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Authors: Brian Christian

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When the diff between two frames of video is too large (this often occurs across edits or cuts), it’s often easier to build a new I-frame than to enumerate all the differences. The analogy to human experience is the moment when, giving up on the insufficient “It’s like ____ meets ____” mode of explanation-by-diff, we say “It’d take me longer to explain it to you than to just show you it” or “I can’t explain it really, you just have to see it.” This, perhaps, as a definition of the sublime?

Diffs and Morality

Thomas Jefferson owned slaves; Aristotle was sexist. Yet we consider them wise? Honorable? Enlightened? But to own slaves in a slave-owning society and to be sexist in a sexist society are low-entropy personality traits. In a compressed biography of people, we leave those out. But we also tend on the whole to pass
less judgment
on the low-entropy aspects of someone’s personality compared to the high-entropy aspects. The
diffs
between them and their society are, one could argue, by and large wise and honorable. Does this suggest, then, a
moral
dimension to compression?

Putting In and Pulling Out:
The Eros of Entropy

Douglas Hofstadter:

We feel quite comfortable with the idea that a record contains the same information as a piece of music, because of the existence of record players, which can “read” records and
convert the groove-patterns into sounds … It is natural, then, to think … decoding mechanisms … simply reveal information which is intrinsically inside the structures, waiting to be “pulled out.” This leads to the idea that for each structure, there are certain pieces of information which
can
be pulled out of it, while there are other pieces of information which
cannot
be pulled out of it. But what does this phrase “pull out” really mean? How hard are you allowed to pull? There are cases where by investing sufficient effort, you can pull very recondite pieces of information out of certain structures. In fact, the pulling-out may involve such complicated operations that it makes you feel you are putting in more information than you are pulling out.

The strange, foggy turf between a decoder pulling information out and putting it in, between implication and inference, is a thriving ground for art criticism and literary translation, as well as that interesting compression technique known as
innuendo
, which thrives on the deniability latent in this in-between space. There’s a kind of eros in this, too—
I don’t know where you (intention) end and I (interpretation) begin
—as the mere act of listening ropes us into duet.

Men and Women: (Merely?) Players

Part of the question of how good, say, a compressed MP3 sounds is how much of the original uncompressed data is preserved; the other part is how good the MP3
player
(which is usually also the decompressor) is at guessing, interpolating the values that weren’t preserved. To talk about the quality of a
file
, we must consider its relationship to the player.

Likewise, any compression contests or competitions in the computer science community require that participants include the size of the decompressor along with their compressed file. Otherwise you get
the “jukebox effect”—“Hey, look, I’ve compressed Mahler’s Second Symphony down to just two bytes! The characters ‘A7’! Just punch ’em in and listen!” You can see the song hasn’t been compressed at all, but simply moved inside the decompressor.

With humans, however, it works a little differently. The size of our decompressor is fixed—about a hundred billion neurons. Namely, it’s huge. So we might as well use it. Why read a book with the detachment of a laser scanning an optical disc? When we engage with art, the world, each other, let us mesh all of our gears, let us seek that which takes maximum advantage of the player—that which calls on our full humanity.

I think the reason novels are regarded to have so much more “information” than films is that they outsource the scenic design and the cinematography to the reader. If characters are said to be “eating eggs,” we as readers fill in the plate, silverware, table, chairs, skillet, spatula … Granted, each reader’s spatula may look different, whereas the film pins it down:
this
spatula, this very one. These specifications demand detailed visual data (ergo, the larger file size of video) but frequently don’t matter (ergo, the greater
experienced
complexity of the novel).

This, for me, is a powerful argument for the value and potency of
literature
specifically. Movies don’t demand as much from the player. Most people know this; at the end of the day you can be too beat to read but not yet too beat to watch television or listen to music. What’s less talked about is the fragility of language: when you watch a foreign film with subtitles, notice that
only the words
have been translated; the cinematography and the soundtrack are perfectly “legible” to you. Even without “translation” of any kind, one can still enjoy and to a large extent appreciate foreign songs and films and sculptures. But that culture’s books are just so many squiggles: you try to read a novel in Japanese, for instance, and you get virtually nothing out of the experience. All of this points to how, one might say,
personal
language is. Film and music’s power comes in large part from its universality;
language’s doggedly nonuniversal quality points to a different kind of power altogether.

Pursuit of the Unimaginable

Kundera:

Isn’t making love merely an eternal repetition of the same? Not at all. There is always the small part that is unimaginable. When he saw a woman in her clothes, he could naturally imagine more or less what she would look like naked …, but between the approximation of the idea and the precision of reality there was a small gap of the unimaginable, and it was this hiatus that gave him no rest. And then, the pursuit of the unimaginable does not stop with the revelations of nudity; it goes much further: How would she behave while undressing? What would she say when he made love to her? How would her sighs sound? How would her face distort at the moment of orgasm? … He was not obsessed with women; he was obsessed with what in each of them is unimaginable … So it was a desire not for pleasure (the pleasure came as an extra, a bonus) but for possession of the world.

The pursuit of the unimaginable, the “will to information,” as an argument for womanizing? Breadth before depth? Hardly. But a reminder, I think, that a durable love is one that’s dynamic, not static; long
-running
, not long
-standing;
a river we step into every day and not twice. We must dare to find new ways to be ourselves, new ways to discover the unimaginable aspects of ourselves and those closest to us.

Our first months of life, we’re in a state of perpetual dumbfoundedness. Then, like a film, like a word, things go—though not without exception—from inscrutable to scrutable to familiar to dull. Unless
we are vigilant: this tendency, I believe, can be fought.
26
Maybe it’s not so much about possession of the world as a kind of understanding of it. A glint of its insane detail and complexity.

The highest ethical calling, it strikes me, is curiosity. The greatest reverence, the greatest rapture, are in it. My parents tell the story that as a child I went through a few months when just about all I did was point to things and shout, “What’s it!” “Ta-ble-cloth.” “What’s it!” “Nap-kin.” “What’s it!” “Cup-board.” “What’s it!” “Pea-nut-but-ter.” “What’s it!” … Bless them, they conferred early on and made the decision to answer every single time with as much enthusiasm as they could muster, never to shut down or silence my inquiry no matter how it grated on them. I started a collection of exceptional sticks by the corner of the driveway that soon came to hold
every stick
I found that week. How can I stay so irrepressibly curious? How can we keep the bit rate of our lives up?

Heather McHugh: We don’t care how a poet looks; we care how a poet
looks
.

Forrest Gander: “Maybe the best we can do is try to leave ourselves unprotected. To keep brushing off habits, how we see things and what we expect, as they crust around us. Brushing the green flies of
the usual
off the tablecloth. To pay attention.”

The Entropy of English

What the Shannon Game—played over a large enough body of texts and by a large enough group of people—allows us to do is actually quantify the information entropy of written English. Compression relies on probability, as we saw with the coin example, and so English
speakers’ ability to anticipate the words in a passage correlates to how compressible the text should be.

Most compression schemes use a kind of pattern matching at the binary level: essentially a kind of find and replace, where long strings of digits that recur in a file are swapped out for shorter strings, and then a kind of “dictionary” is maintained that tells the decompressor how and where to swap the long strings back in. The beauty of this approach is that the compressor looks only at the binary—the algorithm works essentially the same way when compressing audio, text, video, still image, and even computer code itself. When English speakers play the Shannon Game, though, something far trickier is happening. Large and sometimes very abstract things—from spelling to grammar to register to genre—start guiding the reader’s guesses. The ideal compression algorithm would know that adjectives tend to come before nouns, and that there are patterns that appear frequently in spelling—“
u
after
q
” being a good example, a pairing
so
common they had to alter Scrabble to accommodate it—all of which reduce the entropy of English. And the ideal compressor would know that “pearlescent” and “dudes” almost never pop up in the same sentence.
27
And that one-word sentences, no matter the word, are too curt, tonally, for legal briefs. And maybe even that twenty-first-century prose tends to use shorter sentences than nineteenth-century prose.

So, what, you may be wondering,
is
the entropy of English? Well, if we restrict ourselves to twenty-six uppercase letters plus the space, we get twenty-seven characters, which,
uncompressed
, requires roughly 4.75 bits per character.
28
But, according to Shannon’s 1951 paper “Prediction and Entropy of Printed English,” the average entropy of a letter as determined by native speakers playing the Shannon Game comes out to somewhere between 0.6 and 1.3 bits. That is to say, on average, a reader can guess the next letter correctly
half
the time. (Or, from the writer’s perspective, as Shannon put it: “When we write
English half of what we write is determined by the structure of the language and half is chosen freely.”) That is to say, a letter contains, on average, the same amount of information—1 bit—as a coin flip.

Entropy and the Turing Test

We return to the Shannon Game one last time. Scientists all the way back to Claude Shannon have regarded creating an optimal playing strategy for this game as equivalent to creating an optimal compression method for English. These two challenges are so related that they amount to one and the same thing.

But only now are researchers
29
arguing one step further—that creating an optimal compressor for English is equivalent to another major challenge in the AI world: passing the Turing test.

If a computer could play this game optimally, they say, if a computer could compress English optimally, it’d know enough about the language that it would
know the language
. We’d have to consider it intelligent—in the human sense of the word.

So a computer, to be humanly intelligent, doesn’t even need—as in the traditional Turing test—to respond to your sentences: it need only complete them.

Every time you whip out your mobile and start plowing your thumbs into it—“hey dude 7 sounds good see you there”—you’re conducting your very own Turing test; you’re seeing if computers have finally caught us or not. Remember that every frustration, every “Why does it keep telling people I’m feeling
I’ll
today!?” and “Why in the heck does it keep signing off with
Love, Asian
!?” is, for better or worse, a verdict—and the verdict is
not yet, not just yet
. The line itself is still no match for you. And it’s still no match for the person at the other end.

1.
Claude Shannon: “Joyce … is alleged to achieve a compression of semantic content.”

2.
Length here refers to binary bits, not words of English, but the distinction isn’t hugely important in this case.

3.
This is why, for instance, starting a game of Guess Who?, as I routinely did in the late ’80s, by asking about the person’s gender is a poor strategy: the game only had five women characters to nineteen men, so the question wasn’t as incisive as one that would create a twelve-twelve split.

4.
The problem was how to get an accurate gauge of its volume without melting it down. Thinking about this as he stepped into a public bath, all of a sudden he registered: the water level rose as he got in! You can measure the volume of an irregular object by the amount of water it displaces! Allegedly, he was so excited about this insight that he immediately leaped out of the bath and ran home to work out the experiment, naked and dripping bathwater through the streets, shouting for joy. The word he was shouting was the Greek for “I’ve got it!” and has since become our synonym for scientific discovery:
Eureka
.

5.
As a result, highly compressed files are much more fragile, in the sense that if any of the bits are corrupted, the context won’t help fill them in, because those contextual clues have already been capitalized on and compressed away. This is one of the useful qualities of redundancy.

6.
Not to be confused with
thermodynamic
entropy, the measure of “disorder” in a physical system. The two are in fact related, but in complicated and mathematically strenuous ways that are outside of our scope here but well worth reading about for those curious.

7.
Play the game yourself at
math.ucsd.edu/~crypto/java/ENTROPY/
. It’s fun; plus, moving that slowly and being forced to speculate at every single darn step of the way, you’ll never think about language and time the same way again. Some elementary schools use a variation of the Shannon Game to teach spelling; I’d have my undergraduate poetry workshop students play the Shannon Game to strengthen their syntactical chops. In poems, where the economy of language is often pushed to its breaking point, having a feel for what chains of words will be predictable to a reader is a useful compass.

8.
Fascinatingly, this suggests that blander, more generic, lower-vocabulary, or more repetitive books are harder to search, and harder to edit.

9.
For this reason much swear-bleeping censorship on television makes no sense to me, because if the removed words are cloze-test obvious, then to what extent have you removed them?

10.
Heck, even pickup artists don’t like it. As Mystery puts it, “The location where you first encounter a woman is not necessarily favorable … The music may be too loud for lengthy comfort-building dialogue.”

11.
That the distinctions between the words in “And in an …” are steamrollered by native speakers, especially when talking excitedly—“Nininin …”—is lossy compression. We can afford to render all three words alike because the rules of grammar and syntax prevent other “decompressions,” like “and and an,” or “an in in,” from seeming plausible.

12.
I can’t help noticing that the fifteen-character “Shannon entropy” and five-character “mouth” have both been assigned a two-character substitute—in fact, the
same
two-character symbol, the pronoun “it”—in this sentence: more compression for you.

13.
Any utterance or description or conversation, of course, leaves countless things out. Thus the implication of anything
said
is that it is, in fact, non-obvious. Thus the word “obviously” (or the phrase “of course”) is always at least slightly disingenuous—because anything said must be at least
somewhat
surprising and/or informative in order to
be
said. (Everything said has a presumption of ignorance behind it. This is why stating the obvious is not only inefficient, but frequently offensive. Yet the opposite, too much left unsaid—as Shannon shows us in the value of redundancy, and as expressions like “when you assume you make an ass out of u and me” indicate—has its own risks.)

14.
“A girl on the stairs listens to her father / Beat up her mother,” it begins, and ends with what might be a reference to either the mother or the girl: “Someone putting their tongue where their tooth had been.”

15.
David Bellos, director of the Program in Translation and Intercultural Communication at Princeton, speculates that firmly “generic” books may be easier for computers to
translate:
“If you were to take a decidedly jaundiced view of some genre of contemporary foreign fiction (say, French novels of adultery and inheritance), you could surmise that since such works have nothing new to say and employ only repeated formulas, then after a sufficient number of translated novels of that kind and their originals had been scanned and put up on the web, Google Translate should be able to do a pretty good simulation of translating other regurgitations of the same ilk … For works that are truly original—and therefore worth translating—statistical machine translation hasn’t got a hope.”

16.
See, e.g., Columbia University clinical psychologist George Bonanno’s “Loss, Trauma, and Human Resilience: Have We Underestimated the Human Capacity to Thrive After Extremely Aversive Events?”

17.
As a confederate, it was often the moments when I (felt I) knew what the judge was typing that I jumped the Q&A gun. This suggests a way in which Shannon Game entropy and the (much less well understood) science of barge-in may be related: a link between the questions of
how
to finish another’s sentences, and
when
.

18.
“You know, if people spoke completely compressed text, no one would actually be able to learn English,” notes Brown University professor of computer science and cognitive science Eugene Charniak. Likewise, adults would find it much harder to distinguish gibberish at a glance, because every string of letters or sounds would have at least
some
meaning. “Colorless green ideas sleep furiously” is, famously, nonsensical, but requires a second’s thought to identify it as such, whereas “Meck pren plaphth” is gibberish at a glance. A language that was compressed for maximum terseness and economy wouldn’t have this distinction.
Another casualty of an optimally compressed language (if anyone could learn it in the first place) would be
crossword puzzles
. As Claude Shannon noted, if our language was better compressed—that is, if words were shorter, with almost all short strings of letters, like “meck” and “pren” and all sorts of others, being valid words—then it would be much harder to complete crossword puzzles, because wrong answers wouldn’t produce sections where no words seemed to fit, signaling the error. Intriguingly, with a
less
well-compressed language, with more non-word letter strings and longer words on average, crossword puzzles would be nearly impossible to
compose
, because you couldn’t find enough valid words whose spellings crisscrossed in the right way. The entropy of English is just about perfect for crossword puzzles.

19.
This sentence read best when I made my examples all nouns, but lest you think that this process happens only to (somewhat uncommon) nouns, and not to
everyday
adjectives and adverbs, I hope you don’t think so
anymore. Anything
and
everything
can do it.

20.
The American Heritage Book of English Usage
, §8. (That § symbol, being outside both alphabet and punctuation, is probably the entropy value of half a sentence. I get a satisfying feeling from using it. Ditto for other arcane and wonderfully dubbed marks like the pipe, voided lozenge, pilcrow, asterism, and double dagger.)

21.
The most recent statistics I’ve seen put global cell phone subscriptions at 4.6 billion, in a global population of 6.8 billion.

22.
Dave Matthews Band’s “You and Me” is, to my knowledge, the first major radio single to have its lyrics written on an iPhone—suggesting that text prediction may increasingly affect not only interpersonal communication but the production of art.

23.
Including underneath the word “ain’t,” despite its having been in steady use since the eighteenth century. It returns 83,800,000 results on Google and was said in the 2008 vice presidential debate.

24.
In October 2008, an online petition over twenty thousand strong helped persuade Apple to allow users, once they download the new version of the iPhone firmware, to disable auto-correction if they wanted.

25.
Some artists are actually
using
compression artifacts and compression glitches to create a deliberate visual aesthetic, called “datamoshing.” From art-world short films like Takeshi Murata’s “Monster Movie” to mainstream music videos like the Nabil Elderkin-directed video for Kanye West’s “Welcome to Heartbreak,” we’re seeing a fascinating burst of experiments with what might be called “delta compression mischief.” For instance, what happens when you apply a series of diffs to the
wrong
I-frame, and the wall of a subway station starts to furrow and open uncannily, as though it were Kanye West’s mouth?

26.
E.g., Timothy Ferriss: “My learning curve is insanely steep right now. As soon as that plateaus, I’ll disappear to Croatia for a few months or do something else.” Not all of us can disappear to Croatia at whim, but the Shannon Game suggests, perhaps, that simply asking the right questions might work.

27.
This sentence itself being one, and perhaps the only, exception.

28.
(log
2
27 = 4.75)

29.
Florida Tech’s Matt Mahoney for one, and Brown’s Eugene Charniak for another.

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