Before I talk about Gulliver's Travels, I would like to throw out some questions on waves;
A friend of mine is a physics concentrator and we discussed some of the principals of waves in relation to dimensions. What we discovered is an extract from Walter Strauss's book "Partial Differential Equations" which addresses how waves behave in different dimensions;
Huygens's principle [a principle that allows us to see sharp images or hear any sound that is carried through the air without echoes] is false in two dimensions. For instance, when you drop a pebble onto a calm pond, surface waves are created which (approximately) satisfy the two dimentional wave equation with a certain speed c, where x and y are horizontal coordinates. A water bug whose distance from the point of impact is p experiences a wave first at a time t=p/c but thereafter continues to feel ripples. These ripples die down, like t (to the) -1 but theroretically continue forever. (Physically, when the ripples become small enough, the wave equation is not really valid anymore as other physical effects begin to dominate.) One can speculate what it would have been like to live in Flatland, a two dimensional world. Communication would be difficult because light and sound waves would not propogate sharply. It would be a noisy world! It turns out that if you solve the wave equation in N dimensions, that signals propogate sharply (i.e Huygens's principle is valid) only for dimensions N = 3,5,7,.......Thus three is the "best of all possible"dimension, the smallest dimension in which signals propogate sharply!
This concept is interesting because we can imagine a wave in lineland - it comes and goes and that is it - we can chart sound as it waves through the air on computers and yet this passage tells us that in two dimensions (Flatland) the waves will continue forever. My question is this; What would waves look like or appear to be in the fourth dimension and will they continue forever like those in Flatland?
Gulliver's Travels After reading the first part of the book in the Norton Anthology I found the begining two letters to be very interesting, mainly because of how Swift had to deal with the manipulation of the publisher. In the letter from Gulliver to "His Cousin Sympson" (Benjamin Motte, the manipulating publisher) in which Swift defends his work and attempts to take it to the publisher as a whole. "But pray, how could that which I spoke so many years ago, and at about five thousand leagues distance, in another reign, be applied to any of the Yahoos, who are now said to govern the herd." Of course Swift fully believed that everything written about the Yahoos applied today and was outraged to think that it should be spoiled and "tamed." The reply he gets from Sympson is as follows - "I now venture to send them (the papers i.e book) out into the world; hoping they may be, at least for some time, a better entertainment to our young noblemen, than the common scribbles of politics and party." What Sympson was driving at is that for noblemen, it is far more pleasant to read of fantastical adventures to far off lands which have no connection to the society of the day, than to feel attacked and scorned. After reading this in relation to Flatland, I begin to wonder whether Abbott encountered much publisher manipulation or pressure to restrict his satiristic licence. Last friday in our discussion we were asked to imagine how the book was recieved by the audience of the day. And I replied that I thought that perhaps the satire was distant enough to be unrecognized by some of the audience. And where it was recognized, the societal attack was not too offensive because of the mathematical, science fiction approach. As opposed to the more digestible Lilliput or Yahoos who had hair skin bones and all the rest of it. And could therefore be quickly compared to English society. My comment was quickly shot down by someone who believed that it was obvious to everyone that the book was satirical by the depiction of women.