"Since the extra dimensions beyond spacetime that physicists talk about are all spatial dimensions (or 'space-like' as some prefer to say), thinking about how the simplest spatial dimensions relate one to another gives us tools for imagining the more complex ones. The key to remember with all this is that each additional spatial dimension is at 'right angles' to the one before: so each new dimension allows an observer to see 'around the corner' in a way that was unattainable from the previous dimension. This time, let's work through the dimensions with that idea in mind."
(Rob Bryanton, October 2009)
Rob Bryanton (2006). "Imagining the Tenth Dimension: A New Way of Thinking About Time and Space", Trafford Publishing.