I am not a linguist or historian. These are purely my musings of formed by trying to learn from Google University, and then being fanciful. If you are a linguist or historian, PLEASE enlighten me. Furthermore, I write this fully aware of the silliness and cultural insensitivity put forth in the "how foreign cultures think" department about my parents' first language. Enough disclaimers. Fanciful musings:
First of all, from what I could tell, and according to someone more knowledgeable, it is not actually true that the Amandawa don't have an idea of abstract time. That doesn't make this situation uninteresting. What they seem to lack, according to the paper (PDF) the BBC article quotes, is a concept of cyclic time (among a few other things).
The seasonal and diurnal time interval systems can therefore properly be thought of as cognitive, cultural and linguistic schemas, but they differ from more familiar calendric and clock schemas in that there is no evidence that they are conceptualized by speakers as being cyclical in structure.
When the Amondawa are asked to describe their day or year, the consistently come up with a curvilinear structure.
No participants attempted to create a circular, cyclic representation. It is unclear whether the curvilinear responses were a result of a compromise between an intended rectilinear configuration and the length of human reach, or signify that neither cyclicity nor rectilinearity are relevant to the Amondawa seasonal schema.
That's just cool! I have no desire to exoticize these people, but possibly curvilinear time?!
This is where Japanese math comes in: there are numerous examples of different ways of thinking about information leading to different insights about the world. Apparently, mathematics in Japan developed, at least in part, by studying sticks on a grid. As a result, by the time of the Edo era (1603-1868), Japanese mathematicians were centuries ahead of Europe in term of being able to solve large linear systems (matrix calculations), but very far behind in terms of other concepts in abstract math. I'm sorry I have no citations for this factoid, I learned it during a dinner conversation. I haven't gone to GU about it yet.
This is where I intentionally confuse anecdote with the singular of data for the amusement of my imagination. What new insight about the world does a curvilinear (or a strictly linear, without the cyclic component) view of time give? Maybe nothing. But it's fun to fantasize.
I leave with a deep thought from the tenth doctor:
People assume that time is a strict progression of cause to effect, but *actually* from a non-linear, non-subjective viewpoint - it's more like a big ball of wibbly wobbly... time-y wimey... stuff