KDnuggets : News : 2001 : n25 : item21    (previous | next)


From: Lev Goldfarb
Date: Fri, 30 Nov 2001 13:57:58 -0400 (AST)
Subject: A paper: "What is a structural measurement process?"
The following paper, whose abstract is attached below, proposes a
far-reaching (biologically inspired) generalization of the classical
concept of measurement process, based on the ETS model for structural
representation proposed by us earlier, and attempts to explain it on a
simple "shape example". The paper also attempts to clarify the radical
differences between the two kinds of "measurement" processes. Thus, we
address a very broad scientific context within which it might be useful to
treat the proposed ETS model.



Best regards,




                   Lev Goldfarb and Oleg Golubitsky

ABSTRACT.  Numbers have emerged historically as by far the most popular
form of representation. All our basic scientific paradigms are built on
the foundation of these, numeric, or quantitative, concepts. Measurement,
as conventionally understood, is the corresponding process for (numeric)
representation of objects or events, i.e., it is a procedure or device
that realizes the mapping from the set of objects to the set of numbers.
Any (including a future) measurement device is constructed based on the
underlying mathematical structure that is thought appropriate for the
purpose. It has gradually become clear to us that the classical numeric
mathematical structures, and hence the corresponding (including all
present) measurement devices, impose on "real" events/objects a very rigid
form of representation, which cannot be modified dynamically in order to
capture their combinative, or compositional, structure. To remove this
fundamental limitation, a new mathematical structure--evolving
transformation system (ETS)--was proposed earlier. This mathematical
structure specifies a radically new form of object representation that, in
particular, allows one to capture (inductively) the compositional, or
combinative, structure of objects or events. Thus, since the new structure
also captures the concept of number, it offers one the possibility of
capturing simultaneously both the qualitative (compositional) and the
quantitative structure of events.
    In a broader scientific context, we briefly discuss the concept of a
fundamentally new, biologically inspired, "measurement process", the
inductive measurement process, based on the ETS model. In simple terms,
all existing measurement processes "produce" numbers as their outputs,
while we are proposing a measurement process whose outputs capture the
representation of the corresponding class of objects, which includes the
class projenitor (a non-numeric entity) plus the class transformation
system (the structural class operations). Such processes capture the
structure of events/objects in an inductive manner, through a direct
interaction with the environment.

KDnuggets : News : 2001 : n25 : item21    (previous | next)

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