Why do extra dimensions have to be "curled up"? This is my first post to this forum. I'll start with a question that has bothered me for a long time. T. Kaluza suggested to Einstein that the equations describing fundamental forces and fields could be simplified if the possibility of real extra dimensions of space were considered. It seems to me that from the outset of that suggestion, people rejected the idea because they thought that if such extra dimensions exist, we should be able to see them or otherwise detect them. Klein addressed this "problem" by suggesting that the extra dimensions were compactified or rolled-up. This was the Kaluza-Klein idea of a hyperspace in which all but three spatial dimensions were rolled-up so we can't detect them. As far as I can tell, there have been only two objections to Kaluza's original idea which require contaminating (IMHO) it with Klein's addition: 1. If large extra dimensions exist, we should be able to detect them, and, 2. Large extra dimensions would require that inverse square laws would necessarily become inverse cube (or higher) laws. I think these objections can easily be dealt with as follows: 1. If our 4-space (i.e. Einstein-DeSitter 4-D space-time continuum) is in fact a 4-manifold (equivalent, I believe, to what cosmologists currently call a 4-brane), then structures and features in the manifold could have the same properties as they would if the 4-space were not a manifold embedded in higher-D space. An analogy would be that geometric structures drawn on a sheet of paper cannot, in principle, somehow "get up off the paper" and achieve access to any part of the 3-space, in which the sheet of paper is embedded, that is not on the paper. The structures are the same whether or not the "paper" is embedded in 3-D space. Since everything (except possibly the observer's consciousness) that is involved in any observation of our world is a 3-D structure (objects, apparatus, eyes, etc.) it is reasonable to expect that we would not be able "get up out of our 3-D space" in order to access anything outside our manifold. 2. The topology of a 4-manifold could be identical to that of a 4-space which does not happen to be an embedded manifold. Thus there is no reason why inverse square laws shouldn't hold in the 4-manifold. An analogy would be that the density per acre of a fixed number of sheep in a circular pasture varies inversely with the radius. The fact that the pasture is a 2-manifold embedded in 3-space does not require that the sheep density follows an inverse square law. It seems possible to me, as Plato suggested, that extra-dimensional objects may produce effects in our manifold, just as 3-D objects can cast 2-D shadows. If this is the case, it would seem possible that some of our more elusive "objects" such as electrons and photons might be manifestations of such effects. My questions to you are: 1. Are there reasons, other than the two I listed, for requiring Klein's approach of "curling up" extra dimensions? 2. Are there errors in my argument for dismissing those two reasons?