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
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
insights and challenging 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 design
Only we optimize We often appear use
vastly complex solutions to
achieve incredibly simple
outcomes...

Whilst Mother Nature...
Only evolves systems
Only 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 generalities
Analogue 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....
Air
Water
Earth
Machines
Lifeforms
Fluids
Solids
Chemicals
Radiation
Information

What’s in THE BOX ?
s(t) h(t) o(t)
Chemical
Physical
Information/Data Processing
Mathematical
Natural
Unnatural
Biological
Electrical
Electronic
Mechanical
Computational
+++
Optical
Acoustic
Organic
Inorganic
Life 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
e(t)
f(t)

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...

Size
Scale
Complexity
Connectivity
Sophistication
Connectivity
MTBF
Speed
Agility
Reliability
Testability
Predicability
Responsivity
Common/General system traits

Size
Scale
Complexity
Connectivity
Sophistication
Connectivity
MTBF
Speed
Agility
Reliability
Testability
Predicability
Responsivity
Often difficult
to define
with
any great
precision

Size
Scale
Complexity
Connectivity
Sophistication
Connectivity
MTBF
Speed
Agility
Reliability
Testability
Predicability
Responsivity
Cost MTTR Latency
Power Heat Resources
Often difficult
to define
with
any great
precision

s(t) h(t) o(t)
s1(t)
s2(t)
s3(t)
si(t)
o1(t)
ok(t)
o3(t)
o2(t)
hi(t)

s(t) h(t) o(t)
s1(t)
s2(t)
s3(t)
si(t)
o1(t)
ok(t)
o3(t)
o2(t)
hi(t)
Simple
Singular
Linear
Complex
Multi - I/O
Linear
Non-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

Complex System - Key Features I
s(t) = Stimulus
h(t) = Operator
o(t) = Output }
the environment
s1(t)
s2(t)
s3(t)
si(t)
o1(t)
ok(t)
o3(t)
o2(t)
hi(t)

s(t) = Stimulus
h(t) = Operator
o(t) = Output }
the environment
s1(t)
s2(t)
s3(t)
si(t)
o1(t)
ok(t)
o3(t)
o2(t)
hi(t)
X

s(t) = Stimulus
h(t) = Operator
o(t) = Output }
the environment
s1(t)
s2(t)
s3(t)
si(t)
o1(t)
ok(t)
o3(t)
o2(t)
hi(t)
X X
May be violated by design
or implementation error ++

s(t) = Stimulus
h(t) = Operator
o(t) = Output }
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 X
May be violated by design
or implementation error ++

Response matches need
Symbiotic with the environment
Predictable, reliable, with a fast recovery time
Upgrades and changes not traumatic or risky
Shocks are not terminal or unduly debilitating
Reproducible, 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)
si(t)
o1(t)
ok(t)
o3(t)
o2(t)
hi(t)

Complex System - Key Features II
s1(t)
s2(t)
s3(t)
si(t)
o1(t)
ok(t)
o3(t)
o2(t)
hi(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.ex
Predictable
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.ex
Predictable
input states
Un Predictable
Huh !!!

How come ???
input states
Un Predictable
Memory Dynamic/Stochastic non-linearities Input/Output uncertainties FeedbackVariability
Delay Dynamic/Stochastic conﬁgurations Conditional uncertainties FeedforwardVariability
Dynamic non-linearities
Dynamic conﬁgurations

Examples
input states
Un Predictable
Weather Markets War People

Examples
input states
Un Predictable
Network
Trafﬁc
Large Bio
Entities
Chance
Gambling
Atomic
Interactions

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’
Or

Huh ?
That’s a story for another day
AND
Systems 1.1

AND NOW
This Weeks Assignment!

Read everything you
can on Entropy and
come back....
...prepared to discuss
and debate

the
journey
has
Begun

Systems 1.0 What They Should Have Told You in Class

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