Dealing With a 5d World
I was trying to understand that once you get to see how the equation leads you too a understanding of that 5d world it allowed you to entertain all possibility based on this position.
Extra dimensions sound like science fiction, but they could be part of the real world. And if so, they might help explain mysteries like why the universe is expanding faster than expected, and why gravity is weaker than the other forces of nature.
Three dimensions are all we see -- how could there be any more? Einstein's general theory of relativity tells us that space can expand, contract, and bend. If one direction were to contract down to an extremely tiny size, much smaller than an atom, it would be hidden from our view. If we could see on small enough scales, that hidden dimension might become visible.
Here are some thoughts to consider?:)
Klein's Ordering of Geometries
A theorem which is valid for a geometry in this sequence is automatically valid for the ones that follow. The theorems of projective geometry are automatically valid theorems of Euclidean geometry. We say that topological geometry is more abstract than projective geometry which is turn is more abstract than Euclidean geometry.
A VIEW OF MATHEMATICS by Alain CONNES
Most mathematicians adopt a pragmatic attitude and see themselves as the explorers of this mathematical world" whose existence they don't have any wish to question, and whose structure they uncover by a mixture of intuition, not so foreign from poetical desire", and of a great deal of rationality requiring intense periods of concentration.
Each generation builds a mental picture" of their own understanding of this world and constructs more and more penetrating mental tools to explore previously hidden aspects of that reality.
Nature's Greastest Puzzle
This is a torus (like a doughnut) on which several circles are located. Unlike on a Euclidean plane, on this surface it is impossible to determine which circle is inside of which, since if you go from the black circle to the blue, to the red, and to the grey, you can continuously come back to the initial black, and likewise if you go from the black to the grey, to the red, and to the blue, you can also come back to the black.
Reichenbach then invites us to consider a 3-dimensional case (spheres instead of circles).
Figure 8 [replaced by our Figure 2] is to be conceived three-dimensionally, the circles being cross-sections of spherical shells in the plane of the drawing. A man is climbing about on the huge spherical surface 1; by measurements with rigid rods he recognizes it as a spherical shell, i.e. he finds the geometry of the surface of a sphere. Since the third dimension is at his disposal, he goes to spherical shell 2. Does the second shell lie inside the first one, or does it enclose the first shell? He can answer this question by measuring 2. Assume that he finds 2 to be the smaller surface; he will say that 2 is situated inside of 1. He goes now to 3 and finds that 3 is as large as 1.
How is this possible? Should 3 not be smaller than 2? ...
He goes on to the next shell and finds that 4 is larger than 3, and thus larger than 1. ... 5 he finds to be as large as 3 and 1.
But here he makes a strange observation. He finds that in 5 everything is familiar to him; he even recognizes his own room which was built into shell 1 at a certain point. This correspondence manifests itself in every detail; ... He is quite dumbfounded since he is certain that he is separated from surface 1 by the intervening shells. He must assume that two identical worlds exist, and that every event on surface 1 happens in an identical manner on surface 5. (Reichenbach 1958, 63-64)
THOMAS BANCHOFF has been a professor of mathematics at Brown University in Providence, Rhode Island, since 1967. He has written two books and fifty articles on geometric topics, frequently incorporating interactive computer graphics techniques in the study of phenomena in the fourth and higher dimensions
Today, however, we do have the opportunity not only to observe phenomena in four and higher dimensions, but we can also interact with them. The medium for such interaction is computer graphics. Computer graphic devices produce images on two-dimensional screens. Each point on the screen has two real numbers as coordinates, and the computer stores the locations of points and lists of pairs of points which are to be connected by line segments or more complicated curves. In this way a diagram of great complexity can be developed on the screen and saved for later viewing or further manipulation
Current research said something abut how the brain/mind can assume the reality in terms of randomness or end up realizing some chaotic function? Well, if such chaos is measured in the heat of thinking I am surprised we do not end up in some brain/mind heat death?:)
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