7.4 Conclusions
“Gravitation by Condensation” is offered as a way to explain the phenomenology
suggested by the Mandelbrot Set and the remarkable way it fits to the ideas of top
theorists. The advantages of this theoretical construction are that it resembles
Newtonian or Einsteinian gravity at shorter scales but inherits the accelerating
expansion at the largest scales that is seen in DGP gravity and cascading DGP,
because it arises in a similar higher-dimensional framework. But a single context for
all of this—condensation that proceeds from spaces with higher dimension, creates
the current conditions, and explains the force of gravity—is provided by the Mandelbrot Set and its associated figures. Of course, we must assume that M is higherdimensional, residing in the quaternions and octonions, but this is reasonable. We
note that Kricker and Joshi (1995) used the Mandelbrot Set to map associative and
non-associative regions in the octonions, in a paper on bifurcations in the octonionic
quadratic. So we know there are natural correspondences to explore for brave souls
prepared to deal with the complexity of octonion algebra. Thankfully, there are now
tools available, helping to make the difficult calculations more routine to implement.
Rick Lockyer has made available an octonion calculation package for NodeJS
(Lockyer 2018) that I have been test driving, which offers some capabilities that
will assist further research. However, the features of M seen along the real axis, such
Fig. 7.4 Misiurewicz point at ~ (À1.543689, 0i) illustrating an event horizon/quantum critical
point (on left) and the condensation process (on right)
74
J. J. Dickau
“Gravitation by Condensation” is offered as a way to explain the phenomenology
suggested by the Mandelbrot Set and the remarkable way it fits to the ideas of top
theorists. The advantages of this theoretical construction are that it resembles
Newtonian or Einsteinian gravity at shorter scales but inherits the accelerating
expansion at the largest scales that is seen in DGP gravity and cascading DGP,
because it arises in a similar higher-dimensional framework. But a single context for
all of this—condensation that proceeds from spaces with higher dimension, creates
the current conditions, and explains the force of gravity—is provided by the Mandelbrot Set and its associated figures. Of course, we must assume that M is higherdimensional, residing in the quaternions and octonions, but this is reasonable. We
note that Kricker and Joshi (1995) used the Mandelbrot Set to map associative and
non-associative regions in the octonions, in a paper on bifurcations in the octonionic
quadratic. So we know there are natural correspondences to explore for brave souls
prepared to deal with the complexity of octonion algebra. Thankfully, there are now
tools available, helping to make the difficult calculations more routine to implement.
Rick Lockyer has made available an octonion calculation package for NodeJS
(Lockyer 2018) that I have been test driving, which offers some capabilities that
will assist further research. However, the features of M seen along the real axis, such
Fig. 7.4 Misiurewicz point at ~ (À1.543689, 0i) illustrating an event horizon/quantum critical
point (on left) and the condensation process (on right)
74
J. J. Dickau