Am I going too fast to carry my readers with me to these obvious conclusions? Surely a moment’s reflection, and a single instance from common life, must convince everyone that our whole social system is based upon Regularity, or Equality of Angles. You meet, for example, two or three tradesmen in the street, whom you recognize at once to be tradesmen by a glance at their angles and rapidly bedimmed sides, and you ask them to step into your house to lunch. This you do at present with perfect confidence, because everyone knows to an inch or two the area occupied by an adult Triangle: but imagine that your tradesman drags behind his regular and respectable vertex, a parallelogram of twelve or thirteen inches in diagonal:⁠—what are you to do with such a monster sticking fast in your house door?

But I am insulting the intelligence of my readers by accumulating details which must be patent to everyone who enjoys the advantages of a residence in Spaceland. Obviously the measurements of a single angle would no longer be sufficient under such portentous circumstances; one’s whole life would be taken up in feeling or surveying the perimeter of one’s acquaintances. Already the difficulties of avoiding a collision in a crowd are enough to tax the sagacity of even a well-educated Square; but if no one could calculate the Regularity of a single Figure in the company, all would be chaos and confusion, and the slightest panic would cause serious injuries, or⁠—if there happened to be any women or soldiers present⁠—perhaps considerable loss of life.