Let's try something--let me know if you have difficulty Let's try something. Everybody imagine an expanding three-sphere. When cosmologists give you the balloon analogy, that is what they are trying to illustrate. the balloon is just the 2D analog of the 3-sphere. It is easy to imagine the 3-sphere (math'ians call it S3) You just have to imagine the experience of living in it and moving around in it--what that would be like. It is hardly any different from the usual experience moving around in usual space---if the three-sphere is a large one---except for one slight detail. I've noticed that some people probably newcomers at PF don't seem to "get" the balloon analogy. It is an example of a finite, boundaryless expanding space which can serve as a springboard to mentally comprehending the 3D version of the same thing. A 3-sphere is also a finite boundaryless space---and the balloon surface is just the LOWER DIMENSIONAL ANALOG OF IT---if you can picture it at all then you will be able to imagine expansion: distances between points increasing at a percentage rate. If everybody takes the (*easy*) first step of imagining S3 before they come into Cosmology forum, then maybe we wont have to repeat the same explanations over and over. If there is some reason why it is DIFFICULT for anybody, I would very much like to know, as it might help us improve explanations. So let's try this. Anybody who wants to share their way of picturing the three-sphere please do! I will sketch one or two ways I have of thinking of it and feel free to criticize if you find them not helpful or if you can come up with an approach that works better. Before continuing with this, I'm going to wait a while to give anyone who wants a chance to respond, and say what is their preferred way of picturing S3, if they want.