Synthesized answer
The author provides evidence that the social life in Flatland rests upon the fundamental fact that Nature wills all Figures to have their sides equal [1]. If sides were unequal, angles might be unequal, necessitating the ascertainment of each angle by feeling, which would be too tedious and lead to a collapse of civilization [1]. The author also presents the argument that expediency, along with Nature, approves of regularity of conformation. The Law reinforces this by treating "Irregularity of Figure" as equivalent to or worse than moral obliquity and criminality [2].
As an example of the importance of regularity, the author describes how one can confidently invite Tradesmen to lunch because the area occupied by an adult Triangle is known. However, if a Tradesman had an irregular shape, like a parallelogram, it would create a problem for entering a house [3]. The author also explains how, through long training and experience, educated classes can discriminate between different social orders by sight. This ability is possible due to the presence of fog, which causes figures to appear as straight lines that dim away from the center, with the rate of dimming indicating the figure's…
Synthesized from the book passages below. Chat with the book on Feynman for follow-up.
From the book
adult’s size, when added together, is two feet or a little more. But the size of our sides is not under consideration. I am speaking of the _equality_ of sides, and it does not need much reflection to see that the whole of the social life in Flatland rests upon the fundamental fact that Nature wills all Figures to have their sides equal. If our sides were unequal our angles might be unequal. Instead of its being sufficient to feel, or estimate by sight, a single angle in order to determine the form of an individual, it would be necessary to ascertain each angle by the experiment of…
eaders 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…
ivilization might relapse into barbarism. 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 every one that our social system is based upon Regularity, or Equality of Angles. You meet, for example, two or three Tradesmen in the street, whom your recognize at once to be Tradesman 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…
e rapidly into the fog;_ and what appear to me as the Merchant’s extremities, viz. D and E, will be _very dim indeed_. On the other hand in the case of (2) the Physician, though I shall here also see a line (D′A′E′) with a bright centre (A′), yet it will shade away _less rapidly_ to dimness, because the sides (A′C′, A′B′) _recede less rapidly into the fog:_ and what appear to me the Physician’s extremities, viz. D′ and E′, will not be _not so dim_ as the extremities of the Merchant. The Reader will probably understand from these two instances how—after a very long training…
f which shall be reserved for the next section. § 6 Of Recognition by Sight I am about to appear very inconsistent. In the previous sections I have said that all figures in Flatland present the appearance of a straight line; and it was added or implied, that it is consequently impossible to distinguish by the visual organ between individuals of different classes: yet now I am about to explain to my Spaceland critics how we are able to recognize one another by the sense of sight. If however the Reader will take the trouble to refer to the passage in which Recognition by Feeling is…