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This volume offers a fundamentally different way of conceptualizing
time and reality. Today, we see time predominantly as the
linear-sequential order of events, and reality accordingly as
consisting of facts that can be ordered along sequential time. But
what if this conceptualization has us mistaking the "exhausts" for
the "real thing", i.e. if we miss the best, the actual taking place
of reality as it occurs in a very differently structured,
primordial form of time, the time-space of the present? In this new
conceptual framework, both the sequential aspect of time and the
factual aspect of reality are emergent phenomena that come into
being only after reality has actually taken place. In the new view,
facts are just the "traces" that the actual taking place of reality
leaves behind on the co-emergent "canvas'' of local spacetime.
Local spacetime itself emerges only as facts come into being - and
only facts can be adequately localized in it. But, how does reality
then actually occur? It is conceived as a "constellatory
self-unfolding", characterized by strong self-referentiality, and
taking place in the primordial form of time, the not yet
sequentially structured "time-space of the present". Time is seen
here as an ontophainetic platform, i.e. as the stage on which
reality can first occur. This view of time (and, thus, also space)
seems to be very much in accordance with what we encounter in
quantum physics before the so-called collapse of the wave function.
In parallel, classical and relativistic physics largely operate
within the factual portrait of reality, and the sequential aspect
of time, respectively. Only singularities constitute an important
exemption: here the canvas of local spacetime - that emerged
together with factization - melts down again. In the novel
framework quantum reduction and singularities can be seen and
addressed as inverse transitions: In quantum physical state
reduction reality "gains" the chrono-ontological format of
facticity, and the sequential aspect of time becomes applicable. In
singularities, by contrast, the inverse happens: Reality loses its
local spacetime formation and reverts back into its primordial,
pre-local shape - making in this way the use of causality
relations, Boolean logic and the dichotomization of subject and
object obsolete. For our understanding of the relation between
quantum and relativistic physics this new view opens up
fundamentally new perspectives: Both are legitimate views of time
and reality, they just address very different chrono-ontological
portraits, and thus should not lead us to erroneously subjugating
one view under the other. The task of the book is to provide a
formal framework in which this radically different view of time and
reality can be addressed properly. The mathematical approach is
based on the logical and topological features of the Borromean
Rings. It draws upon concepts and methods of algebraic and
geometric topology - especially the theory of sheaves and links,
group theory, logic and information theory, in relation to the
standard constructions employed in quantum mechanics and general
relativity, shedding new light on the pestilential problems of
their compatibility. The intended audience includes physicists,
mathematicians and philosophers with an interest in the conceptual
and mathematical foundations of modern physics.
This volume offers a fundamentally different way of conceptualizing
time and reality. Today, we see time predominantly as the
linear-sequential order of events, and reality accordingly as
consisting of facts that can be ordered along sequential time. But
what if this conceptualization has us mistaking the "exhausts" for
the "real thing", i.e. if we miss the best, the actual taking place
of reality as it occurs in a very differently structured,
primordial form of time, the time-space of the present? In this new
conceptual framework, both the sequential aspect of time and the
factual aspect of reality are emergent phenomena that come into
being only after reality has actually taken place. In the new view,
facts are just the "traces" that the actual taking place of reality
leaves behind on the co-emergent "canvas'' of local spacetime.
Local spacetime itself emerges only as facts come into being - and
only facts can be adequately localized in it. But, how does reality
then actually occur? It is conceived as a "constellatory
self-unfolding", characterized by strong self-referentiality, and
taking place in the primordial form of time, the not yet
sequentially structured "time-space of the present". Time is seen
here as an ontophainetic platform, i.e. as the stage on which
reality can first occur. This view of time (and, thus, also space)
seems to be very much in accordance with what we encounter in
quantum physics before the so-called collapse of the wave function.
In parallel, classical and relativistic physics largely operate
within the factual portrait of reality, and the sequential aspect
of time, respectively. Only singularities constitute an important
exemption: here the canvas of local spacetime - that emerged
together with factization - melts down again. In the novel
framework quantum reduction and singularities can be seen and
addressed as inverse transitions: In quantum physical state
reduction reality "gains" the chrono-ontological format of
facticity, and the sequential aspect of time becomes applicable. In
singularities, by contrast, the inverse happens: Reality loses its
local spacetime formation and reverts back into its primordial,
pre-local shape - making in this way the use of causality
relations, Boolean logic and the dichotomization of subject and
object obsolete. For our understanding of the relation between
quantum and relativistic physics this new view opens up
fundamentally new perspectives: Both are legitimate views of time
and reality, they just address very different chrono-ontological
portraits, and thus should not lead us to erroneously subjugating
one view under the other. The task of the book is to provide a
formal framework in which this radically different view of time and
reality can be addressed properly. The mathematical approach is
based on the logical and topological features of the Borromean
Rings. It draws upon concepts and methods of algebraic and
geometric topology - especially the theory of sheaves and links,
group theory, logic and information theory, in relation to the
standard constructions employed in quantum mechanics and general
relativity, shedding new light on the pestilential problems of
their compatibility. The intended audience includes physicists,
mathematicians and philosophers with an interest in the conceptual
and mathematical foundations of modern physics.
In Natural Communication, the author criticizes the current
paradigm of specific goal orientation in the complexity sciences
and proposes an alternative that envisions a fundamental
architectonics of communication. His model of "natural
communication" encapsulates modern theoretical concepts from
mathematics and physics, in particular category theory and quantum
theory. From these fields it abstracts precise concepts such as to
constitute a terminological basis for this theory which offers the
opportunity to open up novel ways of thinking about complexity. The
author is convinced that it is only possible to establish a
continuity and coherence with contemporary thinking, especially
with respect to complexity, through looking into the past.
This unique book provides a self-contained conceptual and technical
introduction to the theory of differential sheaves. This serves
both the newcomer and the experienced researcher in undertaking a
background-independent, natural and relational approach to
'physical geometry'. In this manner, this book is situated at the
crossroads between the foundations of mathematical analysis with a
view toward differential geometry and the foundations of
theoretical physics with a view toward quantum mechanics and
quantum gravity. The unifying thread is provided by the theory of
adjoint functors in category theory and the elucidation of the
concepts of sheaf theory and homological algebra in relation to the
description and analysis of dynamically constituted physical
geometric spectrums.
If there is a central conceptual framework that has reliably borne
the weight of modern physics as it ascends into the twenty-first
century, it is the framework of quantum mechanics. Because of its
enduring stability in experimental application, physics has today
reached heights that not only inspire wonder, but arguably exceed
the limits of intuitive vision, if not intuitive comprehension. For
many physicists and philosophers, however, the currently
fashionable tendency toward exotic interpretation of the
theoretical formalism is recognized not as a mark of ascent for the
tower of physics, but rather an indicator of sway-one that must be
dampened rather than encouraged if practical progress is to
continue. In this unique two-part volume, designed to be
comprehensible to both specialists and non-specialists, the authors
chart out a pathway forward by identifying the central deficiency
in most interpretations of quantum mechanics: That in its
conventional, metrical depiction of extension, inherited from the
Enlightenment, objects are characterized as fundamental to
relations-i.e., such that relations presuppose objects but objects
do not presuppose relations. The authors, by contrast, argue that
quantum mechanics exemplifies the fact that physical extensiveness
is fundamentally topological rather than metrical, with its proper
logico-mathematical framework being category theoretic rather than
set theoretic. By this thesis, extensiveness fundamentally entails
not only relations of objects, but also relations of relations.
Thus, the fundamental quanta of quantum physics are properly
defined as units of logico-physical relation rather than merely
units of physical relata as is the current convention. Objects are
always understood as relata, and likewise relations are always
understood objectively. In this way, objects and relations are
coherently defined as mutually implicative. The conventional notion
of a history as "a story about fundamental objects" is thereby
reversed, such that the classical "objects" become the story by
which we understand physical systems that are fundamentally
histories of quantum events. These are just a few of the novel
critical claims explored in this volume-claims whose
exemplification in quantum mechanics will, the authors argue, serve
more broadly as foundational principles for the philosophy of
nature as it evolves through the twenty-first century and beyond.
If there is a central conceptual framework that has reliably borne
the weight of modern physics as it ascends into the twenty-first
century, it is the framework of quantum mechanics. Because of its
enduring stability in experimental application, physics has today
reached heights that not only inspire wonder, but arguably exceed
the limits of intuitive vision, if not intuitive comprehension. For
many physicists and philosophers, however, the currently
fashionable tendency toward exotic interpretation of the
theoretical formalism is recognized not as a mark of ascent for the
tower of physics, but rather an indicator of sway-one that must be
dampened rather than encouraged if practical progress is to
continue. In this unique two-part volume, designed to be
comprehensible to both specialists and non-specialists, the authors
chart out a pathway forward by identifying the central deficiency
in most interpretations of quantum mechanics: That in its
conventional, metrical depiction of extension, inherited from the
Enlightenment, objects are characterized as fundamental to
relations-i.e., such that relations presuppose objects but objects
do not presuppose relations. The authors, by contrast, argue that
quantum mechanics exemplifies the fact that physical extensiveness
is fundamentally topological rather than metrical, with its proper
logico-mathematical framework being category theoretic rather than
set theoretic. By this thesis, extensiveness fundamentally entails
not only relations of objects, but also relations of relations.
Thus, the fundamental quanta of quantum physics are properly
defined as units of logico-physical relation rather than merely
units of physical relata as is the current convention. Objects are
always understood as relata, and likewise relations are always
understood objectively. In this way, objects and relations are
coherently defined as mutually implicative. The conventional notion
of a history as "a story about fundamental objects" is thereby
reversed, such that the classical "objects" become the story by
which we understand physical systems that are fundamentally
histories of quantum events. These are just a few of the novel
critical claims explored in this volume-claims whose
exemplification in quantum mechanics will, the authors argue, serve
more broadly as foundational principles for the philosophy of
nature as it evolves through the twenty-first century and beyond.
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