I've mentioned Greg Egan's "Orthogonal" trilogy (_The Clockwork Rocket_, _The Eternal Flame_, and _The Arrows of Time_) in which the interval between two events isn't x^2 + y^2 + z^2 - t^2 as in our universe, but x^2 + y^2 + z^2 + t^2. In other words, there is no distinction between the time and space dimensions. The perceived time dimension is simply the direction of your worldline, which can point in literally any direction. As in our universe, people traveling at close to the same speed will almost perfectly agree on the direction of the time axis. He has since written _Dichronauts_, in which the interval between two events is x^2 + y^2 - z^2 - t^2. Roughly speaking, there are two space axes and two time axes. But people experience linear time, just as in our universe and in the "Orthogonal" universe. The main difference from our universe is that the three axes that aren't your personal time axis don't all act alike. For instance objects can't rotate around a vertical axis by 45 degrees or more. Smaller rotations result in the object elongating. Some people are born facing east, others facing west. To look in the opposite direction you need to bend way forwards or way backwards. There would be no point in facing north or south even if you could, since no light travels in those directions. Also, energy works rather differently than in our universe. See http://www.gregegan.net/DICHRONAUTS/00/DPDM.html for more information on the physics. There's a similar page for the physics of the Orthogonal trilogy, http://www.gregegan.net/ORTHOGONAL/00/PM.html I could be wrong, but I think that swapping all the signs makes no difference, so there are only the three possibilities, all the same signs (Orthogonal), three and one (our universe), and two and two (Dichronauts). Those novels are perfect for people who enjoyed learning physics so much that they wish they could do it all again.