It is a great pity when the editor of a great writer fails to understand that writer, and thus ends up committing the very error the writer is attacking; but, as Shakespeare said, "That 'tis true 'tis pity, and pity 'tis 'tis true."
Recently, I was reading the collection, G.K. Chesterton: Essential Writings, edited and introduced by one Mr. William Griffin. Mr. Griffin, in this fine volume ("fine" in the double sense of being both excellent and small), has gathered selections from Mr. Chesterton's various writings, both short and long, which contain elements of the author's spiritual wisdom (the book being part of the Modern Spiritual Masters Series). In addition to headnotes and endnotes to each selection, Mr. Griffin also composed an introduction for the volume, dealing with various aspects of Chesterton, the man and the writer. Of all his observations about Mr. Chesterton, perhaps the oddest is his observation that, upon a second reading, his writings appear curiously full of four items: noses, umbrellas, elves and griffins (concerning the last, he notes that Chesterton once referred to himself in his autobiography as a "Fabulous Griffin," 39).
As I was devouring this book (for I love writing of all sorts, and Chesterton is one of my favorite flavors), I noticed something very curious about a few of the endnotes Mr. Griffin appended to the selected passages therein. In addition to the mere fact that there were notes at all—in stark contrast to Chesterton's own opposition to such things—in addition to the fact that the notes at times seem to assume a high degree of cultural ignorance in the reader (do we really need the word "clockwork" defined for us?)—there was one very sad bit of misunderstanding on Mr. Griffin's part that, unfortunately, appeared in the notes to two separate excerpts.
First, in an excerpt entitled "The Impatient Patient," Chesterton contrasts the rigidity of mathematical truth with the flexibility of imaginative invention, noting that, while Shakespeare was free to do whatever he liked with Romeo, "you cannot finish a sum how you like" (111). In response to the statement of this simple fact, Mr. Griffin gives the following note: "This statement may be true but, alas for Chesterton, it's not to say that 2 plus 3 always equals 5; it depends upon the base number of the mathematics" (112).
Again, in another selection (from the fourth chapter of Orthodoxy, "the Ethics of Elfland,") Mr. Chesterton distinguishes between the necessary truths of mathematics and the contingent truths of nature, observing of scientists that, "They talked as if the fact that trees bear fruit were just as necessary as the fact that two and one trees make three. But it is not" (133). In his notes, Griffin quotes Chesterton's words about two trees and one making three, then says, "only in a base-10 mathematics; even in Chesterton's time mathematicians were already imagining an infinite number of other basimals, in most of which two and one wouldn't necessarily make three" (138-39).
I give these statements in the exact words of the writers, along with proper documentation, because it is necessary if we are to understand Mr. Griffin's error, and it is a simple but significant one. Mr. Griffin's error is one of semantics—or semiotics—of signs and symbols. Put simply, he confuses numbers, which are concepts concerning quantity, with numerals, which are written symbols that refer to numbers, and do so directly, without the intervening symbolism of words.
Thus, while it may be so that "2 + 3 = 5" is only true in a mathematical system with a base number of six or more (in a base-five system, for example, it would be "2 + 3 = 10"), the statement "two and three is five" is always true; for two trees and three trees do make five trees, whether you write the equation for it "2 + 3 = 5" in a decimal system, or "2 + 3 = 10" in a base-five system. Ironically, Griffin's mention of a "base-10 mathematics" can only mean what he wishes it to mean if we assumed a decimal system. He should have written "base-ten." Chesterton's statements were about the numerical relationships themselves; Griffin's "corrections" (alas), apply only to the question of how to represent them using the Arabic numerals which, as Chesterton would no doubt remind us, we have only had for a few short centuries.
Ironically, Griffin commits the very errors of overly-narrow thinking that Chesterton so often opposed with his vast intellect and enormous literary output. If Chesterton were somehow to return to us (as Neil Gaiman has happen—after a fashion—in the second volume of his Sandman series, The Doll's House), he would most certainly object vehemently to these pedantic and ultimately erroneous quibbles. I envision him beating Mr. Griffin soundly about the head with his swordstick (no doubt expostulating appropriately as he goes: "Take that! You dishonor your name, sir! And that! Where are your wings of imagination? You cannot fly! You cannot stalk! You only crawl! I am a Griffin, sir! You are none!"), or perhaps—and this by far the worse punishment—he would simply sit on him.
The relationship between numbers and numerals is yet one more fascinating area of semiotics, and can be exploited to inventive literary ends by those who understand it (as Robin Wilson shows in his book on Lewis Carroll), but as this essay illustrates, the world of mathematics can be a perilous field for those who venture into it unprepared. With all due respect to Mr. Griffin, perhaps he should stick to the literary aspects of the works he treats, and leave the numbers game (or the numerals game) to the mathematicians.
