While reading Paul Halmos’ 1970 essay How To Write Mathematics, I was motivated to reveal how I write essays and blog posts. So, here are my comments on Halmos’ essay along with the underlying structure I use as a copywriter to pump out more than 4,000 words a day, six days a week.
Paul R. Halmos was a Hungarian-Jewish born American mathematician who died in 2006 at the age of 90. After reading his How To Write Mathematics essay, I was struck by the simplicity of his arrangement and I was moved to refresh the confidence in my own methods of communication. On looking further into Halmos, I was tickled to find that he had pursued a Ph.D in philosophy before refocusing on mathematics after failing the oral exam necessary for his masters’. Having myself pursued philosophy before being sidelined by illness, I feel sympathy. Regardless, Halmos’ essay — like all good philosophy, like all good essays! — remains relevant because it was written by a man who loved philosophy looking to demonstrate its vibrancy and elegance. How to Write Mathematics was written for pre-thesis math students who did not experienced the same fortification as Halmos, and were very likely incomprehensible when translating numbers to the page.
Through reading Halmos, we find that writing mathematics has its own unique foibles, and that the students for which the essay was written therefore navigate suitably unique challenges. Out of empathy to the author, I find the essay to be a sort of paean to living philosophy, an apology for his own offense against her. How to Write Mathematics reads as an unlabeled attempt at founding a new English language written school of persuasion from a man who was unable to defend himself out loud, despite its introduction to the world as a digestible guide for the college-aged calculator.
The full essay is available here, and I would now like to offer my own personalized comments on structure. Not for the eggheads, but for the bloggers and other newfound essayists of the world.
Let us begin by rounding on the proper object of an essay qua essay.
The perfect novel is not structured the same as the perfect short story, likewise the perfect poem and the perfect joke. But novels, poems, short stories and jokes are all fiction and non-fiction, while essays are authored to define and promote real-world assertions that are judged on truth value. Works of fiction and non-fiction may attempt to demonstrate the truth value of an assertion through narrative, but these assertions are subordinate to the greater work. Such works intend to provoke an emotional response. Compared “I loved this novel,” and “This is a good essay,” with “This is a good novel” and “I loved this essay.” The goodness of the work is in its structure, and to describe a work as a “good essay” is more informative than to describe a work as a “good novel.” In fact, “This is a good novel” is often followed by “But I didn’t love it.” Essays do not require an emotional review, because they are not in pursuit of an emotional response. Essay-like books such as political narratives are not essays, because they are organized according to the style of the author. Political books have a wider narrative, and it’s that extra fluff takes away from the thesis and opens the author and her assertion up to unnecessary criticism.
I have titled this post How to Write the Perfect Essay; a title I have chosen carefully. There is no such thing as a singular perfect essay but with practice we can all participate in the higher form of the perfect essay.
Since my focus here is on the deliverance of essays, I want to focus on the point of an essay which is to accurately communicate an assertion. Now, it is true that all words and their appropriate collections have a material form. The shape of the letters, the ink on the paper, the vibrations of sound are all material, and we use our material-collecting eyeballs and ear holes to take in the string of inputs that make up a communique. When humans are presented with a string of material information, we attempt to sort it for meaning, like someone unpacking a bag of groceries who wants to shelve each item instead of leaved it unsorted and unexamined on the counter. We look for meaning even when there is none, such as the discovery of faces in the clouds. Or, we look for meaning in a song and get stuck on the nonsense of I Am The Walrus.
When someone examines your essay, you ought not impede their search for its meaning by adding clouds or eggmen, or making it difficult for them to decide whether the information is necessary. An excess passage is excess material to sort, and the human brain can only keep so many unsorted thoughts on the counter at once before the material becomes unmanageable. Don’t bring home groceries you don’t intend to use, and don’t introduce concepts that are irrelevant to supporting your thesis statement. State your intention clearly. Tell your reader what you’re going to say, and how you’re going to say it. Respect the time your reader is giving you.
An essay that is to-the-point remains timeless if you write as if you were participating in history, not a trend.
In contemporary times, the proper use of language to communicate has branched into a two party system. In one corner, you have John Searle and the acceptance of modern scientific notions into language (e.g. the inclusion of the study of attention spans, which is valuable for speechwriting) and in the other corner you have the postmodernists under the absurd Jacques Derrida, who has decided that since white men invented language, all language is tainted by whiteness and maleness. Halmos’ essay was written around the time that the two started fighting over language, but it was written not as a third party alternative but in seclusion from trends. Instead of partaking in the style at the time, Halmos looked to the classics: Ancient Greek concepts of logic are clearly front and center in How to Write. Further, this Greek school finds agreement with Biblical revelation. Billions of us believe we have been granted a numbered and ordered universe.
But thou hast arranged all things by measure and number and weight. Wisdom 11:20
We are permitted to seek order, and it is good to do so.
It is more fulfilling to read an orderly essay than it is to be exposed to the disgraceful House of Wax postmodernist pooling miasma that consumes the inherited and celebrated logic of if this then that. We are privileged to read the clear thoughts of men who lived and died millennia ago. By writing clearly, and plainly, you are participating in the tradition that opened the western world to the stars above and to the men long dead by keeping it simple.
We on the ground are unable to create perfection but it is within our domain (that’s a pun) to pursue the the perfection of the formal (another pun) essay. Therefore I recommend you to avoid essay structures that seek a emotional complaint as its thesis statement, because an emotionally charged complaint is the dominion of novels and poetry. The addition of jokes and unnecessary literary references into your essay makes you anxious to hear back praise on your cleverness, not your thesis. A essay has a core. And it is that single fertilized egg that is the essay’s kernel, its thesis statement, that will grow and expand into a stronger, more robust and defensible essay. The fewer assertions you introduce, the less likely you will be pulled into several different directions of growth. In other words, don’t try to carry twins.
As Halmos says,
“Complete honesty makes for greatest clarity.”
I’ll add that a 13 word sentence is preferable to a 14 word sentence. Again, it’s for the sake of clarity.
For example, the thesis statement of this post is that an essay is the expanded form of a logical sentence.
Within this assertion are several questions. What is the goal of an essay? Will the hallmarks of a good essay change in the future? What, exactly, must be expanded? How do I identify the focus of my argument? What, exactly, constitutes a logical argument?
A good sentence, like a good essay, contains a subject and object and gives them a place in time. Here are some ways to extend the above thesis sentence in order to stress different aspects of its assertion without changing the interpretation of the assertion.
- As a communication device, an essay is the expanded form of a logical sentence.
- An essay structure that will always be accepted and understood is the expanded form of a logical sentence.
- An essay is best written utilizing multiple examples to show the expanded form of a logical sentence.
- An essay is the expanded form of a focused and singular logical sentence.
- An essay is the expanded form of a logical sentence that demonstrates a syllogism delivered with clear grammar.
Moving word-by-word and concept-by-concept through the entire sentence is the proper structure for an assertion, and therefore the proper structure for an essay. In order to write an essay, you need a thesis statement that denotes subject, object and a place in time. If you’re having trouble finding your short thesis statement, write your conclusion first. The conclusion is your final analysis of the essay and repeats your argument with reference to the buttressing you introduced as part of your expanded proof.
Review this post and you’ll notice that it indeed follows the “expanded sentence” method I’ve used here. But, I’m missing a piece: the only thing left for me to touch upon is to explain syllogisms. For this, my footnote, I would recommend Aristotle and my man Socrates.
Thank you for reading. I write for conservatives.