Dear Igor, Dear Pedro
and Colleagues,
When someone has spent as much time and effort as Igor has on developing
and presenting a concept of information, the least one can do is study and
comment on it carefully. Now, I happen to disagree with Igor on some pretty
fundamental issues, but I believe my critique, and the response from him I hope
we will all see, may suggest new ways of approaching our favorite topic. I take
as references both his long note of 20 December 2010, to which Pedro referred,
and his summary of it 19 April 2011.
1. General Remark
The key ontological
property for Igor is identity: he thinks that a “Science of Information” must
use a single, unified unique definition of information. On the other hand
“information is a continuous evolving process” that exists in both simple and
complex forms. It is not clear why, except from a kind of habit, one needs to
have a single, static definition for an evolving process. But, you and he will
say, he states that information is heterogeneity! Yes, but it is heterogeneity
to the exclusion of homogeneity, which for anything real is an abstraction. It
is the identity of exclusion (please see next point).
2. The Definitions of Homogeneity and Heterogeneity
Igor’s definitions are
a restatement of the principle of exclusivity in standard set theory and the
standard concept of similarity and difference. This makes his definitions of
homo- and heterogeneity fully equivalent to elements of classical bivalent
propositional logic. In my opinion, it is impossible for such a logic and such
definitions
to apply to information as a process, moving as it does between partially
homogeneous
and heterogeneous elements.
3. Information-as-Heterogeneity
Igor states that his
definition of information-as-heterogeneity, stable for a finite time, “can
describe information (heterogeneity) of any nature”. This statement perhaps
anticipates
the subsequent discussion, but it is not clear as it stands. In the complete
note it is stated that “the measure of the degree of heterogeneity or
information is Shannon’s information entropy
*and other information characteristics (information divergence, joint entropy,
communication information)*”. However, these “other information
characteristics”, which in my view may be the most significant ones for further
discussion, are not indicated, nor is if and how they function in measurement.
4. Information and Observers
Igor is of course
correct when he observes (sorry) that the advent of Observers results in new
levels of complexity (or hierarchies) of information, limited by the
informational characteristics of the “lowest level”, that is the physics and
chemistry of our world. I also agree that it is most useful to see information
as a universal property or process component of the world.
However, I would like
to call attention to the most interesting citation Igor makes in his April,
2011 note from the
work of A. D. Ursul to the effect that “information is a variety which one
object contains about the other (in the process of their interaction (which can
also be self-referential))”.
This for me is an
essential point: we do not need to make absolute separations between observer
and observed, Observer 1 and Observer 2 (both “objects” and “subjects”) and the
information, in slightly different words, that is a product of their
interaction, the interactive process. I am not convinced, then, that the
standards and definitions of each Observer will be totally disjoint. Rather
(with some good will), some partially if not completely compatible
interpretations of information will be possible.
5. Perception and Thinking
As a final point, I
note Igor’s statement that “the concept of information reflects … also the
*property*
of perception and thinking, as well as the “objectively real property of
inanimate and animate objects of nature and society”. I would argue that the
use of “objectively” here diminishes the value of the qualitative features of
information that the simple definition of it as heterogeneity cannot provide,
but that we somehow would like to capture.
My suggestion is that Igor’s
designation of perception and thinking as “properties” is perhaps misplaced.
Mark Burgin’s suggests (elsewhere) that perception and thinking are complex
operators. Individual instances of perceptive and cognitive acts result from
the application of those operators, which both constitute information and from
which new information can emerge. I also prefer to think of perception and
thought as complex processes, also “objectively real”, albeit more difficult to
work with.
As always, I look forward to comments on and criticisms of my ‘dialectics’.
Best wishes,
Joseph
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