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Some bending space is needed to understand how the picture of Einstein's theory of relativity, gravity works. To illustrate the basic ideas, physicists often resort to gravitational bending example of the two-dimensional space, the surface area or saddle or donut. In these examples, we are familiar with the three-dimensional space surrounding surface so that we can easily envisage the curvature. The trick is what corresponding to the curvature perception of our own three-dimensional space is the same.           Space, the Final Frontier     "Egocentric." "Ethnocentric." A variety of words in the English language describe the tendency of people to get locked into a limited perspective. "Anthropocentric" is a favorite word in some circles of astronomy. It describes the tendency of scientists, as well as Star Trek writers, to conjure up alien life forms that are fundamentally similar to us, not just physically, but emotionally and socially, with our motivations, drives, and dreams. The anthropic principle — that the Universe is as it is because we exist — is a related idea. In the never-ending battle to expand our perspectives, I write this to call attention to the existence of another limited, rarely questioned, viewpoint that affects us all: trispatiocentrism. Trispatiocentrism is the attitude that the "normal" three-dimensional space of our direct perceptions is all there is and all that matters.   This word arose in my substantial writing-component course at the University of Texas in Austin. We were exploring the nature of space and time with a particular emphasis on spaces of various dimensions. I wanted a word to connote the notion that our three-dimensional world view carries with it unrecognized restrictions. I came up with "trispatiocentric" and its obvious variations.   There is a serious scientific side to this. Some understanding of curved space is needed to picture how Einstein's theory of gravity works. To illustrate the basic ideas, gravitational physicists often have recourse to examples of curved two-dimensional spaces, the surfaces of spheres or of saddles or of doughnuts. In these examples, our familiar three-dimensional space surrounds the surface so that we can easily envisage the curvature. The trick is to try to perceive what the corresponding curvature of our own three-dimensional space is like. The goal is to understand the arcanae of Einstein's theory: black holes, wormholes, time machines and the ramifications of string theory. In this context, it is quite natural for a logical, if naïve, mind to ask: if the surface of a sphere curves in a three-dimensional space, then must our three-dimensional space curve in some four-dimensional space?   For the non-naïve, these issues arise at the forefront of modern physics, the attempt to construct a "theory of everything." This theory will allow us to understand the raging singularities predicted to be at the centers of black holes and from which the Universe was born. Singularities represent the place where our current concepts of space and time, indeed all of physics, break down. The most successful current attempts to develop a new understanding of space and time are based on "string theory," where, to be self-consistent, the "strings" that constitute the fundamental elements of nature exist in a space of ten dimensions. Thus these developments have led physicists to ponder higher dimensions, perhaps ones so tightly packed we cannot perceive them directly. They speak in terms of surfaces or membranes in a space of p-dimensions and call them "p-branes." Alas, I cannot resist pointing out that all this is not for pea brains like me. It is, however, the stuff that will push back the frontiers of knowledge...             — J. Craig Wheeler, Cosmic Catastrophes: Exploding Stars, Black Holes, and Mapping the Universe, Chapter 14 – Beyond: the Frontiers                 Indexes/11