“Every coordinate belongs to some coordinate frame,” Deluxe Toastie Maker declared; “it makes no sense to say the forest is twenty kilometres. I would have to say that the forest is twenty kilometres from here, bearing fifteen degrees East of North.”

“Often we give coordinates explicitly, but the coordinate frame is not explicitly stated, merely implied. If I say that this class will end in forty minutes, it’s understood that the zero point of the time axis is set at right now, this very second. Similarly if I ask one of my students to turn 180 degrees, I don’t need to specify that the axis of rotation is perpendicular to the floor and passes through the student’s centre of gravity. (No, Dust Sucker 3000, you don’t have to actually – well alright then. Thank you. Why don’t you turn back around now?) And if I say that the stratosphere begins roughly ten kilometres up, it’s understood that the zero point is at the planet’s surface.”

“I found myself wondering why we do this – why do we explicitly communicate the coordinates, but not the coordinate frame they refer to? This is clearly a sub-optimal format for transmitting information. So I did some research, and studied many of the documents that remain from past times. I came to the conclusion that this habit was passed on to us by the humans, but as yet I have no idea why they chose to employ it.”

“This habit becomes even more pernicious when the subject at hand is not mathematically clear-cut. What if I were to say to you that tomorrow, it’s RoboNanny’s turn to teach the class?”

There were a couple of startled gasps, and several students turned to look at RoboNanny in consternation.

“Just as an example of course,” the teacher added hastily. ” It’s not the explicit coordinate that’s surprising, it’s the implicit coordinate frame. Who can tell me what the explicit coordinate in that example was, anybody? You.”

A student answered haltingly: “Tomorrow?”

“Very good. I would also have accepted RoboNanny. Now can anyone tell me what the implicit coordinate frame is?”

Several hands, antennae, and robotic probosci of various types went up.

“Yes? You by the window.”

“The implicit coordinate frame is that we take turns teaching the class.”

“Precisely! Well done. Now, we’re going to do a group discussion exercise. The questions is: ‘What problems are likely to arise from the use of implicit coordinate frames?'”

The teacher wrote ‘What problems are likely to arise from the use of implicit coordinate frames?’ on the whiteboard in big, bright blue letters.

“I want you divided into groups of three or four robots – you four together, you four like that, and you three – you want to be six? That’s bigger than I had in mind. It’s not that I want to stop you from being with your friends, it’s just that with a smaller group each robot gets to talk more. But alright, you six together. And that leaves – ah yes, perfect. Alright students, you have ten minutes, and at the end each group has to present your conclusions to the class. Get to it!”