This forum is so laden with frivolous responses such as the two above concerning sugar, that it is difficult to find meaningful responses any more.
I have read your link to hyperspace and have the following comments
1. The author himself points out that 3-d space is characterized by the inverse r squared law, whereas 4-d space is characterized by an inverse cube law. He mentions this early in his essays, but never returns to it. As far as I can tell, since science has only found an inverse square law, hyperspace is ruled out.
2. He mocks string theory, yet string theorists recently revived the possibility of a small (micro to millimeter 4th dimension) to explain several problems. Alexander himself has investigated this experimentally and found that the inverse square law holds in the sub-mm regime
3. A serious problem is that if there actually were 4 large space dimensions, we would not be here to discuss it. In 4-d space the amount of mass density in the universe is great enough to make the universe almost immediately recollapse right after the big bang. Kip Thorne's book on black holes explains that. For example, in 2-d space, mass density of our universe is too weak to ever make a black hole. That is why stable galaxies tend to be 2-d spirals. Black holes can form in 3-d but the universe at the present mass density is open. We need the addition of a cosmological constant to make the universe flat. In 4-d space, the universe is very closed- so much that it would not exist today. So 3-d is the only number of space dimensions that can produce a viable universe.
I read the essays rather quickly. So if I missed the most interesting aspects of it please so advise me and I'll check it out.