"Mathematical Landscapes" is an art and writing series about the connections between science, mathematics and surreal art in which one can observe the truth between many layers of twisted realities.
This work also combines the thought of what consciousness could be - seen through the eyes of a mathematician and logician!
The concepts of the interplay between both mathematical structures as well as physical processes creates new insights about solutions to very odd logical mysteries, called 'paradoxes'.
The main thoughts are implications of Hofstadter's Gödel Escher Bach and the ideas of Gödel's Incompleteness...
People who enjoyed this book may perhaps find 'Mathematical Landscapes' interesting as well.
Underlined are these texts with 22 unique artworks where 're-occuring symbols' appear in each one. If you want to find out more, this book might give you the answers.
by Max Tegmark
ISBN 978-0307599803
by Peter Atkins
ISBN 978-3150190319
by Hermann Haken
ISBN 978-3854525035
by Douglas R. Hofstadter
ISBN 978-0465026562
These four books shaped the logical foundation of the project Mathematical Landscapes.
...An introduction to Thermodynamics by Atkins that beautifully portraits the four laws of thermodynamics and gives insight to processes of heat and energy up to terms of a phenomenon called "chaos"...
A very short, but quite interesting, book by Haken about synergetics - the science of interaction, as Haken put it in his book. In this book the reader can understand how orderly structures can emerge out of chaos.
The bridges I've built between these two topics (thermodynamics and synergetics) give a quite beautiful insight about how our universe behaves. In combination with Hofstadter's Godel, Escher, Bach that's mainly about Godel's incompleteness underlines these bridges as well. Godel's incompleteness can be implicated as the principle that a formal system can either be self-referent (, thus paradox) or incomplete, because the self-referent system can't be proven nor disproven OUTSIDE that system (like the semantic rules of mathematical logic); Thus a system that would be complete needs to be proven or disproven by ITSELF, which makes it self-referent and thus paradox.
These three books are like three sides of one and the same thought pattern; They explain and somewhat build up on each other.
The 4th book by Tegmark offers an example of Hofstadter's thought about "tangled hierarchies". It is about multiverses of four levels. In the upshot the biggest structure can be the smallest as well, and vice versa.
It is a quite delicate example of the tangled hierarchies used by Hofstadter. This tangled hierarchy of the biggest structure being the smallest as well creates a common paradox.
...and where paradoxes appear, Godel's incompleteness isn't far away as well...
This sums up what I try to display in my artworks of Mathematical Landscapes.