Pilote Tempête
12th May 2014, 06:25
From http://unconventional-wisdom.info/Page_2.html:
Extra dimensions would be describing a space invisible to us which would be totally in the imagination as it would be completely undefined and there would be no explanation of how it could exist and extra dimensions have no names and no quantities. As well, there are serious contradictions in descriptions of extra dimensions as they are said to be small (they have size, therefore volume, therefore 3 dimensions), are extended (have length), and are curled up (have shape, i.e., 3 dimensions). Spatial dimensions are measures of space so they cannot themselves have size nor shape and can't have anything in them, no more than length, height, and width. Or hyperspace would be a parallel universe or parallel universes which would themselves have 3 spatial dimensions each. Since physicists state there are 10 or 23 of these extra spatial dimensions they are not speaking of parallel universes because they would have to be a cluster of these universes to make up the total, so they, the spatial dimensions, would be in multiples of 3, which doesn't add up to 10, 11, nor 23. Also, such clustering is not postulated in any model of parallel universes. And physicists and cosmologists consider extra dimensions and parallel universes to be separate issues, which they are. (Kaku confuses dimensions with parallel universes on p. 22 of Hyperspace, refering to Riemann and Riemann never even mentioned parallel universes and his theory had nothing to do with them; Clifford Pickover does the same with his book Surfing Hyperspace: Undersatnding Higher Universes in 6 Easy Lessons, which is appropriately structured as fiction).
There are 14 types or meanings of dimensions in math (the size of a matrix, the number of elements in a basis in a vector space, of Hilbert space, of algebraic variety, and a manifold, simplex (Lesbegue or topological), Krull, Hausdorff, Hamel, box-counting, fractal, and inductive dimension, the power of a physical quantity (such as length, time or mass), and spatial dimension) and only 1 refers to physical space (the last one), so we shouldn't be confusing them either--what we are talking about are physical spatial dimensions only. Most spaces in math are abstract, not physical; physical space is also the domain of physics.
Some confuse spatial dimensions with directions and axes, but they are neither directions nor axes--and a figure with 4 or more axes is still in 3-D. The so-called hyperspaces in "multidimensional" geometry are really in 2- or 3-D, including the hypercube-tessaract, which is just a combination of 2 cubes which can be folded out into a cruciate configuration of 8 cubes, all in 3-D, and the Coxeter graphs. A hypercube is actually 2 cubes with their corners connected by lines forming a parallelogram, and the tessaract is actually a cube within a cube, with lines connecting their corners. And an ant on a cylinder, used as an example of extra dimensions by Green in The Elegant Universe, is also in 3-D.
As well, hyperspace would encompass normal space, just as 3-D space encompasses 2-D space, so if hyperspace existed it wouldn't be small nor curled up and we would be able to see it. The reason that we can't see it is because our bodies (or any biological beings) can't exist in more than 3D any more than they can in less than 3D, not because, as some argue, we can't visualize them in our minds. In other words, the reason we can't see them is because they don't exist. Put another way, what scientists speak of when they talk about hyperspace and extra dimensions is contrary to nature and reality and makes no sense whatsoever. (Philosopher A.N. Whitehead rightly refered to the 5th dimension as fiction (Singh, Great Ideas in Modern Mathematics, 1959, p. 302, Dover)). Also, some, e.g. Martin Grumiller of the Vienna University of Technology's Institue of Theoretical Physics, postulate a 2-D Universe (length and width) according to the holographic model of the Universe (Science Daily. 2009. How Many Dimensions in the Holographic Universe? sciencedaily.com). In the over 150 years since the idea of extra dimensions was introduced by Riemann in his Uber die Hypothesen welche der Geometrie zu Grunde liegen (On the Hypotheses Which Lie at the Foundation of Geometry) in 1854 there has never been any experimental nor observational evidence for them whatsoever.
There are certain anomalies in networked machines known to most electrical engineers which, according to Gabriel Kron, who did work on the torsion field using tensor analysis (developed by Gregorio Ricci-Curbastro c. 1890, and known then as tensor calculus, as a generalization or extension of vector analysis and deals with vector and scalar relations and coordinate systems)(Penguin Dictionary of Mathematics; Britannica On-Line, Wikipedia) in the 1930s, can be explained only by extra dimensions (Joseph Farrell, Secrets of the Unified Field, 2008, Adventures Unlimited). However, a tensor is an abstract geometric entity and its space is abstract so its dimensions are not physical (Penguin Dictionary of Mathematics; Britannica On-Line, Wikipedia), so Kron's higher dimensions actually refer to abstract mathematical space, not physical space. In other words, Farrell, and others apparently, confuse abstract space with physical space.
Extra dimensions would be describing a space invisible to us which would be totally in the imagination as it would be completely undefined and there would be no explanation of how it could exist and extra dimensions have no names and no quantities. As well, there are serious contradictions in descriptions of extra dimensions as they are said to be small (they have size, therefore volume, therefore 3 dimensions), are extended (have length), and are curled up (have shape, i.e., 3 dimensions). Spatial dimensions are measures of space so they cannot themselves have size nor shape and can't have anything in them, no more than length, height, and width. Or hyperspace would be a parallel universe or parallel universes which would themselves have 3 spatial dimensions each. Since physicists state there are 10 or 23 of these extra spatial dimensions they are not speaking of parallel universes because they would have to be a cluster of these universes to make up the total, so they, the spatial dimensions, would be in multiples of 3, which doesn't add up to 10, 11, nor 23. Also, such clustering is not postulated in any model of parallel universes. And physicists and cosmologists consider extra dimensions and parallel universes to be separate issues, which they are. (Kaku confuses dimensions with parallel universes on p. 22 of Hyperspace, refering to Riemann and Riemann never even mentioned parallel universes and his theory had nothing to do with them; Clifford Pickover does the same with his book Surfing Hyperspace: Undersatnding Higher Universes in 6 Easy Lessons, which is appropriately structured as fiction).
There are 14 types or meanings of dimensions in math (the size of a matrix, the number of elements in a basis in a vector space, of Hilbert space, of algebraic variety, and a manifold, simplex (Lesbegue or topological), Krull, Hausdorff, Hamel, box-counting, fractal, and inductive dimension, the power of a physical quantity (such as length, time or mass), and spatial dimension) and only 1 refers to physical space (the last one), so we shouldn't be confusing them either--what we are talking about are physical spatial dimensions only. Most spaces in math are abstract, not physical; physical space is also the domain of physics.
Some confuse spatial dimensions with directions and axes, but they are neither directions nor axes--and a figure with 4 or more axes is still in 3-D. The so-called hyperspaces in "multidimensional" geometry are really in 2- or 3-D, including the hypercube-tessaract, which is just a combination of 2 cubes which can be folded out into a cruciate configuration of 8 cubes, all in 3-D, and the Coxeter graphs. A hypercube is actually 2 cubes with their corners connected by lines forming a parallelogram, and the tessaract is actually a cube within a cube, with lines connecting their corners. And an ant on a cylinder, used as an example of extra dimensions by Green in The Elegant Universe, is also in 3-D.
As well, hyperspace would encompass normal space, just as 3-D space encompasses 2-D space, so if hyperspace existed it wouldn't be small nor curled up and we would be able to see it. The reason that we can't see it is because our bodies (or any biological beings) can't exist in more than 3D any more than they can in less than 3D, not because, as some argue, we can't visualize them in our minds. In other words, the reason we can't see them is because they don't exist. Put another way, what scientists speak of when they talk about hyperspace and extra dimensions is contrary to nature and reality and makes no sense whatsoever. (Philosopher A.N. Whitehead rightly refered to the 5th dimension as fiction (Singh, Great Ideas in Modern Mathematics, 1959, p. 302, Dover)). Also, some, e.g. Martin Grumiller of the Vienna University of Technology's Institue of Theoretical Physics, postulate a 2-D Universe (length and width) according to the holographic model of the Universe (Science Daily. 2009. How Many Dimensions in the Holographic Universe? sciencedaily.com). In the over 150 years since the idea of extra dimensions was introduced by Riemann in his Uber die Hypothesen welche der Geometrie zu Grunde liegen (On the Hypotheses Which Lie at the Foundation of Geometry) in 1854 there has never been any experimental nor observational evidence for them whatsoever.
There are certain anomalies in networked machines known to most electrical engineers which, according to Gabriel Kron, who did work on the torsion field using tensor analysis (developed by Gregorio Ricci-Curbastro c. 1890, and known then as tensor calculus, as a generalization or extension of vector analysis and deals with vector and scalar relations and coordinate systems)(Penguin Dictionary of Mathematics; Britannica On-Line, Wikipedia) in the 1930s, can be explained only by extra dimensions (Joseph Farrell, Secrets of the Unified Field, 2008, Adventures Unlimited). However, a tensor is an abstract geometric entity and its space is abstract so its dimensions are not physical (Penguin Dictionary of Mathematics; Britannica On-Line, Wikipedia), so Kron's higher dimensions actually refer to abstract mathematical space, not physical space. In other words, Farrell, and others apparently, confuse abstract space with physical space.