Abstracting systems from phenomena
Copyright 2021 Graham Berrisford. A chapter in the book https://bit.ly/2yXGImr. Updated 23/08/2021 14:42
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This
chapter helps you avoid confusion by disentangling descriptions of activity
systems from reality the of physical entities and phenomena. Don’t worry if you
don’t get all the ideas first time through. When they reappear in later
chapters, you may find it helps to return here.
Contents
Abstracting
activity systems from physical entities
Relating
abstract activity systems to physical entities
The
realization of an abstract activity system in reality
Dependencies
in reality between independent systems
Abstracting
activity systems from social entities.
What people call “systems thinking” ranges
from the softest of sociology to the hardest of physics and mathematics. Some
generalize across these different domains of knowledge by defining a system as
a whole made of parts. The trouble is that every individual entity you can see
or name is divisible into separately describable parts. If the term system is to be
useful, more than a vacuous noise word, more than a synonym for entity,
then it must have some more particular meaning.
The universe is an ever-unfolding process from
the big bang onwards. We observe, envisage and describe the universe by carving
up space and time.
From the continuous expanse of space, we carve
out discrete structures - entities and actors. And from the continuous flow of
change over time, we carve out discrete behaviors - events and activities.
Structure examples |
Behavior
examples |
Solar system |
Orbit |
Planet |
Rotation |
Volcano |
Eruption |
Animal |
Heart beat, life |
Motor cycle |
Two-stroke cylinder cycle |
Business |
Billing process |
Every structure has a life time over which it
changes – whether cyclically or progressively. An aggregate entity is a collection
of elementary entities that interact – whether cyclically or progressively.
Every behavior, be it cyclic or progressive, is
constrained by the laws of nature or other rules. An activity system is
a pattern of behavior we observe or envisage in what one or more entities do
over time – as in cybernetics, system dynamics and soft
systems methodology.
The first big cause of confusion is the use of
the word “system” for both aggregate entities and activity systems. The second
is the presumption that one aggregate entity corresponds to one activity
system. In general, the relationship is between them is many-to-many.
“It is important to stress Ashby defined a system not as something that exists in nature. A system consisted of a set of variables chosen for attention and relationships between these variables, established by observation, experimentation, or design." Ashby’s student Krippendorff writing in 2009 on Ashby’s Information Theory
Every activity system in the real world
is “soft” in the sense its boundary is determined by its observer/describer/designer.
In operation, it is dynamic in the sense it changes from state to state and/or produces outputs from inputs
in a way that is regular or repeatable enough to be
modelled by an observer/describer/designer.
Ashby
distinguished reality from description. He distinguished a physical entity
(which he sometimes called the real 'machine') that is observable as changing over
time from the countless regular systems we might abstract from observing that
entity.
2/5. It will be
appreciated that every real 'machine' embodies no less than an
infinite number of variables, most of
which must of necessity be ignored. Ashby’s “Design for a Brain”
3/11 “At this point we must be clear about how a “system” is to be defined. Our first impulse is to point at a [physical entity] and to say “the system is that thing there”. This method, however, has a fundamental disadvantage: every material object contains no less than an infinity of variables and therefore of possible systems. … Any suggestion that we should study “all” the facts is unrealistic, and actually the attempt is never made. [We must] pick out and study the facts that are relevant to some main interest that is already given.” (Ashby’s “Introduction to Cybernetics”)
Ashby’s
wording was not entirely consistent between, and even within, his books. It
seems fair to say however that his real 'machine'
is some material object(s) that can be observed as behaving in the way
described by an abstract system.
In both cybernetic and in system dynamics, the abstract system is a set of state variable types, and rules for activities that change the values of those state variables over time. Then, a real 'machine' is a physical entity that can realize an abstract system – near enough.
The larger
and more complex the physical entity, the less of its behavior an observer can
abstract into a system description. Consider how five observers may see
the same card school.
Observer |
The
system they abstract from a card school |
A card player |
a poker game |
An economist |
a system to transfer money from less skilled to more skilled. |
A psychologist |
a system in which players are conditioned by occasional and near random rewards to repeat a behavior. |
A sociologist |
a system in which players swap anecdotes and bond socially |
A heating engineer |
a system that generates heat and so reduces the host’s heating bill |
The system an observer abstracts from the phenomena depends on the interest they bring to their observation. The graphic below shows how different observers/describers observe or envisage different activity systems in one physical entity, and create or use abstract descriptions of those systems.
[jpg missing from on-line display]
The graphic is a description in which the phrase “a game or tennis” or “a beating heart” is a proxy for a real-world system in operation.
Suppose a heart surgeon’s abstract system is this a model of a heart beat.
1. The atria walls contract and force blood into the ventricles.
2. The ventricles walls contract and force blood from the heart into the lungs and body.
3. The
atria fills with blood (and the cycle begins again).
The model above represents a physical system (an actual heart beat) performed by a physical entity (a heart). The physical activity system, though inseparable from the physical entity, is only that part or aspect of the entity that is correlatable with the abstract system description.
The graphic is a little too neat. It shows observers abstracting distinct systems. In practice, the systems abstracted by observers may be independent, nested or overlapping. For example, from the body of an animal, specialists might model several overlapping, systems related to digestion.
Abstract
systems are descriptions that typify some behavior. Physical entities are
individuals. The relationship between them is many to many.
Admittedly,
in conversation, we do often correlate one physical entity with one system. For
example, we might speak of a physical machine (like a steam engine, or an
organism like you or me) as being a system. By way of contrast consider the
entity that so many “system thinkers” focus on - a human society. This is very
different in character.
About
the entity of interest |
Steam engine |
Organism |
Human society |
Is it a
bounded solid entity, locatable in space? |
Yes |
Yes |
No. It is a
network of parts distributed in space. |
Does its
boundary enclose its parts, visibly and tangibly? |
Yes |
Yes |
No. It has no
visible or tangible boundary. |
Does it
realize a specification encoded in a design or genotype? |
Yes |
Yes |
No. Its
structures and behaviors are fluid, not determined by a specification. |
Does it have
a single main purpose? |
Yes. Moving
things. |
Yes. Gene
propagation. |
No. It
continually evolves to meet the disparate purposes of disparate stakeholders. |
Are its
parts primarily dedicated to its purpose? |
Yes |
Yes |
No. Each
actor is agent with their own aims who divides their time between different
social entities, some in competition or conflict. |
The trouble
for coherent systems thinking is this: the relationship between abstract
activity systems and physical entities is many to many. First one
physical entity may realize or participate in several abstract systems.
One physical
entity |
may realize many abstract systems |
One rain forest |
may capture carbon
in tree trunks, and feed squirrels |
One card school |
may play many
games (poker, whist and pizza sharing) |
One orchestra |
may perform many
different musical scores |
One computer |
may execute many
different programs, or be used as a doorstop |
One human being |
exhibits heart beat,
digestion and breathing systems |
And conversely, one abstract activity system may be realized by many physical entities.
One abstract
system |
may be realized by many physical entities |
“Carbon capture” |
realized by
photosynthesis in countless rain forests |
“Poker” |
followed in the
playing of games by many card schools |
One musical score |
performed by many
orchestras |
One program |
executed by many
computers |
“Digestion” |
exhibited by many
human beings |
Generally speaking, one abstract
system may represent (idealize, typify, codify, defined the behavior of)
several physical entities. One physical entity may realize (embody, exemplify,
manifest, behave as defined by) several abstract systems.
In a sociological context, one social entity can realize several social activity systems. And conversely, one social activity system can be realized by several social entities.
Some go as far as to say activity systems are purely abstractions; they exist only in models; don’t exist in the natural world, which is misleading, because a physical activity system exists whenever a physical entity – near enough - realizes an abstract system.
Below, Ashby’s real 'machine' is divided into two
aspects. There is a physical activity system - a
performance of the defined activities, giving values to the defined variables.
And there is a physical entity - some actor(s) able to
perform the activities in the system (and possibly activities in many other
systems).
Realizations can be imperfect. We can model the way a pendulum behaves – near enough. However, when operating out of doors, buffeted by a wind, the behavior of the real machine will depart from that of our ideal machine.
Realizations can change. The genome of an organism can be seen as codifying the structures and behaviors of a biological system. So, when a bacterium acquires some genetic material from another bacterium, from then on, it will realize a different system.
A physical entity (be it a machine, animal or social entity) is always more than any activity system realizes. And when we model a system, we do so at one level of the hierarchy of sciences introduced in the previous chapter.
A social entity behaves in ways above and beyond the biology of its individual members. It has been suggested that the nature/nature influence on human abilities is 70/30. Whatever the true proportion, much of what a human actor does is not defined in its genome. Some behavior is shaped by the actor’s experience, education and roles in social interactions that are constructed to meet some goals.
Observers may abstract countless independent systems from observation of one physical entity, such as a human being. The three systems in the table below are independent in that their models do not overlap or connect.
|
S1 |
S2 |
S3 |
Abstract system |
Heartbeat model |
Digestive system model |
Contract signing model |
Physical system |
A beating heart |
The digestion of food |
The signing of a contract |
Physical entity |
A heart |
Teeth, stomach, intestines etc. |
Brain, eyes, hand etc. |
However, in reality, S3 depends on the successful operation of S1 and S2. Moreover, all three systems depend on a body’s nervous system. Similarly, on your computer, your spreadsheet and browser applications are independent systems, yet both depend on your computer’s operating system. And more generally, any two systems may be related indirectly by their dependence on another (server, platform or infrastructure) system.
Despite the dependencies in reality between what is described as independent systems, there is no prospect of modelling the whole of a human being (all its physical, biological, psychological, social behaviors) in one abstract system. We can only study and define tiny aspects of the whole as a system.
4/16. “Up till now, the systems considered have all seemed fairly simple, and it has been assumed that at all times we have understood them in all detail. Cybernetics, however, looks forward to being able to handle systems of vastly greater complexity: computing machines, nervous systems, societies.” (Ashby’s “Introduction to Cybernetics”.)
If cybernetics is to be applied to a computer, not only must the material reality of that computer be massively simplified, but also, the physical components of the computer must be distinguished from the countless applications systems the computer may offer its users.
Similarly, if cybernetics is to be applied to a society (a set of communicating actors), not only must that social entity be massively simplified, but also, its physical components (the actors) must be distinguished from the roles they play in completing actions.
"The
first decision is what to treat as the basic elements of the social system. The
sociological tradition suggests two alternatives: either persons or
actions." David Seidl 2001
Person-centric social entity thinking
is one thing; action-centric activity systems thinking is another. Both
are useful views, but the “system” in one is not the “system” in the other. It
is unfortunate that even highly respected systems thinkers have flipped from
one to the other, in speaking or writing. If systems thinking is to advance,
thinking about a social entity must be distinguished from thinking about an
activity system it may perform or participate in.
A first social activity system
Think of a card school. The quantity of money in front of
each player is a variable that is increased and decreased by playing hands in a
game of poker. The card school is a social entity that can be seen as a
physical system when and where it plays a game of poker.
|
A
game of poker |
Abstract
system |
The rules of the game and roles for players |
Physical
system |
A game of poker, in which defined variables change value |
Physical
entity |
A card school, whose members are able to play the game |
Again, the relationship is many to many. One activity system can be realized by several social entities (the game of poker can be realized by many card schools). Conversely, one social entity can realize several activity systems (the card school can play whist, or share a pizza). There is much more to know about a card school than its playing of games. Its members can act in many other social entities, some of which may conflict or compete with each other.
A second social activity system
A composer conceives and organizes the musical notes an orchestra (a social entity) should play in a symphony (an activity system).
|
A
symphony |
Abstract
system |
A symphony score: musical notes and how they relate to each other. |
Physical
system |
Symphony performance: outputs notes as sounds in a venue. |
Physical
entity |
Orchestra members employed to play roles in a performance. |
The symphony score does not address the whole of the social entity that is an orchestra. The composer addresses only the roles that orchestra members play in sounding musical notes, and the kinds of instrument they need to play their roles. The description of roles, notes and resources add up to the complex type that is a symphony score. At run time, in a performance supervised by a conductor who keeps things in order, orchestra members cooperate to realize the abstract symphony score in a performance.
Composers <observe &
envisage> Symphony performances
Describers
<create and use> Symphony scores
Symphony scores
<represent> Symphony performances
A third social activity system
A business architect describes or designs the activities a business (a social entity) is to play regular business operations (an activity system).
|
A
business |
Abstract
system |
Business activity model (as in soft systems methodology) |
Physical
system |
Business operations that realize the model above |
Physical
entity |
Actors employed to play roles in business operations. |
An enterprise typically realizes a mess of countless different activity systems, some duplicated, some uncoordinated and some in conflict (which is the problem that enterprise architecture was invented to address). At run time, in operations supervised by managers who keeps things in order, human actors cooperate to realize the abstract system in the everyday performance of their roles and processes
Business architects <observe & envisage> Business operations
Business architects <create and use> Business activity models
Business activity models <represent> Business operations
Abstraction in system dynamics
The same layering can be seen in a closed system of feedback loops, as may be modelled using system dynamics.
|
System
dynamics in general |
Abstract
system |
Quantitative variables connected by flows (rules for change) |
Physical
system |
Real-world interactions between things or qualities below |
Physical
entity |
A selection of related material entities and/or qualities of them |
In philosophy, ontology is about what things are, independent of observation. By contrast, epistemology is about what we know of things, and empiricism is about what we can know by observation. Science is empirical; it does say what a physical entity “really is”; only that it matches (near enough) some theory or model we have.
Cartography is empirical; it does say what a territory “really is”; only that it matches (near enough) some map we have. It involves three relations of the kind we have seen above.
Mappers <observe and envisage> Territories.
Mappers <create and use> Maps.
Maps <represent> Territories.
In some later
chapters, this book represents such relations using a triangular graphic. For
example, read the graphic below from left to right.
Cartography |
Maps <create and use> <represent> Mappers <observe & envisage> Territories |
The map is not the territory, but the two must be correlated well enough to help map users find things. Bear in mind however that one phenomenon can be described in several ways. Different maps, showing different features, may be drawn of one territory. You may use different maps for country walks, planning journeys, driving, studying geographic features, studying demographic features. And you may need to find or buy a new map now and then.
Bear in mind also that no description is complete. A territory is infinitely complex; a map cannot be a complete or perfect representation of it. A map is an abstraction that shows only enough that we can find or learn what we need to.
Composers
(describers) define the notes and instruments required for symphony
performances (described things) in symphony scores (descriptions).
Composers <envisage> Performances
Composers <create> Symphony scores
Symphony scores <represent> Performances
The composer does not address the whole of the social entity that is an orchestra. The composer addresses only the roles that orchestra members play in sounding musical notes, and the kinds of instrument they need to play their roles. All the documented role, note and resource types add up to a complex type we call the symphony score.
Symphonies |
Symphony
scores <create and
use>
<represent> Classical
composers <observe and
envisage> Symphony performances |
At run time, conductors
use a score to drive an orchestra, beat by beat, to perform the symphony in a
discrete event-driven way. Thus, supervised by a conductor who keeps
things in order, an orchestra realizes the abstract symphony score in a
performance.
Systems thinking is empirical; it does not insist a physical entity is a system, only that its behaviour (near enough) matches some system model we have.
The designer of a business activity system cannot address the whole of the social entity that is a business. The designer addresses the roles that business actors play in a performance of the business system, and the kinds of resource they need to play those roles.
The designer describes entity types like customer, event types like order and payment, process types like billing, and rule types like order value = order amount * unit price. All these entity, event, process, data and rule types add up to a complex type we may call an abstract activity system.
Business
activity systems |
Abstract activity systems <create and use> <represent> Business architects <observe
and envisage> Physical operations |
At run time, supervised by managers who keep thing in order, business actors realize the abstract activity system in a physical activity system that consumes inputs, creates business data and uses it to decide how to respond to events.
In cybernetic terms, a business activity
system of this kind can be seen as a machine that imitates what comes naturally
to animals. It detects events, interprets their significance in the
light of memories retained, and responds by acting in a way that serves the
interests or aims of the business, machine or animal.
The more general triangle below relates describers to descriptions and phenomena. Note that a description in the mind is at the top of this triangle, not the left.
Episteomology |
Descriptions <create and use> <represent> Describers
<observe
and envisage> Phenomena |
In the first three parts of this book, don’t worry about the
triangles. Treat them as informal graphics that illuminate the text. In the
fourth part, the semantics of the triangle are more important, because it turns
out there is an essential difference between our
triangle and comparable triangles you can find in semiotics and philosophy.
My education (in psychology, biology and the philosophy of science) leads me to the conclusion that a government institution, or a university, is not a system. Rather, it is a social entity (in which the basic elements are actors) that employs and participates in several human activity systems (in which the basic elements are actions). Accordingly, this chapter has distinguished abstract systems from physical or social entities that realize them. Later, this will be important to how we think of systems in practical enterprise architecture.
This final section includes a few more remarks on description and reality.
Analytical and synthetic thinking are often
contrasted as though people do one or the other. In practice, we interleave the
two processes. Analysis is what we do in reverse-engineering, when we observe
and describe an existing thing by dividing it into parts and then
drawing a map, or studying how parts interact to produce so-called “emergent
properties”.
Synthesis is what we do in forward
engineering, when we envisage and design a new thing by relating parts
so as to produce some desired or required emergent properties. Synthetic design
involves not only creating connections between things but also describing them.
This book does not say much about the design process, but it does discuss the
product - a description of what is designed.
Aside: when we speak of the design of
a natural system, we refer to a structure and/or behavior that is an outcome of
evolution. You might think of evolution as an opportunistic kind of design
process, and a genome as a special kind of description.
The system
defined in an event-driven model of a dynamic system is a model of individual
entities and events. Below are four related entity types, documented in the
style of relational data analysis. The identifiers are underlined. The
relationships are indicated by asterisks.
Housing
market: entity types |
|||
City |
House |
Residence |
Person |
City
Name Total
Houses Houses
For Sale |
City
Name* Address Owner
Person id * For Sale
Status For Sale
Price |
Person
id * Address
* |
Person
Id Person
Name |
To complete
an entity-event model, one defines the events that create entities, update the
values their of attributes and remove them. Key events here may include Put
House On Market, Buy House, and Remove House From Market, along with discrete
events to register and remove an entity of each type.
By
contrast, a system dynamics model is a model of aggregate quantities at
a statistical level.
Housing market: system dynamics
model |
||
Growth in |
Feedback loop |
Growth in |
Houses
for Sale |
decreasesà ßincreases |
Average
House Price |
However,
models of individuals and aggregates are naturally entangled. First, an
individual entity can have an aggregate property, such as a bank account level,
or a number of children. Second, we may be able to describe a stock, population
or aggregate not just in terms of its quantity, but also as an individual
entity with attributes like name, weight, volume, average size, unit price,
whatever. And using agent-based modelling software, we can represent the
individuals in a statistical model, such as the fish in a shoal, as dots on a
screen.
The chapter
on dynamics discusses abstracting from the individual to the aggregate
level.
Ashby wrote that a regulator’s model of a target must be isomorphic with the target that is regulated, meaning, the elements and relationships in the model must be correlatable with elements and relationships in the reality. This isomorphism is logical rather than physical.
Two models or descriptions are homomorphic
when one is an abstraction or elaboration of the other. A higher-level
description may be more abstract (by composition or generalisation); a
lower-level description may be more elaborate (extended by decomposition or
specialization). Homomorphism may be seen as a special case of isomorphism.
Two things are said to be isomorphic
when they are similar in shape or pattern, such that the elements of one can be
correlated with the elements of the other. Systems thinkers use the term with
various meanings that bear closer examination, because some are more useful
than others. The classification below elaborates on the one in Ashby’s
Introduction to Cybernetics (6/8).
Passive structure isomorphism
This occurs when two passive
structures resemble each other in shape. At least three varieties may be
distinguished.
Natural isomorphism occurs when passive structures are
paired by the laws of nature, like an image to its reflection in a mirror, or a
photograph to its negative
Description-to-reality isomorphism occurs when icons or symbols
correspond (by design) to reality, like a statue to a person, or a map to a
territory.
Symbol-only isomorphism has no significance. For example;
· This sentence’s words are structurally
isomorphic to the words below.
· John Kennedy was the thirty-fifth
president of the United States.
Activity system isomorphism
This occurs when two activity systems resemble
each other in structure and/or behavior. Again, at least three varieties may be
distinguished.
Behavior-only isomorphism. Ashby called this the “strictest”
kind of isomorphism. Two “black box” systems may behave the same, regardless of
their internal structure. So, interchanging them cannot be detected by testing
their input-to-output behavior. Such encapsulation of systems and components
has been a basic principle of every software design fashion since 1970 (modular
programming, object-oriented design, component-based design, service-oriented
architecture, microservices, etc).
Full isomorphism. Two systems may not only behave in a
similar way, but also have similar internal structures, like the mechanical and
electrical machines in Ashby’s figure 6/8/1. The output display dials show
measures of different qualities.
Ashby’s
isomorphic systems |
||
|
Mechanical
system |
Electrical
system |
Input
parameter |
First shaft: degree of rotation |
Potentiometer: voltage |
Components |
Spring: stiffness |
Inductor: inductance |
Fly wheel: inertia |
Resistor: resistance |
|
Liquid trough: friction |
Capacitor: capacitance |
|
Output
variable |
Second shaft: degree of rotation |
Current meter: sum of currents |
[jpg missing from on-line display]
Structure-only isomorphism. Lastly, two systems may have the same
structure, but behave differently, as in the correlation drawn by Stafford Beer
between the structure of the human nervous system and the management structure
of a business. This is the weakest kind of isomorphism. At best, it provides a
teacher with an analogy for use in education.
The later chapter on Beer’s ideas
suggests this last kind of isomorphism can mislead people about the nature of
one or other of the two things compared.