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DIMENSIONS 
Indistinguishable vacuumsThe volume of an ndimensional sphere increases with r^n, r = the radius of the sphere. When space has a high negative curvature, homogeneous and isotropic (everywhere the same and in all directions the same) then volume increases faster with r than its volumeformula describes for flat space. Suppose we have a 5dim sphere in flat space. Its volume increases with r^5. When not mentioned otherwise in this page all considered spaces are static, that is: not changing in time, constant in time. Suppose we too have a 4dim sphere in highly negative curved space. The curvature is such the volume increases with the r^5. I assume such a negative curved space can exist. I mean, the volume increase to be proportional to r^5 in every point of space and in all directions, while the sphere is 4dim. I don’t know whether this assumption is right but in this page I assume curvature can be adjusted like that. Suppose you are a 3dimensional observer “O”. You observe a matter distribution of C60 molecules around you, just ordinary 3dimensional C60 molecules. All molecules are standing still with respect to you. You can measure the apparent diameter of a molecule and thus infer the distance r to you  if not, you should use a bigger type of molecule. The distribution has a quite low average density, the nearest molecules are about 1 kilometer away. The observed distribution is isotropic but the observed numberofmolecules m at a certain distance r increases with r^5; m is proportional to r^5. We state that the following possibilities have identical observations of matter distribution. Provided those spaces can exist physically, they are indistinguishable for the observer O and thus for O, as “experienced” by O, will superpose. 1) A flat 3dim space in which C60 molecule density increases in space with r^5, being r the distance to the observer; 2) A flat 5dim space with homogeneous and isotropic distribution of C60 molecules; 3) A highly negative curved 4dim space of the described kind with homogeneous and isotropic distribution of C60 molecules; 4) A 3dim flat expanding space with homogeneous and isotropic distribution of C60 molecules, in which the expansion simulates the effects of the highly negative curved 4dim space of number 3. I tried to discuss its existence in page 4 of the storyline EXPANSION OF THE UNIVERSE, the column at the right. The observer observes its local environment to which he, she or it belongs, as being 3dim. The transition between your local 3dim space and the space further away around you is, as to speak, “not your business”. It consists of vacuum that you cannot observe. Consider the molecules within a sphere of r = 10 km. In the second possibility (flat 5dim space) no molecules can be found with a mutual distance larger than 20 km. They can see that from each other. In possibility 3 the molecules with largest mutual distance, this distance certainly will exceed 20 km. But that is not of your business. The mutual distance consists of vacuum that you cannot observe. The molecules have no mind or memory, they will not give a sign to you what they see. Initially we assume such signs to be absent and the superposition will be there. Later, if there arises some sort of memory or any indication of mutual distance, this would be decisive and forces you into a choice. Then you are in flat 5dim space. Or in highly curved 4dim space. Or in flat 3dim space with a peculiar C60 molecule distribution  peculiar but not forbidden. Or in flat 3dim expanding space. You will have to find out. If space turns out to be 4dim or 5dim, how then the transition is made between your local environment, obviously being 3dim, and the 4dim or 5dim space further away? I don’t know, but IF nature provides an existable way THEN those possibilities will superpose. Well, I guess under normal circumstances this will not be the case. But circumstances have been not normal in the far past. Nor are they everywhere in space. NEXT PAGE Up CONTACT 
