Curiosity: Trans-dimensional Loupe
Of ferman: Fernando Mancebo Rodriguez--- Personal page. ----Spanish pages

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Curiosity: Trans-dimensional Loupe.


Friends, in order to explain and make myself understand about the fourth dimension 4D (or exponential dimension of space), we are going to build an imaginary device consisting of a hypothetical and ideal loupe with which we could travel (viewing) through the fourth dimension of 4D space.
This loupe (which in physics we could define as "ideal loupe") contains a turning or navigation wheel, with which we are giving a capacity of vision and magnification to the loupe indefinitely, that is, by turning the navigation wheel we can increase (or decrease) the field of view of the loupe without scope limit.
Therefore, it would have two directions of rotation:
1.- To right, to increase the size of the observed objects until penetrating them and their components indefinitely.
As well as to attract them to those who are in long distances.
2.- To left, to move them away and expand the field of vision indefinitely.
For example,
A.- If in our living room we take an apple and focus the loupe on it and begin to turn the navigation wheel indefinitely (to the right), we will first see its molecules, then its atoms, then the particles of these atoms, the matter and energy of these particles, and so on down to the infinitesimally small.
B.- But if instead of turning the navigation wheel to the right we turn it to the left, then we will begin to see the apple shrink, and that inside the loupe we begin to see our living room in its entirety; then our entire house will be seen, then our entire town, then our entire country, then the entire earth, ... our solar system ... our galaxy ... all the galaxies from the Big-bang , and so on.
Well, the interesting thing about this whole trip is that we have done it through the fourth dimension of space, and with it we have understood a little about what this dimension consists of.
We have also learned that due to the characteristics of our observation or vision capacity and the application this ideal loupe that this fourth dimension consists on a double property:
1.- In the approach or moving away from us (observed by the loupe) of any element. (in 3D, plane dimension)
2.- The indefinite penetration into the interior of objects, or the indefinite outward expansion of our vision and observation field. (4D exponential space dimension)



Well, I understand that mathematics has to be adapted and measured to physical realities, and not the other way around.
For example in this 4D that we are exposing and in the simplest way possible.
We take as adjustment base the 3D Cartesian Coordinates (x,y,z), which to convert them into 4D we compose them with another dimension N (natural numbers) 4D = (x,y,z).N = (Nx, Ny , Nz).
If we now multiply and solve all these products one after another, we will thereby be inflating or enlarging an initial small cube (ie. 1 m^3), up to an infinite dimensional cube, for example a cube containing the entire universe.
We can also get it by substituting the natural number N for the rational number Q, and we will be able to build a smaller and smaller cube to infinity.
Well, this is all spatial math and perfectly understandable and adjustable.
And it is at the same time, the fourth dimension 4D, both arithmetic and geometric, as well of space and time.