
c.
Seth Bullock, 2006
Motivations
Each definition attempts to formalise an intuition.Systems can be placed on a continuum:
Both regular and random systems are simple - their aggregate behaviour is straightforward to explain (e.g., pendulum, ideal gas)
Complex systems are more difficult to understand due to the “entwined” nature of their parts.Standard “divide-and-conquer” approaches to explanation are limited, here.
Com
ple
xit
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Regularity
Seth Bullock, 2006
Beyond Intuition
Much hinges on unpacking what we mean by intuitive terms: “straightforward” or “difficult”.
If we cannot formalise them, then to claim that one system is more complex than another is just to claim that we currently find it harder to understand.
Seth Bullock, 2006
Problems
Some of the formalisms have obvious problems:Kolomogorov complexity measures predictability in a system. Homogeneous Systems → Low KC Regular, Periodic Systems → Higher KC Complex, Chaotic Systems → Even Higher
KC Totally Random Systems → Highest KC
It is the intermediate systems that we want to single out.
Seth Bullock, 2006
Emergence
Low-level interactions bring about systemic organization in complex systems. How?
System-level behaviour “emerges” from the low-level interactions of individual system components in a non-trivial manner.But again, much hinges on what we mean by “non-trivial”.
Seth Bullock, 2006
Emergent = Mysterious?
Andy Clark points out that when a number of small children tip a see-saw, we gain little by tagging this as “emergent behaviour”.
But reserving “emergent” for systems that are currently unexplained (or perhaps inherently inexplicable)…
“robs the notion of immediate scientific interest”
Seth Bullock, 2006
Four Kinds of Emergence
Clark again:1.collective self-organization2.un-programmed functionality3.interactive complexity4.incompressible unfoldingNo time to deal with all four.
Each drives at an account of the opacity in the relationship between a system’s levels of description that is not subjective.
Seth Bullock, 2006
Non-linearity
Simplifying:To the extent that a system’s interactions are non-linear, an account of their impact on global behaviour will be increasingly involved.
For “non-linear” read: multiple, ecologically embedded non-additive, inseparable, heterogeneous interactive, asynchronous, lagged, or
delayed.
Seth Bullock, 2006
Naturalising Emergence
A continuum: non-linearity in a system’s interactions corresponds with a notion of complexity and emergence.
Between simple (weight) and irreducibly complex (protein folding) sit moderately complex systems with challenging but tractable.
Seth Bullock, 2006
Issues
These ideas are not new. People have been fretting about these questions for a long time.Given this, can we expect significant progress any time soon?First, let's look at some stumbling blocks that have prevented complexity ideas from entering the mainstream of science and particularly engineering...
Seth Bullock, 2006
Plurality
Lack of consensus on defining complexity is sometimes taken to reflect poorly on the field. diverse communities → multiple definitionsA single tightly-defined concept may be impossible/undesirable.We might expect a cluster of ideas to share a common centre of gravity.Increased interdisciplinarity could accelerate this? Some evidence that this is happening already.
Seth Bullock, 2006
Subjectivity
“behaviour is emergent if it surprises us ”“a system is complex when we find it hard to understand”
Limits scientific utility.
Non-linearity is not subjective. Can it be made core to notions of complexity and emergence?N.b. Complex systems may of course remain counter-intuitive even when we have a full theory in place.
Seth Bullock, 2006
Complicated vs. Complex
“Well, you are talking about complexity, but a car is not complex it's just complicated.”Complicated systems: difficult, but succumb to divide-and-conquer approaches. a car’s turning circle
Complex systems are different: Hofstadter’s “thrashing” e.g.
“Why can't you just open up the computer, find the number ‘35’ and change it to ‘50’?”Complicated is easier to cope with than complex?
Seth Bullock, 2006
Complications
But complicated systems are often complex:
Cars do exhibit “unwanted functionality”. Software does suffer from “emergent” bugs
And complex systems do exhibit complicatedness:
the body’s many modular sub-systemsIf this were not so (i) engineering would be much easier, (ii) science would be much much harder.
complexity arises from complication complication evolves in complex systems
The distinction is not clear-cut.
Seth Bullock, 2006
PredictabilityComplexity = Unpredictability = Untrustworthy?
← Simple Gas Complex Pigs →
Low-level behaviour is unpredictable (gas molecules bouncing around, pigs pigging about).Yet, some high-level behaviours are predictable.
E.g., Stock control must be reliable, therefore we cannot use a complex systems approach, and must eradicate complexity from our systems!
Seth Bullock, 2006
Explicability not Predictability
It is relatively easy to explain how more gas increases temperature (ideal gas law) but not easy to explain how more pigs brings about an abrupt phase transition in pig violence. For simple (linear) systems:
a small change to a system’s components → a small change at the system level
For complex (non-linear) systems:a small change to a system’s
components → large/small/no change at the system level
Seth Bullock, 2006
Example
The periodic table organises and labels these transitions. But it does not explain them.Complexity science is in the process of building it's own periodic table, but we are not there yet.
If we add a proton to each atom of a bar of gold, radical but predictable change occurs.