Synthesized answer
The provided passages do not explicitly define "Enlargement of THE IMAGINATION." However, they illustrate the process of using imagination through analogy.
In one instance, a Sphere prompts the narrator to imagine a point moving northward to create a line, then a line moving eastward and westward to create a square. The Sphere then asks the narrator to stretch his imagination to conceive of a square moving upward, out of Flatland altogether [2]. This suggests that "Enlargement of THE IMAGINATION" involves extending concepts and geometric figures to new dimensions or directions through an analogous process [2, 3]. The narrator's enthusiastic aspirations to explore higher dimensions while in a state of ecstatic imagination further emphasize this concept [3].
Synthesized from the book passages below. Chat with the book on Feynman for follow-up.
From the book
imagination, or the baseless fabric of a dream. [Illustration] PREFACE TO THE SECOND AND REVISED EDITION, 1884. BY THE EDITOR If my poor Flatland friend retained the vigour of mind which he enjoyed when he began to compose these Memoirs, I should not now need to represent him in this preface, in which he desires, fully, to return his thanks to his readers and critics in Spaceland, whose appreciation has, with unexpected celerity, required a second edition of this work; secondly, to apologize for certain errors and misprints (for which, however, he is not entirely…
and Magicians. After a long pause he muttered to himself, “One resource alone remains, if I am not to resort to action. I must try the method of Analogy.” Then followed a still longer silence, after which he continued our dialogue. _Sphere_. Tell me, Mr. Mathematician; if a Point moves Northward, and leaves a luminous wake, what name would you give to the wake? _I_. A straight Line. _Sphere_. And a straight Line has how many extremities? _I_. Two. _Sphere_. Now conceive the Northward straight Line moving parallel to itself, East and West, so that every point in it leaves behind it…
s really Thoughtland, then take me to that blessed Region where I in Thought shall see the insides of all solid things. There, before my ravished eye, a Cube moving in some altogether new direction, but strictly according to Analogy, so as to make every particle of his interior pass through a new kind of Space, with a wake of its own—shall create a still more perfect perfection than himself, with sixteen terminal Extra-solid angles, and Eight solid Cubes for his Perimeter. And once there, shall we stay our upward course? In that blessed region of Four Dimensions, shall we linger at the…
t a moving Square produce—did not this eye of mine behold it—that blessed Being, a Cube, with _eight_ terminal points? And in Four Dimensions shall not a moving Cube—alas, for Analogy, and alas for the Progress of Truth, if it be not so—shall not, I say, the motion of a divine Cube result in a still more divine Organization with _sixteen_ terminal points? Behold the infallible confirmation of the Series, 2, 4, 8, 16: is not this a Geometrical Progression? Is not this—if I might quote my Lord’s own words—“strictly according to Analogy”? Again, was I not taught by my Lord that as in a…
rance of Priests and Women, under a new Legislation, may not be recognized; if so, a word or two will make it obvious. Imagine a woman duly decorated, according to the new Code; with the front half (_i.e._, the half containing the eye and mouth) red, and with the hinder half green. Look at her from one side. Obviously you will see a straight line, _half red, half green_. [Illustration] Now imagine a Priest, whose mouth is at M, and whose front semicircle (AMB) is consequently coloured red, while his hinder semicircle is green; so that the diameter AB divides the green from the red.…