

Alt.Fractals:
A
visual guide to fractal geometry and design

ISBN 0955706831 
Fractals
are Officially Cool.
Where most books on the subject concentrate on
mathematical theory, Alt.Fractals
takes a graphical approach. Starting with the fractal "standards" – the
Sierpinski Triangle and Pyramid, Menger Sponge, Julia and
Mandelbrot Sets – Alt.Fractals
explores the world of variations one step removed from the usual
textbook versions.
With over two hundred diagrams
and additional thumbnails giving constructional details, Alt.Fractals
is is a fascinating browsing experience for the newcomer, a key
resource for anyone interested in fractal designs, and an essential
bookshelf reference for the expert.
b&w, 232 pages, 225 illustrations


The
Abyss of Time: An architect's history of the Golden
Section

ISBN 0955706815 
Martin
Hutchinson
spent years researching possible links between the Fibonacci
Series (and the Golden Section)
and
ancient architecture. His basic premise was that not only did
there seem to be a common prehistoric unit of measurement (related to
Alexander Thom's “megalithic yard”), and
a recurring appearance of proportions similar to the
Golden
Section in many old
structures, but that the two might be related: when it came to
constructing systems of weights and measures, ancient builders
seemed to have been using the Fibonacci Series ( 1, 1, 2, 3,
5,
8, 13,
21, 34, 55 ... ) as a logical way of assembling larger
building blocks
from smaller units. As we ascend the Fibonacci Series, the ratio
between adjacent pairs of numbers becomes evercloser to the Golden
Section, so marking out a
cathedral floorplan with the Fibonacci ratio “34:55” would give the
building “Golden Section”like proportions without any
advanced mathematics.
The early recognition and use
of the Fibonacci series (Hutchinson argued) might have been the reason
for the otherwiseinexplicable appearance of “thirteen” in many
premetric measurement systems, since thirteen is an awkward prime
number that can't be divided down into convenient smaller units, and to
modern eyes, there would be no obvious reason for using it. Thirteen
would, however, necessarily appear in a scale based on the Fibonacci
Series.
Hutchinson lectured on the
subject in the
1960's, but the planned publication of "Abyss" was
stalled by his death in 1973.


Relativity
in
Curved Spacetime: Life without special relativity

ISBN 0955706807
ISBN 0955706823 
Relativity
theory is usually considered to consist of two main parts: a restricted
theory that assumes flat spacetime ("special
relativity"), and
a more ambitious model (Einstein's "general theory of
relativity") that allows curved
spacetime. The general theory is assumed to reduce to the "special"
theory over small regions of spacetime.
However,
towards the end of his life, Einstein seemed to have lost confidence
in this twostage approach, and appeared to be
presenting the
adoption of special relativity as a historical fluke, and
suggesting that
he
no longer believed that it was valid to model physics in the absence of
curvature "I do not believe that such an attitude,
although historically understandable, can be objectively justified ...
I do not believe that it is justifiable to ask: what would physics look
like without gravitation?" (Scientific
American,
April 1950).
Einstein's later notion of
curvature
as a fundamental aspect of physics invalidates many of our
current ideas about how relativity theory ought to operate, and in
"Relativity in Curved Spacetime", Eric
Baird
examines what we really know about relativity
theory, looks at
potential problems with the special and general theories, and examines
how a "curvaturebased" model might depart from current theory.
Adopting
a groundup approach, the book makes heavy use of illustrations to
explain some basic principles of relativity theory, and also has
chapters on black holes, wormholes, cosmology and warp drive theory.
The latter part of the book looks at some of the ways that logical
systems can break down, and examines logical black holes, Titanic
Syndrome, why computers crash, and what Pi tells us about
mathematicians. The conclusion, that we might well have
committed ourselves to the wrong theory of
relativity, may make some physicists uncomfortable.


