Hyperwebster and the Universe’s Longest Game of Scrabble
Infinity is famously difficult to picture. You can imagine huge numbers or things repeating into the horizon, fractals that appear to go on forever, but since infinity never stops, it’s impossible to really consider everything that could go into it.
So, food for thought – what if we didn’t have to think about infinity as a never-ending string of numbers? Why not make it about words?
The Hyperwebster is a thought experiment that allows us – perhaps even better than with numbers – to make a sort of illustration of the infinite while attempting to glean some small perspective on the vastness not only of boring, abstract mathematical theories, but more importantly, on the limits of our languages.
Since infinity is so immeasurably vast, cognitively strange, most of us just don’t even bother trying to think about it much; we simply accept that it’s some sort of impossible number that exists, but also doesn’t exist because reasons and math and whatever, man.
Very simply put, the Hyperwebster is the universe’s largest dictionary. It’s not just large, it’s actually infinite – it’s infinitely infinite. This sounds redundant, I know, but I’ll clarify shortly and you’ll see what I mean.
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Eat your heart out, Oxford
Very much-not-dead British mathematician Dr. Ian Stewart, a science fiction writer and fun science promoter, devised this simple-yet-not-so-simple “dictionary” experiment as a response to the more famous line paradox in which there is an infinite number of points on a straight line.
Indeed, there is in fact an infinite number of points on even an infinitely short section of this line. No matter how close together you make the points, you can always zoom in then fill in the gaps.
Stewart, thinking of another way to visualize this line thing, decided to use an infinite “dictionary.” Like any English dictionary, it is based on the 26 letters of the English alphabet, beginning, shockingly, with A.
But unlike a normal dictionary, instead of being composed only of “real” words (cat, dog, snorkel, hippopotomonstrosesquipedaliophobia, etc),2 the Hyperwebster is made up of every possible arrangement of letters and no punctuation or spaces. As the great majority of the words are useless gibberish, the dictionary does not include definitions.
Worst game of Scrabble ever
Let’s imagine that our Hyperwebster is metaphysically contained within an infinitely large library packed with procedurally generated, never-ending scrolls.
This great library is maintained by a very patient and extraordinarily tired immortal librarian who wants to track down good words so she can play and win the universe’s least exciting game of infinite Scrabble – or as I am rebranding it, Everscrabble©. Just like any other game of traditional Scrabble, Everscrabble© is played on an infinite board that goes on in every direction, forever. It was originally designed by the Germans because they wanted to play traditional Scrabble, but kept running out of space. True story.
We’ll name our librarian Susie.
Starting at the top is easy, and Scroll I begins like this:
A, AA, AAA, AAAA, AAAAA…. and so on and so forth into infinity. Just an infinite string of A – the universe’s longest scream.
Scroll II is a bit more annoying:
AB, ABA, ABAA, ABAAA…
Then of course it becomes:
AC, ACA, ACAA, ACAAA….
You see where this is going.
Naturally, the following scrolls will eventually (for argument’s sake, anyway) go:
B, BB, BBB, BBBB, BBBBB….
BA, BAA, BAAA….
BBA, BBAA, BBAAA….
And now for some time, Susie is left with the insufferable, eternal bleating of immortal sheep. Old MacDonald’s personal Purgatory. Susie’s existence is exhausting.
To make things even worse, we then see:
BAB, BABB, BABBB, BABBB…
BAC, BACC, BACCC, BACCCC….
If I haven’t lost you yet, things become even more complex to think about. This is the part where I reiterate that this library is infinitely infinite – not only is each scroll infinitely long, there is also an infinite number of scrolls. Each of the alphabet’s 26 letters begin to repeat themselves to create their first word, each scroll adding another repetition (in this example I’ll continue with B), in each consecutive scroll until we see something like:
BBBA, BBBC, BBBD…
BBBBA, BBBBC, BBBBD…
BBBBBA, BBBBBC, BBBBBD….
Eventually, the first word in each of these scrolls would itself be nearly, but never quite, infinitely long, and the next would be one letter longer. Tragically, at this point, we will never find “true” English words as we know them.
To my knowledge, and please correct me if you know of an example, there are no “legitimate” English words that begin with a string of consecutive Bs longer than BB. We do see some abbreviations, such as BBB, which stands for many things, BBBB, which stands for slightly fewer things including but not limited to Big Bailey’s Birdwatching Bonanza, the NASDAQ code for Blackboard Inc. and Big Bad Beetleborgs. BBBBB and BBBBBB are only useful as placeholders, for example, in New Zealand bank account formats, and beyond that, it’s a lonely infinity of nothing but B.
If you want to feel powerful and create additional infinities, there’s no reason you can’t start adding punctuation. This would help with the sentences, books, and narratives contained within.
What makes this perfectly alphabetized insanity interesting is that contained somewhere within the endless rows of these endless scrolls of endless alphabet soup resides every “true” word in the English language.
It takes her a while, but when Susie digs through the endless scrolls, she can discover every combination of words ever said by English speakers, every conversation that will ever occur in the future, or that won’t occur, every misspelling, typo, tidbit of Internet slang, covfefe… It’s all there.
Susie will encounter every single answer to every single question she or the world has ever had. She’ll find every insult that was ever hurled at someone, every insult that was held back. Every declaration of war, every news article, every English poem, lyric or book ever written or that will ever be written, and all of those that will never be written. Susie will even discover this post, in its entirety, exactly as I’m writing it. But she’ll also discover a version of this post in which I use a synonym somewhere, make a few typos, and a version in which this post is about World War I trench warfare in the Italian Alps fought between Santa, Caligula, the sound of one hand clapping and Enya riding an ultraviolet triceratops made of sushi.
We can very much liken the Hyperwebster to the multiverse theory wherein there’s an infinite number of parallel universes in which everything that could happen, has happened or is happening. This idea proposes that there’s a world in which I’m a squid, one in which you are and are not Schrodinger’s Cat, and a world in which you and I do not exist.
The Hyperwebster is exactly the same, it simply deals with words. We could even make the deep, philosophical suggestion that the Hyperwebster is really just the user manual for the multiverse.
The Library of Babel
The certainty that everything has already been written annuls us, or renders us phantasmal. -Jorge Luis Borges Click To Tweet
If this whole thing sounds somewhat familiar, you might be a fan of Argentinian science fiction writer Jorge Luis Borges, who in the 1940s, composed a series of short stories including The Library of Babel, and whose words lead me to believe he was not hugged often as a child.
I swear that when I started writing this that the whole library thing seemed like a clever setting for explaining Hyperwebster, and I had not yet discovered Borges’ work. I thought that the proper place for any infinite compendium of words should be in a library, so I made a library and put Susie and my Hyperwebster in it.
In any case, Borges beat both Ian Stewart and I to the punch with his own somewhat less mathematical but nonetheless still awesome story, which imagines a universe comprised of endless hexagonal rooms in which people live with only the most basic necessities, and that contains something similar to a Hyperwebster.
Like our Hyperwebster, this library contains books made up of infinite and random orderings of the (originally Spanish) alphabet and its basic punctuation and spaces. Also contained is every actual book ever written, that will be written, that could be written, and every possible mutation or variation of those books. All books are also translated into all languages both living and extinct.
What starts out sounding like the setting of a bookworm’s erotic utopia quickly becomes a leather-bound nightmare. In what feels more like Satan’s bedtime story, the residents of the library are born, live and die within this world of mostly nonsensical drivel and, due to the extent of the books’ rampant and meaningless fuckery, are super stressed out. So stressed out, actually, that they’ve reached the point of insanity, murder, suicide, and the creation of extremist factions and cults with bizarre tendencies that make the worst cases of obsessive compulsive disorder sound like a mild annoyance with a messy filing cabinet. Grim.
The Library of Babel is actually one of the best things I’ve read in a really long time, and I ferociously recommend that you read it. It’s a super short story so you can probably make the time, I read it on the train going to work.
Doesn’t have to be a library
There are other ways of looking at a Hyperwebster that generally come to the same conclusion. There’s no need for the the scrolls to be infinite in number.
If you decide that instead of creating a new book every time you go from A, AA, AAA, AAAA… to AB, ABA, ABAA…, that you simply make 26 scrolls, one for each letter, you’d have more or less the exact same situation. 26 scrolls makes for a pretty lame infinite library with an awful lot of empty shelves, though, so I deliberately spread them out for mental aesthetics. Ultimately, the format is less important than the contents.
Another example of a Hyperwebster that I read was this one, which used the 26 volume model and envisioned a printing company rather than a library. This writer focused less on the enormity of the words contained within the dictionary, and more about the math that you could experiment with when you realize that you can just remove the first character from each book (or scroll) – eventually allowing you to bring the library back to a single volume, which ends up saving multiple infinities worth of ink and paper. At least infinity can be eco-friendly!
Furthermore, this thought experiment isn’t, at its heart, very different from the Infinite Monkey Theorem, which imagines chimpanzees or monkeys with typewriters, suggesting that immortal chimps typing away all day would eventually compose the entire works of Shakespeare – and everything else – simply by smashing their keyboards at random.
Fun story: in 2003, some scientists actually did this with macaques. It didn’t really work because monkeys suck, but it still illustrated some interesting stuff. They typed merely 5 pages over 4 weeks, mostly just pushed “S”, smashed the keyboard with a rock, and defecated all over everything. To be fair, a few weeks is sort of a weak sample size next to eternity.
Why is Hyperwebster cool?
Sometimes, it’s just fun to zoom out on things, grab some perspective, and experiment with our thoughts. Usually when I do it, I fall into a deep rabbit hole of research and reading and end up coming with weird new stuff to talk about.
You can easily imagine Susie and her scrolls. You can imagine looking down the hallways of the library, stretching into a papery oblivion, like when you stand between two mirrors and look into an ever-shrinking and always eerily satisfying tunnel of repetition, casually flirting with a feeling that exists ever so slightly outside your comfort zone.
Other than having a new math term to talk to all your nerdy friends about, taking time to think about these things – especially when it comes to words – can help us realize what the limits of our languages are – or are not. Of course, we’ll never be able to visualize all of the possibilities for word combinations, sentences, stories ever written or spoken, but we can grasp a teaspoon of the enormity and take that with us. Sometimes it feels like all the poems that could be written, all the songs and stories, have already been created. Hyperwebster is there to remind us that they most definitely have not.
Your Hyperwebster doesn’t have to be written in English either. You could use any written language, or even conceive of an interlinguistic Ultrahyperwebster – a word I spontaneously invented and a library that contains all possible combinations of all possible written characters from every language and script, and era. One that features words mixed between one language and another, or a thousand – making the infinitely infinite, infinitely larger.
Just, don’t try playing Everscrabble© in Chinese. That’s where I draw the line.
Susie will never finish pouring over her collection of scrolls, but she’ll undoubtedly discover some stupendous words for her game along the way. When she gets there, hippomonstrosesquipedaliophobia has a word value of 65 points.2 Susie, being immortal, will not only find that word in a scroll some day. In fact, she’ll find it an infinite number of times – an infinite number of scrolls will actually consist entirely of an infinitely long repetition of that single word.
The eternal Susie will never get there on her own, but if she somehow skipped to the end, somewhere down there she would finally be able to catch some Z, ZZ, ZZZ, ZZZZs…
Apex-editor of Languages Around the Globe, collector of linguists, regaler of history, accidental emmigrant, serial dork and English language mercenary and solutions fabricator. Potentially a necromancer. All typos are my own.
