# [Fis] “model” and “mental model”

```Dear FIS Colleagues,
```
```

I agree with Joseph and Pedro that:

“There are no ideal meta-observers; we are all, to a certain extent, both
meta-observers of the discussion and participants in it. This is not a simple
vertical hierarchy. We move between these two roles, switching from actualizing
one to the other.”

What I think is that from point of view of the observed system, object, event,
etc., it is better to say “external observer” and “internal observer” in
corresponded cases just because “this is not a simple vertical hierarchy”.

Now, let me continue with little explanation about “model” and “mental model”.

If one will visit the Wikipedia he/she will find series of examples of concept
“model” [1].

As Marx Wartofsky remarks [2], the concept "model" has been used for denotation
of the very large class of phenomena: mechanical, theoretical, linguistic, etc.
constructions. He gave a good definition of the model relation and in [2] he
made clear the main characteristics of the models. His definition is as follow:

“

The model relation is triple M:

M: (S, x, y)

where "S" is subject for whom "x" represents "y".

In other words only in this relation and only for the subject "S" the entity
"x" is a model of the entity "y".

“

The easy but not serious definition of the “mental model” is to say: “it is a
model in the subject’s consciousness”.

Again, in Wikipedia, there are several examples [5].

This way is not good because it is very difficult to answer the question: who
is “the subject” in this case?

So, we need another definition.

In mathematics, a structure on a set, or more generally a type, consists of
additional mathematical objects that, in some manner, attach (or relate) to the
set, making it easier to visualize or work with, or endowing the collection
with meaning or significance. A partial list of possible structures are
measures, algebraic structures (groups, fields, etc.), topologies, metric
structures (geometries), orders, events, equivalence relations, differential
structures, and categories.

Sometimes, a set is endowed with more than one structure simultaneously; this
enables mathematicians to study it more richly. For example, an order induces a
topology. As another example, if a set both has a topology and is a group, and
the two structures are related in a certain way, the set becomes a topological
group.

Mappings between sets which preserve structures (so that structures in the
domain are mapped to equivalent structures in the co-domain) are of special
interest in many fields of mathematics. Examples are homomorphisms, which
preserve algebraic structures; homeomorphisms, which preserve topological
structures; diffeomorphisms, which preserve differential structures; [3], and
the functors which preserve category structures.

To avoid misunderstandings with concepts Subject, agent, animal, human,
society, humanity, living creatures, etc., in [4] we use the abstract concept
“INFOS” to denote every of them as well as all of artificial creatures which
has features similar to the former ones.

Here we are interested only of three features of Infos: receptors, effectors,
and memory. Infos has possibility to reflect the reality via receptors and to
operate with received reflections in its memory. The opposite is possible - via
effectors Infos has possibility to realize in reality some of its
(self-)reflections from its consciousness.

If the following diagram exists and if it is commutative, then it represents
all modeling relations:

- in reality: real models,

- in consciousness: mental models;

- between reality and consciousness: perceiving data and creating mental models.

It is easy to imagine the case when the Infos realizes its reflections using
its effectors, i.e. relation between consciousness and reality: realizing
mental models and creating data. In this case the receptors’ arrows should be
replaces by opposite effectors’ arrows.

In mathematical terms in diagram above:

― Source “s” and Recipient “r” are structured sets;

― Infos is an intelligent system;

― “e” is a mapping from s in r which preserves (all or partial) structures;

― mental source “si” and mental recipient “ri” are structured sets;

― “ei” is a mapping from si in ri which preserves (all or partial) structures.

Finally, the task of the external observer is to create the diagram above by
using some experimental data and staying outside the system (consciousness) -
above the dotted line.

Respectively, the internal observer does the opposite. The task of the internal
observer is to create the diagram above by using some (experimental) data and
staying inside the system (consciousness) – below the dotted line.

Friendly greetings

Krassimir

[1] https://en.wikipedia.org/wiki/Model

[2] M.W.Wartofsky. Models. Representation and the Scientific Understanding.
D.Reidel Publishing Company, Dordrecht: Holland /Boston: USA, London: England/,
1979.

[3] http://en.wikipedia.org/wiki/Mathematical_structure

[4] Kr. Markov, Kr. Ivanova, I. Mitov. Basic Structure of the General
Information Theory. IJ ITA, Vol.14, No.: 1, 2007. pp. 5-19.

[5] https://en.wikipedia.org/wiki/Mental_model

PS: If the diagram is not visible after posting in FIS-list I shall duplicate
this message presenting it by symbols.

From: PEDRO CLEMENTE MARIJUAN FERNANDEZ
Sent: Sunday, March 04, 2018 9:36 PM
To: joe.bren...@bluewin.ch
Cc: fis@listas.unizar.es
Subject: Re: [Fis] Meta-observer?

Dear Colleagues,

I am reluctant to discuss the information matters related to our language as
they too easily mess things up. But Eric Werner short paper (2010, Science 329,
629-630) makes a very adequate remark in the context of Shannon's theory and
biologic information that may also apply to language use: "The meaning of a
message is determined by how it affects the informational and intentional state
of the agent. Agents coordinate their actions by using communication to adjust
their respective strategies so that they cohere to achieve their interlocking
goals."

The point on "interlocking goals" by Werner brings me to the centrality of life
cycles (synchronization of lives), in all quarters pertaining to the biological
and to the social, and also in our languages. But they are not still recognized
as a central concern to ponder. They are like the water for the fish, that
invisible stuff which permeates our societies.

which I concur. In actuality, the full world of disciplines with all their
institutional collective bodies, Institutes, Departments, Journals, Reviewers,
Meetings, formal and informal gatherings, etc. constitute a thought collective
well beyond the individual. In our case, the "meta" complexity is well
credited, as the problems around information cross along some of the deepest
conundrums: from a new evolutionary/cellular theory to the absence of an
efficient central theory of neurosciences (&consciousness); from quantum
information (&measurement&coherence interpretations) to cosmology; from the
relationship with entropy to the information society, and of course including
the new "dataism" to be discussed soon.

And this is my second cent of the week.

Best--Pedro

On Sat, 3 Mar 2018 02:58:28 +0100 (CET) "joe.bren...@bluewin.ch" wrote:

Dear Pedro and All,

If I go back to Pedro's original note, I see a further aspect which might be
worked into its discussion. There are no ideal meta-observers; we are all, to a
certain extent, both meta-observers of the discussion and participants in it.
This is not a simple vertical hierarchy. We move between these two roles,
switching from actualizing one to the other. Recognition of both should help
accomplish what I have tried to propose, namely, that we force ourselves to
emphasize someone else's work in our proposals, rather than our own.

Best regards,

Joseph

----Message d'origine----
De : pcmarijuan.i...@aragon.es
Date : 28/02/2018 - 05:34 (PST)
À : fis@listas.unizar.es
Objet : [Fis] Meta-observer?

Dear FISers,

Although I share Terry's concern, I do not think that

p>expostulating one's general framework is going to facilitate the
p>discussions. Perhaps opposite, as it will introduce a trend towards
generalization that fortifies the perspectival differences and makes

the rhetorics less adjusted to the concrete. The problem basically

resides in the persistent immaturity of the "information synthesis" so

to speak. Defenders of each approach advocate a different "observer",

charged in each case with their favorite conceptualizations. Taking

into account the apparent multitude of dimensions of information, and

its almost unfathomable reach, a "battery" of those observers has to

be in place. And an agile switching among the observers has to be

established. A sort of "attention" capable of fast and furious

displacements of the focus...  helas, this means a meta-observer

or an observer-in-command.

But what sort of reference may such a

metaobserver arbitrate? There is no conceivable book of rules about

the switching between heterogeneous disciplinary bodies.

I see

only one way, imitating the central goal of nervous systems: the

metaobserver should finally care about our collective social life. It

was Whitehead, as far as I remember, who put it: "to live, to live

better." In each level of organization it is the life cycle of the

concerned entities and the aggregates built upon them what

matters.

Information is not only about logic-formal

aspects. It is the bread and butter of complexity, that which allows

contemporary social life.

So, in the coming session about

"dataism" we can also explore these themes.

Best--Pedro

/blockquote>

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