Clippings

“The best thing for being sad,” replied Merlin, beginning to puff and blow, “is to learn something. That’s the only thing that never fails. You may grow old and trembling in your anatomies, you may lie awake at night listening to the disorder of your veins, you may miss your only love, you may see the world about you devastated by evil lunatics, or know your honour trampled in the sewers of baser minds. There is only one thing for it then—to learn. Learn why the world wags and what wags it. That is the only thing which the mind can never exhaust, never alienate, never be tortured by, never fear or distrust, and never dream of regretting. Learning is the only thing for you. Look what a lot of things there are to learn.”

…they are both completely still, silent … enclosed in their insensitive casing… The poverty of their sensorial stimuli perhaps drives them to a concentrated, intense mental life, leads them to a crystalline inner awareness. . . . Perhaps the eros of tortoises obeys absolute spiritual laws…

…young people are taking better advantage of social tools, extending their capabilities in ways that violate old models, not because they know more useful things than we do, but because they know fewer useless things than we do. I’m old enough to know a lot of things, just from life experience. I know that newspapers are where you get your political news and how you look for a job. I know that music comes from stores. I know that if you want to have a conversation with someone, you call them on the phone. I know that complicated things like software or encyclopedias have to be created by professionals. In the last fifteen years, I’ve had to unlearn every one of those things and a million others, because those things have stopped being true.

The most merciful thing in the world, I think, is the inability of the human mind to correlate all its contents. We live on a placid island of ignorance in the midst of black seas of infinity, and it was not meant that we should voyage far. The sciences, each straining in its own direction, have hitherto harmed us little; but some day the piecing together of dissociated knowledge will open up such terrifying vistas of reality, and of our frightful position therein, that we shall either go mad from the revelation or flee from the deadly light into the peace and safety of a new dark age.

To me … mathematical experience goes to the heart of what it means to be human. And I’ll go even further and say that mathematics, this art of abstract pattern-making—even more than storytelling, painting, or music—is our most quintessentially human art form. This is what our brains do, whether we like it or not. We are biochemical pattern-recognition machines and mathematics is nothing less than the distilled essence of who we are.

Lower School Math. The indoctrination begins. Students learn that mathematics is not something you do, but something that is done to you. Emphasis is placed on sitting still, filling out worksheets, and following directions. Children are expected to master a complex set of algorithms for manipulating Hindu-Arabic symbols, unrelated to any real desire or curiosity on their part…

Middle School Math. Students are taught to view mathematics as a set of procedures, akin to religious rites, which are eternal and set in stone. … Contrived and artificial “word problems” will be introduced in order to make the mindless drudgery of arithmetic seem enjoyable by comparison. Students will be tested on a wide array of unnecessary technical terms, such as ‘whole number’ and ‘proper fraction,’ without the slightest rationale for making such distinctions. Excellent preparation for Algebra I.

Algebra I. So as not to waste valuable time thinking about numbers and their patterns, this course instead focuses on symbols and rules for their manipulation. The smooth narrative thread that leads from ancient Mesopotamian tablet problems to the high art of the Renaissance algebraists is discarded in favor of a disturbingly fractured, postmodern retelling with no characters, plot, or theme. … Students must also memorize the quadratic formula for some reason.

Geometry. Isolated from the rest of the curriculum, this course will raise the hopes of students who wish to engage in meaningful mathematical activity, and then dash them. Clumsy and distracting notation will be introduced, and no pains will be spared to make the simple seem complicated. The goal of this course is to eradicate any last remaining vestiges of natural mathematical intuition, in preparation for Algebra II.

Algebra II. The subject of this course is the unmotivated and inappropriate use of coordinate geometry. Conic sections are introduced in a coordinate framework so as to avoid the aesthetic simplicity of cones and their sections. Students will learn to rewrite quadratic forms in the variety of standard formats for no reason whatsoever. Exponential and logarithmic functions are also introduced in Algebra II, despite not being algebraic objects… Why Geometry occurs in between Algebra I and its sequel remains a mystery.

Trigonometry. Two weeks of content are stretched into a semester length by masturbatory definitional runarounds. Truly interesting and beautiful phenomena, such as the way the sides of a triangle depend on its angles, will be given the same emphasis as irrelevant abbreviations and obsolete notational conventions, in order to prevent students from forming any clear idea as to what the subject is about. Students will learn such mnemonic devices as “SohCahToa” and “All Students Take Calculus” in lieu of developing a natural intuitive feeling for orientation and symmetry. …

Pre-Calculus. A senseless bouillabaisse of disconnected topics. Mostly a half-baked attempt to introduce late-nineteenth-century analytic methods into settings where they are neither necessary nor helpful. Technical definitions of limits and continuity are presented in order to obscure the intuitively clear notion of smooth change. As the name suggests, this course prepares the student for Calculus, where the final phase in the systematic obfuscation of any natural ideas related to shape and motion will be completed.

Calculus. This course will explore the mathematics of motion, and the best ways to bury it under a mountain of unnecessary formalism. Despite being an introduction to both the differential and integral calculus, the simple and profound ideas of Newton and Leibniz will be discarded in favor of the more sophisticated function-based approach developed as a response to various analytic crises that do not really apply in this setting, and that will of course not be mentioned. To be taken again in college, verbatim.

…never was a wolf in sheep’s clothing as insidious, nor a false friend as treacherous, as high school geometry. It is precisely because it is school’s attempt to introduce students to the art of argument that makes it so very dangerous.

Posing as the arena in which students will finally get to engage in true mathematical reasoning, this virus attacks mathematics at its heart, destroying the very essence of creative rational argument, poisoning the students’ enjoyment of this fascinating and beautiful subject, and permanently disabling them from thinking about math in a natural and intuitive way.

The mechanism behind this is subtle and devious. The student-victim is first stunned and paralyzed by an onslaught of pointless definitions, propositions, and notations, and is then slowly and painstakingly weaned away from any natural curiosity or intuition about shapes and their patterns by a systematic indoctrination into the stilted language and artificial format of so-called “formal geometric proof.”