Hi Marcin and Richard,
Thank you for focusing on the core of the work. I have tried to find the
main points of Marcin's "general question", which in a way is an answer to
Richard's wish for a definition of information.
Let me republish those statements in Marcin's posting to which I would like
to add my opinion. For didactic reasons, I have changed the sequence of the
thoughts Marcin raises.
Q: "I strongly believe that only a definition of information based on the
concepts with firm philosophical foundations can be of any value for the
development of information science. This is why I have proposed probably the
oldest, and for sure thoroughly examined philosophical problem
of "one vs. many" as a background for the concept of information. "
A: The definition of information which will in my opinion survive the next
few years is: "information is that what we neglect as we conduct an
addition" or "For any given collection of parts, information is the extent
of the deviation of the probability for the given collection of parts to the
probability of the most usual collection of parts."
This approach presupposes a-priori gravitational centers for parts. Up to
now, we established the properties of the collection by taking the property
of its "unit element" (the least individuated element, the unit most devoid
of properties) and multiplied by the number of units. So we say conceptually
7 = 7*1. In the new approach, we take NOT the unit element, but the - new
concept - "central element" as the most representative of all of the
elements. The distinction between the unit element and the central element
is of first importance.
The central element is the element with the most probable collection of
properties. It will be a part of the most probable summand/s and carry the
most probable number and kinds of symbols (in fact, it will carry only
fractions of a distinguishing symbol, but this fraction is > 0.)
So, we see a deviation in the result. It does make a difference whether we
calculate the properties of a set based on the idealised unit or the most
probable unit.
The central element is to be thought as that {unit, fish, bird, person, ...}
that is in the midst of the swarm. The cross-hair of the most probable
properties gives one the type, properties and place - and therefore density
- of the central element. (One can demonstrate the typical unit on the left
side of an = in an addition to have statistical properties, these
transcending both the individual addition and the result of the addition.)
Hope that the idea has gotten across:
A: yes, there is a definition of information.
B: each actual state we encounter is as much full of information as it is
deviating to the most probable state.
C: the most probable state is devoid of information: it is the origo,
etalon, the reference point itself.
D: the element incorporating (realising) the most probable state is called
the central element. It is conceptualised as the mass point (schwerpunkt) of
a swarm. Relative to this, the others are "somehow otherwise", that is:
possessing a degree of information.
Q: "The reference to biological taxonomy brings another argument for
informational taxonomy. ... It can help in the development of information
science. ... if a genus/species definition of information is just an option,
why should we expect that a taxonomy of information can help. ...
I am looking for the definition in this classical genus/species
(or genus/differentia) form. I have formulated in this form the definition
which I have proposed ..."
A: We find the central element by superimposing statistical search routines
on each other. (find the most usual /age, weight, hair colour, .../ and the
person/s agreeing to all these is/are the central element). Each cut is a
first-order cut. (Grouping people acc to the probability of their birthday
is as legitimate as acc to the probability of their earnings.) Second-order
cuts split the first-order subsets. (Sunday-born people earn more than
Friday-born people, or, in the highest quintile of earnings there are
disproportionately more Sunday than Monday people, etc.) The disparity
between the most dense and the second-most dense subsegment is where the
importance lies. The cuts "between" two first-order cuts are cuts of the 2nd
order. There is a clear hierarchy among cuts, with a few equally legitimate
readings of the order of cuts.
Q: "The mutual relations of concepts related to information are important
for its understanding. It is some form of looking for understanding
information from the (conceptual) inside. ... However, I think that more
important is to find an appropriate perspective on the concept of
information from the outside. How is the concept of information related to
the other concepts?"
A: In my opinion, we pay now the price for having idealised uniformity over
diversity. (Animals with a CNS that remembers /=re-recognises, =discovers
similarities, =prefers uniformity signals over diversity signals/ do have a
reproductive advantage, so we are hard-wired to prefer similarity to
diversity.)
De-constructing all that what we have built up without regard to the
diversity component in concatenations of units will be a long and
complicated affair. The reverse engineering happens most usefully by
re-building from the bottom up, by evolving the concept of units and
operations based on diversity.
Q: " ... naive and incorrect belief that the more general concept we want to
define (information is such a general concept,) the more "common sense"
concepts should be used in explanation (definiendum.) ... This is the
reason why so popular is an "explanation" of information by "uncertainty"
(originally, probably because of its "scientific" association with quantum
mechanics and the Uncertainty Principle.)"
A: Quite often, it is not the intrinsic truth of a thought that will
determine whether it will be a culturally accepted axiom, but some other
aspects as well. The self-evident truths seldom contradict common sense. On
the opposite, it is rather the definitions - decrees, dogmas - which may
evolve away from common sense and obvious reason.
It is much more trendy, jazzy and splashy, not to speak of Wow! effect of
fame and richesse if you find an audience where you can feed them with
highly complicated nonsense, than a simple and obvious, self-evident truth.
The contortions of tortured minds come up with ideas like the uncertainity
principle, quantum esoterics and affinity of informed agents towards each
other unless they are noble, in which case they refrain from interaction
with the non-noble. Our concepts about the world are filled up to the hilt
with religious and anthropomorphic (animalistic) ideas (like centri-fugal
forces /=fleeing the center, like a criminal flees a jail/).
It is much less poshy to say that we have been conned into a make-believe
world of uniformity with absolutely no individuality of the units. Diversity
matters, and if the scientists make themselves a world in which there is no
diversity, they play peek-a-boo with themselves.
In psychology, we have a term: "artefact". This describes the effects of the
surroundings, requisites, circumstances of an experiment. Quite many of the
findings of science appear to turn out to be the effects of the artefact
that we discount diversity without giving a thought to the costs of doing
so. Like there is no free lunch, there is no standardisation without loss of
individuality/diversity. If we standardise into well-behaved,
undistinguishable units with no individual properties and expect collections
of such to behave as we expect, then we are perplexed that things happen
which should not happen if every unit was as devoid of individuality as we
decreed them to be. One can build himself a lovely world of illusions, it
just does not fit into reality. The deviation between reality and how I
expect it to be is not mysterious at all. It is my expectations which were
too much overidealised.
To re-callibrate our concepts in order to find them aligned BOTH with
similarity and diversity, we should begin a reverse engineering task. A kind
of "truth and reconciliation commission" would be in order, in science, too.
Let us hope FIS will turn out to be one of the seeds for a more realistic
view of science.
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Received on Thu Mar 16 11:18:03 2006
