Chances are you, being the literate person you are, have probably read some science fiction in your life. Or, less probably, a geometry text book. So you understand that the zeroth dimension is a point, the first a line, the second a plane, the third space, and (through whatever exciting imagery) the fourth is space-time. And you know what it means when I say a group of points, or the entities they represent, (the pyramids at Giza, the price of a good versus the supply, the descending quality of M. Night Shyamalan’s movies), is linear. They lie on a line.

But what about when I say thoughts are linear? Linear thinking is a progression from one thought (the conjunct of your premises), to its logical consequence, then to its logical consequence, and so on. A train of thought. This is the skeleton of mathematical proof and any good expository writing (hopefully your PWR paper). The creation of documents representing linear thought processes is both easy and useful. A linear argument, from a single point of view, is the easiest to communicate. But linearity can also be restricting. Imagine an ant walking along a taut string as if he could only travel along that line. Now imagine a multi-dimensional being folding the string, bringing the two ends together. All of a sudden the ant has teleported from one point on the line to another.

It is a familiar story, I know. Personally, I’m indebted to Madeleine L’Engle, and I’m sure we’re both ultimately indebted to E. A. Abbott. But until recently I hadn’t thought of how these illustrations of spatial linearity related to linearity of reasoning. Every step is necessary when traveling in only one dimension, even when traveling between thoughts. Without height as a dimension, there’s no way to leap. Conversation is one place we might look for instances of multi-dimensional ideas. Consider two distinct linear arguments together and you’ve outlined something that has to exist on a plane. You’ve added a dimension. This is one appeal of the dialogue as an argument structure.

It also seems like a lot of literature is dedicated to transcending linearity. Through metaphor you can run multiple trains of thought on the same fuel. And by writing down your thoughts, documenting your data points, you lessen the cognitive load of keeping track of them. This allows you to look back and draw new lines, in different directions, on what you’ve already created.

This is the premise of the game “Sentences,” developed by George Hokkanen ‘12. Recommended for 2-3 players. Requires pencil or pen, paper or whiteboard. The concept is simple: start with a sentence, any sentence, and think about it. A lot. Strip it down so far it would make Derrida blush. Define words, define their definitions, define how they relate to one another, to the reader, to you. Take notes. Notation is important. Explore your concepts in this way until you reach another sentence: another point you’d like to plot. Build outward from that. Aim for new sentences to tie into the existing sentences in as many ways as possible. Stray from these rules to taste. In the end, you should have a structurally interesting thought-object.

Sound dull? It’s not. Because if you like to think (and I’d like to think most of you do like to think), this is a fun way to do it. Even if a certain sentence isn’t particularly potent by itself, the game invigorates it, at least for the players. This is a thinking game more than a writing game: a systematized way to sculpt ideas about anything. Philosophy. Operating systems. Language. Psychology. I’d love to see history or chemistry majors set loose on this.

The first time I played, things took a turn to metacommentary. I saw the ultimate object of the game as to represent everything. Which is the tenth dimension, of course, according to a YouTube video I’d seen earlier that day. Hokkanen remarked that this might be a good guiding force and wrote on our note page: We are going to everything.

But we needed a first sentence. Someone suggested a boat. We liked the imagery.

Sentence (1): We are on a boat getting to a place.

(2) Stock the yar vessel with fuel* and guidance*. (3) Buoyed up on the sea of understanding, pull up the anchor of convention. (4) Let the wind* fill the sails*, and we’re on our way into the unknown.

Our fuel was language, our guidance, structure. We were mapping the sea as we went, so far as we could perceive from the bow. The winds were ideas, our minds the sails. How you get to everything:

(5) A rogue wind blows demanding whence and whither. Whence? What’s land?

(6) We come from ignorance, a dry place…

Whither? “If we’re going to everything, we’re mapping bounds of the ocean, right? We’re seeking our limits,” I offer.

“Our limits, hm?” Hokkanen says, and squints at me. “I wonder if we’d ever think to look up.”

Sentence (6 (b)) …we are going to the end of the page.

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