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Re: How Does One go From the 4th Dimension to the Fifth?Posted by Ramanujan12 on September 23, 2003 at 07:11:45: In Reply to: How Does One go From the 4th Dimension to the Fifth? posted by sol on September 22, 2003 at 14:29:30: Sol Thanks for inviting me to this forum. So many topics posted here and I am eager to read them all. But first I will assimilate some Ideas in relation to GR because this seems to be an overarching area of importance. One of my ideas about GR I have had recently is it's ideal connection to geometries in other areas of Classical physics such as the classical mechanics of Newton, fluid theories, simple surface theories, Minkowski dimension, chromodynamics, and the work of Laplace. What I like to conceptualize is the idea of a Neo-Classical re-interpretation of physics from the intuitive geometry of GR and even simpler models which may be used as a Neo-Classical generalization for hyperspace in extremely high dimensions. Modern physics in M and QST theories lately focuss too much on certain domains of thought and becomes, what I like to state as being: "too groupy". Not just in it's group-theoretic-centric models but also as a clique or group in modern thought. This is rather novel way of looking at it. Much of the work on QST from the 80's done by Kaku and Witten is of high iterest ie. Wittens papers on the Morse-stratified realizations of Abelians. A kind of Neo-Classical rendering of high-dimensions would be a beautiful model for GUT but it could only be formulated by re-interpreting calculus from a modern point of view ie. in terms of smooth ifinitesimal calculus SIC (multivariated calculus), synthetic differential geometry SDG, and founding quantum statistical models using abstact probability (derivation theory, martingales, cell functions, and star blankets). I think this is perhaps were the true mystical intuitions of hyperspace can occur; by not confining GR, SR, and classicism to 6-dimensions by a unique turn rather towards re-interpreting, on a philosophical level, what dimensionality actually means for linear and non-linear functions. This seems to resemble the direction taken by the contemporaries of Einstein, namely Hermann Weyl and Felix Klein. Both Weyl and Klein being mathematical physicists and philosophers who speculated in the intuitive manner the way Einstein did for physics. It is intersting to look at GR in the manner of pure theoretics; aluded to in Hacking's "Representing and Intervening" which harboured seeds to the awakening of intuitive studies of experimentation in natural sciences which corrects the imbalance of reliance upon experimental results in favour of intuitive theories. In other words the natural sciences can be done from inside the mind by assimilating concepts and knowledge in the form of working out cosmology and quantum potentials as experiments of thought, as experiments that yield discovered natures and their own results. Perhaps it is more sufficient to describe the type or species of data on which GR is founded as an idealization of what is inherently real for nature and inherently real in the sense of allways being an idealization a priori and a postriori. This idealization is also akin to the amazing results of GR for high-energy physics. Such things as the equivalence of inertial and gravitational mass demonstarted in the Emotvos experiment, uderstanding the perihelion of Mercury, the bending of light by massive gravitational objects, gravitational lensing; and the discovered gravitational red shift surveys for spectral lines. This is were the work of interdisciplinary's like Weyl , who continued Einsteins progress outside the quantum movement, is worth looking into as a model of introspection as "Neo-Classical" hyperdimensional physics. Weyl overcame the dualism beteen the electric force and gravity which suggests that GR, and SR, was incomplete, and that following in the mental footsteps of Einstein in math, physics, philosophy etc. could in fact be associated with freedom and creativity for the future reallization of greater unifications. The idea of an alternative master narative in physical science, such as Neo-Classical high-dimensionality, may require the re-interpreting of 20th-Century physics as a movement between essence/unity/transcendence and novelty/ disunity/objective experimentation. This idea takes the route of anti-reductionism and complexity where solid state physics, rather than elementary particle theories, is exemplary. Solid states here unites with a smooth surface geometry for mechanical tensor models, and most importantly engineering! I can't imagine GR and quantum physics mathematically resonating without a very model-theoretic understanding of dimensions from which it comes together in the higher spaces. Model-theoretic here means the pure modeling of mathematical representations that are the logical root of all maths. And model theory, as it is termed, is the same thesis and defines dimensions in the exact same context as does classsical and modern engineering! From this basis of modeling equations and engineering analysis can be reconstituted from the basic principles of reality as we perceive it. However dimensions mean something completely different from this base than they do in model-excluded mathematics which has forgotten it's base. Dimensions are defined as actual metrics themselves, not metrics in the sense of the topological school ie. points set to the deformations of space, but in the school of engineering they are given as units of measurement which human beings give definition. GR in this perspective may then be understood as a human experience defined by Einstein himself in his use of the Riemmanian and Lorentzian systems. Neo-Clasical modeling of higher-dimensions would be like engineering equations as a re-setting from those of the past, from the lost mathematics of the mid-20th Century, in the form of 1-dimensional, 2-dimensional, 3-dimensional processes and surfaces as complexes for 7-dimensional, 15-dimensional, and or 27-dimensional exemplars governing the space we allready inhabit! As Kaku has stated before on Art Bell interviews that common denominator being that: the dimensions are all arround us, occupying the 3rd-dimension, even in this very room they are right in front of our noses. I would further state that in order to penetrate these other dimensions, these higher dimensions etc. we must fully make a radical new shift in the way we use our tools, mathematical tools, physical tools, machines, and philosophy. Starting from mathematical physics we could re-invest our notions of meaning, re-root the modeling of what constitutes mathematical physics, dissolving the Hilbert-Hamiltonian conjugations and actually, via history, fully understand what these greats in the past may have realy been triying to say. As for GR, I would do the same, by placing myself in Eisteins slippers and ask ones self - what it all means; is the relative realy absolute and is the absolute realy relative? And for Newton and Leibniz I would ask myself; are real numbers realy complex or are complex numbers realy real? These are inspirational questions that need to be adressed, and if they have already, then perhaps they need to be adressed in light of a new language.
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