Systems 1.0 What They Should Have Told You in Class

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

Definitions

What do we mean

by a system ?

“A group of interacting, interrelated,

or interdependent elements forming

a complex whole”

Not entirely satisfactory...

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...

But what a lot of words,

disjointed concepts and

examples to remember...

...might we do better ?

‘A system takes energy, matter,

information, and transforms its

nature’

Ergo; Systems are ‘essentially entropic’

S = k log W

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...

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 !

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...

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...

“Perfection is the enemy of

Good Enough”

Defining ‘good enough’ is not always trivial and is generally the biggest challenge !

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

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

What’s in THE BOX ?

s(t) h(t) o(t)

ChemicalPhysicalInformation/Data ProcessingMathematicalNaturalUnnatural

BiologicalElectricalElectronicMechanicalComputational+++

Optical AcousticOrganicInorganicLife forms+++

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

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

But many of our systems are of a much higher order with hundreds of feedback and feedforward loops...

They also have hundreds of diverse inputs and outputs and cannot be fully flood, or combinatorially tested...

SizeScaleComplexityConnectivitySophisticationConnectivity

MTBFSpeedAgility

ReliabilityTestability

PredicabilityResponsivity

Common/General system traits

MTBFSpeedAgility

Often difficult to define with any great precision

MTBFSpeedAgility

Cost MTTR LatencyPower Heat Resources

Often difficult to define with any great precision

s(t) h(t) o(t)

s1(t)s2(t)s3(t)

o3(t)o2(t)

s(t) h(t) o(t)

s1(t)s2(t)s3(t)

o3(t)o2(t)

SimpleSingularLinear

ComplexMulti - I/OLinearNon-Linear

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

All known, understood, well described

and characterized, bounded, and well

behaved with causality preserved

Complex System - Key Features I

s1(t)s2(t)s3(t)

o3(t)o2(t)

s1(t)s2(t)s3(t)

o3(t)o2(t)

s1(t)s2(t)s3(t)

o3(t)o2(t)

X XMay be violated by design or implementation error ++

s1(t)s2(t)s3(t)

o3(t)o2(t)

X Any one or more or all of these

conditions may no longer true

X XMay be violated by design or implementation error ++

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)

Simple System - Key Features II

s(t) h(t) o(t)

Sometimes we cannot satisfy this wish list 100%

Complex System - Key Features II

s1(t)s2(t)s3(t)

o3(t)o2(t)

Complex System - Key Features II

s1(t)s2(t)s3(t)

o3(t)o2(t)

Almost by definition we cannot satisfy this wish list 100%

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

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

Un Predictable

Huh !!!

How come ???

Un Predictable

Memory Dynamic/Stochastic non-linearities Input/Output uncertainties Feedback VariabilityDelay Dynamic/Stochastic configurations Conditional uncertainties Feedforward Variability

Dynamic non-linearitiesDynamic configurations

Examples

Un Predictable

Weather Markets War People

Examples

Un Predictable

Network Traffic

Large BioEntities

ChanceGambling

AtomicInteractions

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

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 !

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 !!!

How can we be so sure ?

Because the universe is governed by Entropy

‘Gods Celestial Ratchet’

That’s a story for another day

Systems 1.1

AND NOW

This Weeks Assignment!

Read everything you can on Entropy and come back....

...prepared to discuss and debate

journey

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