What's information,
for
an organism or intelligent
machine?
How can a machine or organism mean?
Preprint of chapter to appear in a book on Information and
Computation
to be published by World Scientific Publishing Co. 2011
Edited by
Dr. Gordana Dodig-Crnkovic (Mdlardalen University, Sweden) and
Dr. Mark Burgin (UCLA, USA)
This html file was automatically generated from latex by 'tth' and
is likely to contain errors and omissions. For a definitive version,
which may also be more up to date, please use the pdf version:
here.
Abstract
Words and phrases referring to information are now used in many
scientific and non-scientific academic disciplines and in many forms of
engineering. This chapter suggests that this is a result of increasingly
wide-spread, though often implicit, acknowledgement that besides
matter and energy the universe contains information
(including information about matter, energy and information) and many of
the things that happen, including especially happenings produced by
living organisms, and more recently processes in computers, involve
information-processing. It is argued that the concept "information"
can no more be defined explicitly in terms of simpler concepts than any
of the other deep theoretical concepts of science can, including
"matter" and "energy". Instead the meanings of the words and phrases
referring to such things are defined implicitly in part by the
structure of the theories in which they occur, and in part by the way
those theories are tested and used in practical applications. This is
true of all deep theoretical concepts of science. It can also be argued
that many of the pre-scientific concepts developed by humans (including
very young humans) in the process of coming to understand their
environment are also implicitly defined by their role in the theories
being developed. A similar claim can be made about other intelligent
animals, and future robots. An outline of a theory about the processes
and mechanisms various kinds of information can be involved in is
presented as partial implicit definition of "information". However
there is still much work to be done including investigation of varieties
of information processing in organisms and other machines.
Contents
1 Introduction
1.1 The need for a theory
1.2 Is biological information-processing special?
1.3 Questions seeking answers
2 Uses of the word "information"
2.1 Confusions
2.2 This is not "information" in Shannon's sense
2.3 Misguided definitions
2.4 The world is NOT the best representation of itself
2.5 Disagreements about information bearers, representations
2.6 Computation and information
2.7 Not all information is true
3 Is "information" as used here definable?
3.1 The inadequacy of explicit definitions
3.2 Concepts implicitly (partially) defined by theories using them
3.3 Evaluating theories, and their concepts
3.4 The failure of concept empiricism and symbol-grounding theory
4 Information-bearers, information contents.
4.1 Users, bearers, contents, contexts - physical and virtual
4.2 Changing technology for information-bearers
4.3 A common error about bit patterns and symbols
4.4 Many forms of representation
4.5 "Self-documenting" entities
5 Aspects of information
5.1 Information content and function
5.2 Medium used for information bearer
5.3 Same content, but different function
5.4 Processing requirements for different media
5.5 Potential information content for a user
5.6 Potential information content for a TYPE of user
5.7 Information content shared between users
5.8 Ambiguity, noise, and layers of processing
5.9 Information content for a user determined partly by context
5.10 Information-using subsystems
5.11 Layers of interpretation in epigenesis
6 Conclusion
6.1 An implicitly defined notion of "information"
6.2 Life and information
6.3 Information processing in virtual machines
6.4 Finally: Is that everything?
1 Introduction
The question "What is information?", like "What is matter?" and
"What is energy?", cannot have a simple answer in the form of a
non-circular definition. Answering such a question involves answering a
host of related questions. Answers to the second and third cannot be
given without presenting deep and complex theories about how the
physical universe works. The theories, along with links to experimental
methods, instruments and observation techniques, provide the only kind
of definition possible for many of the concepts used in the physical
sciences: implicit definition. Moreover, the answers are always subject
to the possibility of being revised or extended, as the history of
physics shows clearly: old concepts may be gradually transformed as the
theories in which they are embedded are expanded and modified -
sometimes with major discontinuities, as happened to concepts like
"matter", "energy" and "force" in the work of Newton and Einstein,
for example. Lesser transformations go with improved instruments and
techniques for observation, measurement, and testing predictions. So
concepts, have a continuing identity through many changes,
like rivers, growing organisms, nations, and many other things
.
1.1 The need for a theory
"Information" (in its oldest, and still growing, use), is another
such concept. So answering the question "What is information?"
will require developing a deep and complex theory of how parts of
the universe that use or interact with information work, for
instance entities (information users) that do various things with
information: acquiring, manipulating, combining, deriving, storing,
retrieving, comparing, analysing, interpreting, explaining,
indexing, annotating, communicating, and above all using
information for practical purposes. Information cannot play a role
in any process unless there is something that encodes or expresses
the information: an "information bearer" (B), and some user (U)
that takes B to express information I (i.e. interprets B). The same
bearer B may be interpreted differently by different users, and the
same user, U may interpret B differently in different contexts (C).
We need a theory that explains the different ways in which a
bearer B can express information I for U in context C, and what
that means. I shall henceforth use "representation" to refer to
any kind of information bearer, and will later criticise some
alternative definitions, in Section 2.3.
Such a theory will have to mention different kinds of information-users
and information-bearers (physical and non-physical), as well as
different kinds of information content, and the different ways
information-bearers can be related to the information they carry, often
requiring several layers of interpretation, as we'll see. The theory
will also have to survey varieties of information users, with different
sorts of information processing architectures, interacting with
different sorts of environment, using information-bearers
(representations) that have different structures, and use different
media (physical and non-physical).
Questions to be addressed include: What are the requirements for U to
treat B as expressing a meaning or referring to something? What are the
differences between things that merely manipulate symbolic structures
and things that also understand and make use of information they
associate with those structures, for example, deriving new information
from them, or testing the information for consistency?
Compare [ SearleSearle 1980].
1.2 Is biological information-processing special?
Many of the questions have a biological context. In what ways do
organisms acquire, store, extract, derive, combine, analyse, manipulate,
transform, interpret, transmit, and use information? Which of these are,
or could be, replicated in non-biological machines? If not all of them,
then why not? Is there something special common to all forms of
biological information processing?
1.3 Questions seeking answers
More general questions of a more philosophical kind that need to be
answered include, whether "information" is as important a concept for
science as "matter" and "energy", or just a term that is bandied
about, with changing meanings, by undisciplined thinkers? Is it reasonable
to think of the universe as containing matter, energy and information,
with interdependencies between all three, or is there only matter and
energy, in various static and changing configurations?
Why is a simple explicit definition for "information" impossible? Is
it like some older scientific concepts, not explicitly definable, but
implicitly definable by developing powerful explanatory theories that
use the concept? Is information something that should be measurable as
energy and mass are, or are its features mainly structures to be
described not measured (e.g. the structure of this sentence, the
structure of a molecule, the structure of an organism)? How does this
(centuries old) notion of information (or meaning) relate to the more
recent concept of information as something measurable?
Are there conservation laws for information, or is that idea refuted by
the fact that one user can give information to another without losing
any? Moreover, it is even possible for me to say something that gives
you information I did not have. (Compare the role of relay switches in
electrical power circuits.)
This document attempts to give partial answers to these questions, and
to specify requirements for more complete answers. I shall attempt to
sum up what I think many scientists and engineers in many disciplines,
and also historians, journalists, and lay people, are talking about when
they talk about information, as they increasingly do, even though they
don't realise precisely what they are doing. For example the idea of
information pervades many excellent books about infant development, such
as , without being explicitly defined. I shall try to
explain how a good scientific theory can implicitly define its main
theoretical concepts, and will sketch some of the main features of a
theory of the role of information in our universe. A complete theory
would require many volumes. In several other papers and presentations
cited below, I have presented some of these ideas in more detail.
2 Uses of the word "information"
2.1 Confusions
Unfortunately, there are many confusions about both the
content of the notion of "information" (what we mean by it, how
it should be defined, whether it can be given any precise
definition) and its status (e.g. as a theoretical term in
scientific theories, or as a loose and ill-defined, though currently
fashionable, concept). The word may be a source of so much confusion
that a better one is needed, but it is too late to propose a
replacement, and there is no obvious candidate. "Meaning" is just
as bad, or worse, since it often refers to an intention (what did
you mean to do?), or the importance of some event or object (what's
the meaning of the election result?), whereas information does not
have to be the content of anyone's intention, and can be devoid of
importance.
Some philosophers talk about "propositional content" but the
normal interpretation of that phrase rules out information expressed
in non-propositional forms, such as the information in pictures,
maps, videos, gestures, and perceptual systems. So I shall stick to
the label "information", and attempt to explain how it is used in
many everyday contexts and also in scientific (e.g. biological)
contexts. The word is also used in this sense in engineering, in
addition to being used in Shannon's sense, discussed further in
Section 2.2.
The phrase "semantic information" is as pleonastic as the phrase
"young youths", since information, in the sense under discussion, is
semantic. It is sometimes useful to contrast syntactic information with
semantic information, where the former is about the form or structure of
something that conveys information, whereas the semantic information
would be about the content of what is said. ("Content" is metaphorical
here.) For instance, saying that my sentences often have more than eight
words gives syntactic information about my habits, whereas saying that I
often discuss evolution or that what I say is ambiguous or unoriginal
gives semantic information, or, in the latter case, meta-semantic
information. Likewise, we provide syntactic information about a
programming language (e.g. how it uses parentheses) or semantic
information (e.g. about the kinds of structure and transformations of
structure that it can denote). We can distinguish the "internal"
semantics of a programming language (the internal structures and
processes the programs specify) from its "external" semantics, e.g.
its relevance to a robot's environment, or to a company's employees,
salaries, jobs, sales, etc.
2.2 This is not "information" in Shannon's sense
There is another, more recent, use of the word "information" in
the context of Shannon's "information theory" .
But that does not refer to what is normally meant by "information"
(the topic of this paper), since Shannon's information is a purely
syntactic property of something like a bit-string, or other
structure that might be transmitted from a sender to a receiver
using a mechanism with a fixed repertoire of possible messages. If a
communication channel can carry N bits then each string
transmitted makes a selection from 2N possible strings. The
larger N is, the more alternative possibilities are excluded by
each string actually received. In that syntactic sense longer
strings carry more "information". Likewise the information
capacity of a communication channel can be measured in terms of the
number of bits it can transfer in parallel, and the measure can be
modified to take account of noise, etc. Shannon was perfectly aware
of all this. He wrote
"The fundamental problem of communication is that of reproducing at
one point either exactly or approximately a message selected at
another point. Frequently the messages have meaning; that is they refer
to or are correlated according to some system with certain physical or
conceptual entities. These semantic aspects of communication
are irrelevant to the engineering problem."
. [My emphasis.]
It is worth noting that although he is talking about an engineering
problem of reproducing a message exactly, doing that is not what
most human communication is about. If you ask me a question, my
answer may fill a gap in your information, allowing you to make
inferences that I could not make. Both of us may know that, and that
could be the intention of my answer. On a noisy phone line that
could happen if you knew in advance that the answer was either
"elephant" or "fly". If I say "fly" and you hear "spy", the
fact that my precise message was not transmitted accurately does not
matter: you can tell that I did not say "elephant", and proceed
accordingly. A pupil's questions or comments may give a teacher
information that the pupil would not understand, e.g. about how to
continue a lesson. So communication in intelligent systems depends
on, but is far more than, mere signal transmission. It also uses
context, general knowledge of the world, more or less sophisticated
interpretation mechanisms, and reasoning capabilities. Shannon's
work is summarised, with strong warnings about extending it beyond
the context of electromechanical signal transmission in
.
Having a measurable amount of information in Shannon's sense does not,
in itself, allow a string to express something true or false, or to
contradict or imply something else in the ordinary senses of
"contradict" or "imply", or to express a question or command. Of
course, a bit string used in a particular context could have these
functions. E.g. a single bit could express a "yes" or "no" answer to
a previously asked question, as could a "continue" or "stop"
command. In some contexts, that single bit may indirectly convey a great
deal of information. "Is everything Fred wrote in his letter true?"
"Yes."
2.3 Misguided definitions
[ BatesonBateson 1972] describes "a bit of information" and later "the
elementary unit of information" as "a difference that makes a
difference".1 This is widely misquoted as offering a
definition of "information" rather than "a bit/unit of
information". He seems to be thinking of any item of information as
essentially a collection of "differences" that are propagated
along channels. This is far too simplistic - and perhaps too
influenced by low level descriptions of computers and brains. An
alternative approach is to define "information" implicitly by a
complete theory, as happens for many scientific concepts. This paper
attempts to present substantial portions of such a theory, though
the task is not completed. Section 3.2 explains how
theories can implicitly define the concepts they use and
6.1 relates this to defining "information".
What it means for B to express I for U in context C cannot be given any
simple definition. Some people try to define this by saying U uses B to
"stand for" or "stand in for" I. For instance, Webb writes "The
term `representation' is used in many senses, but is generally
understood as a process in which something is used to stand in for
something else, as in the use of the symbol `I' to stand for the author
of this article" [ WebbWebb 2006]. This sort of definition of
"representation" is either circular, if standing for is the same thing
as referring to, or else false, if standing in for means "being used in
place of". There are all sorts of things you can do with information
that you would never do with what it refers to and vice versa. You can
eat food, but not information about food. Even if you choose to eat a
piece of paper on which "food" is written that is usually irrelevant
to your use of the word to refer to food. Information about X is
normally used for quite different purposes from the purposes for which X
is used. For example, the information can be used for drawing
inferences, specifying something to be prevented, or constructed, and
many more. Information about a possible disaster can be very useful and
therefore desirable, unlike the disaster itself.
So the notion of standing for, or standing in for is the wrong notion to
use to explain information content. It is a very bad metaphor, even
though its use is very common. We can make more progress by considering
ways in which information can be used. If I give you the information
that wet whether is approaching, you cannot use the information to wet
anything. But you can use it to decide to take an umbrella when you go
out, or, if you are a farmer you may use it as a reason for accelerating
harvesting. The falling rain cannot so be used: by the time the rain is
available it is too late to save the crops.
The same information can be used in different ways in different contexts
or at different times. The relationship between information content and
information use is not a simple one.
2.4 The world is NOT the best representation of itself
In recent years, an erroneous claim, related to confusing representing
with standing in for, has found favour with many, namely the claim that
"the world is its own best representation".
Herbert Simon pointed out long ago that sometimes the
changes made to the environment while performing a task can serve as
reminders or triggers regarding what has to be done next, giving
examples from insect behaviours. The use of stigmergy, e.g. leaving
tracks or pheromone trails or other indications of travel, which can
later be used by other individuals, shows how sometimes changes made to
the environment can be useful as means of sharing information with
others. Similarly if you cannot be sure whether a chair will fit through
a doorway you can try pushing it through, and if it is too large you
will fail, or you may discover that it can go through only if it is
rotated in some complex way.
The fact that intelligent agents can use the environment as a store of
information or as a source of information or as part of a mechanism for
reasoning or inferring, does not support the slogan that the world, or
any part of it, is always, or even in those cases the best
representation of itself (a) because the slogan omits the role of the
information-processing in the agent making use of the environment and
(b) because it sometimes is better to have specific instructions, a map,
a blue-print or some other information structure that decomposes
information in a usable way, than to have to use the portion of the
world represented, as anyone learning to play the violin simply by
watching a violinist will discover.
In general, information about X is something different from X itself.
Reasons for wanting or for using information about X are different from
the reasons for wanting or using X. E.g. you may wish to use information
about X in order to ensure that you never get anywhere near X if X is
something dangerous. You may wish to use information about Xs to destroy
Xs, but if that destroyed the information you would not know how to
destroy the next one until you are close to it. It may then be too late
to take necessary precautions, about which you had lost information.
[ DreyfusDreyfus 2002] wrote "The idea of an intentional arc is meant to
capture the idea that all past experience is projected back into the
world. The best representation of the world is thus the world itself."
As far as I can make out he is merely talking about expert servo
control, e.g. the kind of visual servoing which I discussed in
.
But as any roboticist knows, and his own discussion suggests, this
kind of continuous action using sensory feedback requires quite
sophisticated internal information processing
[ GrushGrush 2004]. In such cases "the world" is not nearly enough.
2.5 Disagreements about information bearers, representations
Brooks also wrote a series of papers attacking symbolic AI, including
. He repeatedly emphasises the need to test working
systems on the real world and not only in simulation, a point that has
some validity but can be over-stressed. (If aircraft designers find it
useful to test their designs in simulation, why not robot designers?)
Moreover, he disputes the need for representations (information bearers
constructed and manipulated by information users), saying: "We
hypothesize (following Agre and Chapman) that much of even human level
activity is similarly a reflection of the world through very simple
mechanisms without detailed representations," and "We believe
representations are not necessary and appear only in the eye or mind of
the observer." A critique of that general viewpoint is presented in
, which mostly deals with [ BrooksBrooks 1990],
in which he goes further:
"The key observation is that the world is its own best model. It
is always exactly up to date. It always contains every detail
there is to be known. The trick is to sense it appropriately and
often enough."
That's impossible when you are planning the construction of a skyscraper
using a new design, or working out the best way to build a bridge across
a chasm, or even working out the best way to cross a busy road, which
you suspect has a pedestrian crossing out of sight around the bend. The
important point is that intelligence often requires reasoning about what
might be the case, or might happen, and its consequences: and that
cannot be done by inspecting the world as it is. Recall that
information bearers and things they represent have different uses
(Section 2.3).
2.6 Computation and information
It is sometimes suggested, e.g. in [ SearleSearle 1980], that computation is
concerned only with syntax. That ignores the fact that even in the
simplest computers bit patterns refer to locations and instructions,
i.e. they have a semantic interpretation. An extreme view in the
opposite direction is expressed by [ DenningDenning 2009]: "The great
principles framework reveals that there is something even more
fundamental than an algorithm: the representation. Representations
convey information. A computation is an evolving representation and an
algorithm is a representation of a method to control the evolution".
A position close to Denning's will be developed here, though his view
of computation (i.e. information-processing) is too narrow.
2.7 Not all information is true
Some people, for example the philosopher Fred Dretske, in his contribution to
, claim that what we ordinarily mean by "information"
in the semantic sense is something that is true, implying that it is
impossible to have, provide or use false information. False information,
on that view can be compared with the decoy ducks used by hunters. The
decoys are not really ducks though some real ducks may be deceived into
treating the decoys as real - to their cost! Likewise, argues Dretske,
false information is not really information, even though some people can
be deceived into treating it as information. It is claimed that truth is
what makes information valuable, therefore anything false would be of no
value.
Whatever the merits of this terminology may be for some philosophers,
the restriction of "information" to what is true is such
a useless encumbrance that it would force scientists and robot designers
(and philosophers like me) to invent a new word or phrase that had the
same meaning as "information" but without truth being implied. For
example, a phrase something like "information content" might be used
to refer to the kind of thing that is common to my belief that the noise
outside my window is caused by a lawn-mower, and my belief that the
noise in the next room is caused by a vacuum cleaner, when the second
belief is true while first belief is false because the noise outside
comes from a hedge trimmer.
The observation that humans, other animals and robots, acquire,
manipulate, interpret, combine, analyse, store, use, communicate,
and share information, applies equally to false information and to
true information, or to what could laboriously be referred to as the
"information content" that can occur in false as well as true
beliefs, expectations, explanations, and percepts, and moreover, can
also occur in questions, goals, desires, fears, imaginings,
hypotheses, where it is not known whether the information content is
true. So in constructing the question "Is that noise outside caused
by a lawnmower?", a speaker can use the same concepts and the same
modes of composition of information as are used in formulating true
beliefs like: "Lawnmowers are used to cut grass", "Lawnmowers
often make a noise", "Lawnmowers are available in different
sizes", as well as many questions, plans, goals, requests, etc.
involving lawnmowers. Not only true propositions are valuable: all
sorts of additional structures containing information are useful.
Even false beliefs can be useful, because by acting on them you may
learn that they are false, why they are false, and gain additional
information. That's how science proceeds and much of the learning of
young children depends heavily on their ability to construct
information contents without being able to tell which are true and
which are false. The learning process can then determine the
answers. This will also be important for intelligent robots.
For the purposes of cognitive science, neuroscience, biology, AI,
robotics and many varieties of engineering, it is important not to
restrict the notion of "information" to what is true, or even to
whole propositions that are capable of being true or false. There
are information fragments of many kinds that can be combined in many
ways, some, but not all, of which involve constructing propositions.
Information items can be used in many other processes. The uses of
information in control probably evolved before other uses of
information in biological organisms, including, for example,
microbes. Explaining how and why other uses evolved, such as forming
memories, predictions, questions and explanations, along with
increasingly sophisticated mechanisms to support them, is a task for
another occasion. Some hypotheses are sketched in .
3 Is "information" as used here definable?
3.1 The inadequacy of explicit definitions
In order to understand how a concept like "information" can be used in
science without being definable, we need to understand some general
points from philosophy of science. Shannon's notion of information was
defined precisely [ ShannonShannon 1948] and has had important applications in
science and engineering. Nevertheless, for reasons given above, that
concept is not what we need in talking about an animal or robot that
acquires and uses information about various things (the environment, its
own thinking, other agents, future actions, etc.), even though Shannon's
notion is relevant to some of the mechanisms underlying such processes.
Can we define this older, intuitive, more widely used, notion of
information?
After many years of thinking about this, I have concluded that
"information" in this sense cannot be explicitly defined without
circularity. The same is true of "mass", "energy" and other deep
concepts used in important scientific theories.
Attempts to define "Information" by writing down an explicit
definition of the form "Information is ...." all presuppose some
concept that is closely related ("meaning", "content",
"reference", "description", etc.). "Information is meaning",
"information is semantic content", "information is what something is
about" are all inadequate in this sense.
This kind of indefinability is common in concepts needed for deep
scientific theories. Attempts to get round this by "operationalising"
theoretical concepts fail. For example, there are standard methods of
measuring mass and energy, but those do not define the concepts,
since the measuring methods change as technology develops, while the
meanings of the words remain mostly fixed by their roles in physical
theories. The measurement methods define what are sometimes called
"bridging rules" or "correspondence rules", which link theories to
observations and applications.
[ CarnapCarnap 1947] called some of them "meaning postulates".
All this was known to early 20th century philosophers of science, some
of whom had tried unsuccessfully to show that scientific concepts are
definable in terms of the sensory experiences of scientists, or in terms
of "operational definitions" specifying how to detect or measure
physical quantities .
The absence of any explicit definition does not mean either that a word
is meaningless or that we cannot say anything useful about it. The
specific things said about what energy is and how it relates to force,
mass, electrical charge, etc., change over time as we learn more, so the
concepts evolve. Newton knew about some forms of energy, but what he
knew about energy is much less than what we now know about energy, e.g.
that matter and energy are interconvertible, and that there are chemical
and electromagnetic forms of energy. Growing theoretical knowledge
extends and deepens the concepts we use in expressing that knowledge
. That is now happening to our concept of
information as we learn more about types of information-processing
machine, natural and artificial.
3.2 Concepts implicitly (partially) defined by theories using them
If concepts are not all defined in terms of sensory experiences or
measurement operations, how do we (including physicists) manage to
understand the word "energy"? The answer seems to be: such a word
mainly acquires its meaning from its role in a rich, deep, widely
applicable theory in which many things are said about energy, e.g. that
in any bounded portion of the universe there is a scalar
(one-dimensional), discontinuously variable amount of it, that its
totality is conserved, that it can be transmitted in various ways, that
it can be stored in various forms, that it can be dissipated, that it
flows from objects of higher to objects of lower temperatures if they
are in contact, that it can be radiated across empty space, that it can
produce forces that cause things to move or change their shape, etc.
(All that would have to be made much more precise for a physics text
book.)
If a theory is expressed logically, and is not logically inconsistent,
and its undefined concept labels are treated as variables ranging over
predicates, relations and functions, then there may be a non-empty set
of possible models for the set of statements expressing the theory,
where the notion of something being a model is illustrated by lines,
points, and relations between them being a model for a set of axioms for
Euclidean geometry, and also certain arithmetical entities being a model
for the same axioms. This notion of model was first given a precise
recursive definition by Tarski but the idea is much older, as explained
in [ SlomanSloman 2007 3]. I think the core idea can be generalised to
theories expressed in natural language and other non-logical forms of
representation including non-Fregean forms of representation, but making
that idea precise and testing it are research projects (compare
[ SlomanSloman 1971]). The models that satisfy some theory with undefined
terms will include possible portions of reality that the theory could
describe. Insofar as there is more than one model, the meanings of the
terms are partly indeterminate, an unavoidable feature of scientific
theories. [ SlomanSloman 1978,Chap 2] explains why it is not usually
possible to completely remove indeterminacy of meaning. Compare
[ CohenCohen 1962].
Adding new independent postulates using the same undefined terms will
further constrain the set of possible models. That is one way to enrich
the content of a theory. Another way is to add new undefined concepts
and new hypotheses linking them to the old ones. That increases the
complexity required of a piece of reality if it is to be a model of the
theory. Other changes may alter the set of models and increase the
number of things that are derivable from the theory, increasing the
variety of predictions. Some changes will also increase the
precision of the derived conclusions, e.g. specifying predicted
processes or possible processes in more detail. Adding new "meaning
postulates", or "bridging rules", linking undefined terms to methods
of measurement or observation, as explained above, can also further
constrain the set of possible models, by "tethering" (label suggested
in [ Chappell SlomanChappell Sloman 2007]) the theory more closely
to some portion of reality. As science progresses and we learn more
things about energy. the concept becomes more constrained - restricting
the possible models of the theory, as explained in
[ SlomanSloman 2007 3]. This gradual increase in understanding would not
be possible if the initial concepts were fully determinate. Far from
requiring absolutely precise concepts, as normally supposed, some
scientific advances depend on (partial) indeterminacy of concepts.
3.3 Evaluating theories, and their concepts
For concepts that are implicitly defined by their role in the
theory, the evaluation of the concepts as referring to something real or
not will go along with the evaluation of the theory. How to evaluate
scientific theories is itself a complex and difficult question and there
are many tempting but shallow and inadequate criteria. I think the work
of Lakatos extending and refining Popper's ideas
[ LakatosLakatos 1980] is of great value here, in particular insofar as it
draws attention to the difficulty of evaluating or comparing theories
conclusively at a point in time. Instead it often takes time before we
can tell whether the research programme associated with a theory is
"progressive" or "degenerating". It always remains possible for new
developments to resurrect a defeated theory, as happened to the
corpuscular theory of light.
Doubt is cast on the value of a theory and its concepts if the theory
does not enhance our practical abilities, if it doesn't
explain a variety of observed facts better than alternative theories, if
all its predictions are very vague, if it never generates new research
questions that lead to new discoveries of things that need to be
explained, if its implications are restricted to very rare situations,
and if it cannot be used in making predictions, or selecting courses of
action to achieve practical goals, or in designing and steadily
improving useful kinds of machinery, In such cases, the concepts
implicitly defined by the theory will be limited to reference within the
hypothetical world postulated by the theory. Concepts like "angel"
and "fairy" are examples of such referentially unsuccessful concepts,
though they be used to present myths of various sorts, providing
entertainment and, in some cases, social coercion.
These ideas about concepts and theories were elaborated in
[ SlomanSloman 1978,Chap 2], which pointed out that the deepest advances in
science are those that extend our ontology substantively, including new
theories that explain possibilities not previously considered. How
concepts can be partly defined implicitly by structural relations within
a theory is discussed further in [ SlomanSloman 1985, SlomanSloman 1987]. These ideas
can be extended to non-logical forms of representation, as discussed in
[ SlomanSloman 2008 2].
3.4 The failure of concept empiricism and symbol-grounding theory
Because a concept can be (partially) defined implicitly by its role in a
powerful theory, and therefore some symbols expressing such concepts get
much of their meaning from their structural relations with other symbols
in the theory (including relations of derivability between formulae
including those symbols) it follows that not all meaning has to come
from experience of instances, as implied by the theory of concept
empiricism. Concept empiricism is a very old philosophical idea, refuted
by [ KantKant 1781], and later by philosophers of science in the 20th
century thinking about theoretical concepts like "electron", "gene",
"neutrino", "electromagnetic field". (For more on Concept
Empiricism, see: [ PrinzPrinz 2005, MacheryMachery 2007].)
Unfortunately, the already discredited theory was recently reinvented
and labelled "symbol grounding theory" . This
theory seems highly plausible to people who
have not studied philosophy, so it has spread widely among AI theorists
and cognitive scientists, and is probably still being taught to
unsuspecting students. Section 3.2 presented "symbol
tethering" theory, according to which meanings of theoretical terms are
primarily determined by structural relations within a theory,
supplemented by "bridging rules". Designers of intelligent robots will
have to produce information-processing architectures in which such
theories can be constructed, extended, tested and used, by the robots,
in a process of acquiring information about the world, and themselves.
Marvin Minsky in also talks about
"grounding" but in a context that neither presupposes nor supports
symbol-grounding theory. He seems to be making a point I agree with,
namely that insofar as complex systems like human minds monitor or
control themselves the subsystem that does the monitoring and
controlling needs to observe and intervene at a high level of
abstraction instead of having to reason about all the low level details
of the physical machine. In some cases, this can imply that the
information that such a system has about itself is incomplete or
misleading. I.e. self-observation is not infallible, except in the
trivial sense in which a voltmeter cannot be misled about what its
reading of a voltage is, as explained in .
The rest of this paper attempts to outline some of the main features of
a theory about roles information can play in how things work in our
world. The theory is still incomplete but we have already learnt a lot
and there are many possible lines of development of our understanding of
information processing systems in both natural and artificial systems.
4 Information-bearers, information contents.
4.1 Users, bearers, contents, contexts - physical and virtual
As explained in Section 1.1, an information-bearer B (a
representation) can express information I for user U in context C. The
user, U, can take B to express information about something remote, past,
future, abstract (like numbers), or even non-existent, e.g. a situation
prevented, or a story character.
The expressed information can be involved in many processes, for
instance: acquiring, transforming, decomposing, combining with other
information, interpreting, deriving, storing, inferring, asking,
testing, using as a premiss, controlling internal or external behaviour,
and communicating with other information-users. Such processes usually
require U to deploy mechanisms that have access to B, to parts of B, and
to other information-bearers (e.g. in U's memory or in the environment).
The existence of information-bearers does not depend on the existence of
what they refer to: things can be referred to that do not exist.
Mechanisms for this were probably a major advance in biological
evolution. Example information-bearers explicitly used by humans include
sentences, maps, pictures, bit-strings, video recordings, or other more
abstract representations of actual or possible processes. At present
little is known about the variety of information bearers in biological
systems, including brains, though known examples include chemical
structures and patterns of activation of neurons. In some cases the
information-bearers are physical entities, e.g. marks on paper or
acoustic signals, or chemicals in the blood stream. But many
information-bearers in computing systems, e.g. lists of symbols, the
text in a word-processor, are not physical entities but entities in
virtual machines (see Section
6.3). The use of virtual machines in addition to physical
machines has many benefits for designers of complex information
processing systems.
[ SlomanSloman 2009 6] argues that evolution produced animals that use
virtual machines containing information bearers, for similar reasons.
The problem of explaining what information is includes the problem of
how information can be processed in virtual machines, natural or
artificial. (In this context, the word "virtual" does not imply
"unreal"2.)
The bearer is a physical or virtual entity (or collection of entities)
that encodes or expresses the information, for that user in that
context. Many people, in many disciplines, now use the word
"representation" to refer to information-bearers of various kinds,
though there is no general agreement on usage. Some who argue that
representations are not needed proceed to discuss alternatives that are
already classified as representations by broad-minded thinkers.
Such factional disputes are a waste of time.
4.2 Changing technology for information-bearers
Early general purpose electronic computers used only abstract
bit-patterns as forms of representation, though the physical
implementation of the bit-patterns varied. Over the years since the
1940s many more information-bearers have been developed in computers,
either implemented in bit patterns, or in something else implemented in
bit-patterns, e.g. strings, arrays, lists, logical expressions,
algebraic expressions, images, rules, grammars, trees, graphs,
artificial neural nets, and many more. These are typically constructed
from various primitive entities and relationships available in virtual
machines though they are all ultimately implemented in bit-patterns,
which themselves are virtual entities implemented in physical machines
using transistors, magnetic mechanisms in disc drives, etc. The use of
such things as error-correcting memories and raid arrays implies that
the bits in a bit pattern are virtual entities that do not correspond in
any simple way to physical components.
This use of bit-patterns as a form of representation is relatively
recent, although Morse code, which is older, is very close. Long before
that, humans were using language, diagrams, gestures, maps, marks in the
sand, flashing lights, etc. to express information of various kinds
[ DysonDyson 1997]. And before that animal brains used still unknown
forms of representation to encode information about the environment,
their motives, plans, learnt generalisations, etc.[ SlomanSloman 1979, SlomanSloman 2008 2].
It is arguable that all living organisms acquire and use information,
both in constructing themselves and also in controlling behaviour,
repairing damage, detecting infections, etc.3
Information-bearers need not be intentionally constructed to
convey information. For example, an animal may hear a sound and derive
the information that something is moving nearby. The original
information-bearer is a transient acoustic signal in the environment
produced unintentionally by whatever moved. The hearer constructs an
enduring information-bearer (representation) that may be retained long
after the noise has ended. The physical signal does not
intrinsically carry that information, though for a particular user it
may do so as a result of prior learning. However, in a different
context, the same noise may be interpreted differently. So the
association between bearer and information content can depend not only
on user but on context: information (or meaning) involves at least a
four-termed relation involving B, I, U, and C.
4.3 A common error about bit patterns and symbols
It is sometimes claimed that in Shannon's sense "information" refers
to physical properties of physical objects, structures, mechanisms. But
not all bit-strings are physical. For example, it is possible to have
structures in virtual machines that operate as bit-strings and are used
for communication between machines, or for virtual memory systems,
especially when bit-strings are transmitted across networks in forms
that both use data-compression and error correcting mechanisms based on
redundancy. A similar mistake was made by Newell and Simon
when they proposed that intelligent systems need to use
"physical symbol systems", apparently forgetting that many symbols
used in AI systems are not physical entities, but entities in virtual
machines (see Section 6.3).
4.4 Many forms of representation
There are many forms in which information can be expressed. Some are
very general, including logic, human languages, and various structures
used in computer databases. They are not completely general insofar as
there may be some things, e.g. information about irregular continuous
spatial or temporal variation, that they cannot express fully. Other
forms of representation are more specialised, e.g. number notations,
notations for differential and integral calculus, musical notation, and
various styles of maps. What characterises a form of representation is a
collection of primitives, along with ways of modifying them, combining
them to form larger structures, transformations that can be applied to
the more complex items, mechanisms for storing, matching, searching, and
copying them, and particular uses to which instances of the form can be
put, e.g. controlling behaviour, searching for plans, explaining,
forming generalisations, interpreting sensory input, expressing goals,
expressing uncertainty, and communication with others. The representing
structures may be physical objects or processes, or objects or processes
in virtual machines. The use of virtual machine forms of representation
allows very rapid construction and modification of structures without
having to rearrange physical components. In computers instead of
physical rearrangements there are merely banks of switches that can be
turned on and off, thereby implementing changes to virtual network
topology and signals transmitted, in terms of which higher-level virtual
machine representations can be implemented.
Humans often use forms that are Fregean [ SlomanSloman 1971] insofar as they
use application of functions to arguments to combine information
items to form larger information items. Examples include sentences,
algebraic expressions, logical expressions and many expressions in
computer programs. Purely Fregean forms of representation use only
function application, whereas impure forms also use spatial or temporal
order, and other relationships in the bearer's medium, as
[ BatesonBateson 1972] noted. For example, the programming language Prolog
uses ordering of symbols as well as the function-argument relationship,
as significant.
The 1971 paper argued, against [ McCarthy HayesMcCarthy Hayes 1969], that non-Fregean
forms of representation, e.g. analogical representations, are often
useful, and should be used in AI alongside logic and algebra. For
example, information may usefully be expressed in continuously changing
levels of activation of some internal or external sensing device, in
patterns of activation of many units, in geometrical or topological
structures analogous to images or maps, in chemical compounds, and many
more. Despite some partial successes, this has proved easier said than
done.
Exactly how many different forms exist in which information can be
encoded, and what their costs and benefits are, is an important
question that will not be discussed further here. One of the profound
consequences of developments in metamathematics, computer science,
artificial intelligence, neuroscience and biology in the last century
has been to stretch our understanding of the huge variety of possible
forms of representation , including some forms that
are not decomposable into discrete components, as sentences, logical
expressions, and bit strings are, and some which can also change
continuously, unlike Fregean representations.
Besides analogical and Fregean forms of representation many others have
been explored, including distributed neural representations and forms of
genetic encoding. [ MinskyMinsky 1992] discusses tradeoffs between
some symbolic and neural forms. There probably are many more forms of
representation (more types of information-bearer) than we have
discovered so far. Some philosophers use the misleading expression
"non-conceptual content" to refer to some of the non-Fregean forms of
representation - misleading because it presupposes that concepts (units
of semantic content) can only be used in propositional formats. We can
achieve greater generality by using the label "concept" wherever there
are re-usable information components that can be combined with others in
different ways whether in propositions, instructions, pictures, goal
specifications, action-control signals, or anything else.4
Obviously, a representation may convey different information to
different users, and nothing at all to some individuals (e.g. humans
listening to a foreign language). Moreover, the very same
information-bearer can convey different information to the same user at
different times, in different contexts, for example, indexical
expressions, marks in the sand, shadows, etc. (Further examples and
their implications are discussed below in Section 5.9 and
in .)
The continued investigation of the space of possible forms of
representation, including the various options for forming more complex
information contents from simpler ones, and the tradeoffs between the
various options, is a major long term research project.
This paper is mostly neutral as regards the precise forms in
which information can be encoded.
4.5 "Self-documenting" entities
It is normally assumed that we cannot talk about the information
expressed by or stored in a bearer B without specifying a user (or type
of user) U. However, it is arguable that any object, event, or
process is intrinsically a bearer of information about itself (a
"self-documenting" entity), though not all users are equally able to
acquire and use the information that is available from the entity. So a
twig lying in the forest is a bearer (or potential bearer?) of
information about its size, shape, physical composition, location,
orientation, history, and relationships to many other things. Different
information users can take in and use different subsets or impoverished
forms of that information, depending on their sensory apparatus, their
information processing architecture, the forms of representation they
are able to use, the theories they have, and their location in relation
to the twig. (Compare the notion of "intrinsic information" in
[ ReadingReading 2006].)
Besides the "categorical" information about the parts, relationships,
properties, and material constitution of an object or process that can
be discovered by an appropriately equipped perceiver, there is also less
obvious "dispositional" information about processes it could be part
of, processes that it constrains or prevents, and processes that could
have produced it. These are causal relationships. Intelligent perceivers
make a great deal of use of such information when they perceive
affordances of various kinds. Gibson's notion of "affordance"
[ J J. GibsonJ J. Gibson 1979] focuses on only a subset of possible processes and
constraints, namely those relevant to what a perceiver can and cannot
do: action-affordances for the perceiver. We need to generalise that
idea if we are to describe all the different kinds of information a
perceiver can use in the environment, including proto-affordances,
concerned with which processes are and are not physically possible in
the environment, epistemic affordances, concerned with what
information is and is not available and vicarious affordances,
concerned with affordances for other agents, all described in
[ SlomanSloman 2008 1]. Some animals are able to represent
meta-affordances: information about ways of producing, modifying,
removing, or acquiring information about, affordances of various kinds.
Information-users will typically be restricted in the kinds of
information they can obtain or use, and at any time they will only
process a subset of the information they could process. They will
typically not make use of the majority of kinds of information
potentially available. For instance, detailed, transient, metrical
information about changing relationships will be relevant during
performance of actions such as grasping, placing, catching or avoiding,
but only more abstract information will be relevant while future actions
are being planned, or while processes not caused by the perceiver are
being observed [ SlomanSloman 1982]. States of an
information-processing system (e.g. the mind of an animal or robot) are
generally not just constituted by what is actually occurring in the
system but by what would or could occur under various conditions - a
point made long ago in [ RyleRyle 1949].
The information-processing mechanisms and forms of representation
required for perceivers to acquire and use information about actual and
possible processes and causal relationships are not yet understood. Most
research on perception has ignored the problem of perceiving
processes, and possibilities for and constraints on
processes, because of excessive focus on perceiving and learning about
objects.
5 Aspects of information
5.1 Information content and function
Items of information can have different aspects that need to be
distinguished, of which three important examples are content,
function (or use, or causal role) and the medium in which
information is expressed, or represented, where each of those can be
further subdivided.
It is possible for the same information content (e.g. that many parents
abuse their children by indoctrinating them) to be put to different
uses. E.g. it can be stated, hypothesised, denied, remembered, imagined
to be the case, inferred from something, used as a premiss, used to
explain, used to motivate political action, and many more. Those could
all be labelled "declarative" uses of information. An item of
declarative information can be true or false, and can imply, contradict,
or be derived from, other items of factual information. It can also
provide an answer (true or false) to a question, or a description of
what needs to be achieved for an item of control information to be
successful, e.g. for a command to be obeyed.
The same content can also occur in other information uses, e.g.
"interrogative" and "imperative" uses: formulating requests for
information and specifying an action to be performed (or modified,
terminated, suspended or delayed, etc.), for instance asking whether it
is the case or exhorting people to make it false by changing their ways.
An important use that is hard to specify is in conditionalising some
other information content, which could be a statement, intention,
command, question, prediction. Examples: "If it's raining take an
umbrella", "If it's raining, why aren't you wet?" There is usually
no commitment regarding truth or falsity of the condition, in such uses.
Like questions, imperative uses of information are not true or false,
though particular processes can be said to follow or not follow the
instructions. Just as some declarative information contents are
inconsistent, and therefore incapable of being true, likewise, some
instructions are inconsistent, and therefore impossible to execute (e.g.
"Put seven balls into an empty box and, put red marks on ten of
them").
5.2 Medium used for information bearer
From the earliest days of AI and software engineering it was clear that
choice of form of representation could make a large difference to the
success of a particular information-processing system. Different
expressive media can be used for the various functions: vocal
utterances, print, internet sites, use of sign language, political
songs, etc. The same content expressed in print could use different
fonts, or even entirely different languages. But some information
contents cannot be adequately expressed in some media, e.g. because, as
J.L.Austin once quipped: "Fact is richer than diction"
[ AustinAustin 1956]. Some kinds of richness are better represented in
a non-Fregean medium, e.g. using static or moving images, or 3-D models.
A pre-verbal child, or a non-human animal, can have percepts whose
content specifies a state of affairs in the environment; and can
have intentions whose content specifies some state of affairs to be
achieved, maintained or prevented. It is unlikely that toddlers, dogs,
crows, and apes use only linguistic or Fregean forms of representation,
though there are many unanswered questions about exactly which other
forms or media are possible.
Many information-bearers use static media, like sentences, pictures, or
flowcharts, whereas some use dynamic media, in which processes are
information-bearers, e.g. audio or video recordings, gestures, play
acting, and others. If the dynamic representation is repeatedly produced
it may be represented by some enduring static structure that is used to
generate the dynamic process as needed - e.g. a computer program can
repeatedly generate processes. I suspect the role of dynamic
information-bearers and static encodings of dynamic information-bearers,
in animal intelligence, and future intelligent robots, will turn out to
be far more important than anyone currently realises, not least because
much information about the environment is concerned with processes
occurring, and processes that could occur.
Earlier, in 4.5, we mentioned self-documenting entities,
which potentially express information for various kinds of information
user simply in virtue of their structure, properties and relations.
These information bearers do not depend for their existence on users.
They can be contrasted with the sensory signals and other transient and
enduring information bearers constructed by information users. An
element of truth in the view of Brooks criticised above
(2.5) is that in some cases the presence of
self-documenting entities reduces (but does not eliminate) the need for
an information user to construct internal representations. Moreover,
during performance of actions, force-feedback and visual feedback can be
used to provide fine-grained control information that reduces the
reliance on ballistic control, which may be inaccurate.
Another way of putting the point about control using feedback is that
the changing relationships to external objects produced when
performing physical actions can be useful self-documenting aspects
of the environment, helping with control. They can also be useful for
other observers (friendly or unfriendly!) who can perceive the actions
and draw conclusions about the intentions and motives of the agent - if
the viewers have appropriate meta-semantic information-processing
capabilities. In that sense, intentional actions can serve as unintended
communications, and it is conjectured in
[ SlomanSloman 2008 2] that fact played a role in evolution of languages
used intentionally.
5.3 Same content, but different function
Items of information with the same declarative content can be given
different functional roles in an information user. For example, the same
thing can be stated to be true and either asked about or commanded to be
made or kept true. It can also be wondered about, hypothesised, imagined
regretfully, treated as an ideal, etc.
The philosopher R.M. Hare introduced the labels
"Phrastic" and "Neustic" to distinguish the semantic content of an
utterance and the speech act being performed regarding that content,
e.g. asserting it, denying it, enquiring about its truth value,
commanding that it be made true, etc. The concept of "information
content" used here is close to Hare's notion of a "Phrastic", except
that we are not restricting semantic content to what can be expressed in
a linguistic or Fregean form: other media, including maps, models,
diagrams, route-summaries, flow-charts, builders' blue-prints, moving
images, 3-D models, and other things, can all encode information
contents usable for different functions. Moreover, not all uses are
concerned with communication between individuals: information is
processed in perceiving, learning, wanting, planning, remembering,
deciding, etc.
[ SlomanSloman 1979, SlomanSloman 2008 2]. We therefore need to generalise the
Phrastic/Neustic distinction to contrast content and function in many
different information media, including information expressed in
diagrams, maps, charts [ SlomanSloman 1971], and also whatever forms are used
in animal brains or minds. In many cases the "neustic" is not
expressed within the representation but simply by its role in an
information processing architecture, as explained in
[ SlomanSloman 2009 1], or in some aspect of the context, e.g.
the word "Wanted" above a picture of a human face.
Questions, requests, commands, desires, and intentions, can all be
described as examples of "control information", because their
information-processing function (the neustic aspect), involves
making something happen, unlike factual information, which, in itself,
has no implications for action, although it can have implications in
combination with motives, conditional plans, etc. Control information
(and what should be done) is commonly found in kitchen recipes, computer
programs, knitting patterns, legal documents, etc. There must be many
forms implemented in animal brains.
Summing up: When information is used we can distinguish the content of
the information (phrastic) from the use that is being made of it
(neustic). The latter may be explicitly indicated in the medium, or
implicitly determined by the subsystem of the user that the bearer is
located in, or the context. We can also distinguish different
information media, e.g. linguistic, Fregean, pictorial, hybrid, static,
dynamic, etc. Each of these can be further subdivided in various ways,
only some of which have already been explored in working artificial
systems.
5.4 Processing requirements for different media
One of the achievements of AI research in the last half-century has been
the study of different information media, and analysis of different
information processing mechanisms required for dealing with them,
including sentences, algebraic expressions, logical expressions, program
texts, collections of numerical values, probability distributions, and a
variety of analogical forms of representation, including pictures,
diagrams, acoustic signals, and more. There are many ways in which
information media can vary, imposing different demands on the mechanisms
that process them.
One of the most important features of certain media is their
"generativity". For example, our notations for numbers, sentences,
maps, computer programs, chemical formulate, construction blue-prints,
are all generative insofar as there is a subset of primitive information
bearers along with ways in which those primitives can be combined to
form more complex bearers, where the users have systematic ways of
interpreting the complex bearers on the basis of the components and
their relationships. This is referred to as a use of "compositional
semantics", where meanings of wholes depend on meanings of parts and
their relationships, and sometimes also the context [ SlomanSloman 2006 2].
If an organism had only six basic actions, and could only process
bearers of information about complex actions made up of at most three
consecutive basic actions, then it would have restricted generativity,
allowing for at most 216 complex actions. Some organisms appear to have
sensor arrays that provide a fixed size set of sensor values from which
information about the environment at any time can be derived. In
contrast, humans, and presumably several other species, do not simply
record sensor values but interpret them in terms of configurations of
entities and processes in the environment, e.g. visible or tangible
surface fragments in various orientations changing their mutual
relationships.
If the interpretation allows scale changes (e.g. because of varying
distances) and sequential scanning of scenes, both of which are
important in human vision, the user can construct and interpret
information bearers of different kinds and degrees of complexity. The
mechanisms involved may have physical limits without being limited in
principle, in which case the animal or machine may have "infinite
competence" (explained more fully in [ SlomanSloman 2002]). Even when the
competence is not infinite, compositionality implies the ability to deal
with novelty, a most important feature for animals and robots inhabiting
an extremely variable environment. Closely related to this are the
ability to plan complex future actions and the ability to construct
new explanations of observed phenomena.
A more complete exposition would need to discuss different ways in which
information bearers can be combined, with different sorts of
compositional semantics. One of the major distinctions mentioned in
Section 4.4 is between and Fregean and other forms of
composition. As explained in [ SlomanSloman 1971], the systematic complexity
of forms of representation can provide a basis for reasoning with
information-bearers: deriving new conclusions from old information by
manipulating the bearers, whether Fregean or not. Logical inference
and geometric reasoning using diagrams two special cases among many.
5.5 Potential information content for a user
The information in B can be potentially usable by U even though U has
never encountered B or anything with similar information content. That's
obviously true when U encounters a new sentence, diagram or picture for
the first time. Even before U encountered the new item, it was
potentially usable as an information-bearer. In some cases, though not
all, the potential cannot be realised without U first learning a new
language, or notation, or even a new theory within which the information
has a place.
You cannot understand the information that is potentially available to
others in your environment if you have not yet acquired all the concepts
involved in the information. For example, it is likely that a new-born
human infant does not have the concept of a metal, i.e. that is not part
of its ontology [ SlomanSloman 2009 2]. So it is incapable of acquiring
the information that it is holding something made of metal even if a
doting parent says "you are holding a metal object". In humans a
lengthy process of development is required for the
information-processing mechanisms (forms of representation, algorithms,
architectures) to be able treat things in the environment as made of
different kinds of stuff, of which metals are a subset. Even longer is
required for that ontology to be extended to include the concepts of
physics and chemistry. In part that is a result of cultural evolution:
not all our ancestors were able to acquire and use such information.
5.6 Potential information content for a TYPE of user
It is possible for information to be potentially available for a
TYPE of user even if NO instances of that type exist. For example,
long before humans evolved there were things happening on earth that
could have been observed by human-like users using the visual
apparatus and conceptual apparatus that humans have. But at the time
there were no such observers, and perhaps nothing else existed on
the planet that was capable of acquiring, manipulating, or using the
information, e.g. information about the patterns of behaviours
of some of the animals on earth at the time. (This is related to the
points made about self-documenting entities in 4.5.)
There may also be things going on whose detection and description
would require organisms or machines with a combination of
capabilities, including perceptual and representational capabilities
and an information-processing architecture, that are possible in
principle, but have never existed in any organism or machine and
never will - since not everything that is possible has actual
instances. Of course, I cannot give examples, since everything I can
present is necessarily capable of being thought about by at least
one human. Weaker, but still compelling, evidence is simply the fact
that the set of things humans are capable of thinking of changes
over time as humans acquire more sophisticated concepts, forms of
representation and forms of reasoning, as clearly happens in
mathematics, physics, and the other sciences. There are thoughts
considered by current scientists and engineers that are beyond the
semantic competences of any three year old child, or any adult human
living 3000 years ago. If the earth had been destroyed three
thousand years ago, that might have relegated such thoughts to the
realm of possible information contents for types of individual that
never existed, but could have.
5.7 Information content shared between users
It is sometimes possible for a bearer B to mean the same thing (convey
the same information content I) to different users U and U′,
and it is
also possible for two users who never use the same information-bearers
(e.g. they talk different languages) to acquire and use the same
information.
This is why relativistic theories of truth are false. It cannot be true
for me that my house has burned down but not true for my neighbour. In
principle we have access to the same sources of information in the
world.
5.8 Ambiguity, noise, and layers of processing
Media can also vary in the extent to which they allow information to be
expressed ambiguously. For example, some cases are totally unambiguous,
e.g. the association between bit patterns and CPU instructions or memory
addresses in a computer. In a virtual memory system, a bit pattern
uniquely identifies a location in a virtual memory, but the mapping to
physical memory locations is context sensitive. In natural languages and
many forms of pictorial or map-like representation, local details are
ambiguous and finding a global interpretation for a complex
information-bearer can include searching and problem solving, possibly
using constraint propagation and background knowledge, illustrated below
in 5.9.
In some cases the medium requires several layers of interpretation,
using different ontologies, to be coordinated, e.g. acoustic, phonetic,
morphemic, syntactic, semantic and social, in the case of speech
understanding systems. Other layers are relevant in visual systems, such
as edge features, larger scale 2-D features, 3-D surface fragments, 3-D
structures, layers of depth, 3-D processes involving interacting
structures, intentions of perceived agents, etc. [ TrehubTrehub 1991] offers
a theory about how such layers might be implemented neurally, but there
remain many unknowns about how vision works.
In some cases, the requirement for layers of interpretation is the
result of engineering designs making use of compression, encryption,
password protection, zipping or tarring several files into one large
file, and many more. In other cases, the layers are natural consequences
of a biological or engineering information-processing task, e.g. the
layers in visual information processing.
Some information-bearers include various amounts and kinds of noise,
clutter, and partial occlusion, sometimes causing problems that require
collaboration between interpretation processes at different levels of
abstraction. Where multiple layers of processing are coordinated,
ambiguities in some layers may be resolved by interpretations in other
layers, possibly using background knowledge [ SlomanSloman 1978,Chap 9].
This is sometimes described as "hierarchical synthesis", or "analysis
by synthesis" [ NeisserNeisser 1967]. A related view of
layers of interpretation is presented in [ H. Barrow TenenbaumH. Barrow Tenenbaum 1978].
Although there has been much research on ways of extracting information
from complex information-bearers, it is clear that nothing in AI comes
close to matching, for example, the visual competences of a
nest-building bird, a tree-climbing ape, a hunting mammal catching prey,
a human toddler playing with bricks and other toys. In part, that is
because not even the requirements have been understood properly
[ SlomanSloman 2008 1].
5.9 Information content for a user determined partly by context
There are lots of structures in perceptual systems that change what
information they represent because of the context. E.g. if what is on
your retina is unchanged after you turn your head 90 degrees in a room,
the visual information will be taken to be about a different wall even
if retinal images are unchanged because the two walls have the same
wallpaper. The new interpretation uses the information that the head was
turned. Many examples can be found in .
[ SlomanSloman 1971] showed how a particular line can represent
different things in a 2-D image of a 3-D scene, depending on its
relationships to other fragments. Determining whether a vertical line in
a picture represents a horizontal mark on the floor or a vertical line
on a wall generally requires use of context. Similar problems arise in
language processing, e.g. determining whether "with" introduces a
prepositional or adverbial phrase in "He watched the boy with
binoculars".
Some information-bearing structures express different information for
the same user U in different contexts, because they include an explicit
indexical element (e.g. "this", "here", "you", "now", or
non-local variables in a computer program).
Another factor that makes it possible for U to take a structure B to
express different meanings in different contexts can be that B has
polymorphic semantics: its semantic function (for U, or a class of
users) is to express a higher order function which generates semantic
content when combined with a parameter provided by the linguistic or
non-linguistic context. E.g. consider: "He ran after the smallest
pony". Which pony is the smallest pony can change as new ponies arrive
or depart. More subtly, what counts as a tall, big, heavy, or thin X can
vary according to the range of heights, sizes, weights, thicknesses of
Xs in the current environment and in some cases may also depend on why
you are looking for something tall, big, heavy , etc.
There are many more examples in natural language that lead to incorrect
diagnosis of words as vague or ambiguous, when they actually express
precise higher order functions, applied to sometimes implicit arguments,
e.g. "thin", "long", "efficient", "heap". Other examples
include spatial prepositions and other constructs, which can be analysed
as having a semantics involving higher order functions some of whose
arguments are non-linguistic, discussed in [ SlomanSloman 2006 2].
A more complex example is: "A motor mower is needed to mow a meadow"
which is true only if there is an implicit background assumption about
constraints on desirable amounts of effort or time, size of meadow, etc.
So a person who utters that to a companion when they are standing in a
very large meadow might be saying something true, whereas in a different
context, where there are lots of willing helpers, several unpowered
lawnmowers available, and the meadow under consideration is not much
larger than a typical back lawn, the utterance would be taken to say
something different, which is false, even if the utterances themselves
are physically indistinguishable. Moreover, where they are standing does
not necessarily determine what sort of meadow is being referred to. E.g.
they may have been talking about some remote very large or very small
meadow.
The influence of context on information expressed is discussed in more
detail in relation to Grice's theory of communication, in
, along with implications for the evolution of
language. The importance of the role of extra-linguistic context in
linguistic communication can be developed in connection with indexicals,
spatial prepositions, and Gricean semantics, into a theory of linguistic
communications as using higher order functions some of whose arguments
have to be extracted from non-linguistic sources by creative
problem-solving. This has implications for language learning and the
evolution of language. It also requires the common claim that natural
languages use compositional semantics, to modified, to allow context to
play a role. The use of non-local variables can have a similar effect in
programming languages. It seems very likely that brain mechanisms also
use context-modulated compositional semantics.
5.10 Information-using subsystems
An information-user can have parts that are information users. This
leads to complications such as that a part can have and use some
information that the whole would not be said to have. E.g. your immune
system and your digestive system and various metabolic processes use
information and take decisions of many kinds though we would not say
that you have, use or know about the information.
Likewise there are different parts of our brains that evolved at
different times that use different kinds of information, even
information obtained via the same route, e.g. the retina or ear-drum, or
haptic feedback. Input and output devices can be shared between
sub-systems that use them for different purposes, possibly after
different pre- or post- processing, as explained in [ SlomanSloman 1993].
Some sub-systems are evolutionarily old and shared with other species,
some are newer, and some unique to humans.
An example is the information about optical flow that is used in humans
to control posture, without individuals being aware of what they are
doing [ Lee LishmanLee Lishman 1975]. More generally, it is likely that human
information processing architectures include many components that
evolved at different times, performing different functions, many of them
concurrent, some of them surveyed in [ SlomanSloman 2003]. The
subsystems need not all use the same forms of representation, and
individual subsystems need not all have access to information acquired,
derived, constructed or used by others. In particular, some will use
transient information that is not transferred to or accessible by other
subsystems.
That is why much philosophical, psychological, and social theorising is
misguided: it treats humans as unitary and rational information users.
That includes Dennett's intentional stance and what Newell refers to as
"the Knowledge level". For example, the philosophical claim that only
a whole human-like agent can acquire, manipulate and use information is
false. To understand biological organisms and design sophisticated
artificial systems, we need what [ McCarthyMcCarthy 2008] labels "the
designer stance". Unfortunately education about how to be a designer of
complex working systems is not part of most disciplines that need it.
5.11 Layers of interpretation in epigenesis
There is a different kind of use of information: when the user is
constructing itself! In that process there are not sensors and motors
transferring information and energy between the organism and its
environment. The processes by which genetic information is used in
organisms are very complex and varied. The use of information provided
genetically can be very indirect, involving many stages, several of
which are influenced by the environment (e.g. maternal fluids, or soil
nutrients), so that the interpretation process required for development
of an organism, is highly context sensitive.
In many cases, much of the information from which the processes start is
encoded in molecular sequences in DNA, specifying, very indirectly, how
to construct a particular organism by constructing a very complex
collection of self-organising components, which themselves construct
more self-organising components. The interpretation of those sequences
as instructions depends on complex chemical machinery assembled in a
preceding organism (the mother) to kick-start the interpretation
process. The interpreting system builds additional components that
continue the assembly, partly influenced by the genetic information and
partly by various aspects of the environment. During development, the
ability to interpret both genetic and environmental information changes,
partly under the influence of the environment. So the standard
concept of information encoded in the genome is over-simple theory.
(Many details are discussed in [ Jablonka LambJablonka Lamb 2005]. The importance of
cascaded development of layered cognitive mechanisms influenced by the
environment is discussed in [ Chappell SlomanChappell Sloman 2007]. See also
[ DawkinsDawkins 1982].)
The problems of interpreting and using visual and genetic information
show that the role of the user U in obtaining information I from a
bearer B in context C may be extremely complex and changeable, in ways
that are not yet fully understood. That kind of complexity is largely
ignored in most discussions about the nature of information, meaning,
representation, but it cannot be ignored by people trying to design
working systems.
6 Conclusion
In Section 3 it was claimed that it is not possible to
define explicitly, precisely, and without circularity, what we mean by
"information", in the semantic sense that involves not merely having
some syntactic or geometric form but also having the potential to be
taken by a user to be about something. So subsequent sections
presented an implicit definition in the form of a first-draft
informal theory about the role of information in our world.
6.1 An implicitly defined notion of "information"
What was said above in Section 3.2 about "energy"
applies also to "information". We can understand the word
"information" insofar as we use it in a rich, deep, precise and widely
applicable theory (or collection of theories) in which many things are
said about entities and processes involving information. I suspect that
we are still at a relatively early stage in the development of a full
scientific theory of information, especially as there are many kinds of
information processing in organisms that we do not yet understand.
Some of the contents of a theory of information have been outlined in
previous sections, elaborating on the proposition that a user U can
interpret a bearer B as expressing information I in context C. Among the
topics mentioned include the variety of sources of information, the
variety of information-bearing media (about which we still have much to
learn), the variety of structures and systems of information-bearers
(syntactic forms), the variety of uses to which information can be put
(including both communicative and non-communicative uses), the variety
of information contents, the variety of ways in which information
contents can change (e.g. continuously, discretely, structurally, etc.),
the different kinds and degrees of complexity of processes required for
interpreting and using the information in particular bearers, the
variety of information-using competences different users (or different
parts of the same user) can have, the potential information available in
objects not yet perceived by information users, and more. We already
have broader and deeper understanding of information in this sense than
thinkers had a thousand years ago about force and energy, but there is
still a long way to go.
Unlike Shannon's information, the information content we have been
discussing does not have a scalar value, although there are partial
orderings of information content. One piece of information I1 may
contain all the information in I2, and not vice versa. In that case we
can say that I1 contains more information. I1 can have more information
content than both I2 and I3, neither of which contains the other. So
there is at most a partial ordering. The partial ordering may be
relative to an individual user, because giving information I1 to an user
U1, may allow U1 to derive I2, whereas user U2 may not be able to derive
I2, because U2 lacks some additional required information. Even for a
given user, the ordering can depend on context.
Information can vary both discontinuously (e.g. adding an adjective or a
parenthetical phrase to a sentence, like this) or continuously (e.g.
visually obtained information about a moving physical object). More
importantly, individual items of information can have a structure: there
are replaceable parts of an item of information such that if those parts
are replaced the information changes but not necessarily the structure.
Because of this, items of information can be extracted from other
information, and can be combined with other information to form new
information items, including items with new structures. This is
connected with the ability of information users to deal with novelty,
and to be creative. Moreover, we have seen that such compositional
semantics often needs to be context sensitive (or polymorphic), both
human language and other forms of representation.
It can be stored in various forms, can be modified or extended through
various kinds of learning, and can influence processes of reasoning and
decision making. Information can also be transmitted in various ways,
both intentionally and unintentionally, using bearers of many kinds.
Some items of information allow infinitely many distinct items of
information to be derived from them. (E.g. Peano's axioms for
arithmetic, in combination with predicate calculus.) Physically finite,
even quite small, objects with information processing powers can
therefore have infinite information content. (Like brains and
computers.)
There is a great deal more that could be said about our current theories
about information, but that would take several volumes. Many additional
points are in papers in the bibliography, and in other books and
journals, as well as in human common sense.
6.2 Life and information
Some of the most important and least well understood parts of a theory
about information are concerned with the variety of roles it plays in
living things, including roles concerned with reproduction, roles
concerned with growth, development, maintenance and repair, roles
concerned with perception, reasoning, learning, social interaction, etc.
The limitations of our understanding are clearly displayed in the huge
gaps between the competences of current robots (in 2009) and the
competences of many animals, including human infants and toddlers. For
many very narrowly prescribed tasks it is possible to make machines that
perform better than humans (e.g. repeatedly assembling items of a
certain type from sets of parts arrayed in a particular fashion), but
which are easily disrupted by minor variations of the task, the parts,
or the starting configuration. Aliens who visited in 1973 and saw what
the Edinburgh robot Freddy could do, as described in
[ Ambler, Barrow, Brown, Burstall, PopplestoneAmbler . 1973] and shown in this video
http://groups.inf.ed.ac.uk/vision/ROBOTICS/FREDDY/Freddy_II_original.wmv,
might be surprised on returning 36 years later to find how little
progress had been made, compared with ambitions expressed at that time.
Every living thing processes information insofar as it uses (internal or
external) sensors to detect states of itself or the environment and uses
the results of that detection process either immediately or after
further information processing to select from a behavioural repertoire,
where the behaviour may be externally visible physical behaviour or new
information processing. (Similar points are made in [ ReadingReading 2006]
and in Steve Burbeck's web site
http://evolutionofcomputing.org/Multicellular/BiologicalInformationProcessing.html)
In the process of using information an organism also uses up stored
energy, so that it also needs to use information to acquire more energy,
including the energy required for getting energy.
There are huge variations between different ways in which information is
used by organisms, including plants, single celled organisms, and
everything else. For example, only a tiny subset of organisms appear to
have fully deliberative information processing competence, as defined in
[ SlomanSloman 2006 1]. As explained in Section 5.10 there
can also be major differences between the competences of sub-systems in
a single information-user.
6.3 Information processing in virtual machines
A pervasive notion that has been used but not fully explained in this
paper is the notion of a virtual machine. Our understanding of
requirements for and possible ways of building and using them has
gradually expanded through a host of technical advances since the
earliest electronic computers were built.
Because possible operations on information are much more complex and far
more varied than operations on matter and energy,
engineers discovered during the last half-century, as evolution appears
to have "discovered" much earlier, that relatively unfettered
information processing requires use of a virtual machine rather than a
physical machine, like using software rather than cog-wheels
to perform mathematical calculations. A short tutorial on virtual
machines and some common misconceptions about them can be found in
[ SlomanSloman 2009 6]. See also [ PollockPollock 2008]. One of the
main reasons for using virtual machines is that they can be rapidly
reconfigured to meet changing environments and tasks, whereas
rebuilding physical devices as fast and as often is impossible. It is
also possible for a physical machine to support types of virtual machine
that were never considered by the designer of the physical machine.
Similarly, both cultural evolution and individual development can
redeploy biological information processing systems in roles for which
they did not specifically evolve.
In [ SlomanSloman 2009 6] I suggested that the label
"Non-physically-describable-machine" (NPDM) might have been preferable
to "virtual machine" (VM) because the key feature is having states and
processes whose best description uses concepts that are not definable in
terms of the concepts of the physical sciences. Examples are concepts
like "winning", "threat", "rule", "pawn", "checkmate",
relevant to virtual machines that play chess. These VMs/NPDMs are
nothing like the old philosophical notions characterised by
[ RyleRyle 1949] as referring to "The Ghost in the Machine", for we are
not talking about mysterious entities that can continue existing after
their physical bodies have been completely destroyed. The crucial point
is that the nature of the physical world allows networks of causation to
exist that support processes in such virtual machines that not only
cause other virtual machine processes to occur but can also influence
physical machines, for example when a decision taken by a running chess
program causes the display on a computer screen to change
[ SlomanSloman 2009 5]. A crucial step in evolution was the development of
causal networks, including sub-systems running in parallel, in virtual
machines that could be their own information-users.
This contradicts a number of common mistakes, such as the assumption
that information-processing machines have to operate serially, that they
have to use only programs installed by a designer, and that they cannot
be aware of what they are doing, or why they are doing it, or decide to
change their goals. Such mistakes might be overcome if more people
studied AI, even if only designing relatively simple agents, as proposed
in [ SlomanSloman 2009 4].
Although we (or at least software engineers and computer scientists,
unlike most philosophers in 2009) understand current virtual machines
well enough to create, modify, debug, extend and improve them, the
virtual machines that have been produced by biological evolution are
another matter: their complexity, their modes of operation, the best
ways to describe what they do and how they do it, still defeat
scientists, though many subscribe to various personal favourite theories
of consciousness, or whatever. Some of them think the known phenomena
cannot possibly be explained in terms of information-processing
machinery, though in most cases that is because their concept of
information-processing is too impoverished - e.g. because based on the
notion of a Turing machine, whose relevance to this topic was challenged
in [ SlomanSloman 2002]. For example, Turing machines are limited to
discrete operations, whereas there is no reason to assume that all
information-processing has to be so limited, though it could turn out to
be the case that no physical machine could support truly continuous
information manipulation. Others take it for granted that brains are
information-processing machines, but do not yet understand what
information they process or how they do it. For instance, major
features of human and animal vision remain unexplained.
6.4 Finally: Is that everything?
It is clear that what I have written so far does not come near
exhausting our current notion of information, though it gives an
indication of the diversity of phenomena and mechanisms involved.
Moreover since most of this was not known a hundred years ago it shows
that we are in the process of discovering more about information through
scientific and engineering research, though progress has not been as
fast as many hoped.
This is just the beginning of an analysis of relationships between
information, bearers, users, and contexts. What is written here will
probably turn out to be a tiny subset of what needs to be said about
information. A hundred years from now the theory may be very much more
complex and deep, just as what we know now about information is very
much more complex and deep than what we knew 60 years ago, partly
because we have begun designing, implementing, testing and using so many
new kinds of information-processing machines. The mechanisms produced by
evolution remain more subtle and complex, however.
I doubt that anyone has yet produced a clear, complete and definitive
list of facts about information that constitute an implicit definition
of how we (the current scientific community well-educated in
mathematics, logic, psychology, neuroscience, biology, computer science,
linguistics, social science, artificial intelligence, physics,
cosmology, and philosophy) currently understand and use the word
"information". But at least this partial survey indicates how much we
have already learnt.
Some physicists seek a "theory of everything", e.g.
[ J D. BarrowJ D. Barrow 1991, DeutschDeutsch 1997]. However, it does not seem
likely that there can be a theory that is recognisable as a
physical theory from which all the phenomena referred to here would be
derivable, even though all the information-processing systems I have
referred to, whether natural or artificial, must be implemented in
physical systems. I suspect that we are in the early
stages of understanding how the physical world can support non-physical
entities of which simple kinds already exist in running virtual machines
in computers, including virtual machines that monitor themselves, and
use information about what is happening inside them to take decisions
that alter their internal and external behaviours.
My own view has been, for several decades, that as regards information
processing our state of knowledge could be compared with Galileo's
knowledge of physics. He was making good progress and laying foundations
for future developments: including developments he could not possibly
imagine.
One of the drivers of progress in science (and philosophy) is improved
understanding of what is not yet known. I believe the ideas
sketched here help us to focus more clearly on aspects of information
processing that are not yet understood. Doing that in far more
detail with far more specific examples, can
help to drive advances that will produce new, deeper, more general
explanations. But only time will tell whether this is what Lakatos would
call a progressive or a degenerating research programme.
Acknowledgements
I am grateful to Gordana Dodig-Crnkovic and Christophe Menant for useful
comments on an earlier draft. This is a much revised version of my
attempt to answer a question asking what "semantic information" is,
posted on the MINDMECHANISMS discussion forum. My original answer,
posted on 20th Sep 2006, is available online at
http://www.jiscmail.ac.uk/cgi-bin/webadmin?A2=ind0609&L=mindmechanisms&T=0&P=1717
as part of a thread with subject "Analysis of conscious functions".
Comments and questions by several readers led to major improvements.
Many of the points made here were previously also made piecemeal over
several years in contributions to the Psyche-D discussion list, now
archived at
http://www.archive.org/details/PSYCHE-D, and in papers
and
presentations on my web site, listed in the bibliography. Discussions by
email and face to face with many colleagues have helped to shape the
ideas presented here. It was Max Clowes who first introduced me to
computational ways of thinking about philosophical problems.
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doi:10.1088/1741-2560/3/3/R01
Footnotes:
1In at least two of the essays "The
Cybernetics of `Self': A Theory of Alcoholism" and in "Form
Substance and Difference".
2As explained in
and in various papers and presentations available online
[ SlomanSloman 1985, SlomanSloman 1987, SlomanSloman 2008 2, SlomanSloman 2008 3, SlomanSloman 2009 5]
3This is discussed
in a presentation arguing that there is a sense in which life
presupposes mind (informed control)
http://www.cs.bham.ac.uk/research/projects/cogaff/talks/\#lifemind
4See
also the discussion of alternatives to logical representations in
[ SlomanSloman 1978,Chap7]. [ SlomanSloman 2008 2] argues that
non-communicative "languages" used for perception, learning, planning,
etc., evolved before human languages, some of them using non-Fregean
forms of representation.
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