M2M Day 270: The physics of language (and a book recommendation)

This post is part of Month to Master, a 12-month accelerated learning project. For July, my goal is to solve a Saturday New York Times crossword puzzle in one sitting without any aid.

At the beginning of this month, I remarked that “crossword puzzles can theoretically contain clues and answers from an infinite knowledge base”.

In other words, I was assuming that the contents of any given crossword puzzle are barely correlated to the contents of any other crossword puzzle. I reasoned that every puzzle would contain its own nearly unique set of trivia pulled from some infinite pool of crossword-eligible knowledge.

But, this is quite far from the case. Instead, it seems that there is some kind of physics that governs what can and cannot find its way into a crossword puzzle, resulting in grids with contents that are heavily correlated.

Essentially, creating a clean 15x15 grid of interlocking words requires some reliance on certain patterns of the English language, which forces crossword constructors to lean much more heavily on words better suited to fit into these kinds of grids.

As a result, the same types of words show up over and over again in crossword puzzles, creating patterns that are surprisingly more learnable than I anticipated.

I also suspect that, as crossword constructors uncover these grid-friendly words, they start relying more and more heavily upon them, perpetuating these patterns even further.

Thus, it seems that crossword puzzles are much more finite in scope that I originally thought, which is largely why I was able to improve my solving abilities so quickly. I didn’t actually need to memorize a massive corpus of trivia — instead, I just needed to get an intuitive feel for the common patterns (as dictated by the constraints of the English language).


This Physics of Crossword Puzzles was an idea I’ve been thinking about for the past few days (I had planned to write this particular post earlier this week). So, I was particular surprised when this exact idea was presented to me in an unexpected place…

Yesterday, during my flight to LA, I listened to the audiobook A Mind at Play, which is about mathematician Claude Shannon, the inventor of “Information Theory”.

Information Theory is the mathematics of encoding, storing, and communicating information, which is highly relevant to crossword puzzles. However, I didn’t make this connection when I started the book yesterday morning.

While I was waiting in line at airport security, listening to a part of the book about information redundancy (about 50% of the way through), I finally realized the parallels. I thought: “Wow, this is so related to crosswords. This will be a perfect way to start tomorrow’s Medium post”.

A minute later, the book takes an even more explicit turn…

In his theory of communication, Shannon guessed that the world’s wealth of English text could be cut in half with no loss of information: “When we write English, half of what we write is determined by the structure of the language and half is chosen freely.” Later on, his estimate of redundancy rose as high as 80 percent: only one in five characters actually bear information.
As it is, Shannon suggested, we’re lucky that our redundancy isn’t any higher. If it were, there wouldn’t be any crossword puzzles. At zero redundancy, in a world in which RXKHRJFFJUJ is a word, “any sequence of letters is a reasonable text in the language and any two dimensional array of letters forms a crossword puzzle.” At high redundancies, fewer sequences are possible, and the number of potential intersections shrinks: if English were much more redundant, it would be nearly impossible to make puzzles. On the other hand, if English were a bit less redundant, Shannon speculated, we’d be filling in crossword puzzles in three dimensions.

In other words, according to Shannon, because of the strict structure of the English language, we are just barely able to successfully construct reasonable crossword puzzles. As a result, this strict structure and redundancy come across very strongly within puzzles, creating the patterns I was able to tap into.

If you’re interested in learning more about “Information Theory”, or the about the idiosyncratic life of Claude Shannon, I’d highly recommend the book.

Read the next post. Read the previous post.

Max Deutsch is a product manager at Intuit, the creator of Somebody.io and Rightspeed, and the guinea pig for Month to Master.

If you want to follow along with Max’s year-long accelerated learning project, make sure to follow this Medium account.