Ignore these people. The 4th spacial dimension is not time, and it is definitely not some weird plane of consciousness.
It's an unanswered question why there are 3 spacial dimensions in this universe, and not some other number. There is absolutely no reason why there shouldn't be, and anybody who tells you there is is simply an unimaginative person. All other spacial dimensions are just as mathematically - logically - consistent as these.
To think in terms of the fourth spacial dimension, it is actually extremely easy.
First, picture a dot. This is the 0th spacial dimension. There are no degrees of freedom at all.
Second, imagine this dot splitting like a cell into two dots, some distance apart, and between them, they draw a line, like a spider drawing a thread. You now have a line with two dots at each end; this is the 1st dimension, and there is 1 degree of freedom.
Now, imagine these two dots splitting into four in the same way as before. Separate the two new dots and again join them up with lines. You have a square, the 2nd dimension.
Do it again. Split these four dots into eight, separate them, and you have a cube, the 3rd spacial dimension.
And then do it again. Split the eight dots into sixteen, and separate them. You now have two superimposed cubes. Obviously this is a mere shadow of what a 4 dimensional cube (called a tesseract) actually is because it is not possible for the human neural network to comprehend such things, but nevertheless, it gives you an extremely clear idea of what one is, much like drawing a cube on paper gives you a clear idea what one is, even though the 'depth' cannot be transcribed onto the paper.
In Einstein's theory of general relativity, basically he creates a mathematical framework in which you interpret this fourth dimension as time; but that is a physical theory. It is completely separate from what you wanted to know, which is the mathematical generalisation of n-dimensional forms.
And you can continue to expand upon this; a cube in the 5th spacial dimension will have 32 verticies, a cube in the 6th spacial dimension will have 64 verticies, and so on.
Hope that helped.
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