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'Alt.Fractals' ISBN 0955706831

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": full cover

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 ever-closer to the Golden Section, so marking out a cathedral floor-plan 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 otherwise-inexplicable appearance of “thirteen” in many pre-metric 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": full cover

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 two-stage 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 "curvature-based" model might depart from current theory.

Adopting a ground-up 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.