Dear Jerry and colleagues:
The mathematical community continues to insist that the text has a single
meaningfulness.
So, we must semantically distinguish between the notion of communication
with an exactness and the notion of communication that transfers some degree
of meaningfulness but less than exact.
Perhaps, one migt consider mathematical discourse as precisely the discourse
which does not tolerate ambiguity, and therefore has to abstract from all
contingency. It seems to me that mathematics also evolves differently from
the empirical sciences. (Philosophy is the other case with a deviant
pattern.) For example, we are still able to fully understand Pythagoras and
Euclides, while one would nowadays find it difficult to explain phlogiston
theory. Thus, the evolutionary patterns are different.
Herbert Simon's concept of "near decomposibility" seems important to me: all
evolving systems remain nearly decomposable because of the contingencies of
the adjacent (windowing) systems. Mathematicians (with the exception of
Louis Kauffman?) seem counterfactually to wish to state the alternative.
Math is perhaps the only science in Popper's World Three. It becomes
evolutionarily relevant insofar as it recombines with other scientific
discourses. The other scientific discourses (e.g., chemistry) specify the
substance which is communicated (distributed) in theoretical terms. Thus,
they develop special theories of communication, while math contributes with
the formal theory of communication for the understanding. The mismatches
drive the research programs.
[ ...]
This suggests that the issue is the distinction between a single unique
meaning for every text (perhaps the goal of mathematics and physics, the
"for all time and place" syndrome,) and the contingencies intrinsic to
biological communication among individual biological organisms.
I would layer individual minds between the biology (body) and the social.
While the individual mind is still very constrained by ("structurally
coupled" to) the biological body, the communication between minds allows for
much more freedom.
[...]
The curious reader is referred to the last chapter of Rosen's "Life Itself"
for this rather fine semantic and syntactic distinction.
Yes, this is certainly worth reading!
With best wishes,
Loet
PS. This is my second posting to the list this week. Thus, I will not be
able to react any further except offline.
_____
Loet Leydesdorff
Amsterdam School of Communications Research (ASCoR)
Kloveniersburgwal 48, 1012 CX Amsterdam
Tel.: +31-20- 525 6598; fax: +31-20- 525 3681
<mailto:loet@leydesdorff.net> loet@leydesdorff.net ;
<http://www.leydesdorff.net/> http://www.leydesdorff.net/
<http://www.leydesdorff.net/knbecon> The
Knowledge-Based Economy: Modeled,
Measured, and Simulated
<http://www.universal-publishers.com/book.php?method=ISBN&book=1581126956>
The Self-Organization of the Knowledge-Based Society;
<http://www.universal-publishers.com/book.php?method=ISBN&book=1581126816>
The Challenge of Scientometrics
Cheers
Jerry
Jerry LR Chandler
Research Professor
Krasnow Institute for Advanced Study
George Mason University
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Received on Tue Feb 7 08:42:43 2006
