Dear Krassimir,
thank you for undertaking this project of an "Anthology of Contemporary
Ideas on Information".
Let me take up your kind encouragement (not published in fis) and offer the
following contribution (through fis, in order to be able to request the
colleagues to offer their comments: thanks):
(let me hope that the word processor of the fis server will deal correctly
with the formattings used)
The Algorithm of Information Content
The approach we propose needs some introduction, as it makes use of
combinations of techniques which have not been used together.
1) Material we work with
We begin by creating elements of a set.
The set we construct to demonstrate how to establish information content
consists of realisations of the logical sentence *a+b=c. *That is, if we
use *d *distinguishing categories of elements, we shall have a set that
contains the elements *{(1,1), (1,2), (2,2), (1,3), (2,3), (3,3), (1,4),
(2,4), …., (d,d)}. *These elements we refer to as *(a,b), a <=b.*
The number *n *of the elements of the set is of course dependent of *d*, *n
= f(d). * *n = d(d+1)/2.*
While the *principle *of information management is valid over a wide range
of values of *d*, it can be shown (OEIS A242615) that for reasons of
numerical facts, the *efficiency *of information management is the highest
when using *d=16, *which yields *n=136. *Nature also appears to use the
mathematically optimal method of information transmission.
2) What we look into the material 1: properties of the elements
We use the set of elements created such as a kind of Rorschach cards,
looking aspects into them.
We use, next to the traditional aspects *{a, b, c=a+b}* some additional
aspects of *a+b=c *also, namely *{u=b-a, k=2b-a, t=3b-2a, q=2a-b, s=(d+1) -
(a+b), w=3a-2b},* that is, altogether *9 aspects of a+b=c. *
Users are of course free and invited to introduce additional or different
aspects to categorise logical sentences with. The *number* of aspects needs
not to be higher of 8 if they are used in combination (we refer here again
to the facts discussed in OEIS A242615), and as to the *kinds* of aspects:
one is always open to improvements.
3) What we look into the material 2: properties of the set
We impose sequential orders on the elements of the set, using combinations
of aspects.
We generate *sequencing aspects * by using always 2 of the 9 *primary
aspects, *by creating sequential orders within the set such that each of
the primary aspects is once the *first* and once the *second *ordering
aspect. That is, we sequence the set on the criteria *{ab, ac, ak, au, …,
as, aw, ba, bc, bu, …, bw, ca, cb, …, cw, ka, kb, …, …, wt, ws}. * This
brings forth 72 sequential enumerations of the elements of the set. Of
these, about 20 are actually different. (The inexactitude regarding the
number of identical sequential enumerations has to do with the *sequence*
of the primary aspects and will be of fundamental importance in the course
of the applications of the model.)
The 72 different sequences the elements – of which some are different in
name only - of the set have been brought into are called the *catalogued
sequences. *These are by no means random but are as closely related to
each other as aspects of *a+b=c *can be closely related to each other. Each
of the catalogued sequences is equally legitimate and each is an implicated
corollary of *a+b=c, *now having been made explicit (=realised).
4) What we observe within the material 1: logical conflicts
We will not ignore conflicts between place and inhabitant, inhabitant and
place.
It is obvious that 2 different catalogued orders unveil logical conflicts.
If in order *αβ* element *e *is to be found on place *p1* and in order *γδ*
element *e *is to be found on place *p2*, there is apparently a conflict.
The same conflict can also be stated by using the formulation: If in order
*αβ* on place *p *element *e1* is to be found and in order *γδ *on place *p
*element *e2* is to be found, there is apparently a conflict.
We observe potentially or actually conflicting assignments of a sequential
number *{1..n}* to one and the same element of the set, in dependence of
which of the catalogued orders we deem to be actually the case. As we
decline to entertain an epistemological attitude of human decisions
creating and ceasing logical conflicts, we look into methods of solving
these potential and realised conflicts. As the two orders *αβ* and *γδ*, if
they are different, create dislocations of the elements relative to their
own conceptions of which is the correct place for an individual element to
be in, we speak of *a consolidation of dislocations* that we aim at.
5) What we look into the material 3: series of place changes
We transform linear arrangement *αβ* into linear arrangement *γδ*.
We have observed that if we once order the set sequentially according to
sorting order *αβ* (say, e.g. on arguments: *a,b*), and then again on a
different sorting order *γδ* (say, e.g. on arguments: *b,a*), then we have
conflicting assignments of places to most of the elements. (This example is
worked through in great detail in OEIS A235647. The sequence: *{(1,1),
(1,2), (2,2), (1,3), (2,3), (3,3), (1,4), (2,4), …., (d,d)} *shows the set
to be sorted on arguments *b,a*, while the sequence *{(1,1), (1,2), (1,3),
…, (1,d), (2,2), (2,3), …, (2,d), (3,3), (3,4), (3,d), …., (d,d)} *shows
the set to be sorted on arguments *a,b.*)
The position of an element *(a,b) *in the linear sequence that has been
created by sorting the set on arguments *b,a*
is given by (1),
* x = position ( (a,b), d, (b,a) ) = b* (b-1) / 2 +
a
(1)*
The position of an element *(a,b) *in the linear sequence that has been
created by sorting the set on arguments *a,b*
is given by (2),
* x = position ( (a,b), d, (a,b) ) = d*(d + 1) / 2 – ( d – a + 1 ) * ( d –
a + 2 ) / 2 + ( b – a + 1) (2)*
where the SYNTAX is:
x resulting position of element
position ( *(a,b)*, d, (a,b) ) elements with numerical values a,b
position ( (a,b), *d, *(a,b) ) number of distinct categories, resulting
for number of elements in set *n = d*(d+1)/2*
position ( (a,b), d, (*a,b*) ) sorting order resulting from first
criterium: a, second criterium: b
We now visualise a series of *travels - bumps – pushes – travels – bumps –
pushes – travels - … - travels. *In this vivid imagination about how the
reordering, from order according to *αβ* into order according to *γδ*,
actually takes place, one starts off with the first element one encounters
in the present order *αβ *and moves it to its new place in order *γδ. *There,
the element *bumps* into that element which occupies that place in this
moment. This element is then *pushed* out of its place and *travels* to its
new place, where it *bumps *into that element which occupies its place, *pushes
*that element out of its place, which then *travels *etc. etc. etc. until
the Last element of the cycle *travels *to that place which has been
vacated by the first element one has started the reorder with. On that
place a void has been the case since the first element of the cycle had
begun its *travel.*
6) What we observe within the material 2: a web of paths
We see tautologies, compromises and discontinuities.
Extending the concept demonstrated above on a rearrangement from sorting
order *(a,b)* into sorting order *(b,a) *onto rearrangements from any of
the 72 catalogued orders into any different of the catalogued orders, we
arrive at 72*71/2 = 2.556 *transitions, *where each transition
contains 136 *steps.
*This gives us a *Basic Table of Transitions *that has 347.616 rows. Each
row contains the data *from_order, into_order, value_a, value_b, cycle_nr,
step_in_cycle, place_from, place_to. *
Of these data, one may construct many planes and some spaces. The *place_from,
place_to *values are coordinates on a plane, of which the axes are
named *from_order,
into_order, *and the x,y values are the integers that represent the
sequential place of the element in the respective sequential orders.
In some cases, one can observe that spaces can be constructed with 3
rectangular axes. For more details on this observations, please generate
the tables on your own computer, or see the discussion in *Learn To Count
In Twelve Easy Steps [1], *or *Natural Orders [2].*
The cycles connect points of planes, in some cases: point that have
coordinates in 3 dimensions.
7) What we observe within the material 3: logical relations
The entries in our databases are connected among each other in manifold
ways, both in commutative and also in sequential enumerations.
We now come to the information content of a communication. The concept we
now put forward is an improvement on the Shannon concept. In the Shannon
understanding of data transmission, the communication points out 1 place
within a limited range and transmits the relevant value which can be {0,1}.
Here, we also use a limited range – namely the number of elements of the
corpus of a cycle – and transmit the value of 1 element. In a
visualisation, we bend the section of the number line which Shannon
imagines straight, albeit limited, until it becomes a closed cycle. In this
loop, we point out, *which* of the elements of the loop we mean, and
also, *which
loop *this element is included in.
When identifying a pupil in a class of n pupils, we can proceed with
Shannon and:
1) Line up the pupils,
2) Give each pupil 1 sequential number
3) Transmit repeatedly, which half of the line-up the pupil is included
in.
Our approach would be:
1) Do not line up the pupils, but rather sort them on
a) hair colour
b) age
c) weight
d) height
e) voice pitch
f) etc. (One can read off OEIS 242615, how many properties can maximally be
used with n pupils.)
2) Establish, who would change places with whom if a linear reorder
would take place from property “x” into property “y” (in this example,
there are 5*4/2=10 reorders); which cycles the individual pupils would
belong to;
3) Transmit, the how-many-eth (starting, say, from the smallest element
of the corpus) of the elements in the corpus of
4) Which cycle.
In the former method, one knows the number of bits needed to identify 1 of
n elements in a set. In the latter method, one can learn and one can adapt.
In the former method, the elements have no relationships among each other:
the method is well suited to transmit data that can be random. The latter
method uses the immanent facts of belonging-to among elements that exist
prior to human knowledge.
The formal approach to the idea of information points out, that a
communication about the facts of which elements of the cycle are those that
are *not meant *gives one knowledge about, *which cycle* is the element
meant included in. There is de facto no clean-cut distinction between the
description of “the others” as to whether “the others” are not meant,
because they are of a different category or rather they are of the same
category but just not the one that one wants to point out: this because in
biological reality the clean-cut distinction does not exist (there being no
independent concept of a background without any properties in biologic
epistemology).
2017-10-07 20:06 GMT+02:00 Krassimir Markov <mar...@foibg.com>:
> Dear FIS Colleagues,
>
> It is time for my second post this week.
>
> Many thanks to Christophe Menant (for the profound question) and to all
> colleagues (for the very nice and useful comments)!
>
> **********************
>
> Christophe Menant had written:
> “However, I'm not sure that “meaning” is enough to separate information
> from data. A basic flow of bits can be considered as meaningless data.
> But the same flow can give a meaningful sentence once correctly
> demodulated.
> I would say that:
> 1) The meaning of a signal does not exist per se. It is agent dependent.
> - A signal can be meaningful information created by an agent (human
> voice, ant pheromone).
> - A signal can be meaningless (thunderstorm noise).
> - A meaning can be generated by an agent receiving the signal
> (interpretation/meaning generation).
> 2) A given signal can generate different meanings when received by
> different agents (a thunderstorm noise generates different meanings for
> someone walking on the beach or for a person in a house).
> 3) The domain of efficiency of the meaning should be taken into account
> (human beings, ant-hill).
> Regarding your positioning of data, I'm not sure to understand your
> "reflections without meaning".
> Could you tell a bit more?“
>
> Before answering, I need to make a little analysis of posts this week
> connected to my question about data and information. For this goal, below
> I shall remember shortly main ideas presented this week.
>
> Citations:
>
> Stanley N Salthe:
> “The simple answer to your question about data is to note the word's
> derivation from Latin Datum, which can be compared with Factum.”
>
> Y. X. Zhong:
> “It is not difficult to accept that there are two concepts of information,
> related and also different to each other. The first one is the information
> presented by the objects existed in environment before the subject's
> perceiving and the second one is the information perceived and understood
> by the subject. The first one can be termed the object information and the
> second one the perceived information. The latter is perceived by the
> subject from the former.
> The object information is just the object's "state of the object and the
> pattern with which the state varies". No meaning and no utility at the
> stage.
> The perceived information is the information, perceive by the subject from
> the object information. So, it should have the form component of the
> object (syntactic information), the meaning component of the object
> (semantic information), and the utility component of the object with
> respect to the subject's goal (pragmatic information). Only at this stage,
> the "meaning" comes out.”
>
> Karl Javorszky:
> “Data is that what we see by using the eyes. Information is that what we
> do not see by using the eyes, but we see by using the brain; because it is
> the background to that what we see by using the eyes.
> Data are the foreground, the text, which are put into a context by the
> information, which is the background. In Wittgenstein terms: Sachverhalt
> and Zusammenhang (which I translate – unofficially – as facts /data/ and
> context /relationships/)”.
>
>
> Dai Griffiths:
> “I'm curious about your use of the word 'dualistic'. Dualism usually
> suggests that there are two aspects to a single phenomenon. As I interpret
> your post, you are saying that information and meaning are separate
> concepts. Otherwise, we are led to inquire into the nature of the unity of
> which they are both aspects, which gets us back where we started.
> So I interpret 'dualistic' here to mean 'two concepts that are intertwined
> in the emergence of events'. Is this parallel to, for example, atomic
> structure and fluid dynamics (perhaps there are better examples)? If so,
> does that imply a hierarchy (i.e. you can have information without
> meaning, but not meaning without information)? This makes sense to me,
> though it is not what I usually associate with the word 'dualistic'.”
>
> Guy A Hoelzer:
> “If you start by explicitly stating that you are using the semantic notion
> of information at the start, I would agree whole heartedly with your post.
> I claim that physical information is general, while semantic information
> is merely a subset of physical information. Semantic information is
> composed of kinds of physical contrasts to which symbolic meaning has been
> attached. Meaningfulness cannot exist in the absence of physical
> contrast, but physical information can exist independently of sensation,
> perception, cognition, and contextual theory.”
>
> Jose Javier Blanco Rivero:
> “What is information at some stage of the process becomes data on other.”
>
> Loet Leydesdorff:
> "Data" is "given" or "revealed" by God.
> The search for an intuitive definition of information has led to unclear
> definitions. In a recent book, Hidalgo (2015, at p. 165), for example, has
> defined “information” with reference “to the order embodied in codified
> sequences, such as those found in music or DNA, while knowledge and
> knowhow refer to the ability of a system to process information.” However,
> codified knowledge can be abstract and—like music—does not have to be
> “embodied” (e.g., Cowan, David, & Foray, 2000).
> Beyond Hidalgo’s position, Floridi (2010, p. 21) proposed “a general
> definition of information” according to which “the well-formed data are
> meaningful” (italics of the author). Luhmann (1995, p. 67) posits that
> “all information has meaning.” In his opinion, information should
> therefore be considered as a selection mechanism. Kauffman et al. (2008,
> at p. 28) added to the confusion by defining information as “natural
> selection.”
> Against these attempts to bring information and meaning under a single
> denominator--and to identify variation with selection--I argue for a
> dualistic perspective (as did Prof. Zhong in a previous email).
> Information and meaning should not be confounded. Meaning is generated
> from redundancies (Bateson, 1972, p. 420; Weaver, 1949; see Leydesdorff et
> al., 2017).
>
> Lars-Göran Johansson:
> “I am an empiricist and nominalist, accepting Occam’s razor: one should
> not assume more entities than necessary. And assuming that Information is
> a property, an entity, is not necessary. We can proceed with scientific
> research, using any information concept we think useful, without assuming
> it refers to anything.”
>
> Robert K. Logan:
> “So now for my definition of information as can be found in the book:
> • Data are the pure and simple facts without any particular structure or
> organization, the basic atoms of information,
> • Information is structured data, which adds meaning to the data and gives
> it context and significance,
> • Knowledge is the ability to use information strategically to achieve
> one's objectives, and
> • Wisdom is the capacity to choose objectives consistent with one's
> values and within a larger social context.”
>
> Stanley N Salthe:
> “ {facts {data -->information {knowledge {understanding}}}} “
>
> End of citations.
>
> Once more, thank you for the nice reasoning!
> I agree with all above!
>
> What is missing?
> Why we could not come to common understanding if practically we all talk
> about the same phenomenon and share the same idea?
>
> We all agree that there exist two dualistic forms of information (“what is
> information at some stage of the process becomes data on other”):
>
> - External information for the agent (Informational entity,
> interpreter, human brain, etc.) called “object information” (“data,
> information without meaning, what we see by using the eyes; physical
> information; "given" or "revealed" by God; pure and simple facts
> without any particular structure or organization, the basic atoms of
> information!”);
>
> - Internal information for the agent (interpreter, human brain, etc.)
> called “perceived information” (“syntactic information+semantic
> information+pragmatic information; seen by using the brain; semantic
> information; structured data, which adds meaning to the data and
> gives it context and significance!”).
>
> What we have is the equation:
>
> “Internal information” = “external information reflected by the agent“ +
> “subjective for the agent meaning (or semantic)”.
>
> But, the internal information for one agent is external for all others and
> has no meaning (semantic) for them until they reflect it anyway (via some
> secondary reflections created in the environment by the first agent) and
> add a new meaning.
>
> This way we have seen that the meaning (semantic) is separated from the
> external and internal information and exist only in a special case. I.e.
> we have the same phenomenon in both cases plus some agent depended
> reaction - adding the meaning (“semantic; structured data, which adds
> meaning to the data and gives it context and significance”).
>
> Finally, the problem with naming the pointed phenomenon has risen. I
> prefer to call it a “reflection” because of way it is generated - by
> reflection from the environment via all possible sensors of the agent.
>
> Now, it is not good for me (Occam’s razor!) to use name “information” for
> all the cases pointed above (External information and Internal
> information). I prefer to use concept “information” only in the second
> case - Internal information. For the first case (External information) I
> prefer to use concept “Data”.
>
> So, we come to what I had written:
>
> Data = Reflection;
> Information = Reflection + Meaning.
>
> **********************
>
> I plan to publish the text above (between stars) in the next issue of the
> International Journal “Information Theories and Applications”. Because of
> this, I kindly ask colleagues, who are cited in the text as well as all
> other, to give me permission to cite them and to send to me a proper
> citation of publication where the presented ideas are published. If the
> ideas are not published please give me permission to cite your post in the
> list.
>
> Please, take in account that I have no money to buy publications, so all
> citations have to be in open access and corresponded links have to be
> given.
> Not open access publications do not exist for me!
>
> Friendly greetings
> Krassimir
>
>
>
>
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