Let's suppose that we want to relate two quantities that correspond to a palpable reality, for example two lengths of a certain object, and give us the following measurements: 2 and 1/2, 3 and 1/3, 4 and 1/4... n and 1/n. Being n a natural number. The division between them does not offer us any conflict, it will be 4, 9, 16... n2, the times quantity is giving us that a quantity is major than other one. Nevertheless there are relations that can give ambiguities if we allow ourselves to guide for the result purely mathematically. For example, if we concentrate on the figure that the classic fractal represents called flake of Koch and his construction, we see that in every iteration we replace a segment of 3 units with four segments of a unit: exactly the relation between log 4/log 3 gives us the dimension fractal of the figure, which is 1.261859 … If what we want to relate there are two lengths represented by any natural number N and his inverse one 1/N, on having found the relation similar to the previous one, of the flake of Koch, we are with a negative value,-1, a negative dimension for a fractal, when physically he has not any sense, since the dimension fractal is always equal to the topológica (or apparent dimension) more a more irregular the dimensional, so much major coefficient is the fractal. 
Mathematician and logician, Kronecker was defending that the arithmetic and the analysis must be founded in the entire numbers doing without the irrational and imaginary ones. He was an author of a phrase much known between the mathematicians: "God did the natives; the rest is a work of the man" (Eric Temple Bell 1986, p.477. Men of Mathematics). This is the question, in our case we must turn 1/N and N in two new natural numbers than on having been related, to express the value that represents the dimension of the object, us of a coherent result with the reality that we are observing. The figures that continue to this paragraph clarify to us the way to be taken to find a possible solution, for this particular case.
We see the construction of a figure when N=3, N=4 and N=5. In the first figure if we give the value 3 nearby, his perimeter will be 27 (33), but if we give him the value 1/3, his new perimeter will be 3. This way it happens for N=4 ó N=1/4, etc, and in general for any value N and 1/N (with N finite, although so big as let's want). It will always happen that if the side is N the perimeter will be N3 and if the side is 1/N the perimeter will be N, without for it it changing the form of the figure. The natural conversion will be the one that the measurements couple transforms (1/N, N) in (N, N3) and the irregular value,-1, which we were finding for the dimension fractal of the curve would turn into 3. This value would give him to the curve the aptitude to fill the space. It is a fractal with entire dimension, of form similar to the case of a pure random movement, which from every N2 steps realized only moves away N, from any arbitrary point of reference that we consider, and therefore it has a dimension fractal equal to 2, capable of filling the plane.
In fact, for our case (1/N, N), infinite conversions exist, they answer to the expression:
Dim. fractal (*) = 1 + 2/logL (N), being L (N) the value of the side that we consider, like function of N. For L (N) = 1/N we have the value-1, for L (N) =N, the value corresponds to him 3, as we have said. For values of natural exponent more negatives (1/N2) and major the dimension approaches asintóticamente to l. For major values of N, as N2, N3, or of much major exponent the value asintótico will be also 1.
In the end we cannot trust blindly in the value that the mathematics give us, since the world that they represent is much wider than the real world and we will always need our common sense, in the analysis of the opposing results. On the other hand, paradoxically, sometimes the opposite happens: the common sense blinds us and prevents us to see a reality deeper that sublies in the mathematical results.
(*) Taking logarithms in base N
Duality T, (1/N, N) Like simple curiosity, on the values exchange 1/N and N, and like culturilla on ropes theory, all this can remind the called Dualidad-T to us:
In the expression that represents the squares of the energies of the excitements of a rope in a space with a curved dimension or compactada, K. Kikkawa and M. Yamanaka in 1984, observed that the formula keeps on having the same aspect if we do the exchange R 1/R. Being R I remove microscopically of the dimension that bows.
From a physical point of view this indicates that the energies of the excitements of a rope, when there is an extra radio dimension R, it is the same that that of a rope when the radio is 1/R. Not already the energies, but all the physical properties of both systems are exactly the same ones. It attracts attention, so when R it increases 1/R it decreases, contradicting the experience of the daily life, which says to us that the small things differ from the big ones. For a rope it is not like that.
On "Unification and duality theoretically of ropes", to see the number of August, 1998 of Investigation and Science, of Luis E. Ibáñez Santiago. Watch The Good Wife S01E17 Heart now
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