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This volume presents essays by pioneering thinkers including Tyler
Burge, Gregory Chaitin, Daniel Dennett, Barry Mazur, Nicholas
Humphrey, John Searle and Ian Stewart. Together they illuminate the
Map/Territory Distinction that underlies at the foundation of the
scientific method, thought and the very reality itself. It is
imperative to distinguish Map from the Territory while analyzing
any subject but we often mistake map for the territory. Meaning for
the Reference. Computational tool for what it computes.
Representations are handy and tempting that we often end up
committing the category error of over-marrying the representation
with what is represented, so much so that the distinction between
the former and the latter is lost. This error that has its roots in
the pedagogy often generates a plethora of paradoxes/confusions
which hinder the proper understanding of the subject. What are wave
functions? Fields? Forces? Numbers? Sets? Classes? Operators?
Functions? Alphabets and Sentences? Are they a part of our map
(theory/representation)? Or do they actually belong to the
territory (Reality)? Researcher, like a cartographer, clothes (or
creates?) the reality by stitching multitudes of maps that
simultaneously co-exist. A simple apple, for example, can be
analyzed from several viewpoints beginning with evolution and
biology, all the way down its microscopic quantum mechanical
components. Is there a reality (or a real apple) out there apart
from these maps? How do these various maps interact/intermingle
with each other to produce a coherent reality that we interact
with? Or do they not? Does our brain uses its own internal maps to
facilitate "physicist/mathematician" in us to construct the maps
about the external territories in turn? If so, what is the nature
of these internal maps? Are there meta-maps? Evolution definitely
fences our perception and thereby our ability to construct maps,
revealing to us only those aspects beneficial for our survival. But
the question is, to what extent? Is there a way out of the
metaphorical Platonic cave erected around us by the nature? While
"Map is not the territory" as Alfred Korzybski remarked, join us in
this journey to know more, while we inquire on the nature and the
reality of the maps which try to map the reality out there. The
book also includes a foreword by Sir Roger Penrose and an afterword
by Dagfinn Follesdal.
This book explores the premise that a physical theory is an
interpretation of the analytico-canonical formalism. Throughout the
text, the investigation stresses that classical mechanics in its
Lagrangian formulation is the formal backbone of theoretical
physics. The authors start from a presentation of the
analytico-canonical formalism for classical mechanics, and its
applications in electromagnetism, Schroedinger's quantum mechanics,
and field theories such as general relativity and gauge field
theories, up to the Higgs mechanism. The analysis uses the main
criterion used by physicists for a theory: to formulate a physical
theory we write down a Lagrangian for it. A physical theory is a
particular instance of the Lagrangian functional. So, there is
already an unified physical theory. One only has to specify the
corresponding Lagrangian (or Lagrangian density); the dynamical
equations are the associated Euler-Lagrange equations. The theory
of Suppes predicates as the main tool in the axiomatization and
examples from the usual theories in physics. For applications, a
whole plethora of results from logic that lead to interesting, and
sometimes unexpected, consequences. This volume looks at where our
physics happen and which mathematical universe we require for the
description of our concrete physical events. It also explores if we
use the constructive universe or if we need set-theoretically
generic spacetimes.
This book explores the premise that a physical theory is an
interpretation of the analytico-canonical formalism. Throughout the
text, the investigation stresses that classical mechanics in its
Lagrangian formulation is the formal backbone of theoretical
physics. The authors start from a presentation of the
analytico-canonical formalism for classical mechanics, and its
applications in electromagnetism, Schroedinger's quantum mechanics,
and field theories such as general relativity and gauge field
theories, up to the Higgs mechanism. The analysis uses the main
criterion used by physicists for a theory: to formulate a physical
theory we write down a Lagrangian for it. A physical theory is a
particular instance of the Lagrangian functional. So, there is
already an unified physical theory. One only has to specify the
corresponding Lagrangian (or Lagrangian density); the dynamical
equations are the associated Euler-Lagrange equations. The theory
of Suppes predicates as the main tool in the axiomatization and
examples from the usual theories in physics. For applications, a
whole plethora of results from logic that lead to interesting, and
sometimes unexpected, consequences. This volume looks at where our
physics happen and which mathematical universe we require for the
description of our concrete physical events. It also explores if we
use the constructive universe or if we need set-theoretically
generic spacetimes.
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Vovoh (Paperback)
Francisco Antonio Doria
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R724
Discovery Miles 7 240
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Ships in 10 - 15 working days
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The revolutions that Gregory Chaitin brought within the fields of
science are well known. From his discovery of algorithmic
information complexity to his work on Goedel's theorem, he has
contributed deeply and expansively to such diverse fields.This book
attempts to bring together a collection of articles written by his
colleagues, collaborators and friends to celebrate his work in a
festschrift. It encompasses various aspects of the scientific work
that Chaitin has accomplished over the years. Topics range from
philosophy to biology, from foundations of mathematics to physics,
from logic to computer science, and all other areas Chaitin has
worked on.It also includes sketches of his personality with the
help of biographical accounts in some unconventional articles that
will provide a rare glimpse into the personal life and nature of
Chaitin.Compared to the other books that exist along a similar
vein, this book stands out primarily due to its highly
interdisciplinary nature and its scope that will attract readers
into Chaitin's world.
Current mathematical models are notoriously unreliable in
describing the time evolution of unexpected social phenomena, from
financial crashes to revolution. Can such events be forecast? Can
we compute probabilities about them? Can we model them? This book
investigates and attempts to answer these questions through
Goedel's two incompleteness theorems, and in doing so demonstrates
how influential Goedel is in modern logical and mathematical
thinking. Many mathematical models are applied to economics and
social theory, while Goedel's theorems are able to predict their
limitations for more accurate analysis and understanding of
national and international events.This unique discussion is written
for graduate level mathematicians applying their research to the
social sciences, including economics, social studies and
philosophy, and also for formal logicians and philosophers of
science.
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