In my book, Creative Historical Thinking, I consider why people conceive of time in different shapes, and what effect this might have on how we shape chronologies, how we write and think about history, and how we communicate with each other.
Spatial representations of time can be idiosyncratic, but they also have a social, collective function, especially in printed form, when they are intended to communicate knowledge.
The early 19th century U.S. seems to have been a period in which Americans negotiated how they would illustrate time. Newspapers, almanacs, and textbooks all presented spatial representations of time. With the rise of the market, and the increase in printed material, these illustrations competed for prominence.
In many cases, spatial representations of time are limited by the materials they were printed on. Alamanacs and pocket-books, for example, tended to be tall and narrow, leading to vertical structures of time. Textbooks were more squarish, music books could be longer on their x-axis, and newspapers, while big enough for any illustration, were limited by the print technology of the day.