How Many Novels Can There Be?

I like reading. I like writing. When you’ve been writing for a while, you start to get really obsessed with word counts. Anybody you talk to about publishing something you’ve written will want to know your word count. For short fiction, you sometimes get paid by the word. And the number of words in the thing you’ve written determines whether it counts as a short story, a novella, a novel, as War and Peace, or as an encyclopedia.

Every year, I participate in National Novel-Writing Month. Unless, you know, I don’t feel like it. But I’ve participated more years than not, and I’ve produced a surprising number of novels. Every single one of them terrible, but that’s not NaNoWriMo’s fault. The goal in NaNoWriMo is to write a novel of at least 50,000 words in 30 days. And I got to thinking: how many novels that length are there?

Well, in the English language, there are somewhere between 100,000 and 1,000,000 words. But you’ll be able to understand 95% of everything written in English by knowing only the 3,000 most common ones. After all, even though it’s a valid word, people generally don’t go around calling each other antipodean anymore.

The question is: “How many 50,000-word novels are possible, using mostly the 3,000 most common words?” The naive answer is to allow each word to be any of those 3,000, which means the number of possible novels is 3,000^(50,000). That’s 1.155 x 10^173,856. You’ll be happy to know that this number is so large that, when I tried to copy and paste the full thing into this article, it crashed my browser.

Of course, this will include novels that consist entirely of the sentence “Anus anus anus anus anus!” over and over again, which is so avant-garde it makes me want to go pee on Samuel Beckett. The list will also contain more coherent, although still somewhat dubious works, like Stuart Ashen’s peerless desk reference, Fifty-Thousand Shades of Grey. But Fifty-Thousand Shades of Grey is actually constructed of coherent sentences. (Well, one coherent sentence, at least…) Most of the novels in this ridiculously long list will be more along the lines of “Him could carpet but also because you die but but the but the but the butt.”

We’re working from a flawed assumption: that a text is just a bunch of words stuck together. But unless you’re James Joyce (or, to a lesser extent, Stephanie Meyer), that’s not how it works. A novel is a bunch of words stuck together in a particular way. Although “that that” is grammatically valid (even though it looks weird on the page), “the the” isn’t, and “centipede cheese carpet muffin” is the kind of thing I say when I haven’t been getting enough sleep.

We’ve been working from the assumption that any word is equally likely to follow any other word. That is, that all word-pairs are equally likely. They’re not. “Our way” is a lot more common than “our anus,” for instance. Naively, the probability of any two-word combination is (1 / 3,000)^2, or 1 in 9,000,000. To put it another way, there are 9,000,000 two-word pairs, 25,000 of which would make up our nonsensical novel. It’d be much closer to reality to assume that, on average, there are only 50 words that make sense after a given word (the number will be much higher (in the thousands, I’d imagine), for words like “the”, and lower for words like “hoist.”) So, in reality, there are only 150,000 two-word combinations that make sense.

We could extend this to three-word combinations, but there are two problems with that: 50,000 isn’t evenly divisible by three, and that repeating decimal will drive me crazy. More importantly, the longer your word-block, the more words become possible at the end, until you’re getting close to 3,000 possibilities again. For example: “The” could be followed by any noun in our 3,000-word list. “The man” must be followed by a verb, the start of an adjective phrase (example: “The man I met last summer“), or something like that. “The man talked” will likely be followed by a word like “to” or “about.” But there’s an enormous range of things that the man could be talking to or about, so pretty much any noun or participle is fair game, bringing the number of possibilities back up into the thousands again.

So how many novels can there be? Well, the upper bound is probably (as we’ve seen), (3,000 * 50)^25,000, which is 1.912 x 10^129,402. That’s still a number so large there’s no name for it, but it’s smaller than our first number by almost fifty thousand orders of magnitude, which is something.

But let’s take it one step further. To simplify the math, I’m going to skip right to four-word combinations. And let’s say that any two-word combination forms the start of a phrase, and that the third word in the phrase can only be one of 10 words, on average. And, to take into account the fact that the number of choices start rising again with a long enough phrase, let’s say the fourth word can be any one of 500 words. The number of possible 50,000-word novels is now (3,000 * 50 * 10 * 1,000)^(12,500), or 1.382 x 10^114,701. So we’ve chopped off another ten thousand orders of magnitude. Still, that’s a big number. And, although I don’t have the math or linguistics background to prove it, I’m guessing that’s pretty close to the number of actual, sensible novels you could construct with 50,000 words: it takes into account the rough structure of the English language. This is related to the idea of a Markov Chain, which is a mathematically-formal way of saying “where you’re likely to go next depends on where you’re at now.”

For your amusement, I’m going to back up this post, and try to copy and paste (3,000 * 50 * 10 * 1,000)^(12,500) just below. If you see a horrific salad of numbers, you’ll know it worked. If you see an apology, you’ll know it crashed my browser again. Wish me luck!

Sorry. It didn’t work. Browser crashed again. But that’s probably good news for you, the reader, since, when I pasted the number of possible sensible novels into my word processor, it produced a document 32 pages long consisting of nothing but digits in 12-point Helvetica. I think that’d make most people’s eyes bleed. Or explode. Or sprout wings and fly away.

The moral of this story is: don’t worry about machines taking over the writing of novels. If a computer could output one word of its current novel every Planck time (which is generally agreed to be close to the shortest time interval that makes sense in our physics), the time it would take would be larger than the current age of the universe. And that’s an understatement. It would actually be so much larger than the current age of the universe, that if I were to express it as a multiple (in the same way I say 10^24 is a trillion trillion times larger than 1), then I’d have to write out the word “trillion” 9,558 times just to express it. If I allow the convention that 1 googol googol is (10^100) * (10^100), or 10^200 times bigger than 1, then I’d need to write “googol” over 1,100 times. There is simply no good way to express the size of this number. It’s 10^110,000 times larger than the age of the universe in Planck times, the diameter of the observable universe in Planck lengths, and the number of particles in the universe.

Boy oh boy. I started out talking about novels, and now I’m getting into numbers that trip the circuit breakers in my brain. Math can be scary sometimes. And you wanna know the scariest thing? There are numbers, like Graham’s number and the outputs of the Ackerman function for inputs larger than (6,6), that make the number of possible novels look exactly like zero by comparison, for any practical definition.

…I need to go lie down now. Although I’m probably going to come back later and talk about really enormous numbers, because part of my brain seems to want me to have a stroke.


162 thoughts on “How Many Novels Can There Be?

  1. Another thing which I find fascinating is how many different stories are there really out there to tell? And what classifies whether a story is original or unique, doesn’t everything mirror something to some extent? To what extent does that make it ‘old’, or ‘copied’? Anyways, your post is an idea that I think runs through a lot of our heads but in a much messier way than you’ve phrased it. Love this post.

    • There’s probably actually a way to estimate how many interesting stories there can be, based on number of characters and number of events. You may have just inspired my next article 😀

  2. Books are food for the soul. As I’ve grown, so has my taste in food, based on health concerns, activity and emotional states. What I read now is as different to what I read when I was s teenager. It doesn’t matter the number of books out there, no more than we should feel depressed by the number of restaurants out there that tempt our appetite. Hungry drives consumption and creation. Great article!

  3. Matt On Accident says:

    First off, I refuse to grovel,
    Just like I won’t live in a hovel
    But not so determined
    When the word count won’t end
    So I hereby ban writing a novel!

  4. Pingback: How Many Novels Can There Be? | robotissmiling

  5. The way I choose a book is by the first sentence. If it captivates me I will try to read it. That is why I am glad that there are so many novels out there. You given me moment to appreciate the differences in writer’s styles.

  6. Love writing, and you got me motivated with that link you posted, I’ll be looking into that (though I’m mad for it, I have three jobs if you count being a mother and am involved in a few lawsuits). Second, love your mathematical curiosity, especially that it drove you to bother with mathing it at all.
    The best way to communicate the size of the number was how many pages it filled. Everything else went over my head.

    • I got lucky, in a way: I’m a writer at heart, but I learned enough math in my brief stint as a math major that I can (kind of) communicate huge numbers in a way non-math-people can (hopefully) make sense of.

  7. Enjoyed this article, felt like we were having a conversation and a friendly one at that. Oh and antipodean you’re right we don’t use it a lot, but when I met someone new at work I couldn’t decide from their accent whether they were from Australia or New Zealand so to avoid offending them I just said their accent sounded antipodean and they responded quite happily that they were from South New Zealand. Having said that I’ve never found any other use for it.

  8. Pingback: How Many Novels Can There Be? | elle marr

  9. The views expressed below in this precis are my own.

    ?. Why was Into Happy Havens /http://Smarturl.it/ihh written as a novel?

    Answer. The narrator in a work of fiction is granted an opportunity to express his/her views vividly, with many personal (empiric) opinions about issues which will be rejected in fact based reports.

    The editing process for reports or research findings does not allow such flexibility, nor does it permit or encourage the writer to make any statement which could be regarded as politically incorrect, beyond the ability of the authors to deliver, contrary to any legal or corporate laws, or outside of the terms of reference that set parameters on the research/enquiry before commencement.

    As an example of a ‘reality v perception’ approach, no report/research could include the statement …………

    “ A Welsh windbag who drones on for ages and ages, grazing happily on the southern slopes of the Orals”

    …..as a viable expression of the shared views that exist between Senior & Junior managers in the same organisation.

    The freedom granted to the narrator in a reality based novel enables him/her to make pertinent asides and use humour or romance to illustrate valid and memorable lines which re-enforce the novel to lasting effect.

    Dennis Coates, Year 15.

  10. Pingback: How Many Novels Can There Be? | Vienna Waits For You

  11. Give me this novel, this day
    that is an unnumbered heartbeat

    Let her give me an infinite love
    and I will gather up all her leaves
    however many there would be
    in the her universe expanding and throbbing
    like the bubble of a giggle

    Give me a place
    to stand with love,
    to peddle compassion, yes

    give me the world’s bouquet
    and hard hearts to stand in too.

    Just these and I’ll
    beat the stale hatred
    into the lungs of Love, just

    come down from thin airs
    to see if mountains can wait
    when the valley is sanguine.

    If you give me standing in you to
    untangle the tango, I’ll

    dance with you
    until the flowers
    all clap their red petals

    and we count the petals we pluck:
    “she loves me”
    “she loves me not”

  12. Ian Blázquez says:

    Well, I think the beautiful thing about writing is that, it’s infinite. It’s endless. You may have taken the ‘math path’ to solving the question ‘how many novels can there be?’, and probably that rational path is closer to reality. However, the artist in me says, writing is simply endless. From where I stand, you never included in your calculations that language, any language, is a living thing that keeps on changing, evolving, mutating – bringing up new words and concepts for new experiences. We cannot possibly count that in simply because it’s unpredictable. And the other part of writing that wasn’t added to the equation, is that a same idea can be expressed in many different ways; the same words can express so many different ideas. Just think of the Bible (I’m sorry, but I’m not a believer), it has inspired so many different forms of art, especially stories. How many versions has the Bible produced in the History of Humankind? And I think we are still not over with it. Hopefully, there’s still a very, very long way to go. Just for that, thank God – that’s a quality truly divine. Thank you, I enjoyed your post.

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