![]() If that fourth dimension is time, then each of those infinitely thin layers of 4-space represents a moment in time, and as you move in the positive direction of the fourth dimension, you go forward chronologically. It contains infinitely many infinitely thin 3-spaces like ours. When it is thought of as time, all four dimensions together are called “spacetime.” To understand how it could be that the fourth dimension is time, think of the fourth dimension that has been discussed thus far. However, a popular and arguably less geometric interpretation of the fourth dimension is time. The fourth dimension can be treated as a fourth direction, a dimension fundamentally no different from the three we know, except that it is one we humans do not experience. So, the tesseract is bounded by eight cubes. With a tesseract, there are four coordinates which can be held constant at 1 and -1, and as the other three are varied, cubes are produced. Each of the three coordinates can be held constant at 1 and -1, generating the six squares by which the cube is bounded. Taking 1 of the coordinates, holding it constant at either 1 or -1, and varying the others between 1 and -1 begets a square. ![]() It is the 4-D analogue of the cube, or, to apply the analogy, the tesseract is to the cube as the cube is to the square. The tesseract is an object in the fourth dimension. The aforementioned analogy, "4-D : 3-D :: 3-D : 2-D," however, is useless without a 4-dimensional body to which to apply it. Likewise, our universe is an infinitesimal slice of the fourth dimension. They look like flat, infinitesimal slices of our space. So, when thinking of how the third dimension (our space) appears to 4-dimensional beings in the fourth dimension, one need only think of how 2-dimensional spaces appear to us 3-dimensional beings. Since we can understand the latter situation, we can understand the relation, and since we know that the 3-space object relative to the 2-space observer is analogous to the 4-space object relative to us (3-space observers), we can apply the relation to the problem of conceptualizing 4-dimensional things. Whenever we try to comprehend an object in 4-space or perhaps a movement of a 4-dimensional object along the fourth dimension that passes through our space, we need only think of a being in 2-space trying to comprehend the corresponding object in 3-space. The fourth dimension is a hyperspace, since it is of a higher dimension than ordinary space.Ī More Mathematical Explanation Note: understanding of this explanation requires: * Cartesian coordinates, geometryĮntertaining the notion of hyperspace (i.e., dimensions beyond the third) necessitates being able to conceptualize the fourth dimension, and for that, the analogy "4-D is to 3-D as 3-D is to 2-D" is useful. What, then, is the fourth dimension?Įven though imagining what four dimensions actually looks like may be beyond human capability, we know it requires four numbers to describe any possible point in it. If you're reading this, you know already that the first dimension is a line, the second is a plane, and the third is space. Each coordinate represents a distance from the origin in a certain direction, and each of those directions is perpendicular to the rest. The origin is where every coordinate (however many there are) is zero. The nth dimension requires n numbers to specify the position of a point in it, and no point in that dimension cannot be described by some combination of the n coordinates. What constitutes a dimension? A dimension has an origin and a set of coordinates which each can independently equal any real number. 2.2 Possibilities of the Fourth Dimension. ![]()
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