Information, description and type theories https://lnkd.in/dQNhNbd

A cybernetic view of description and reality

A pragmatic, psycho-biological, constructivist philosophy of systems

Copyright 2014 Graham Berrisford. Now a chapter in “the book” at https://bit.ly/2yXGImr. Last updated 23/01/2021 21:53

 

This chapter follows three others.

·       Description and reality - three principles of description

·       Knowledge as a biological phenomenon

·       Knowledge, truth and types

 

This chapter outlines compatible theories of information, description and types. It presents a mainstream view, in a new way. The view, I believe, is one that most scientists and cyberneticians presume to be true. A new explanatory device is an epistemological triangle. The chapter promotes a type theory that allows fuzziness and transience in how things conform to types (in contrast to a more rigid set theory).

Contents

What it means to describe things (recap) 1

An information and communication theory. 4

A description theory. 8

The evolution of description. 11

A type theory. 14

Conclusions and remarks. 20

 

What it means to describe things (recap)

This chapter is about information and descriptions held in memories and transmitted in messages. For some, reading this chapter requires something of a paradigm shift. This first section contains a few pointers that may help you to avoid misunderstandings later.

 

Systems thinkers describe the world in terms of systems. In more general terms, there are:

1.     Phenomena: things that can be observed in reality or envisaged

2.     Descriptions: that correspond to or represent 1

3.     Describers: who create and use 2 in memories and messages.

 

The triangle below is a simplified version of the story. Read it from left to right: describers <create and use> descriptions <represent> phenomena. Note that a description in the mind is at the top, not the left.

 

Our epistemology

 2 Descriptions

<create and use>              <represent>

3 Describers <observe and envisage> 1 Phenomena

 

A description typifies what is described. Suppose I say “The sun is a yellow, spherical, source of light”. The properties named “yellow”, “spherical” and “source of light” appear in two forms.

·       The description is a compound type, composed of simpler general property types.

·       The phenomenon (the sun) embodies or exhibits those types in particular physical properties.

 

The rest of this introductory section distils points arising from the previous chapters.

 

Recognise “knowledge is a psychological phenomenon”

The universe existed for billennia before life emerged, without there being any knowledge of it. Animals evolved to abstract knowledge from perception of real-world phenomena. Where “knowledge” means information that is accurate enough to be useful. Maturana, a biologist and systems thinker, observed: “knowledge is a biological phenomenon”. In other words, before life, there was no knowledge, description or model of reality.

 

 

Recognize the importance of information processing

All social animals hold information in memory, and communicate it in messages. Humans refined information processing by recording knowledge in writing.

 

Don’t think of information processing as a side issue, peripheral to something else. Our lives and businesses depend on creating, processing, using and sharing information. This is evident from the hundred words below that we have for doing those things.

 

Abstracting, Accounting, Agreeing, Analyzing, Answering, Architecting, Asserting, Attributing, Averaging, Believing, Billing, Briefing, Calculating, Characterizing, Chronicling, Coding, Communicating, Composing, Conceiving, Counting, Deciding, Declaring, Decoding, Defining, Demonstrating, Describing, Designing, Detecting, Directing, Drawing, Elucidating, Encoding, Envisaging, Equating, Explaining, Expressing, Factualizing, Fictionalizing, Generalizing, Hearing, Hypothesizing, Idealizing, Illustrating, Informing, Instructing, Judging, Justifying, Knowing, Lying, Mapping, Measuring, Messaging, Modelling, Narrating, Observing, Orating, Ordering, Perceiving, Picturing, Postulating, Presenting, Proposing, Qualifying, Quantifying, Questioning, Reading, Recording, Recounting, Reifying, Remembering, Rendering, Reporting, Representing, Reproducing, Sensing, Sorting, Speaking, Specifying, Stating, Story-telling, Summarizing, Testing, Theorizing, Thinking, Totaling, Translating, Transmitting, Truth-telling, Typifying, Understanding, Valuing, Verifying, Viewing, Voting Visualizing, Worrying, Writing, X-raying, Yelling, Zeroing.

 

Information processing is central to activity system thinking. At design time, designers observe and envisage systems; and represent them in architectural descriptions. At run time, in operation, those systems detect events, and determine and direct activities performed by actors.

 

Recognize the looseness of natural languages

Synonyms and ambiguities abound in natural language. Consider the terms we use to describe things. We may speak of a thing as having properties, qualities, characteristics, attributes or features. Some use those terms interchangeably; some draw distinctions between them. There is no general agreement as to whether the terms should be distinguished or how.

 

An abiding sin of systems thinking discussion is over generalization. A word from one domain (say, fractal) is used in another, with a different meaning. This does not produce a more general theory of the world. Overloading a word with different meanings makes it ambiguous, and potentially misleading.

 

Recognize that one type can be instantiated in many times and places

Our type theory begins with four assertions:

·       to describe a thing is to typify it

·       to typify a thing is to describe it

·       one type can be instantiated in many things

·       one thing can instantiate (embody, realize, manifest, conform to) many types. 

 

We use the same terms (property, quality, characteristic, attribute and feature) with reference to both:

·       conceptual types (say, length: a measurable distance)

·       instantiations of conceptual types (say, the 100 metre length of a race).

 

Speakers assume that listeners can tell from the context which meaning applies; but it is not always clear.

 

Recognize that descriptions can be complex types

A type is conceptual or intensional definitions of a thing that instantiates the type. There are simple types like length, and complex types such as:

·       the conceptual type that is a symphony score

·       an instantiation of that conceptual type in a symphony performance.

 

Recognize that one phenomenon can be described in several ways

We use a map (mental or documented) to help us understand a territory. The map relates selected features of a territory to each other. The triangle below relates mappers to maps and territories. Read it left to right thus: Mappers <create and use> Maps <represent> Territory.

 

Cartography

Maps

<create and use>          <represent>

Mappers  <observe and envisage> Territories

 

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. And more generally, any phenomenon can be described in several ways. Say, light can be described in terms of waves or particles

 

Recognize that holism is not wholeism

A map is never a complete or perfect representation of a territory. It only needs to tell us enough that we can find or learn what we want.

 

Taking a holistic view of a business does not mean you study the whole of the business, every conceivable element of it. It can mean you observe or envisage elements relevant to your motivation for understanding or describing the business. Then, study or describe how those elements interact to produce outcomes they cannot produce on their own. Or else, you identify some unexplained or desired outcome of the business in operation. Then, you find or describe which elements of the business do or must interact to produce that outcome.

 

Recognize that description can take many physical forms

You may observe or envisage some properties instantiated some phenomenon, now or in the future. And encode those properties in a description or model future use. The description may be held in biochemical, mental, documented or other physical form.

 

There are no metaphysical elements in our (radical constructivist) philosophy

It is not that you have a pure or metaphysical concept in mind, which you may encode in a message, be it spoken or documented. Rather, all human knowledge (mental, documented or other) is a biological phenomenon, part of the human phenome. There is no concept without a conceiver, no description without a describer, no type without a typifier. Every concept or description is an observable phenomenon, encoded in some physical medium,

 

Every description you construct (in mind, on paper or elsewhere) encodes information that represents properties of some other phenomenon. To use that information, you must locate it and decode it. You may do that by reading an internal memory, or by reading an external message.

An information and communication theory

 

This chapter is not about Shannon’s information theory. (Which relates to what can be coded in and retrieved from signals such as radio waves, and about the integrity of data structures.)

 

And we don’t begin here by thinking of information like a linguist or software engineer might do. Millennia before verbal languages and computing, animals encoded input signals into memories. Then decoded memories into the stream of consciousness when determining responses to events. And social animals encoded and decoded messages (say, alarm calls) without needing to learn a language.

 

Try to imagine how you’d mimic these incredibly effective processes in software. Inevitably, you’d find yourself drawn down paths you understand. You’d think of data structures – stored in databases, and transmitted in data flows. You’d presume the need for formally defined languages, symbols, syntax and semantics.

 

But surely, a truly general information theory cannot start from or depend on how software works? It ought to start from the evolution of information created and used by animals. Many animals can not only remember information internally in memories, but also share information messages.

 

Information: a structure or behavior that represents something or phenomenon. More scientifically: “A carries information about B if the state of A is correlated with the state of B.”

 

Read this triangle left to right thus: Animals <create and use> Information <represents> Phenomena.

 

Intelligent life

Information

<create and use>          <represents>

Animals      <observe and envisage>    Phenomena

 

The information at the apex is encoded in memories and messages.

 

Memories and messages: holders of information.

In biology, internal memories and external messages are of different kinds. Memories are neural patterns; messages take the form of sounds, smells and gestures. In software, the distinction between memories and messages is blurred.

 

Communication: the exchange of information between senders and receivers.

Actors may exchange information directly by sending/receiving messages. Or else, indirectly by writing/reading information stored in some memory both can access. They respond to information in messages, often in a way determined by information in memory.

 

Remember: “A carries information about B if the state of A is correlated with the state of B.” A message represents a phenomenon if the structure of the message can be correlated with some features of the phenomenon.

The ubiquity of coding in memories and messages

Ashby’s cybernetics is about how information is stored and communicated. In the processes of creating and using information, rather than its physical form. These processes encode and decode information into and out of physical forms.

 

Ashby observed that in the creation and use of information “coding is ubiquitous”.

To create information is to write or encode a model that represents something. To use information is to read or decode a model, and use it for some purpose.

Nobody understands how our biochemistry encodes thoughts, but those processes exist. Suppose you want me to look at the moon, and ask me to.

·       Your conscious thought is encoded in

o   neural impulses from your brain to your mouth, then

§  vocal chord movements, then

·       sound waves, which translated into

§  ear drum movements, then

o   neural impulses from my ears to my brain, and

·       conscious thought in my mind. During the communication, your request is expressed or encoded in several forms, public and private.

Communication stacks in a communication network

Ashby presented the longer example below. To send and receive the gale warning message involves a succession of coding and decoding steps. Each time a message passes between humans, it passes down and up a communication stack. Down from the sender’s brain to some physical medium for transport. And back up from that physical medium to the receiver’s brain, where the message is stored in memory, at least for a while.

 

“Let us consider, in some detail, the comparatively simple sequence of events that occurs when a “Gale warning” is broad-cast. It starts as

·   a patterned process in the nerve cells of the meteorologist, and then becomes

·    a pattern of muscle-movements as she writes or types it, thereby making it

·    a pattern of ink marks on paper. From here it becomes

·    a pattern of light and dark on the announcer’s retina, then

·    a pattern of retinal excitation, then

·    a pattern of nerve impulses in the optic nerve, and so on through her nervous system. It emerges, while she is reading the warning, as

·    a pattern of lip and tongue movements, and then travels as

·    a pattern of waves in the air. Reaching the microphone it becomes

·    a pattern of variations of electrical potential, and then goes through further changes as it is amplified, modulated, and broadcast. Now it is

·    a pattern of waves in the ether, and next

·    a pattern in the receiving set. Back again to

·    a pattern of waves in the air, it then becomes

·    a pattern of vibrations traversing the listener’s ear-drums, ossicles, cochlea, and then becomes

·    a pattern of nerve-impulses moving up the auditory nerve.

… this very brief account mentions no less than sixteen major transformations

through all of which something [announcer’s the intention] has been preserved,

though the superficial appearances have changed almost out of recognition.” (1956, 8/2)

 

After receiving a message, a listener can verify the accuracy of the warning by watching the weather.

How memories and messages employ coding

If the correspondence between a structure in human memory and the phenomenon it represents is to be useful, the brain must decode the memory by reversing the encoding process. Similarly, if the correspondence between a structure in a message and the phenomenon it represents is to be used as intended, a receiver must decode the message using the same code the sender used to encode it. The meaning of a message only exists in the process of encoding it or decoding it.

 

Representing a structure

Suppose A = a map and B = a territory. And there are correspondences between the structures of the two entities. Then the map carries some information about the territory. And the territory carries some information about the map.

Representing a behavior

Suppose A = a musical score and B = a musical performance. And there are correspondences between the structure of A and the behavior of B. Then the musical score carries information about the process of the performance. And the performance carries information about the structure of the musical score.

 

Remembering a thing

Suppose

·       A = the state of something in the environment. M = the state of a message conveyed by eyesight to your brain#

·       B = the state of a memory in your brain.

 

To register and remember the existence of the thing

·       A is encoded into M

·       M is decoded and encoded into B.

 

Ultimately, the meaning of a memory is not found in the memory alone. It is found in the process by which B is decoded by retrieval and used. This last is the information of most interest to psychology.

 

Communicating an idea

Suppose A = the state of a message sender’s brain. M = the state of the message. B = the state of a message receiver’s brain.

To communicate an idea

·       A is encoded in M

·       M is decoded and encoded into B

 

The aim of human-to-human communication is not to draw a biological correspondence between A and B. How far the structures of two brains can be correlated at the biological level is unclear. By contrast, correspondence at the sociological level can be observed and verified.

Can we distinguish information from data?

 

In business?

A business creates and use data to represent phenomena it must monitor and direct.

To define the meaning of a customer data entity is to define the significance of the real-world customer entity to the business.

In business data modelling, various information/data distinctions have been drawn.

 

People speak of

Information in

Data in

a message or data flow

a memory or data store

analogue form

digital form

on paper

a computer

a conceptual or logical) model

a physical data model

 

Conceptual, logical and physical data models specify business data at different levels of abstraction

The higher-level abstracts from the lower by some permutation of idealisation, generalisation and aggregation.

 

In natural language?

The terms data, information and knowledge are often used interchangeably. The distinctions between them are subtle. You might say a frog’s mind holds a memory of things that resemble the insect type. Suppose the frog detects an instance of the insect type – that is meaningful information. The frog’s eyes encode that information into nerve impulses – a message containing data. Then. The brain decodes that message and responds by encoding a message sent to the frog’s tongue. If the tongue finds and captures the insect, that proves the information to be true, or knowledge.

 

WKID?

To facilitate discussion of social systems, an informal classification is helpful. Several WKID hierarchies have been proposed and criticised. The version below seems the best fit to a system of communicating actors.

 

WKID

meaning

Wisdom

the ability to apply knowledge in new situations.

Knowledge

information that is accurate enough to be useful.

Information

meaning created/encoded or found/decoded in data by an actor.

Data

a structure of matter/energy in which information has been created/encoded or found/decoded

 

For discussion of knowledge, and verifying the truth of information, reading the previous two chapters. The chapter sets out principles of information processing in the form of theories of information, description and types.

In any communication stack, the information/data distinction is recursive. The actors at level N+1 abstract the logical information of interest to them from the physical data structure at level N.

 

Note that any physical structure or motion, of matter or energy, can be used as a data structure or signal. Say,

·       The biochemical structures your brain

·       The shadow on a sundial – to represent the time of day

·       The state of your office door (open or closed) – to tell people whether you are open to visitors

·       Dance movements – to express emotions

·       Words (sounded or written).

 

In general, any phenomenon that is variable, has a variety of values, can be used to store or convey information. The phenomenon is used as data structure when it is

·       encoded to convey information/meaning

·       decoded as conveying information/meaning.

 

There is no information or meaning in a structure on its own. Data creators must perform processes to encode/create meanings in structures. And data users must perform processes to decode/find meanings in structures. This “information” of interest to sociology only exists in those processes. In the intentions or purposes of data creators and the interpretations of data users.

A description theory

 

Epistemology is about what we know of reality, through observation, testing, reasoning and learning from others. The purpose of a description us to help describers understand, respond to or manipulate the described phenomenon. This chapter uses this triangle to relate epistemological concepts.

 

Epistemology

Descriptions

<create and use>        <represent>

Describers <observe and envisage> Phenomena

 

The triangle is only simple graphical device, telling a small part of the story

The semantics of the triangle are defined below.

Describers are actors (natural or artificial) that can encode and decode descriptive models of phenomena.

Descriptions embrace all forms of mental, documented, digital and physical models.

Phenomena are entities, events and processes that can be observed or envisaged in time and space.

 

The relationship between each pair of concepts is many-to-many

One describer can create several descriptions of the same thing. Those descriptions may be compatible or in conflict. Is light waves or particles?). Physicists do not say either model is the “true” model, they say only that each can be useful.

 

Also, several describers can contribute to one description of the same thing. It may well be that none of those describers (say, no one system architect) knows whole description. The resulting description is larger, more complex, consistent and informative than any human memory can be.

 

Both describers and descriptions can be observed as phenomena

Describers are physical actors (natural or artificial), which may be described. Descriptions are physical matter/energy structures, which can be described.

 

To describe a thing is to classify it

A description represents, specifies or idealises a thing that embodies or instantiates the description. A class or type represents, specifies or idealises a thing that embodies or instantiates the type. A type is a description; a description is a type.

 

“Intensional definition” is the process of creating a type or description.

A description expresses a type in the symbols of a particular language. What gives the description meaning is the action of an actor in creating or using it. Encoding is the process of creating the symbols. Decoding is the process of reading and using the symbols.

 

(The encoding and decoding of information is a theme of cybernetics, after Ashby. See article/chapter 4 for that and others ideas drawn from Ashby’s cybernetics.)

 

Many don’t at first grasp the radical nature of this psycho-biological and cybernetic view of description and reality. Note especially

·       Descriptions in the mind are at the top (not the left)

·       Descriptions are often recoded into other descriptions

·       Descriptions are physical phenomena

Descriptions <represent> phenomena

Look to the right-hand side of the triangular relation. Descriptions embrace all kinds mental and digital models, speech and writings, paintings and physical models. A phenomenon is anything that can be observed or envisaged in time and space, including descriptions and describers.

 

Epistemology

Descriptions

<create and use>    <represent>

Describers <observe and envisage> Phenomena

 

Descriptions in the mind are at the top (not the left)

Descriptions at the apex of the triangle can take any form. Any kind of mental or digital model, speech or writing, painting or physical model. Any kind of mental, documented or 3D model, in the head, on the page, carved in stone.

 

It makes no difference. All are created and used to describe something that a describer observes or envisages. All carry information about whatever they represent. All are elements found in the human phenome.

In biology, descriptions in internal memories and external messages are different. In software, they are much the same. All are similar in that they are created to be used by a recaller or receiver.

Describers <create and use> descriptions

Look to the left-hand side of the triangular relation. Describers are actors (natural or artificial) that can encode and decode descriptive models of phenomena. Descriptions embrace all kinds mental and digital models, speech and writings, paintings and physical models.

 

Epistemology

Descriptions

<create and use>   <represent>

Describers <observe and envisage> Phenomena

 

Descriptions are often recoded into other descriptions

Models that mimic reality (say, a model airplane) are recognisable using the basic senses. Models that are encoded or symbolized can only by recognised by a machine that knows the code. Moving from the senses to the head, the head to the page, the page to the head, are all recoding processes.

 

Ashby observed that in thought and communication “coding is ubiquitous”. To create a description is to encode a model that represents some feature(s) of a phenomenon. To use a description is to decode a model, and use it, perhaps to respond or manipulate whatever is described. Thinking and communicating involve translating description from one form to another. However, the triangle cannot possibly show everything, say, the multiple recodings involved in thought or communication.

Describers <observe and envisage> phenomena

Look to the bottom side of the triangular relation. Describers are actors (natural or artificial) that have the ability to encode and decode descriptive models of phenomena. A phenomenon is anything that can be observed or envisaged in time and space, including descriptions and describers.

 

Epistemology

Descriptions

<create and use>   <represent>

Describers <observe and envisage> Phenomena

 

Descriptions are physical phenomena

Many copies of a description can be created and used. If all copies are deleted then the description disappears from the cosmos. In other words, there is no ethereal description aside from what exists in one or more copies of it.

 

Describers may observe a house, a horse, and the largest known prime number, which all exist in time and space, in material reality. The types “prime number” and “largest known prime” exist in countless minds and records. The latest instance of “largest known prime” can be envisaged as the output of an algorithm. But it exists only in records, because it is too large for a human to remember (in 2018 it had more than 23 million digits).

 

Describers can also envisage stuff that might possibly exist. E,g, a unicorn (a fantasy) or the next prime number beyond today’s largest known prime. Neither exist in material reality today, but they and infinite other possibilities may be described.

 

Some portions or aspects of the cosmos may never be envisaged or observed by describers. Conversely, some phenomena envisaged by describers (say, unicorns) may never be realized in the cosmos. Their descriptions exist, but will forever remain inconsistent with reality.

 

By the way, the phenomenon to the right of our triangle may be a description. In which case, the description at the apex may be a translation of it, or some kind of meta description. All that matters to describers is that the description helps them to understand, respond to or manipulate the phenomenon.

 

On the nature of description

All written here about systems is based on the idea that systems are patterns we abstract from physical phenomena. This reflects the outcome of a famous debate between two mathematicians about the meaning of descriptions. Another mathematician (to help me) has distilled the argument between Frege and Hilbert. To learn more, read the next section.

The evolution of description

 

Some philosophers have asked: What is reality? Does it exist or is it only imagined?  By contrast, a psycho-biologist asks: What is a description of reality? And what use is it?

 

Descartes is famously said to have started his philosophy from the premise “I think therefore I am”. Psycho-biologists presume rather more than that. They presume that:

·       Space and time exist

·       Other physical phenomena – things and their effects – exist in space and time.

·       Things that exist include you, me and others we communicate with.

·       Describers may perceive things, remember things and recall things.

·       Describers describe things in memories and in messages.

·       Describers can communicate and share descriptions.

·       There no meaning in a description on its own, meanings exist in the processes of creating and using a description.

 

This chapter looks at descriptive representation from the viewpoint of Darwinian biology. The premise here is that there was no description of reality before life. And description is a tool that emerged as a side effect of biological evolution.

 

Pragmatic constructivists presume there was no description of phenomena before life. Memories and messages are biological phenomenon that evolved to help animals survive. Animals daw on memories to react appropriately to events. Social animals exchange messages to coordinate their activities.

 

A description does not have to be complete or perfect. Far from it; it need only represent things well enough to enable recognition. A cat remembers a mouse’s features well enough that the cat can spot and catch mice

A honey bee remembers the location of some pollen well enough that later, it can direct other bees.

 

Why do social animals encode descriptions in messages? The survival of social animals depends on them sharing knowledge, like where food can be found.

 

The Darwinian question is: Does a description help you to understand, predict and manipulate things in reality, and so, improve your chance of reproducing? Here are some staging posts in the evolution of description

1.     Molecular memory: organisms recognize molecular structures. Neural memory: animals remember things they have seen, heard or otherwise perceived

2.     Social messaging: social animals share descriptions of things in fixed format messages (say, gestures and alarm calls)

3.     Speech: humans encode descriptions in words

 

Writing: humans record descriptions in an external persistent form. Science: humans learn to form theories, predict outcomes and test them in reality. Machine learning: humans create machines that can abstract descriptions from phenomena.

 

The previous chapter discussed information in memory, spoken and written form.

Description in graphical forms

A mapper is concerned with two things. A map - a description that expresses and relates abstract descriptive property types (defined in a key) selected by the mapper. A territory that exhibits or embodies those descriptive types in observable reality.

 

Cartography

 Maps

<draw and read>         <represent>

Mappers       <observe>     Territories

 

Hmm… Is the territory real? Or is merely another description – a mental model - we form of reality?

 

It makes no difference, the phenomenon to the right of our triangle may be a description. In which case, the description at the apex may be a translation of it, or some kind of meta description. All that matters to us, as travellers, is that a map helps us find or learn what we want.

Descriptions in building architecture

The structure of a building in reality, independent of any observer, is infinitely complex and incomprehensible. Given a building, the word architecture might be used for:

·       the visual sensation of building formed by an observer (as seen in reality or in a photograph)

·       one or more architectural drawings of the building (of which several different sets might exist).

 

Architectures as sensed

Archiectures as drawn

 Visual sensations

<form and recall>         <represent>

Humans           <observe>        Buildings

Drawings

<create and use>         <represent>

Architects <observe and envisage> Buildings

Descriptions of colors

Before life, light existed and was reflected from the surfaces of objects. But no color existed in the world then, either as a sensation or a description. Experiments show animal brains manufacture the sensation of color, from a mixture of the light they perceive and their experience. In the first place, a color is a sensation in the neural system, which acts to describe some light radiation, modified by what our brain expects to see. After that, a color can be a verbal description of that sensation – as in Isaac Newton’s rainbow, or a color chart, or a wave length range.

 

Colors in biology

Colors in Newton’s rainbow

 Visual sensations

<form and recall>     <represent>

Animals      <observe>    Light waves

Seven colors

<named>        <represent>

Newton    <observed>  Visual sensations

Descriptions of the universe

Imagination is essential to scientific advance, but it builds on existing knowledge (useful information). Imagination not based on knowledge may lead to nonsense or fantasy.

 

Einstein’s imagination was far more informed by existing knowledge than some might lead you to believe. "The 12-year-old Einstein taught himself algebra and Euclidean geometry over a single summer, and discovered his own original proof of the Pythagorean theorem. Max Talmud says that after he had given the 12-year-old Einstein a geometry textbook, after a short time he “had worked through the whole book. He thereupon devoted himself to higher mathematics... Soon the flight of his mathematical genius was so high I could not follow." His passion for geometry and algebra led the 12-year-old to become convinced nature could be understood as a "mathematical structure". Einstein started teaching himself calculus at 12, and as a 14-year-old he says he had mastered integral and differential calculus". Wikipedia

 

Physics

Mathematical structures

<create and use>           <represent>

Physicists     <observe and envisage>     Nature

Description in mathematics

Mathematicians often say a set may be defined by extension (listing members) or by intension (a type). Strictly, an intensional definition or type defines not a set, but one member of a set.

 

Mathematicians <use> types to <specify the properties of> instances. pattern is a thought, design or other phenomenon that is regular or repeatable. A type is a pattern for zero, one or more things or phenomena that instantiate the type. An instance is an exhibition or embodiment of the properties defined in the type.

 

Mathematics

Types

<create and use>       <are instantiated in>

Mathematicians <observe and envisage> Set members

 

There are simple types (say, individual notes in a musical score). And complex types (say, the scores of complete songs and symphonies). Both describe a phenomenon that is regular and repeatable.      

 

On the nature of mathematical types and descriptions

This chapter starts by saying “holism is not wholeism” and “the map is the territory we understand”. All written here about systems is based on the idea that systems are patterns we abstract from physical phenomena.

This reflects the outcome of a famous debate between two mathematicians about the meaning of descriptions. Another mathematician (to help me) has distilled the argument thus.

 

Frege posited that descriptions (axioms) are imperfect representations of thoughts. And that mathematics is carried out at the level of thoughts rather than descriptions.

The presumption is that we know what geometric entities, such as points and lines, actually are.

 

Hilbert said that, even if we did know, this is irrelevant to understanding of geometry. Since geometry merely defines some relations between some entities. He argues mathematics is carried out at the level of descriptions or models. In geometry, a description is a holistic model - it asserts that particular relationships exist between basic, unanalysed, entities. Those entities can be anything (large or small) that follow the relationships stipulated in the model.

 

Hilbert is now regarded as the winner of the debate, according to the Stanford Encyclopedia of Philosophy,

https://plato.stanford.edu/entries/frege-hilbert/

 

I am told, in short, the debate is whether you regard what is described in geometry as

·       a concrete entity, of which every detail is potentially relevant to answering questions about it

·       an abstract set of relationships between unanalysed entities.

 

In other words, does geometry addresses the whole of a thing (Frege), or only selected features of it that are describable by geometry (Hilbert). The cybernetic system theorist’s answer to this question is firmly in the Hilbert camp.

 

Activity system thinking doesn’t address the whole of a thing. It addresses only those features of a physical entity that can be represented in an abstract system description. For more, read the next part.

A type theory

 

This chapter presents the view that description and knowledge are instruments that evolved alongside life. This part promotes a type theory that allows for fuzziness and transience in the conformance of things to types. 

In contrast to the more rigid set theory you may be familiar with.

From fuzzy matching to describing things in terms of formal types (recap)

We show in our everyday thought, talk and actions that we believe the physical world exists. The existence of a physical reality is not a question worth debating. And clearly, many things in the universe resemble each other – from atoms to mountains to galaxies. The debate is whether concepts or types (“atom”, “mountain”, galaxy”) exist outside of human minds and models.

 

“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.

 

Efficiency demands we cannot respond to every event as though it is new and unique, we must somehow classify things. Wittgenstein suggested we recognize loose “family resemblances” rather than types. However, to remember just one particular thing is to remember some of its features. In effect, that set of features forms a pattern or type that future things can be compared with.

 

A reader says: “since every particular defines a type there is no value in the concept of a "type" so defined.” To contrary, if a man with a gun takes a pot shot at you, then remembering that particular situation is valuable. That is the basis of learning by conditioning in psychology. The type is not the man, it is the description of the man you hold in memory.

 

In nature, the matching of newly-perceived things to past-remembered things may be fuzzy. It has only to be close enough to help us learn from experience. This is the basis of conditioning and learning by trial and error. The memory of one thing serves as a type; since we can match perceived things to that memory. And then respond to a new thing in the light of what we learned from responding to the old thing.

 

In science, the matching of perceived evidence to remembered theories has to be more exact.

 

Formalizing types in verbal descriptions of reality

In describing pollen sources, honey bees describe things that resemble each other. But they don’t discuss what those resemblances are.

 

By contrast, humans can and do discuss the resemblances between things, create types. We invent words (such as yellow, person, payment) to label similar things and qualities. We formalise our sense of family resemblances by defining types. Say, order amount. We document descriptions of entities, events and processes. Say, a billing process. And relate types to each other in logical statements. Say, order value = order amount * unit price.

 

Typication

Types

<create and use>         <represent>

Humans  <observe & envisage> Phenomena 

 

There is no way to know the world “as it is”; the idea doesn’t even make sense. Since Einstein's day, scientists say what we can understand is descriptions we make of the world. The success of science demonstrates the effectiveness of describing phenomena using types and logic. And the success of business demonstrates the effective of designing systems using types and logic. But before we can even begin to think of types, we have to think of things as being discrete, describable and differentiable

Seeing things as discrete, describable and differentiable

2/1. “The most fundamental concept in cybernetics is that of ‘difference’, either that

·       two things are recognisably different, or that

·       one thing has changed with time… We assume change occurs by a measurable jump.” Ashby. 1956

 

The universe is an ever-unfolding process, in which space and time are continuous. But in our perceptions, memorizations and descriptions of phenomena, we divide continuous things and qualities into discrete chunks. This requires what psychologists now call the “just noticeable difference”. The concept is traceable to Ernst Weber a 19th century experimental psychologist

His “difference threshold” (or JND) is the minimum amount by which stimulus intensity must be changed in order to produce a noticeable variation in sensory experience.

Using his eyes, Newton divided the continuous spectrum of light into (first five and later seven) discrete colours. And thousands of years ago, using their ears, musicians divided the continuous spectrum of sound into discrete notes. One actor may use a JND in any physical form to encode information for other actors to read.

Say, I leave the office open door open to convey the information that I am open to visitors.

 

Differentiating things in space at one time

To describe the continuous space of the universe, we differentiate discrete entities. An entity’s boundary may be physical (say, the boundary of a solid in a liquid or gas). Or logical, such as the players in a soccer team, who grouped by sharing the same style of shirt.

 

To describe the continuous qualities of things, we differentiate discrete types. Types appear as qualitative attributes (colors) and quantifiable amounts (height, width and depth).

 

Differentiating changes to one thing over time

Change can be classified in three ways:

·       continuous or discrete

·       state change or mutation

·       natural/accidental or designed/planned.

 

The universe is an ever-unfolding process of continual change. A social entity continuously and naturally mutates. Its members change, and it responds to environmental changes that were not predictable or anticipated.

 

By definition, an activity system is an island of regularity in the universe. A system that continually changes its nature would be a contradiction in terms. If there is no stable pattern, no regularity, no repetition, then there is no system to describe. A system cannot possibly be designed to continually mutate into infinite different systems. Ashby and Maturana, separately, rejected continual mutation as undermining the concept of a system. However, continuous change can be simulated by dividing changes into steps frequent and small enough to appear continuous. Discrete designed mutation (say, system version 1 to version 2).

 

Klaus Krippendorff (a student of Ashby) wrote as follows:

"Differences do not exist in nature. They result from someone drawing distinctions and noticing their effects.”

“Bateson's ‘recognizable change’ [is] something that can be recognised and observed."

 

To describe the passage of time and its effects, we divide its continuous flow into discrete intervals or changes. We differentiate:

·       discrete qualities of a thing: say, asleep to awake

·       discrete versions of a thing: say, caterpillar to butterfly. discrete generations of a thing: say, parent to child.

 

To differentiate discrete qualities, versions and generations is to create descriptive types.

Types as descriptions

Our type theory begins with some assertions

1.     A description typifies a phenomenon as embodying or exhibiting properties.

2.     Types encoded in descriptions are conceptual properties.

3.     Types can be instantiated as physical properties embodied in or exhibited by phenomena.

4.     A description is a type; and a type is a description.

5.     One type can be instantiated in many things

6.     One thing can instantiate (embody, realize, manifest, conform to) many types. 

 

A type classifies things that are similar in some way, to some degree. Two things (say, mouse and caterpillar) can be seen as either:

·       two instances of one type (say, two animals), or

·       instances of two different types (say, one mouse and one caterpillar).

 

Two things (say, green box and blue box) can be seen as either:

·       two instances of one type (say, two boxes), or

·       instances of two different types (say, one green box and one blue box).

 

Typification is so fundamental to our existence we have countless words for ideas about things. Those ideas may be called concepts, qualities, properties, characteristics, features, or attributes. We describe a thing by relating it to general ideas, classes or descriptive types.

 

Say, in general, a human body has height and shape property types. To instantiate a type is to embody, exhibit, exemplify, manifest or realize that type in a particular value. We describe a particular thing as instantiating its descriptive types. Say, In particular, one body’s height is 2 metres and its shape is humanoid.

 

Unfortunately, we are sloppy about distinguishing types from instances. And confusingly, we refer to both general types and particular values as qualities, properties, concepts, characteristics, and attributes.

Descriptions as types

Describers use types (classes, categories) to categorise and describe things. The three essential relationships are:

·       Describers <observe and envisage > phenomena.

·       Describers <create and use> types to help them recognize and deal with phenomena.

·       Types <characterizes> phenomena in terms of their structural and/or behavioral attributes.

 

Types

Types

<create and use>     <characterize>

Describers <observe and envisage > Things

 

A description can been seen as a (perhaps complex, perhaps polythetic) type that identifies properties of the thing described. One description may conceivably be embodied or realized in many physical instances, by many real-world things. Having described one universe, physicists can posit the existence of infinite other universes

 

Describer(s)

One abstract type

Many physical instances

Many physical entities

Composer(s)

One symphony score

Many symphony performances

Many orchestras

Building architect(s)

A set of architecture drawings

Many concrete buildings

Many builders

Business architect(s)

One set of business roles and rules

Many businesses processes

Many business actors

Software engineer(s)

One program

Many program executions

Many computers

Game designer(s)

The rules of “poker”

Many games of poker

Many card schools

 

In each example above, the description is embodied or realized in many instances, by many real-world entities. The description is a concept, a type or typifying assertion. And conversely, a type or typifying assertion is a concept, is a description.

The curious relationship of types to sets

For millions of years, social animals have described things using symbolic gestures or sounds – as an alarm call symbolise dangers. Over many thousands of years, people have described things by typifying them verbally – as an elephant, a planet, or round and yellow. Some words represent mathematical concepts – a triangle, an ellipse, and of course, a number.

 

Many animals can recognise the difference between there being one, two or three things of a type. Ancient peoples quantified the items in a collection using words to represent numbers. About 5 thousand years ago, mathematicians introduced the type “zero”, to describe the emptiness of a collection that has no items. About 2 thousand years ago, mathematicians created the decimal number system. Less than 2 hundred years ago, the mathematician Cantor introduced the concept of a set - a collection of things.

 

Set theory is a branch of mathematical logic, and most often applied to mathematical concepts. Traditionally, set theory begins with this relation: a thing can be a member of a set. 

A set is a collection of members; change the members and you change the set; or rather, you a create a new set.

A set can be described:

·       by extension, by listing its members. Say, The rainbow colours set is {red, orange, yellow, green, blue, indigo, violet}. #

·       by intension, by a type that lists one or more attributes of a member. Say, A vehicle in the vehicle set has wheels, a weight and a fuel type.

 

So, to speak of a set, you need one or other way to define a member. You need either a list of members (an extensional definition), or at least one type (an intensional definition).

Mathematicians usually think of a set as a collection of members across all space and time. However, you can limit the set in two ways, first by extensional definition. Or second, by including space and time limits on the intensional definition of a set member.

 

One type expressed in different ways

What at first sight appear to be two sets, with two different types, can turn out to be equal and the same set.

 

Type name

Type qualities or attributes

Doubled number:

A number exactly divisible by two.

Even number

A number greater than an odd number by one.

 

Since everything conforming to one type must conform to the other, there is only one set.

 

Two types that relate to the same or different sets

A set is identified with its members.

 

Type name

Type qualities or attributes

Your friend

A person whose personal number is in your phone right now.

My friend

A person whose personal number is in my phone right now.

 

Today, we have the same friends, and there is one set.

Tomorrow, when one of us adds or removes a friend from our phone list, there are two different sets.

Over two days, there have been three sets, but the two types have not changed.

 

Three types associated with overlapping sets

Where one set overlaps with another set, or is a subset of another set, there are different sets.

 

Type name

Type qualities or attributes

Person

A homo sapiens who has lived, is living, or will live in the cosmos.

Person of interest

Extends “Person” with the constraint that the Person must recorded in our database

Person alive now

Extends “Person” with the constraint that the current time is after birth and before death

 

Clearly, we can associate sets with types. But people created and used types eons before any set theory was established. You may assume that once set theory was established, it embraced type theory. But today, there several set theories and several type theories. Although a type can be associated with a set, we can define and use types with no knowledge of sets. And while a set is identified with a fixed number of members, there is no need to presume a type has a fixed number of instances.

 

All we need for our system theory is a simple theory of types as tools for describing things. To change a type within a system is to change the system. Replacing one set by another (with more or fewer members) doesn’t affect the design of a system or require system testing. But replacing one type by another is more significant, since it does affect the design of a system and requires system testing.

Polythetic (fuzzy) types

Some mathematicians presume a type is monothetic, meaning every set member embodies every attribute included in the type. Types in softer sciences, in social and business systems, are polythetic, meaning a thing may embody only some of its attributes. And sometimes, no particular attribute is needed for membership of the typified collection of things. Wittgenstein use the example of “game”, which I have tried to define below, with no confidence of convincing you.

 

Type name

Type qualities or attributes

Game

An activity performed for enjoyment, or to practice some skill, or to win some prize, or to gain some advantage

 

Basic set theory doesn’t embrace polythetic types - in which the attributes of a type are optional. Also, it doesn’t allow the conformance of a thing to a type to be fuzzy, or a matter of degree. Say, the people who conform to the type “your friend”.

 

Given such a fuzzy type, the extent of an associated set is debatable – two observers may associate different sets with the same type. This instrumentalist and materialistic view of mathematics may seem radical or strange to many – especially mathematicians. But it seems enough for the purpose of describing “real machines” as “systems”.

Conclusions and remarks

This chapter outlines compatible theories of information, description and types. It presents a mainstream view, in a new way. The view, I believe, is one that most scientists and cyberneticians presume to be true

The new explanatory device is an epistemological triangle. This chapter promotes a type theory that allows fuzziness and transience in how things conform to types (in contrast to a more rigid set theory).

The next chapter summarizes some implications of those theories. It challenges other philosophical triangles, including those of Peirce and Popper. And whether what we think of as universal concepts, types and numbers, existed before life.