Systems 1.0 What They Should Have Told You in Class
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Transcript of Systems 1.0 What They Should Have Told You in Class
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Systems 1.0
cochrane.org.uk
COCHRANE a s s o c i a t e s
ca-global.org
Peter Cochrane
Wednesday, 22 May 13
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Definitions
What do we mean
by a system ?
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“A group of interacting, interrelated,
or interdependent elements forming
a complex whole”
Not entirely satisfactory...
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A functionally related group of elements, especially:
- The human body regarded as a functional physiological unit
- An organism as a whole, especially with regard to its vital processes or functions
- A group of physiologically or anatomically complementary organs or parts
- A group of interacting mechanical or electrical components
- A network of structures and channels, as for communication, travel, or distribution
- A network of related computer software, hardware, and data transmission devices
An organized set of interrelated ideas or principles
- A social, economic, or political organisational form
- A naturally occurring group of objects or phenomena: the solar system.
- A set of objects or phenomena grouped together for classification or analysis
- A condition of harmonious, orderly interaction
- An organized and coordinated method; a procedure
Perhaps a bit more comprehensive...
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But what a lot of words,
disjointed concepts and
examples to remember...
...might we do better ?
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‘A system takes energy, matter,
information, and transforms its
nature’
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Ergo; Systems are ‘essentially entropic’
S = k log W
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Note that we do not fully understand...Energy and Matter
Time and Space
...they may all just shr ink down to space...
...they may just shrink down to space...
...but until we get a GUT this will remain uncertain...
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AXIOM...still not understood by many...
Taking an interest in every system known to mankind pays dividends in providing us with ins ights and cha l leng ing concepts and occasionally , really useful results...
..and we no longer design, deploy and operate our systems in isolation...we live in a world of natural and unnatural systems... evolved and designed...
...and the way they connect coexist and intereact is important especially when life dependency and mission critical issues are at stake !
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Some big differences between
Man and Mother Nature...
Only we designOnly we optimize We often appear use
vastly complex solutions to achieve incredibly simple outcomes...
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Whilst Mother Nature...
Only evolves systemsOnly goes for ‘good enough’ and optimizes nothing
She conceals her underlying complexity at every level of her constructs and activity...
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“Perfection is the enemy of
Good Enough”
Defining ‘good enough’ is not always trivial and is generally the biggest challenge !
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Some broad brush system generalitiesAnalogue dominant
Digital spreading fast
Hybrid Analogue//Digital ubiquitous
What we know advancing rapidly
Our understanding mathematically limited
Made by mankind we all die without them
Made by machine we all die without them
Our species survival depends upon good systems
Our planets survival depends upon good systems
Machine intelligence overtaking us in many areas
Symbiosis necessary man machine partnerships
Challenges formidable but interesting
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What’s in THE ENVIRONMENT?
s(t) h(t) o(t)
Other systems of the same or differing type may be sharing the same space or some part of it, and therefore there can be many obvious and hidden opportunities for aliasing....
AirWaterEarthMachinesLifeforms
FluidsSolidsChemicalsRadiationInformation
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What’s in THE BOX ?
s(t) h(t) o(t)
ChemicalPhysicalInformation/Data ProcessingMathematicalNaturalUnnatural
BiologicalElectricalElectronicMechanicalComputational+++
Optical AcousticOrganicInorganicLife forms+++
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What does the output do?
s(t) h(t) o(t)
In the general case it impacts/changes the environment and the input and is often a grossly non-linear series of loops
e(t)
f(t)
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What’s in THE BOX ?
s(t) h(t) o(t)
What can we describe and define
Optical Acoustic++++++Life forms
o(t) = h[s(t)] = h(s) for ease of notation
o = a + bt + ct2 + dt3 et4 + ft5 is the largest polynomial we can solve for very limited and narrow range of cases
In the absence of a closed form solution we often reduced to using polynomial or some other form of approximate descriptor
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But many of our systems are of a much higher order with hundreds of feedback and feedforward loops...
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They also have hundreds of diverse inputs and outputs and cannot be fully flood, or combinatorially tested...
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SizeScaleComplexityConnectivitySophisticationConnectivity
MTBFSpeedAgility
ReliabilityTestability
PredicabilityResponsivity
Common/General system traits
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SizeScaleComplexityConnectivitySophisticationConnectivity
MTBFSpeedAgility
ReliabilityTestability
PredicabilityResponsivity
Common/General system traits
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SizeScaleComplexityConnectivitySophisticationConnectivity
MTBFSpeedAgility
ReliabilityTestability
PredicabilityResponsivity
Common/General system traits
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SizeScaleComplexityConnectivitySophisticationConnectivity
MTBFSpeedAgility
ReliabilityTestability
PredicabilityResponsivity
Often difficult to define with any great precision
Common/General system traits
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SizeScaleComplexityConnectivitySophisticationConnectivity
MTBFSpeedAgility
ReliabilityTestability
PredicabilityResponsivity
Cost MTTR LatencyPower Heat Resources
Often difficult to define with any great precision
Common/General system traits
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Common/General system traits
s(t) h(t) o(t)
s1(t)s2(t)s3(t)
si(t)
o1(t)
ok(t)
o3(t)o2(t)
hi(t)
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Common/General system traits
s(t) h(t) o(t)
s1(t)s2(t)s3(t)
si(t)
o1(t)
ok(t)
o3(t)o2(t)
hi(t)
SimpleSingularLinear
ComplexMulti - I/OLinearNon-Linear
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All known, understood, well described and characterized, bounded, and well behaved with causality preserved
Contained/bounded in/by some known, or well defined, environment/conditions
Simple System - Key Features 1
s(t) h(t) o(t)
s(t) = Stimulus h(t) = Operator o(t) = Output }
s(t) and o(t) originate and terminate within the environment
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All known, understood, well described
and characterized, bounded, and well
behaved with causality preserved
Contained/bounded in/by some known, or well defined, environment/conditions
Complex System - Key Features I
s(t) = Stimulus h(t) = Operator o(t) = Output }
s(t) and o(t) originate and terminate within the environment
s1(t)s2(t)s3(t)
si(t)
o1(t)
ok(t)
o3(t)o2(t)
hi(t)
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All known, understood, well described
and characterized, bounded, and well
behaved with causality preserved
Contained/bounded in/by some known, or well defined, environment/conditions
Complex System - Key Features I
s(t) = Stimulus h(t) = Operator o(t) = Output }
s(t) and o(t) originate and terminate within the environment
s1(t)s2(t)s3(t)
si(t)
o1(t)
ok(t)
o3(t)o2(t)
hi(t)
X
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All known, understood, well described
and characterized, bounded, and well
behaved with causality preserved
Contained/bounded in/by some known, or well defined, environment/conditions
Complex System - Key Features I
s(t) = Stimulus h(t) = Operator o(t) = Output }
s(t) and o(t) originate and terminate within the environment
s1(t)s2(t)s3(t)
si(t)
o1(t)
ok(t)
o3(t)o2(t)
hi(t)
X XMay be violated by design or implementation error ++
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All known, understood, well described
and characterized, bounded, and well
behaved with causality preserved
Contained/bounded in/by some known, or well defined, environment/conditions
Complex System - Key Features I
s(t) = Stimulus h(t) = Operator o(t) = Output }
s(t) and o(t) originate and terminate within the environment
s1(t)s2(t)s3(t)
si(t)
o1(t)
ok(t)
o3(t)o2(t)
hi(t)
X Any one or more or all of these
conditions may no longer true
X XMay be violated by design or implementation error ++
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Response matches needSymbiotic with the environmentPredictable, reliable, with a fast recovery timeUpgrades and changes not traumatic or riskyShocks are not terminal or unduly debilitatingReproducible, easy to deploy and maintain/repair/replace
Simple System - Key Features II
s(t) h(t) o(t)
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Response matches needSymbiotic with the environmentPredictable, reliable, with a fast recovery timeUpgrades and changes not traumatic or riskyShocks are not terminal or unduly debilitatingReproducible, easy to deploy and maintain/repair/replace
Simple System - Key Features II
s(t) h(t) o(t)
Sometimes we cannot satisfy this wish list 100%
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Complex System - Key Features II
s1(t)s2(t)s3(t)
si(t)
o1(t)
ok(t)
o3(t)o2(t)
hi(t)
Response matches needSymbiotic with the environmentPredictable, reliable, with a fast recovery timeUpgrades and changes not traumatic or riskyShocks are not terminal or unduly debilitatingReproducible, easy to deploy and maintain/repair/replace
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Complex System - Key Features II
s1(t)s2(t)s3(t)
si(t)
o1(t)
ok(t)
o3(t)o2(t)
hi(t)
Response matches needSymbiotic with the environmentPredictable, reliable, with a fast recovery timeUpgrades and changes not traumatic or riskyShocks are not terminal or unduly debilitatingReproducible, easy to deploy and maintain/repair/replace
Almost by definition we cannot satisfy this wish list 100%
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The nature of non-linearity
Linear = Output scales with input in some way: y = ax + b
Non - Linear = Output does not scale with input: e.g. y = a.exPredictable
Non - Linear = I/O does not scale with: e.g. y = f1(x0)+ fs(x1) Seldom or never gives a repeatable output for all input states
Un Predictable
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The nature of non-linearity
Linear = Output scales with input in some way: y = ax + b
Non - Linear = Output does not scale with input: e.g. y = a.exPredictable
Non - Linear = I/O does not scale with: e.g. y = f1(x0)+ fs(x1) Seldom or never gives a repeatable output for all input states
Un Predictable
Huh !!!
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How come ???
Non - Linear = I/O does not scale with: e.g. y = f1(x0)+ fs(x1) Seldom or never gives a repeatable output for all input states
Un Predictable
Memory Dynamic/Stochastic non-linearities Input/Output uncertainties Feedback VariabilityDelay Dynamic/Stochastic configurations Conditional uncertainties Feedforward Variability
Dynamic non-linearitiesDynamic configurations
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Examples
Non - Linear = I/O does not scale with: e.g. y = f1(x0)+ fs(x1) Seldom or never gives a repeatable output for all input states
Un Predictable
Weather Markets War People
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Examples
Non - Linear = I/O does not scale with: e.g. y = f1(x0)+ fs(x1) Seldom or never gives a repeatable output for all input states
Un Predictable
Network Traffic
Large BioEntities
ChanceGambling
AtomicInteractions
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AXIOMS - For Networked // Aliased Systems
Complex Systems are never rendered simpler - without incurring errors/costs !
Simple systems are mostly rendered complex - unless we are very lucky !
Complex systems never get easier to characterise
Simple systems always get more difficult to characterise
Simple systems don’t make the complex simpler
Complex systems always make the simple more complex
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AXIOMS - For Networked // Aliased Systems
Complex Systems are never stronger than their weakest element
Systems are never simpler than their most complex elements
There are lots of simple solutions to complex problems... ....but they are always wrong !
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Should you discover sometime in the future, that any of this is untrue, or does not hold...
....then there is a Nobel Prize waiting for you !!!
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How can we be so sure ?
Because the universe is governed by Entropy
‘Gods Celestial Ratchet’
Or
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Huh ?
That’s a story for another day
AND
Systems 1.1
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AND NOW
This Weeks Assignment!
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Read everything you can on Entropy and come back....
...prepared to discuss and debate
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the
journey
has
Begun
Wednesday, 22 May 13