A Square goes on vacation.
He tells us of a dreaming vision of Lineland. Lineland is a one-dimensional universe in which everything is moving in a line.
There are lines of varying sizes and dots, all seemingly moving at the same velocity. They chirrup.
Square decides to ask one of the lines to explain herself. He gets no reaction at first but, upon increasing demand and turning himself, gets the answer he wishes: He is not talking to a woman, lines in Flatland, but to a man and this man is king of Lineland.
The king explains that all Linelanders see but dots. Men, women, objects, all appear as such. Yet, he knows that he is a line and women or dots, because all Lineland men have two mouths and eyes, while women only have one.
Men’s two mouths produce two voices, one a bass and one a tenor. Women are either sopranos or contraltos. So it is that all Lineland men take two wives, one matching harmoniously to each of their voices.
Once a week, all Linelanders feel compelled to move rhythmically from side to side for 100 paces. On the 51 pulsations, they stop and take up a melodious cry heard throughout Lineland.
If two female Linelanders match in harmony with one male Linelander, they are at once a married threesome and their marriage is consummated, no matter their distance on line.
One of the women will bear twin girls and the other a single boy. This is how Linelands population is maintained.
Square wants to impart his truth to the king, that in his bird’s eye view, he can see they are all either dots or lines. The king is not amused by Square’s ignorance but explains that there is no such thing as seeing, they recognize each other through hearing. The king knows he is the biggest Linelander.
To demonstrate how hearing works, the king calls out to his wives, all in line very far away. His wives, he asserts, know that he is 6.457 inches in space - here, Square corrects him that he surely means length but no! Space IS length to Linelanders! and that they know this because they hear how sound traverses 6.457 inches from one of his mouths to the other.
A Square also wonders how the men know they are not deceived by women (or men) since they cannot tell who is who if one fakes one’s voices. Why don’t they just use feeling?
Appalled, the king reminds Square that actually touching one’s neighbour would potentially kill the women, since their bodies are fragile. Such a crime is punishable by death.
But why, Square wonders, don’t they just turn right or left, aren’t they curious about the other directions?
The king understands not what right and left means. His idea of direction is North-or Southward. He urges Square to explain this right and left, but when Square moves out of the line to demonstrate, the king only sees him vanishing. To him, a Linelander, Square is simply performing strange magic.
Mr. Square is indignant and starts to insult the king as ignorant and inferior.
The king takes up a battle cry and the Linelanders stand at the ready.
A Square awakes.
“Hark, only hark!”