Pragmatic Semiotic Information

[Jon Awbrey]

Pragmatic Semiotic Information • 1
• http://inquiryintoinquiry.com/2024/03/03/pragmatic-semiotic-information-1/

All,

Information • What's it good for?

The good of information is its use in reducing our uncertainty
about an issue which comes before us. But uncertainty comes
in many flavors and so the information which serves to reduce
uncertainty can be applied in several ways. The situations of
uncertainty human agents commonly find themselves facing have
been investigated under many headings, literally for ages, and
the categories subtle thinkers arrived at long before the dawn
of modern information theory still have their uses in setting
the stage of an introduction.

Picking an example of a subtle thinker almost at random, the
philosopher‑scientist Immanuel Kant surveyed the questions of
human existence within the span of the following three axes.

• What's true?
• What's to do?
• What's to hope?

The third question is a bit too subtle for the present frame
of discussion but the first and second are easily recognizable
as staking out the two main axes of information theory, namely,
the dual dimensions of “information” and “control”. Roughly the
same space of concerns is elsewhere spanned by the dual axes of
competence and performance, specification and optimization, or
just plain knowledge and skill.

A question of what's true is a “descriptive question” and
there exist what are called “descriptive sciences” devoted
to answering descriptive questions about any domain of
phenomena one might care to name.

A question of what's to do, in other words, what must be done
by way of achieving a given aim, is a “normative question” and
there exist what are called “normative sciences” devoted to
answering normative questions about any domain of problems
one might care to address.

Since information plays its role on a stage set by uncertainty,
a big part of saying what information is will necessarily involve
saying what uncertainty is. There is little chance the vagaries
of a word like “uncertainty”, given the nuances of its ordinary,
poetic, and technical uses, can be corralled by a single pen, but
there do exist established models and formal theories which manage
to address definable aspects of uncertainty and these do have enough
uses to make them worth looking into.

Regards,

Jon

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[Jon Awbrey]

Pragmatic Semiotic Information • 2
• https://inquiryintoinquiry.com/2024/03/04/pragmatic-semiotic-information-2/

All,

What is information that a sign may bear it?

Three more questions arise at this juncture.

• How is a sign empowered to contain information?
• What is the practical context of communication?
• Why do we care about these bits of information?

A very rough answer to these questions might begin as follows.

Human beings are initially concerned solely with their own lives
but then a world obtrudes on their subjective existence and so they
find themselves forced to take an interest in the objective realities
of its nature.

In pragmatic terms our initial aim, concern, interest, object,
or “pragma” is expressed by the verbal infinitive “to live”, but
the infinitive is soon reified into the derivative substantial forms
of “nature”, “reality”, “the world”, and so on. Against that backdrop
we find ourselves cast as the protagonists on a “scene of uncertainty”.

The situation may be pictured as a juncture from which a manifold of
options fan out before us. It may be an issue of “truth”, “duty”,
or “hope”, the last codifying a special type of uncertainty as to
“what regulative principle has any chance of success”, but the
chief uncertainty is that we are called on to make a choice and
all too often we have very little clue which of the options is
most fit to pick.

Just to make up a discrete example, let us suppose the cardinality
of the choices before us is a finite integer n, and just to make it
fully concrete let us say n = 5. Figure 1 affords a rough picture
of the situation.

Pragmatic Semiotic Information • Figure 1
• https://inquiryintoinquiry.files.wordpress.com/2024/03/pragmatic-semiotic-information-e280a2-figure-1.png

This pictures a juncture, represented by a node marked “O”,
where there are n options for the outcome of a conduct and
we have no clue as to which it must be. In a sense the
degree of the node, in this case n = 5, measures the
uncertainty we have at that point.

The Figure illustrates the minimal sort of setting in which a sign
can make any sense at all. A sign has significance for an agent,
interpreter, or observer because its actualization, its being given
or its being present, serves to reduce the uncertainty of a decision
the agent has to make, whether it concerns the actions the agent ought
to take in order to achieve some objective of interest, or whether it
concerns the predicates the agent ought to treat as being true of some
object or situation in the world.

Regards,

Jon

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[Jon Awbrey]

Pragmatic Semiotic Information • 3
• https://inquiryintoinquiry.com/2024/03/05/pragmatic-semiotic-information-3/

All,

Where is information bred? In reality or in its stead?

The way signs enter the scene is shown in Figure 2.

Pragmatic Semiotic Information • Figure 2
• https://inquiryintoinquiry.files.wordpress.com/2024/03/pragmatic-semiotic-information-e280a2-figure-2.png

The Figure illustrates a scene of uncertainty
which has been augmented by a classification.

In the pattern of classification shown the first three outcomes fall
under the sign “A” and the next two outcomes fall under the sign “B”.

• If the outcomes are things potentially true of an object or situation
then the signs may be read as nomens (terms) or notions (concepts) in
a relevant empirical or theoretical scheme, in effect, as predicates
and predictors of the outcomes.

• If the outcomes are things potentially worth doing to achieve a goal
then the signs may be read as bits of advice or other indicators telling
us what actions to try in a situation, relative to our active goals.

This will give us a practical framework for talking about information and
signs in regard to communication, decision, and the uncertainties thereof.

Regards,

Jon

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[Jon Awbrey]

Pragmatic Semiotic Information • 4
• https://inquiryintoinquiry.com/2024/03/08/pragmatic-semiotic-information-4/

All,

Sense and Obliviscence —

In taking up a study of signs from a pragmatic point of view
we naturally follow the advice of the pragmatic maxim on a way
to make the relationship between our concepts and their objects
as clear as necessary. When it comes to our concept of the objects
called signs we expand our conception of signs to a conception of
their practical effects, conceiving the manifold of experiments
and experiences involved in the use of signs.

In forming that expansion we bring to light many kinds of signs
glossed over in the more conventional focus on “words spoken” and
“words written”, that is, language in the strictest sense. Signs in
pragmatic perspective encompass all the “data of the senses” (“dots”)
we take as informing us about inner and outer worlds, along with the
concepts and terms we use to reason about everything from worlds of
being to fields of action.

Ironically enough, we have just arrived at one of the junctures where it is
tempting to try collapsing the triadic sign relation into a dyadic relation.
For if sense data were so closely identified with objects that we could
scarcely imagine how they might be discrepant then we might imagine one
role of beings could be eliminated from our picture of the world.

If that were true then the only things we'd need to bother informing
ourselves about, via the inspection of sense data, would be yet more
sense data, past, present, or prospective, nothing but sense data.
And that is the special form to which we frequently find the idea
of an information channel being reduced, namely, to a source with
nothing more to tell us about than its own conceivable conducts
or its own potential issues.

Regards,

Jon

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[Jon Awbrey]

Pragmatic Semiotic Information • 5
• https://inquiryintoinquiry.com/2024/03/09/pragmatic-semiotic-information-5/

Uncertainty Measured —

As a matter of fact, at least in the discrete types of cases
we are currently considering, it would be possible to use the
degree of a node, the number of paths fanning out from it, as
a measure of uncertainty at that point. That would give us a
multiplicative measure of uncertainty rather than the sorts of
additive measures we are more used to thinking about — no doubt
someone would eventually think about taking logarithms to bring
measures back to familiar ground — but that is getting ahead of
the story.

To illustrate how multiplicative measures of multiplicity, variety,
or uncertainty would work out, let us take up a simpler example,
one where the main choice point has a degree of four. Figure 3
gives us the picture.

Pragmatic Semiotic Information • Figure 3
• https://inquiryintoinquiry.files.wordpress.com/2024/03/pragmatic-semiotic-information-e280a2-figure-3.png

Regards,

Jon

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[Jon Awbrey]

Pragmatic Semiotic Information • 6
• https://inquiryintoinquiry.com/2024/03/10/pragmatic-semiotic-information-6/

Uncertainty Multiplied —

In our minds' eyes last time we imagined ourselves coming to
a fork in the road and seeing four paths diverge from that point.
Suppose a survey of the scene ahead now shows each path reaching
a point where another decision has to be made, this time a choice
between two alternatives. Figure 4 gives us the picture so far.

Pragmatic Semiotic Information • Figure 4
• https://inquiryintoinquiry.files.wordpress.com/2024/03/pragmatic-semiotic-information-e280a2-figure-4.png

The Figure illustrates the fact that the compound uncertainty, 8, is
the product of the two component uncertainties, 4∙2. To convert that
to an additive measure, one simply takes the logarithms to a convenient
base, say 2, and thus arrives at the not too astounding fact that the
uncertainty of the first choice is 2 bits, the uncertainty of the next
choice is 1 bit, and the total uncertainty is 2 + 1 = 3 bits.

Regards,

Jon

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[Jon Awbrey]

Pragmatic Semiotic Information • 7
• https://inquiryintoinquiry.com/2024/03/11/pragmatic-semiotic-information-7/

Uncertainty Moderated —

In many ways the provision of information, a process which serves to
reduce uncertainty, operates as an inverse process in relation to the
type of uncertainty augmentation which occurs in compound decisions.
By way of illustrating the relation in question, let us return to
our initial example.

A set of signs enters on a setup like that as a system of “middle terms”,
a collection of signs one may regard, aptly enough, as forming a “medium”.

Pragmatic Semiotic Information • Figure 5
• https://oeis.org/wiki/File:Pragmatic_Semiotic_Information_%E2%80%A2_Figure_5.png

The “language” or “medium” in Figure 5 is the set of signs {“A”, “B”}.
On the assumption the initial five outcomes are equally likely it is
possible to associate a frequency distribution (k₁, k₂) = (3, 2) and
thus a probability distribution (p₁, p₂) = (3/5, 2/5) = (0.6, 0.4)
with the language, thereby defining a “communication channel”.

The most important thing at this stage of development is simply to get a
first handle on the “conditions for the possibility of signs making sense”,
but once we have that much in hand we can begin constructing the rough and
ready pieces of information-theoretic furniture we need, like measures of
uncertainty, channel capacity, and the amount of information associated
with the reception or the recognition of a single sign.

Regards,

Jon

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[Jon Awbrey]

Pragmatic Semiotic Information • 8
• https://inquiryintoinquiry.com/2024/03/12/pragmatic-semiotic-information-8/

Information Recapitulated —

Suppose we find ourselves in the classification‑augmented
or sign‑enhanced situation of uncertainty shown in Figure 5.
What difference does it make to our state of information
regarding the objective outcome if we heed one or the other
of the two signs, “A” or “B”, at least, operating on the
charitable assumption we grasp the significance of each sign?

Pragmatic Semiotic Information • Figure 5

• https://inquiryintoinquiry.files.wordpress.com/2024/03/pragmatic-semiotic-information-e280a2-figure-5.png

• Under the sign “A” our uncertainty is reduced from log 5 to log 3.
• Under the sign “B” our uncertainty is reduced from log 5 to log 2.

The above characteristics of the relation between uncertainty
and information allow us to define the “information capacity” of
a communication channel as the “average uncertainty reduction on
receiving a sign”, a formula with the splendid mnemonic “AURORAS”.

Regards,

Jon

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[Jon Awbrey]

Pragmatic Semiotic Information • 9
• https://inquiryintoinquiry.com/2024/03/16/pragmatic-semiotic-information-9/

Information Recapped —

Reflection on the inverse relation between uncertainty and information
led us to define the “information capacity” of a communication channel
as the “average uncertainty reduction on receiving a sign”, taking the
acronym “AURORAS” as a reminder of the definition.

To see how channel capacity is computed in a concrete case
let's return to the scene of uncertainty shown in Figure 5.

Pragmatic Semiotic Information • Figure 5
• https://inquiryintoinquiry.files.wordpress.com/2024/03/pragmatic-semiotic-information-e280a2-figure-5.png

For the sake of the illustration let's assume we are dealing with the
observational type of uncertainty and operating under the descriptive
reading of signs, where the reception of a sign says something about
what's true of our situation. Then we have the following cases.

• On receiving the message “A” the additive measure of uncertainty
is reduced from log 5 to log 3, so the net reduction is (log 5 - log 3).

• On receiving the message “B” the additive measure of uncertainty
is reduced from log 5 to log 2, so the net reduction is (log 5 - log 2).

The average uncertainty reduction per sign of the language is computed
by taking a “weighted average” of the reductions occurring in the channel,
where the weight of each reduction is the number of options or outcomes
falling under the associated sign.

• The uncertainty reduction (log 5 - log 3) is assigned a weight of 3.
• The uncertainty reduction (log 5 - log 2) is assigned a weight of 2.

Finally, the weighted average of the two reductions is computed as follows.

• (1/5) ∙ [ 3 ∙ (log 5 - log 3) + 2 ∙ (log 5 - log 2) ]

Extracting the pattern of calculation yields the following worksheet
for computing the capacity of a two‑symbol channel with frequencies
partitioned as n = k₁ + k₂.

Capacity of a channel {“A”, “B”} bearing the odds of 60 “A” to 40 “B”
• https://inquiryintoinquiry.files.wordpress.com/2024/03/channel-capacity-60-a-40-b-tabletitle.png

In other words, the capacity of the channel is slightly under 1 bit.
That makes intuitive sense in as much as 3 against 2 is a near‑even
split of 5 and the measure of the channel capacity, otherwise known
as the “entropy”, is especially designed to attain its maximum of
1 bit when a two‑way partition is split 50‑50, that is, when the
distribution is “uniform”.

Regards,

Jon

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