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Please note that the constructal theory” also elaborates on the dis- continuities on the macroscopic scale. This engineering theory shows that exact shapes must be used to lose the least amount of energy. Let us first look at geometric fractals. They possess properties such as a non-whole dimension that is strictly higher than the topological dimension, non-differentiability (impossibility to define the tangent) and the presence of infinities. A topological dimension is a classic dimension: point (0), line (1), surface (2), volume (3), hyper-volume (4). A homothety (magnification factor) is the repetition of a topological dimension. A frac- tal dimension is expressed by the ratio of two logarithms: the number of fractals (p iterations) and the magnification factor (q): lam not going into detail here, because it would become even more complex. However, this equation gives us a good idea. Let me simply say that the fractal dimension is, of course, non-Euclidean. The fractal values lie between | and 2 when we follow a curve or between 2 and 3 when we speak of volume. It is remarkable to observe that the micro- scopic world contains fractal objects, such as the protein molecule (a value of 1.7). In 3D time, the fractal nature of time only regards the “time density” dimension as the homothety of a single topological dimension. For comparison purposes, fractal time is to conventional physical time what the fractal dimension is to the Euclidean dimen- sion. Moreover, I think that the fractal nature of space inexorably implies the fractal nature of time, because the two are closely related in special relativity. By accepting the universality of the latter as that of geometric fractals naturally spread across the universe, we also accept the existence of fractal time as the only logical conclusion. Most calcu- lations using Minkowski space-time are validated, give or take a few approximations, because fractal space is usually juxtaposed to fractal time giving the illusion of linear equations; hence the use of integral functions. If space indeed diminishes in the same fractal ratio as the increase of time and, of course, at the same time, then a linear function is perfectly appropriate. The changes will be clear. However, if the tran- sition from one scale to another does not take place simultaneously for space and time, significant differences will be observed, for instance in case of 1) gravity on a very large and very small scale, 2) residual glu- onic interaction (different color charge for quarks) permitting strong interaction, 3) residual electromagnetic interaction connecting two 162 The Science of Extraterrestrials: UFOs Explained at Last * Eric Julien Log p/log q