Mathematics and Logic vs. Shakespeare in Alice in Wonderland

Introduction: Entering the Rabbit Hole of Influence

"The ultimate use of Shakespeare is to let him teach you to think too well, to whatever truth you can sustain without perishing." — Harold Bloom

In Harold Bloom's Shakespeare: The Invention of the Human, the author alludes to the Bard of Avon's ability not only to entertain his readers but to engage them in quizzical and logical puzzles of character that result in their redefinitions of truth and themselves. In Robert Atwan's review of Bloom's book, he likens the bard's "multilayered architecture and dramatic intricacy" to a diagram of a complex hi-fi system. Though the quote and these attributes most definitely describe Shakespeare's plays, they also ring true of the complex logic displayed in Lewis Carroll's Alice's Adventures in Wonderland. Though the greatest plays in the English language and a children's story by a mathematician may not seem similar at first, both literary works present truth as a complex puzzle — a Rubik's Cube for the mind.

A simple perusal of the Bible, Greek mythology, and the Bhagavad Gita suggests that the search for truth has been at the center of literature since its earliest conception. Paul's letter to the Corinthians explains humans' search for truth as seeing "through a glass darkly" (1 Corinthians 13:12), and Sophocles' Oedipus tragedies are nothing more than an allegory for the danger involved in that search. Shakespeare, therefore, cannot be credited with originating the theme of searching for truth, but he can be recognized for his contribution to the logic and mystery of that Rubik's Cube. Though Bloom and scholars like Atwan have long considered Shakespeare the most modern authority on this literary theme, Carroll's use of mathematics and logic in Alice's Adventures in Wonderland allows the more modern author to throw his own Rubik's Cube into the running. Bloom is one of the most respected English literature scholars of the postmodern era, but his assumptions about Carroll and Shakespeare can and should be challenged.

I refuse to accept Bloom's generalizations of Carroll's witty novel with respect to the playwright and poet. In this essay, I suggest that Bloom could be wrong, at least partially. Certainly Alice's Adventures in Wonderland is not devoid of Shakespeare's influence, but it does not fall conveniently into place amongst Bloom's theories. My aim is to comb through Alice's Adventures in Wonderland to find not only references to Shakespeare, but also much grander references to Carroll's own discipline of mathematics and logic.

Upon initial research, I found that Bloom recognized Carroll's literary genius — his "astonishing exuberance in both verse and prose" — but did not excuse him from Shakespeare's influence (Bloom). According to Bloom, "Lewis Carroll is Shakespearean to the degree that his writing has become a kind of Scripture for us" (Bloom 2). Bloom also accused Carroll of "belatedness," suggesting that his revolutionary ideas came too late, once Shakespeare's were already mainstream. Bloom intimates this by arguing that "Carroll's parodies, sometimes brilliant though they are, do not transcend their echoes, do not reverse Carroll's own burden of literary belatedness" (Bloom 2).

Bloom's judgment of Carroll's originality was, at least, unfair, as the parodies in Alice's Adventures in Wonderland comprise only a small element of the novel and intentionally mimic their origins. Furthermore, not only are the parodies purposely belated, but they also exemplify a complex system of logic and mathematics that threatens to rival the great Bard himself. Still, I was pleasantly surprised to find that Bloom appreciated Carroll and found his work worthy of comparison to Shakespeare — though I refused to be pacified by the compliment and pressed forward in search of something greater in Carroll's novel.

Upon reading Alice's Adventures in Wonderland, the reader is at once struck and seduced by the peculiarity of the text. The language is riddled, the characters "mad," and the environment fantastical. Beyond this, it is possible to infer multiple antithetical meanings for almost every aspect presented in the novel. A mock turtle is an animal that resembles a turtle but only once was a turtle; anything with a head can be beheaded, even if it has no body; and the simplest way to correct a white rose is simply to paint it red. The novel is not only "mad," but maddeningly hilarious — its absurdities turn out to make absolute sense. Why else would a lesson be called a lesson unless the number of hours one must take it lessens every day? To those trained to seek out and interpret symbols and motifs, the novel is overwhelmingly ambiguous. Once the reader follows Alice down the rabbit hole, there is no turning back to passive reading; he or she is forced to tussle through the same events and encounters as Alice, making what sense he or she can of the experience. Knowledge and confidence in Wonderland come only through experience, and chaos is avoided only by finding stability.

Upon falling into Wonderland, it quickly becomes apparent that this is a land where language and words are significant, mathematics is rendered unrecognizable, and logical reasoning is a continuing struggle. Or is the logic contained in Wonderland simply too fantastical — in a sense too logical — for the casual reader to understand? As a mathematician, Carroll uses logic several times to prove an argument that seems impossible; he uses an illogical syllogism to make a logical argument for the illogical. When considering whether a bodiless Cheshire cat can be beheaded, the King presents this syllogism:

Premise 1: All things with a head can be beheaded.
Premise 2: The Cheshire cat has a head.
Conclusion: The Cheshire cat can be beheaded.

Any rational human being would understand that something must have both a head and a body to be beheaded, but Carroll uses seamless logic to prove the absolutely illogical — a feat that some may call the mark of a true genius. Far beyond his parodies that mimic Shakespeare, Carroll meets and even exceeds Shakespeare through his use of logic and mathematics. Though the Bard certainly used logic to wind together the complex strings of his plays, using the illogical to prove the logical is nothing "belated." It is, in fact, originally and ingeniously Carroll. By exploring the influence of mathematics and logic on Carroll's writing, I contend that although Shakespeare may have influenced Alice's Adventures in Wonderland, the principles of mathematical and logical reasoning are a grander source of influence on Carroll's novel. They are the only concepts that remain constant and true in Wonderland, and the only method by which chaos is harnessed and order is established.

Bloom's Argument of Shakespearean Influence

Though it is impossible to argue that one can find no evidence of Shakespearean influence in Alice's Adventures in Wonderland, Harold Bloom's suggestion that Carroll's novel is simply a belated tale mimicking Shakespeare's logic and complexities is overstated. Because a syllogism worked well in explaining Carroll's unique literary contribution, a second syllogism will suffice to prove the fallacy in Bloom's argument:

Premise 1: If a literary work is post-Shakespearean and Western, then Shakespeare influenced it.
Premise 2: No other theories are capable of encompassing Shakespeare, and Shakespearean theory encompasses all other theories.
Conclusion: Shakespeare is the dominant source of influence in all Western works of literature that succeed him.

While Bloom's first premise — his argument of Shakespearean influence — seems feasible, his claim that Shakespearean theory dominates all other theories is bold and argumentative; and the extreme conclusion that results is even more disagreeable. Essentially, the fallacy of Bloom's logic is that it overreaches. While it is correct to assume that Shakespeare is perhaps the largest single source of influence on Western literature, one cannot argue that he influenced every piece of literature that succeeded him without becoming somewhat reductive. Take, for instance, genres of modern literature that have sprung up in the modern or postmodern era: the film-inspired novel, Christian fiction, and the murder mystery. Among the novels of these genres one will most likely find some inspirations and allusions pointing back to Shakespeare, but these genres also contain many volumes that do not reference the Bard at all. The studious scholar might point out that nearly every document produced since Shakespeare must have been influenced by him because of the sheer number of vocabulary words he created, but the focus here is literary references and thematic influences.

In Alice's Adventures in Wonderland, evidence of Shakespeare's influence is most noteworthy in Carroll's use of the themes of foolery, communication problems, and identity as it relates to power. Yet, if a grander source of influence outside Shakespeare could account for the text more thoroughly, Bloom's theory would be debased.

A larger source of influence on Carroll's work has already been identified: the influence that came from within himself and his own vocation. The principles of mathematical and logical reasoning are a grander source of influence on Carroll's novel because they are the only concepts that seem to remain constant and true in Wonderland, and they are the only method by which chaos is harnessed and order is established. Alice's Adventures in Wonderland is full of mad hatters, babies that turn into pigs, and foods that make one grow at alarming rates. The world is disorderly and illogical. However, Carroll uses logic to make the illogical logical, thereby establishing order. The very themes of the book are highlighted by this use of logic to tame illogical disorder.

For instance, Alice spends considerable time speaking with the hookah-smoking caterpillar about her size, punctuating nearly all of her sentences with "you know." Clearly, as the caterpillar states, he does not know. Alice intimates that she finds it horrible to be the small size she is, and the caterpillar quickly takes offense, pointing out that he is precisely the size Alice seems so ready to discriminate against. Through the caterpillar's logical replies to Alice's illogical assumptions, the reader not only begins to understand the upside-down atmosphere of Wonderland but also becomes aware of one of Carroll's most prevalent themes: the dynamic of assumptions and offense between strangers in strange lands.

Thus, Carroll's use of logic is ultimately a more influential source in his work than his engagement with Shakespeare. By using logic not only to prove the illogical and make sense of the nonsensical world of Wonderland, but also to highlight his major themes, Carroll himself demonstrates that mathematics and logic were of greater influence on his work than was Shakespeare. Formal logic allows two methods of attacking a conclusion: the first is by disproving one or more of the premises, and the second is by providing an alternative source for the conclusion. In this examination, it is most effective to utilize the first method — examining the premises of Bloom's argument for fallacies and weaknesses that may nullify his conclusion.

Conclusion

In conclusion, it is through mathematics, not Shakespeare, that the chaos of Wonderland is harnessed, nonsense is translated to logic, and Alice is saved from identity crisis and madness. It is through this logic that Carroll seems to make semi-political statements involving strangers and their use of reasoning. For these reasons and many others, mathematical concepts, logic, and patterns prove to be a more reliable and useful basis for interpreting and evaluating Wonderland than comparisons to Shakespeare. Bloom's admiration for Carroll is well-placed, but his insistence on framing Carroll's genius entirely within a Shakespearean inheritance underestimates the degree to which Carroll's own mathematical vocation shaped every layer of his most enduring work.