Is Time single dimensionned?

A physicist at Stanford has just recently published a peer review website for several physics lectures focusing on a single underlying idea that time is not a single dimension of spacetime but rather a local geometric distinction in spacetime." The science is presented quite clearly and originally uses GPS systems as a point of focus.

From the article:
Not too long ago, people thought the Earth was flat, which meant they thought that gravity pointed in the same direction everywhere. Today, we think of that as a silly idea, but at the same time, most people today (including most scientists) still think of spacetime as if it were a big box with 3 space dimensions and 1 time dimension. So, like gravity for a flat Earth, the single time dimension for the 'big box universe' points in one direction, from the Big-Bang into the future. A lot of lip service is given to the idea of "curved spacetime", but the simplistic 3+1 'box' remains the dominant concept of what cosmic spacetime is like.