If you have trouble visualizing dimensions beyond the three that make up our spatial world, you're not alone; threedimensional beings in general lack the capability to perceive in four or more dimensions. Nonetheless, it's possible to imagine higher dimensions using extrapolation exercises. Even with visualization aids, however, you may find imagining these dimensions difficult. If so, be thankful you aren't one of the mathematicians or physicists who try to imagine 10 or more of them.
The ThreeDimensional Coordinate System

You need only a piece of paper to help you understand the three familiar dimensions of space, although there are online interactive tutorials that make it even easier. Start with two points, neither of which have dimensionality, and connect them with a line  that's the first dimension. Draw a perpendicular line through the center of that one, and you've created a two dimensional drawing. To depict the third dimension, imagine drawing a third line through the paper; for convenience, draw it perpendicularly through the intersection point of the other two lines. This gives you a set of axes that you can use to describe the position of any point in threedimensional space.
Time as the Fourth Dimension

Mathematicians call the axes of the threedimensional coordinate system that you just created the x, y and z axes, and they use the coordinates to specify position. Objects in the real world can change position, however, and mathematicians are able to describe that movement by adding a fourth axis  the t axis  to denote time. Albert Einstein introduced the concept of time as the fourth dimension in the Special Theory of Relativity. It is the dimension of the spacetime continuum in which objects move and change, but some physicists consider movements perceived in time as indicators of other spatial dimensions.
A Fourth Spatial Dimension

To understand the perception of higherdimensional shapes, it helps to go back the sheet of paper. If an invisible threedimension shape, such as a sphere, moved through the paper and became visible only when it touched the paper, threedimensional observers would see a series of circles that grew larger and then smaller. An imaginary twodimensional observer on the paper would have less indication of the true nature of the sphere, being able to see only a line changing length. In the same way, fourdimensional figures moving through threedimensional space produce a series of threedimensional shapes that change size, position and orientation, and fifthdimensional shapes have even more cryptic signatures in threedimensional reality.
10 Dimensions and Counting

It isn't possible to draw fourdimensional shapes, but it is possible to perform thought experiments to visualize them. In four dimensions, a threedimensional cube becomes a hypercube, a kind of curledup version of the threedimensional shape. Mathematicians Theodor Kaluza and Oskar Klein were the first to propose a fourth spatial dimension based on this geometry. The idea was developed by mathematicians Eugenio Calabi and ShingTung Yau, who described sixdimensional shapes, called CalabiYau shapes, which are created as microscopic space curls in on itself. These shapes are essential in superstring theory, which is a leading candidate for a Theory of Everything; together with the three dimensions of space and the one of time, they provide the 10 dimensions needed for the mathematics to work.
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