Our spacetime diagram has been a very useful aid to both logic and imagination. Yet it is also unpleasantly complex. The rules that relate the co-ordinates and scales of different observers are too complicated. Now I want to show that this complication arises because, when we thought we were being revolutionary, we were actually being pigheadedly conservative. Our perversity consisted in constructing the diagram in terms of the old familiar time-over-there and distance – even though we knew that these were only relics of slow-speed life, which prove to be nearly useless in high-speed conditions.

Shall we try the effect of working instead with the quantities that are actually measured–the times of sending a signal to an event and receiving one from it (§§7.2–3)? We can call these the radar co-ordinates of the event (cf. §§5.20, 7.1). Now please revise §§6.13–22. We're starting afresh from there.

We need shorthand symbols for these radar co-ordinates. But we're running short of convenient letters of our ordinary alphabet, and so we'll use two Greek letters:

We'll use the capitals for A's radar co-ordinates and small letters for B's. And when we want to talk about these radar co-ordinates in general terms, without specifying an observer, we can speak of ‘the theta’ or ‘the phi’ (just like ‘the time’ and ‘the distance’) of this or that event.