The
evolution of descriptive types
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Actors use types to recognise and describe things to each other.
Where do types come from? Did types and numbers exist before life?
The evolution of concepts and numbers might have run as follows.
Contents
Animals
evolved to perceive the universe in terms of discrete things in space.
Animals
evolved to recognise family resemblances between things.
Animals
evolved to recognise if a group of things gains or loses a member
Animals
evolved to communicate facts about things that resemble each other
Humans
acquired verbal languages to describe things in terms of types
Humans
developed monothetic and polythetic types
Humans learn
to count things of a type
Humans
develop artificial intelligence to create new types
Physicists consider our world to be embedded in a four-dimensional space-time continuum.
It is called a “continuum” because it is assumed that space and time can be subdivided without any limit to size or duration.
Although the real world is continuous, we perceive, describe and model that world in terms of discrete entities and events.
This work proposes the discreteness of things in models of the world evolved through biological evolution.
“At a conscious level, animals tend to interpret the world as discrete things.
We pattern match, then label (not necessarily verbal), then move our limited attention on, which is part of a survival strategy, to categorise things as safe or dangerous.” Ron Segal in discussion with the author
An animal that is able to recognise instances of a type (food item, friend, enemy) is better equipped to survive.
To begin with, animals must have recognised only fuzzy family resemblances, say attractive or repulsive.
An earthworm
knows enough to recognise another worm of the same type – for mating purposes.
Certainly, a worm can recognise others members of the worm set, though it may not remember them, and surely cannot count them.
Experiments show babies, before they have words, can recognise when a small group of things gains or loses a member.
And dolphins can recognise which of two boards has, say, five dots rather than six.
The members of a species must have a similar idea of what food, friends and enemies have in common.
The survival of a social group depends on its members sharing ideas, like where food can be found.
Many animals can communicate facts about things of interest by gestures and/or noises.
Honey bees can communicate the direction and distance of a pollen source.
Astonishingly, experiments suggest honey bees can count up to four and communicate that amount to other bees.
Evolution led to human-level self-awareness and verbalisation, to the use of words to describe things of interest.
Through verbalisation, we define and communicate information about countless types of things.
Consider for example the types: river, rose bush, woman, football match, planet, number and triangle.
All such types are logical abstractions, they are constructs of intelligence.
A type is an abstraction from one or more things we perceive or describe as being similar.
It gives us least a partial idea, model or description of a discrete thing we are interested in.
It describes what is true of an instance, by defining one or more properties to be found in a member of a set.
A set can be defined by extension: by enumerating the members of the set (e.g. by pointing to all the rose bushes in my garden).
More usefully to us, what typifies set members can be defined by intension, by listing properties shared by instances of the type.
|
This thing |
is an instance that |
this type |
|
A rose |
exhibits the properties of |
Rosa: a plant that is bushy, thorny, flowering, woody, and perennial. |
To typify is to describe something.
Less obviously, the converse is true; to describe something is to typify it.
Once you have described one thing, there is no limited to the number of similar things that may exist or be created to the description you made.
This applies all the way up from the simple descriptions/types (binary digit), to large and complex descriptions/types (the specification of a Boeing 737).
A type is a kind of template or pattern, a generalisation to which things may conform.
Fairly obviously, a thing that instantiates a named type (a rose) may have more properties than those in the intensional definition of that type (rose).
Far less obviously, that thing may have less properties than the named type, if we allow a type to be fuzzy or polythetic.
Humans formalised the notion of family resemblances with the concept of a “polythetic type”.
A polythetic type a broad set of criteria that are neither necessary nor sufficient to identify an instance.
Each instance of the type must possess some of the defining characteristics, but none has to be found in every instance.
Having developed the concept of a type, humans learnt how to manipulate it.
A monothetic (Aristotelian) type is a set of characteristics that are both necessary and sufficient in order to identify instances of that type.
Mathematicians developed monothetic types like number and triangle, and set theory.
E.g. The necessary and sufficient description of a prime number is that that is divisible only by 1 and itself.
|
This thing |
is an instance that |
this type |
|
16 |
instantiates the qualities of |
Even number: a number divisible by 2. |
|
A planet |
manifests the idea of |
Planet: a massive body that orbits a star. |
As soon as we humans have a group or type in mind, we can start counting the members of that group or type.
And soon as we can count, we find that many groups and types have something in common.
That is, the total number of members, whatever they are.
We use numbers as types, to describe what groups of the same size have in common.
· “oneness” is the property shared by all groups with one member
· “twoness” is the property shared by any one-thing group to which we have added one.
· “empty (zeroness)” is the property of any group from which we have removed all members.
The human ability to generalise across groups and types of different things led to numbers.
And numbers are the basis of mathematics, hard science and the types used in software.
|
The
basis of mathematics |
|
Numbers <create and use> <abstract quantities of> People <observe and envisage > Instances
of Types |
The question is not so much whether there were numbers before life.
It is whether there were any types before life.
The premise here is that there were no types, no descriptions, before life.
The infinite variety of types we manipulate depend on our ability to identify similarities between things and typify them.
However, there were always things that can (in retrospect) be regarded as similar.
This was first true at the level of atomic particles, then stars and planets.
Numbers did not exist in the form of types before life forms started to create, remember and communicate types
But numbers always
existed in the sense that numerous similar instances of what we now choose to
describe as a type have existed.
In the last century, humans developed machines that can create instances of types in signals.
The by-products of evolution now include computers that can read process types and perform process instances, read data types and create data instances
The latest step is for the machine to create and use types – which is the ability required for artificial intelligence.
There are robots that can perform the magic of abstracting a general type of thing from observations of particular things.
“Theoretical results in machine learning mainly
deal with a type of inductive learning called supervised learning.
In supervised learning, an algorithm is given
samples that are labeled in some useful way.
For example, the samples might be descriptions of
mushrooms, and the labels could be whether or not the mushrooms are edible.
The algorithm takes these previously labeled
samples and uses them to induce a
classifier.
This classifier is a function that assigns labels
to samples including the samples that have never been previously seen by the
algorithm.
The goal of the supervised learning algorithm is to optimize some measure of performance such as minimizing the number of mistakes made on new samples.” Wikipedia
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