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I was trying to get the full understanding of 4th dimension from several year now but it is always difficult to understand because it has different definition in mathematics, physics, and metaphysics.
"Dimensions" are a means of organizing different planes of existence according to their vibratory rate. Each dimension has certain sets of laws and principles that are specific to the frequency of that dimension.
In mathematics the fourth dimension, or a four-dimensional space, is an abstract concept, obtained by taking the rules of our three-dimensional space and generalizing them to a space with one more dimension. It has been studied by mathematicians and philosophers for almost two hundred years, both for its own interest and for the insights it offered into mathematics and related fields.
We live in a world of three dimensions. Well, we only perceive three dimensions. We can hypothesize many more dimensions. But, they are difficult to imagine.
Because of Einstein, we often call time the fourth dimension. Special relativity shows that time behaves surprisingly like the three spatial dimensions. The Lorenz equations show this. Length contracts as speed increases. Time expands as speed increases.
Scientists Predict How to Detect a Fourth Dimension of Space
Scientists at Duke and Rutgers universities have developed a mathematical framework they say will enable astronomers to test a new five-dimensional theory of gravity that competes with Einstein's General Theory of Relativity.