By Samuel Gugliotta
For Variety

MARTIN Gardner edited a book called, “Great Essays in Science.” Among contributions by such noted scientists as Einstein, Fermi, Oppenheimer, Darwin, and others there is a wonderful essay by Gilbert Keith Chesterton (1874-1936) called, “The Logic of Elfland.”
Chesterton was not a scientist. He was a brilliant and prolific writer of imaginative fiction. His works, such as,” The Man Who Was Thursday,” “The Club of Queer Trades,” “The Ball and the Cross” are truly a delight to read. If you haven’t yet discovered Chesterton, I strongly urge you to take the leap into this wonderful world of genius and imagination. You won’t be disappointed.
But what is Chesterton doing in a book of essays on science? Well, its because, “The Logic of Elfland” is an artful essay on the play between the logical constraints on our thinking and the use of fantasy and imagination in discovery and creativity. Both sides of the brain are necessary for intelligent vision, and whether you are artist, poet, or scientist, what Chesterton has to say is seminal and enlightening. There is an artist, poet, and scientist in all of us, whether we know it or not, and Chesterton has a way of reminding us of the forgotten child, full of wonder and joy, that may be slumbering in the dim shadows of our unconscious.
Chesterton begins his essay by noting, rhetorically, that what he believes in are fairy tales. He finds them entirely reasonable and full of common sense. He says, “Compared with them religion and rationalism are both abnormal, though religion is abnormally right and rationalism abnormally wrong.” It is interesting to compare this idea with the words attributed to a Chamorro resistance leader in the late 1600’s: “They call our history a heap of fables. But have we not the same right to call theirs a collection of absurdities?”
What we call “reasonable” or “logical” or “rational” are expressions which, minimally, do not violate the basic laws of logic and mathematics. Such laws are, for example, the Law of Identity, which says that P is P is a necessary truth. Or the Law of Contradiction, which says that P and not-P is a necessary falsehood. Such laws are assumed in all our communication, which would be impossible without them. And from such general principles follow other necessary truths, such as if A is greater than B, B must be smaller than A. In the words of Chesterton, “if the Ugly Sisters are older than Cinderella, it is...necessary that Cinderella is younger than the Ugly Sisters...If Jack is the son of a miller, a miller is the father of Jack.”
Logicians call such necessary statements those which are true in all logically possible worlds, and a world is logically possible if it is logically consistent, no matter how wild. “You cannot imagine, “ says Chesterton, “ two and one not making three. But you can easily imagine trees not growing fruit; you can imagine them growing golden candlesticks or tigers hanging on by the tail.” Even God cannot violate the laws of logic. For example, can an omnipotent being make a stone she cannot lift?
The infinite range of logically possible worlds leaves a great range for the roaming imagination to explore. Einstein imagined his was riding on a beam of light when he discovered the laws of relativity, and who knows what wild dreams Newton was having when the apple hit him on the nose? To see things in new ways, to discover and grow intellectually, takes the infinite expanse of logically possible worlds, and the boldness to use your imagination to explore new paths.
Chesterton’s point, I think, is that we often mistake this logical necessity, which puts constraints on our thinking or expression, with the so-called empirical laws of science and the physical world. The laws of science are not deductive, but inductive generalizations from limited experience.
From the logical point of view, such empirical truths are a subset of all possible worlds, called the naturally possible worlds. That is, those which are compatible or contain the same laws of nature as the actual world.
But from the Humean perspective, what are these “laws of nature” but the expression of observed regularities. We observe one thing following another, but we never observe the necessary connection between the events. I let go of the ball, and it drops, but I never see the force of gravity which holds the yo-yo of motion. The point is that natural necessity is an evolving, changing construct or model by which we interpret our experience. And that model is not sacrosanct; not logically necessary.
Psychologically we tend to develop mind sets. Almost unconsciously we develop habits of perception and expectation. Then we are in the danger of living in a self-created world that has lost all its enchantment, its novelty and potential to surprise us or catch our interest. In the words of Chesterton:
“We have forgotten what we really are. All that we call common sense and rationality and practicality and positivism only means for certain dead levels of our life we forget that we have forgotten. All that we call spirit and art and ecstasy only means that for one awful instant we remember that we forget.”
At a deeper level we could find ourselves in a position where all our expectations have fallen apart. Life is bound to involve us in upheavals which we may never have thought possible, leaving us at a loss of what to do. It is here that we may discover Spirit and the possibility of rebirth. Fantasy and the creative imagination may point to a new reality and a new life, all within the confines of the patterns of logical possibility.
Puzzles
1. When Zeus turned Io into a cow, he said to her, “I will turn you back to a beautiful woman, if you can find two numbers whose difference and quotient are both equal to eleven.” Can you help Io and find the numbers?
2. The magician gave her apprentice the following division: AHHA/A = BHHB. Then she told her to find the digits that replace the letters. Can you help the apprentice?
3. In an old, out of the way used bookstore, Socrates came upon a series of books called, The Secret of the Universe, which were published at seven-year intervals. The seventh book, the last in the series, noted that the sum of the publication years totaled 13,524. The publication date of the first book was faded out, but based on this information, Socrates was able to tell the date of publication of the first book. Can you equal the wisdom of Socrates?
Answers To Last Week’s Puzzles
1. There were two winners for the princess’s hand:
The cube of 300 diminished by the square of 5000 is two million. And so is the cube of 129 diminished by the square of 383.
2. If you chose the digits 7 and 8, you would get the keys to the pearly gates.
3. The pauper gave the dimensions 17/21 by 37/21, and he was a pauper no more!