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“BTW, what are the “extra” dimensions? Can you tell me in layman terms?”

An extra dimension is just a direction something has freedom of movement in, that is 90 degrees away from the next lowest direction it has freedom of movement in. You start with being able to move back and forth on a line, then if you can turn 90 degrees from that line and move side to side, you have a 2nd dimension, and can move around a plane. If you can turn 90 degrees from that plane and move up and down, you have a 3rd dimension. We can speculate mathematically on how things work to any number of dimensions, our brains just can’t visually conceive of more than 3. Our brains tell us there is no other direction we can turn to get to the 4th dimension, but math doesn’t care about that. If we plug in the numbers as if there was a 4th dimension, our equations still work.

For example, in computer programming, we have “arrays” which are just sets of numbers, with a dimension that determines the type of array it is, and a size telling us how many numbers fit in it. So you can have a 1 dimensional array of size 3, which would hold 3 numbers. You could think of this like a line of numbers: (1,2,3)

Then you could have a 2 dimensional array of size 3, which would hold 9 numbers. This is like a box of numbers:
(1,2,3,
4,5,6,
7,8,9)

It wouldn’t be easy to type out here, but I’m sure you could also imagine a 3 dimensional array of size 3, that would be like a cube of numbers, and hold 27 numbers. Now, we can’t visualize a 4 dimensional or 5 dimensional or 6 dimensional array, but we can program a computer to store them and do mathematical operations on them just like all the other kinds. The computer isn’t trying to visualize anything so it just applies the math. It has no idea that “4 dimensional” is not supposed to exist.

So that’s how you get to the point where we can speculate about how different theories work if we had higher dimensions. Even before computers we could work out the mathematics of higher dimensions to a degree, but with computers doing the grunt work it gets a lot easier.