Introducing description theory
The nature and use of
descriptive types
Copyright 2017 Graham Berrisford. One of about 300 articles at
http://avancier.website. Last updated 18/02/2018 21:41
The role of enterprise architects is to observe baseline systems, envisage target systems, and describe both.
So, you might assume it is universally agreed what a “description" is; but this is far from the case.
This paper explores “semiotics” and what might be called “type theory”.
The next paper takes a different – more Darwinian – approach to description and reality.
Contents
Structures
and behaviours in the space-time continuum
Aside on the
evolution of description
Remembering
and communicating information using types
Describing
reality using sign-type pairs
Higher and
lower frames of reference
Case study:
Traffic light system
A system is a subdivision of the universe we can describe as a system.
The presumption here is that reality exists independently of description.
We cannot understand reality directly.
We can only understand reality though our perceptions and descriptions of it.
A description is not the reality it describes; it is a model, or theory, of a reality.
One reality can be modelled from different perspectives, in different descriptions.
Any description is true and valuable as far as it enables us to measure/test/predict selected properties of the reality we describe.
The reality of the universe may be a space-time continuum, with no gaps in space or time.
However, all descriptions of the universe chunk it into discrete things,
There are infinite ways to do this, and many influences on how we do it.
There are physical phase boundaries, such as where a solid (its surface) meets a liquid, gas or space.
Logical or designed boundaries, such as how a chair, tennis match or IBM is bounded by design, specification or law.
Biologically evolved boundaries, since every animal is bounded by the specification in its DNA.
And we also draw arbitrary boundaries, as around the Atlantic Ocean, and our circle of friends.
The things we describe can be touching or separate, nested or overlapping, and cooperative or antagonistic.
They can be nested physically: galaxy, star system, planet, mountain, rock, molecule.
Or biologically: living matter, human race, human, organ, cell, organelle, molecule.
Or logically: organisation, division, unit, team, employee role.
Thing: a subdivision of the universe, locatable in
space and time, describable as instantiating one or more types.
Natural thing: a thing that emerges from the evolution of matter and energy, regardless of description.
Organism: a natural thing whose form is defined by it genes, and engages in the process of Darwinian evolution.
Designed thing: a thing described by an organism before the thing is created.
Albert
Einstein showed the space and time coordinates of an event must be combined to
describe it.
Einstein's
former college teacher, Hermann Minkowski, developed a way to think about the
universe in terms of its geometric qualities.
To
describe reality, we combine the 3 dimensions of space and 1 of time in the
'space-time continuum'.
Space-time
is a 4-dimensional object which does not evolve, it simply exists.
When
we examine a thing in space-time, every part of it is located along its
"world-line" in space-time.
We
can slice that world-line at any point in time to see where that slice is
located in space - at that time.
The term 'continuum' tells us there are no missing points in space or missing instants in time.
Also, both space time can be subdivided with no limit to the smallness of space or the shortness of time.
So, actors and activities can be described in terms of their place in space-time - at the level granularity we choose.
Newton’s laws of motion are useful, though Einstein showed their use to have limits.
Describing the universe as a space-time continuum has proved successful; yet is incompatible with quantum mechanics.
The macro and micro scale views of the universe are different.
Both are true as far as they enable us to predict/measure/test selected properties of a reality at the scale we are interested in.
Systems theory favours the macro scale view.
Meaning, the system’s actors can be found in space, and its activities happen over time.
Taking
structure and behavior views of the universe is to look at how things in space
change over time.
Discrete
structures
There are infinite ways to divide the universe into discrete entities or structures.
Entities can be touching or separate, nested or overlapping, and cooperative or antagonistic.
The most obviously discrete kind of structure is a three-dimensional solid.
A solid in a liquid (a fish in water) a gas (a bird in the air) or a vacuum (a planet in space).
There is one kind of entity nature itself has defined as discrete.
That is, a biological organism, such as a virus, a tree, a fish or a human being.
The form and essential functions of an organism are defined in its DNA.
An entity may be perceived or described as composed of parts distributed in space.
E.g. the solar system, or the human race.
Still, every part of that distributed structure is locatable in space-time.
Discrete
behaviors
A discrete entity or structure is bounded in time as well as space.
It has a life time, stretching from when it starts or is formed to when it ends, disintegrates or is replaced.
And to describe how an entity changes during its life time, we speak of:
· structures in space (stocks, entities or actors)
· behaviors over time (flows, events or activities) that change the state of structures.
E.g. We speak of planets and their orbits in the solar system.
The orbits (behaviors) change the position of the planets (structures) in space.
Discrete
systems
Is every entity a system?
The universe is an ever changing entity in which stuff happens.
IBM is an ever changing entity in which stuff happens.
But if every entity is a system, then the term "system" adds no meaning.
A system theory ought to differentiate a system from any other discrete entity.
Here, a system is composed of discrete structure that performs discrete behaviors.
It is an entity whose behavior is organised, regular or repeatable.
Like any other kind of entity, systems can be touching or separate, nested or overlapping, and cooperative or antagonistic.
But if there is no description of the entity as a system, there is
no testable system, just stuff happening.
To be called a system, an entity must
exhibit (manifest, instantiate, realise) the properties of a system.
There must be a system description (a type or theory) that the entity
conforms to – near enough.
This article refers to mathematics and semiotics; but it is written from the perspective of biology.
A Darwinian explanation of description must start long before mathematics, and before words.
It starts from the notion that organisms can recognise family resemblances between things.
And so recognise when a new thing is of a kind important to survival, or resembles a previously remembered thing.
The next paper tells a story of seven steps that lead to increasingly sophisticated creation and use of “types”.
1. Recognition: sunflowers recognise the sun’s daily repeated passage across the sky.
2. Memory: a predator instinctively recognises things that instantiate the type “prey”.
3. Learning: a predator learns by trial and error to recognise things that instantiate the type “edible thing”.
4. Communication: an animal sounds an alarm call to signal a new instance of the type “danger”.
5. Verbalisation: people use words to signify fuzzy types, leaving open whether a penguin is of the type “bird”.
6. Mathematics and computing: the type “circle” is defined strictly and used in calculations.
7. Artificial intelligence: computers mimic the more human-like typification at step 5.
This article presumes describers have the abilities at stages 4, 5 and 6 above.
So we can describe the structures and behaviors of a system by using words to typify them.
Semiotics is the study of signs and symbols and their use or interpretation.
We describe and understand a thing with reference to familiar types it instantiates.
We use symbols/tokens/signs to signify the types to which that thing belongs - in our view.
“In describing a situation, one is not
merely registering a [perception], one is classifying it in some way, and this
means going beyond what is immediately given.”
Chapter 5 of “Language, truth and logic” A J Ayer.
E.g. the message: “The White House is a building” describes a situation.
It tells us the named thing (“The White House”) instantiates, embodies, exemplifies,
manifests or realises the
named type (“building”).
The type name “building” is a meaningless symbol on its own.
It only becomes meaningful information when mapped to a familiar type
(“a structure with a roof and walls”).
This idea (describing particular things with reference to general types) is very important.
Not only in philosophy, mathematics and computing, but also in everyday human existence.
It is essential to remembering things and communicating about them.
To
describe all the properties of a
physical thing is impossible.
But we can communicate some information
about a thing by associating it with one or more types.
Types (“beautiful”, “yellow” and “fluid”) help us remember, describe and understand things (a daffodil, a river).
Yet the concept of “type” is elusive.
Is a type best seen as a set (as in mathematics), a kind (as in logic), or a law (as in sociology)?
Do types exist independently of things, or of life?
The table below is a (questionable) characterisation of some philosophical positions.
|
Position
statement |
Philosopher |
|
Types exist eternally (regardless of things that instantiate them) |
Plato? |
|
Types exist only when things instantiate
them |
Aristotle? |
|
Things exist only when observed by a life form |
Berkely? |
|
Things existed before life forms used types to describe them |
Kant? |
|
Types can be created by life forms before things instantiate them |
|
People speak of a “type” being manifest in “occurrences”, “instances” and “tokens”. Are these the same?
If you have read or thought about these things, this article may turn your thinking upside down.
In four decades of talking about information and systems, I often find myself saying something like:
“This is an example of a type-instance relationship; do you know what I mean by type and instance?”
Typically, students say “No”, “Vaguely” or “I think so, but am not sure, tell me what you mean”.
This section contains the original explanation I offered, and the very different explanation I give today.
To begin, a type is one or more qualities or properties that similar things share.
It may be seen as crystallising the resemblances between things in a family (cf. Wittgenstein’s family resemblances).
Originally, I illustrated types by tabulating examples in the form of a glossary. E.g.
|
Domain |
Type
name |
Type
definition |
|
Astronomy |
Planet |
A body in space that is large, and orbits
a nearby star. |
|
Star |
A body in space that is large, is incandescent and remote from other stars. |
|
|
Biology |
Person |
An
individual of the species Homo Sapiens. |
|
Bird |
An animal that has feathers, has a beak, can fly. |
|
|
Rose |
A bush that is woody, has thorns, has flowers. |
|
|
Culture |
Bachelor |
A male that is mature, is unmarried. |
|
Design |
Jumper |
A
knitted garment worn over the upper body. |
|
Mathematics |
Circle |
A continuous line which is, at every point, the same distance (the radius) from a central point. |
|
Computing |
Date |
An
identifier for one day in time, a “complex type” composed of day, month and
year. |
And I explained instances as though they are things.
Instances of the planet type are things like Venus and Mars.
Instances of the circle type are things like the full moon, and a circus ring.
Instances of the person type include you.
Instances of the date type include the First of January 1953.
Gradually, I reached the conclusion my original explanation was downright misleading.
My original explanation used the term “type definition”.
Which misleads people, because types are definitions.
A type is what mathematicians call the intensional definition of a set.
Some sets can only be defined by enumerating set members; e.g. this set of randomly chosen words {rose, is, a}.
Our interest here is in cases where set members are definable by an intensional definition; e.g. {2, 4, 6, 8...}.
|
Set
of |
Type
name |
Type
(aka intensional definition) |
|
Even numbers |
Even number |
An integer divisible by two with no
remainder |
A set and a type may be in 1-1 correspondence, but they are different.
A set is the collection of things that instantiate a type; it is the assembly or aggregate of set members.
A type is a description of one set member; a type is an intensional definition of a set member.
The type is the definition of one set member only, the rule for set membership.
The set is all things that meet the definition, follow the rule.
(In computing, a set definition might include additional attributes, like total members, weight, and the date the first member joined the set.)
A set can be empty; and a type (“unicorn”) can exist even though nothing embodies or instantiates it.
Mathematicians say all empty sets are the same “empty set”, since it is enumerable thus { }.
Curiously, the empty set has infinite different types (“unicorn”, “mountain made of sand”, “Platonic ideal you can touch”.
Not only is a type a description, but conversely, a description is a type.
Since given one description, it is always possible to imagine several instances of it.
E.g. Physicists talk about parallel universes, which is to say, the set of universes that conform to the universe type.
Charles Peirce and other philosophers use the term “token” rather than type name.
A token is anything which identifies a thing or a type, it could be
·
a
symbol in a code, such as semaphore or a musical score.
·
a
biochemical mental model, like a sensation of cold, the colour yellow, or an
image of a face.
·
a
physical model, like a painting, a model aeroplane or a drawing of a circle
·
any other structure, sight, sound or smell.
Of course, in most speech and writing we use verbal type names as tokens for types.
|
Token |
Type
(aka intensional definition) |
Things
instantiating the type |
|
Planet |
A large body that orbits a star. |
Venus, Mars... |
|
Even number |
An integer divisible by two with no
remainder |
2, 4, 6, 8... |
You read “Mars is a planet” and (if you know the token-type pair) you understand “Mars is a large body that orbits a star.”
You say “4 is an even number” (if I know the token-type pair) I know what you mean.
My explanation led people confuse to things with instances, so I added a little more.
Not only may several things instantiate one type, but one thing may instantiate many types.
|
This
particular thing |
instantiates |
these
types |
|
The White House |
is a |
“building” and “presidential work place” |
|
A circus ring |
exemplifies |
“circle”
and “arena” |
|
You |
embody |
“tennis player”, “source of heat” and
“shape”. |
Note that neither you nor any other physical thing can be fully described thus.
My original presentation of types as
glossary entries was simplistic
Because several type names (synonyms) may be associated with the same type definition.
|
Two
tokens |
One
type |
|
Human being |
An
individual of the species Homo Sapiens |
|
Person |
And one type name may be associated with several type definitions (homonyms).
|
One
token |
Two
types |
|
Jumper |
One who jumps |
|
A knitted garment worn over the upper body. |
For years, I wrestled with how to pre-empt misunderstandings and explain things better.
The trouble is, tokens and types have a many-to-many relationship.
So the examples I originally presented were not types, they were token-type pairs.
|
Token-type pairs |
|
|
Token |
Type
(aka intensional definition) |
|
Planet |
A large body that orbits a star. |
|
Even number |
An integer divisible by two with no remainder |
|
Human being |
An
individual of the species Homo Sapiens |
|
Person |
An
individual of the species Homo Sapiens |
|
Jumper |
One who jumps |
|
Jumper |
A knitted garment worn over the upper body |
To be honest, my “journey” took years and was more convoluted and confused than set out above.
The last step was to recognise the significance of the fact that these two sentences mean the same.
“Mars is a planet.”
“Mars is a large body that orbits a star.”
Many philosophers presume types (or at least, some types) are unique concepts.
Meaning, “planet”, “even number” and “beauty” are singular abstract concepts.
If that is true, then all appearances of that concept , in brains and documents, are also tokens of that type.
Which means redrawing the last table above.
|
Sign-type pairs |
|
|
Sign
(and token) |
Type
(and token) |
|
Planet |
A large body that orbits a star. |
|
Even number |
An integer divisible by two with no
remainder |
All social and computer systems depend on communication.
And communication depends on sign-type pairs being shared (near enough).
Message senders and receivers must share (near enough) the same sign-type associations.
Otherwise, a message is either meaningless to its receiver, or misunderstood.
People speak of instances/occurrences as being “concrete”, which can be misleading.
Instances can be descriptions, sights, sounds, smells and other intangibles (prayers, memories, truths).
And depending on our frame of reference, an instance can also be a type.
|
This
thing |
Higher
frame of reference |
Lower
frame of reference |
|
A description of roses |
an instance of the type “species definition” |
a type realised in real world roses. |
|
The laws of tennis |
an instance of the type “system description” |
a type realised in actual tennis matches. |
|
The word “planet” |
an instance of the type “word” |
a sign or token of the type “Planet” realised in Venus and Mars |
Mind-bendingly, we may view all particular types as being instances in the set of types.
What to call the type that defines a member of the set of types? How about the meta type?
|
Sign |
Type |
|
The meta type |
The concept of an intensional definition
that contains at least one property |
|
Particular type |
A particular intensional definition,
exemplifying the concept of a property |
|
Instance |
The appearance, in a thing, of properties defined in a type |
Does a type exist outside of life, thought and records of it?
Fortunately for semiotics and system theory, it doesn’t matter how you answer this question, but we shall return to it in part four.
The next part relates semiotics to system theory.
Thing: a subdivision of the universe, locatable in
space and time, describable as instantiating one or more types.
E.g.
Any part of the universe describable as instantiating any of the types below.
E.g.
Any discrete structure, object, behavior, event, or a description (be it mental
or documented).
We may look inside the thing at what it contains, and outside at what things it connects to in the wider environment.
Parts
of the thing may be distributed in space, and seen as things in their own
right.
Set: a collection of things that are similar in
so far as they instantiate (embody, exemplify) one type.
E.g.
The empty set of unicorns.
E.g.
The set of planets in our solar system.
E.g.
The set of a symphony’s performances.
Type: an intensional definition, composed of
property type(s) that describe a thing.
E.g.
A white, horse-like animal with a long horn and cloven hooves.
E.g.
A large body that orbits a star.
E.g.
A substantial piece of orchestral music in several movements.
Instance: an embodiment by one thing of a type, giving
values to the properties of that type.
E.g.
A real world unicorn (were one to exist),
but only in so far as it exemplifies the unicorn type.
E.g.
Venus or Mars, but only in so far as it embodies the planet type.
E.g.
A symphony performance, but only in so far as it instantiates a symphony score,
Sign: a name, image or effect of a thing or a
type, which describers use in recognising, thinking or communicating about that
thing or type.
E.g.
The word “unicorn”, a picture of a unicorn, an effect of its horn (rendering
poisoned water potable).
E.g.
The word “planet”.
E.g.
The term “Beethoven’s ninth”.
Token: an appearance of a sign or a type in a
memory or message.
E.g. Either a sign of the kind above, such as “unicorn”, or a copy of the type
(aka intensional definition).
Semiotics is about describing things.
System
theory is about describing an entity whose behavior is organised,
regular or repeatable.
The table below defines some signs and types used in describing such activity systems.
|
Sign |
Type |
|
Thing |
A describable element of the space-time continuum |
|
Behavior |
A thing that happens over time |
|
Structure |
A thing that exists in space |
|
Active
structure |
A structure that can act, can perform a behavior |
|
Passive
structure |
A structure that is acted on or in by a behavior |
A circus ring is a passive structure, an entity which may
be acted on or in.
It instantiates,
embodies, exemplifies, manifests or realises the
types “circle” and “arena”.
It has a particular value for the radius type, when measured to a chosen
degree of accuracy.
Notice there is fuzziness here, since no circus ring is perfectly
circular.
|
Sign |
Structure
Type |
|
Circle |
A continuous line which is, at every point, the same distance (the radius) from a central point |
|
Arena |
A
place where events are performed |
An
active structure is an entity that can perform a behavior, which may
change the state of the entity or other structures.
A social entity is an active structure that may perform various behavior types,
in parallel and over time.
(One
social entity may manifest several social systems.)
|
Particular
structure |
|
Behavior
types |
|
A
group (John, Joe, Joan and Jo) |
participates in |
games of bridge, games of poker, dinner parties |
|
A planet (Mars) |
performs |
orbits, rotations on axis |
System
descriptions as types
One particular thing may be described by several types; one type may be used to describe several things.
A type defines a thing only in so far as that thing instantiates one or more of that type’s properties.
Things usually have many more properties than any given type; and may have less.
It is a matter of judgement whether a thing that does not instantiate all properties of a type can be regarded as a thing of that type.
One particular entity may fit several systems descriptions; one system description may describe many entities.
A system description defines an entity only in so far as that entity instantiates one or more described system behaviors.
Entities usually have many more properties than any given system description; and may have less.
It is a matter of judgement whether an entity that does not instantiate all of a system description can be regarded as a system of that type.
Consider for example the communication between a traffic signal and drivers.
A traffic signal is an electro-mechanical system, designed to act as a proxy for a traffic policeman.
It displays a tiny range of 4 message instances, using a tiny vocabulary, in a short repeated traffic light cycle.
In this case, we have to use words as proxies for colors, describe behaviors as well as structures.
The theoretical system description includes several variables. E.g. “signal code”.
Each signal code is displayed repeatedly, incrementally populating the set of “signal displays” over time.
|
Sign |
Structure type |
|
Signal |
A
machine for displaying signal values. |
|
Signal
code |
A
color intended to convey a meaning; one in the set {red, red+amber, green,
amber}. |
|
Signal
intention |
A
meaning that a code is intended convey; one in the set {stay, get ready, go,
stop}. |
|
Signal
interpretation |
A
meaning associated with a signal code by a driver (ad hoc) |
|
Sign |
Behavior type |
|
Traffic
light cycle |
A
sequence of signal codes: red, red+amber, green, amber. |
|
Signal
display |
An
occurrence of a signal code, displayed in one traffic light cycle. |
|
Signal
reading |
An
occurrence of signal interpretation, made by a driver in one traffic light
cycle. |
The types are instantiated in the empirical system’s operation,
In action, a traffic signal instantiates (embodies, exemplifies, manifests) most of the types above.
It repeats the traffic light cycle by creating a succession of signal displays.
Each of those displays instantiates (for a few seconds) the more generic signal value.
Within each traffic light cycle, each signal display manifests a particular color code.
Each display encodes a meaning intended by the traffic light designer (e.g amber means “stop”.)
Each reading by a driver decodes a meaning from the display.
Information
v data
On its own, a signal display (an occurrence of amber) has no meaning.
It communicates meaning/information only when a driver reads it and decodes it.
In a successful communication, the intended meaning and received meaning are the same.
But what if the driver reads an amber display as meaning “accelerate” instead of “stop”?
In short, information is data at the point of creation or use.
Meaningful information is not found in data values alone.
It is found in the process when a data creator or user (be it human or machine) maps data values to data types, using a grammar.
(It can help if the data creator sends the data type in the message alongside the data value.)
I didn’t set out to say anything new in this article, and doubt I have done.
Some see the conclusions as controversial but the logic seems inexorable.
Certainly, a type must exist before a describer can use it to describe a thing.
Imagine you saw Venus in the night sky before the type “planet” was conceived, named and defined
Then, you could not describe it as an instantiation of the type named “planet”.
You could only say, ridiculously: “That light in the sky already instantiates all as-yet-undefined types that might be created or used to describe it in future.”
Surely few would presume a
type like “enemy” or “danger” existed before life.
And even fewer would presume that
human-specified types like “football” and “unicorn” existed before life.
Yet many
assume that mathematical types like “circle” exist for eternity – before and
after humans.
Why presume
some types have existed forever while others have not?
Could any types exist before there were describers, before there were life forms?
Conclusions here include:
· There can be no concept without a conceiver, or description without a describer
· Before life, there was no description.
· A type is a description
· All types are tokens, meaning they take a concrete form
· Some tokens are types, others are only signs
· Types do not exist in an ethereal and eternal form, independently of human thought
· There was no Platonic ideal “circle” before it was conceived by a describer
· Mathematical types like “circle” are exceptions rather than the norm.
· Communications depend on types being shared well enough, rather than perfectly, between communicating parties.
For more, see the papers under DESCRIPTION AND REALITY
and/or PHILOSOPHY on the "System Theory"
page at avancier.website.
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