ETTY is able to redraw the pattern of dots and lines under posthypnotic suggestion. She doesn't know which part of the "heavens" was shown to her. In particular, her question about the homeport of the entities remained unanswered. In addition to the main pattern, some of the dots which were not connected stay in her memory and appear in her sketch.
To understand the following discussion, it is very important to first make some things very clear:
Betty likes to know, where the entities do come from. The "leader" answers this question not simply by telling her the name of a certain star system or planet but asks her basically about her knowledge of the universe. He gets the definitive indication that Betty merely knows the number of planets in our solar system and perhaps their names and that she has seen the night sky, of course. Because of this he expresses the wish to impart more knowledge to Betty, and then, after manipulating at the head of the table, he makes visible this "opening" in the wall and with this, the "map".
At this point, we harbour grave doubts about Betty's interpretation that she had seen a "star map".
One can find a central thread in the order of questions in the conversation between Betty and the "leader." The "leader" never directly answers Betty's question where they might come from, but instead asks a question about her astronomical knowledge. It seems that before he can talk to Betty about such complicated things as distant foreign star systems, he has to know if Betty is able to follow him at all. He must learn that Betty has limited knowledge, and comments on this with the remark that he wished that she knew more about "the universe". An understandable desire, similar to trying to explain one's own origin in a distant country to someone who doesn't even know the next crossroad at the end of the street where they live.
Betty would like to know more about the stars and so the teacher makes the map appear and the lesson starts. Without having learned even one chapter, the impatient pupil Betty wants to know again where the entities come from. She cannot talk the teacher out of his teaching concept and so he asks his first question: "Where are you on the map?" This "map" must be of a kind where even Betty has a chance to recognize something, because he now knows that she has only minimal knowledge about her solar system. He doesn't ask her for special items but for the simplest and most obvious: her home. It remains open whether the "home" planet or simply the sun is meant.
Betty doesn't know what to do with this "map." The slightly sarcastic undertone of the teacher proves his disappointment: "If you not know where you are, then it is impossible for me to show you where I am from!" If she is completely unable to solve such a simple problem of identifying her home, then it really makes no sense to continue the lesson. The "map" vanishes. (By the way, nowhere is Betty quoted as saying that the aliens' homeport of the aliens is - or is not- on the "map".)
Was it - according to Mrs. Fish - really Zeta Reticuli that Betty saw in the big circles in the foreground? Should it be just so as to see the strange and far away object (Zeta Reticuli) really big in the foreground and the known and familiar object (the Sun) very small in the background? Were there indications in the "map" that would have made it easier for Betty to recognize the Earth?
Have all the proponents of the "Zeta Reticuli interpretation" missed something?