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Essay

Knowing the World Anew (II): Analog & Digital

Aug 4, 2022·26 min read

The idea for this piece came mostly from the podcast Incomputable and its episode 37: A Vast Resemblance Links All Things. 1

I have listened to that episode many, many times, and I cannot recommend it enough.

As words and symbols go, the difference between Analog and Digital is one you can't afford to ignore.

"Analog" means "a mapping from one continuous change to another continuous change." It is infinitely precise, full of detail, messy and organic, fluid and sensual.

"Digital" simply means "of digits, numerical." It refers to "pointing at other things in a discrete, finite way." It is clearly defined, free of ambiguity, deterministic, computable.

  • Analog is an isomorphic migration between different carriers. Digital belongs to no carrier at all.
  • Analog can be refined and described without end. The description of Digital is finite.
  • Analog is informal. Digital is formal.

A few examples of the distinction:

Sound

Vinyl records and old-style radio broadcasts are Analog. Audio files in digital formats are Digital.

The principle behind a record is to carve the continuous sound waves in the air into the grooves of the disc. Radio works in a similar way: sound waves are continuously turned into electromagnetic signals, and at the receiving end those signals are continuously turned back into sound.

A digital audio file is something else entirely. We have no way to store infinitely fine-grained sound, because that would take infinite storage space, so we have to make compromises.

For a digital audio file there is bit depth (from the quietest to the loudest sound, how many "pitch" possibilities we can have) and sampling rate (how many samples per unit of time we pull from the continuous signal to build the discrete one). The pitches that fall between the two smallest steps, and the changes in the wave within the smallest interval of time, have to be thrown away (rounded off) before the file can sit inside digital memory.

For more, listen to the episode S2E1 MP3 from the podcast "Absence."

Computers

There are two kinds of computers in the world: the analog computer and the digital computer.

To work out where a planet will be a year from now, you could use an orrery to simulate the planet's orbit, then turn a crank to spin it and "speed up time," and read off the planet's future position. That is the Analog way of thinking.

Early in the history of digital computing, analog computers were already doing differentiation and integration with precise gear trains. They predicted lunar eclipses and tides and guided anti-aircraft weapons. But an analog computer can't be programmed. It can only carry out the intent it was built for, and mass production, miniaturization, and commercialization were all very hard, so digital computers overtook it quickly.

When we say "computer" now, we always mean the digital kind. But things are turning. Training a neural network depends on enormous amounts of matrix multiplication, which runs inefficiently on the traditional von Neumann architecture (the digital computer). Now analog microelectronic devices have appeared (compute-in-memory devices) that use analog signals (a continuous range from 0 to 1) in place of digital ones (just 0 or 1), and they can cut energy use dramatically while doing the same job.

For more, watch these two videos on analog computers from Veritasium:

Language

If I ask you "how tall is Mount Everest," and you happen to know, you'll tell me it's 8,848 meters, or more precisely 8,848.86 meters. You can't, and you don't need to, tell me anything else. That is Digital.

But if I ask you "what is Mount Everest like," you'll describe how it towers into the clouds, how the mist wreathes around it, how pure and untouched it is, how it stands there, great and unmoving.

I can keep asking, "Anything else? And then?" and you could seem to go on answering forever. That is Analog.

When Chen Jiaying uses this example, he doesn't bring up the Analog and Digital distinction at all. In his book he uses it to talk about "perceptual speech" and "rational speech." It seems to me that the pair of ideas Chen discusses there, "perception" and "rational knowledge," has a strong resemblance to Analog and Digital.

For more, read Chen Jiaying, Perception, Rational Knowledge, Self-Knowledge, Beijing: Beijing Daily Press, 2022, page 126.

Analog and Digital are a hidden and ambiguous pair of opposites. Trying to draw a clean line between them is itself a Digital act, so for an Analog thinker the two are tangled together and mutually dependent. One of the goals of digitalization is to simulate our real world, and analogy in turn can never escape the need to refer and to quantify.

This section is about Digital alone.

In 37: A Vast Resemblance Links All Things, the host, Bao Ting, says:

"Digital does exactly what our fingers do."

Stretching that a little, here are five things it does:

Counting, quantifying, calculating

The most basic thing Digital does. It needs no further explanation.

Pointing (reference, index, pointer)

One of the most important differences between Digital and Analog is that Digital simplifies and abstracts whatever it points at.

We use GDP and broad market indices to point at the macroeconomic state of two great powers, and we use numbers to stand in for each particular person who died in a war or a pandemic. Using a smaller, more understandable amount of data to point at something far more complex and tangled, stripping away redundant detail so it's easier to discuss and analyze and easier to find patterns inside the chaos: this is the feature and the strength of Digital.

Comparing

A number carries comparison inside it from the start.

When I say a test score is 85, that isn't a lonely 85. It is tied to "higher than 80" and "lower than 90." A single score is bound up with a whole system that judges people on one dimension by comparison.

When you run into a young person at a café, someone who loves the world and is full of hope and confusion about the future, you wouldn't judge them with a system like that, because personality and spark are "incomparable." They are Analog, not Digital. But the moment you hang a "value" on a person, whether it's a height of 180, a salary of a million, or a grade of A+, there is no escaping that tinge of comparison.

When we say "cold, hard numbers," we seem to be reaching for "objectivity," but what we're really reaching for is "comparison."

Digital can't be separated from the ideology of meritocracy. A society where everything can be set on the scale and weighed is by no means an ideal one.

Manipulation and management

Put all of the above together and Digital can serve to manipulate and manage. People often say we are now "controlled by numbers." This doesn't only mean "something is controlling me, and that thing is numbers." It means "it is precisely because numbers exist that I feel controlled." Exam scores, performance reviews, digital management, electronic files, price discrimination through big data, recommendation algorithms. The world of numbers forms one tight, orderly system. It gives humanity the power to cooperate at enormous scale, and it also lets every one of us feel the violence that comes from that same system.

Reasoning without feeling (the Turing machine)

Digital is also the engine driving the explosion of technology. The most important spark of the Scientific Revolution wasn't scientists boldly defying the Church. It was the founding of a tradition of scholarly critique and the mathematization of the natural sciences.

(A small aside: heliocentrism had been proposed over and over since the Greeks, and there were even supporters of it within the Church. The Copernican revolution wasn't about proposing heliocentrism, and the Scientific Revolution didn't happen as simply as the textbooks describe.)

Why does mathematization matter so much? Why does a discipline only earn the name "science" once it has been mathematized? Because mathematization makes "reasoning without feeling" possible. The arguments of philosophers (apart from the rationalists and the logicians) tend to be short. The concepts may be hard to grasp, the thought obscure and deep, but you don't find "long-range reasoning," no airtight, tightly linked proof running on and on. In mathematical physics this is everyday business. Theory papers with proofs running dozens of pages are everywhere.

For just this reason, the Greeks could deduce that the Earth is round (from their grasp of plane geometry, and from watching the horizon and lunar eclipses), and could deduce the circular motion of heavenly bodies, yet they had no possibility, the way modern physicists do, of deducing neutron stars, black holes, the uncertainty principle, and quantum fluctuations out of equations. Mathematics is our only way of doing "long-range, precise reasoning." It lets our sight reach into the microscopic and the cosmic that perception can never touch.

If I had to name a capacity that belongs to humans alone, I wouldn't answer "language" or "intelligence." I would answer, carefully:

Perhaps the capacity for Digital is the one humans have and other animals do not.

Liu Cixin tells this story in his novella Heard It in the Morning:

Just as humanity is about to run an experiment that would destroy the universe, an observer civilization, advanced as gods, forces a halt. To keep any civilization from running a creation-scale experiment that would wreck the cosmos, this civilization has placed warning systems everywhere in the universe. A scientist asks them: when did your warning system on Earth first go off? In Newton's time? In Aristotle's?

The answer comes calmly: "At the end of the Pleistocene, two hundred and seventy thousand years ago, a primitive human looked up at the stars for longer than the warning threshold allowed, showing excessive curiosity about the universe. If that primitive human's few minutes of gazing was the sight of a jewel, then everything you call human civilization since has been nothing but bending down to pick it up."

I love Heard It in the Morning. Liu Cixin's prose was still a little raw when he wrote it, but that doesn't stop the story from being one of the best short and mid-length science fiction works in my mind. The romance of "looking up at the stars" is one no other image can match. Still, I'd feel that the alarm starting to sound from the moment "a primitive human counted on his fingers" fits reality better. The arrival of digitalization let humanity, a weak little civilization that built its walls out of river mud, standing on one small rock in this vast universe, armed only with observation, experiment, and pen and paper, see into the secrets of the great cosmos and the tiny world within.

Of course, Digital has its bad side too. As I said above, digitalization is not an ideology-free process. On the contrary, it carries a kind of violence born of standardization, modernization, and scaling, a structural, top-down alienation and domination of people. And this is exactly the space where Analog and the humanistic spirit ought to step in. That touches on the friction between the two worlds that Analog and Digital span, which I'll leave for section 4.

Digital is more than a double-edged sword. It's more like one dimension of our world (what I'll later call the "realm of numbers"), one of the foundation stones of the modern human world.

The question isn't "when should we use Digital and when shouldn't we?" or "how do we use Digital correctly to make the most of it and avoid the worst?" Digital isn't something you can shake off, or a tool you can take or leave. Digital is the reality we live in. Resisting it is wasted effort. What we should be thinking about is how to coexist with it, how to live alongside it.

This section is about Analog alone.

Digital is intensely rational and loves to sort things into categories. Analog is its opposite. So in the section above, I could carefully sort Digital into types, give it definitions and readings, and explain what Digital is entirely through rational narration. The same method of explanation will not work on Analog.

Ah, how am I supposed to describe Analog to you?

This is the world of the poet, the world of sensibility, the world suffused with the smell of coffee.

Analog is literary. It has a literary logic, a logic built on metaphor and feeling, and it doesn't lean on the logic of Digital. I see someone unhappy, and I wonder whether I've offended them. That is reasoning built on a logic of its own, and it has nothing to do with the airtight logic of Digital.

We can find hidden links and resonances between unrelated things. We can dwell, slowly, on a texture, a mood, a scene, a stretch of experience, one leaf of autumn, one grain of sunlight. That is Analog. Words and feelings are not things you can pull apart. Our private feeling lives inside our words, and feeling can only be expressed through words.

In the broadest sense, "the world" is Analog, because everything we feel of the world around us is "a mapping from one continuous change (the world inside and out) to another continuous change (the feeling in the heart)."

So, just like Digital, Analog is also a dimension of the world. Both are the reality we live in.

So, using Analog versus Digital, we can split the Symbolic into two: I'll call them the "realm of feeling and speech" and the "realm of numbers."

The Symbolic order's transgression upon the Real, the specter of the Real tearing the Symbolic apart. This entanglement of the Real and the Symbolic was a source of destructive force in older societies. But the framework of the Imaginary, the Symbolic, and the Real can't hold the human world of the information age. The theoretical horizons of posthumanism and transhumanism have to be let in.

The human in the information age faces a second entanglement of worlds, which shows up as "the realm of numbers transgressing upon the realm of feeling and speech, the specter of the realm of feeling and speech tearing the realm of numbers apart."

The "realm of feeling and speech" is built on metaphor. Our sense of the real world gets abstracted into symbols and words, and through language a reader "experiences," from their own experience, the experience that another's words point at. So this world is different for every person, fluid, and unfixed.

The "realm of numbers" does away with that fluidity and unfixedness. The world of numbers is built on formal systems. Binary storage is discrete, of finite precision, so it carries quantification, simulation, manipulation, and management. The Real, infinitely precise and complete in its detail, and the realm of feeling and speech, shimmering and wholly subjective, are both impossible to quantify and compute.

...In that Empire, the Art of Cartography attained such Perfection that the map of a single Province occupied the entirety of a City, and the map of the Empire, the entirety of a Province.

In time, those Unconscionable Maps no longer satisfied, and the Cartographers Guilds struck a Map of the Empire whose size was that of the Empire, and which coincided point for point with it.

The following Generations, who were not so fond of the Study of Cartography as their Forebears had been, saw that that vast Map was Useless, and not without some Pitilessness was it, that they delivered it up to the Inclemencies of Sun and Winters.

In the Deserts of the West, still today, there are Tattered Ruins of that Map, inhabited by Animals and Beggars; in all the Land there is no other Relic of the Disciplines of Geography.

(complete text)

Borges, "On Exactitude in Science"

The realm of numbers is a "map." There is a mountain in the world, and on the map it becomes a triangle symbol or a set of contour lines, with a number written beside it to mark the height. Notice that the point of this symbolization is not "the symbol standing in for the real thing" (that is the Symbolic transgressing upon the Real). The point is the process of turning it into numbers, which turns a peak in the real world into something quantifiable, something computable. However fine the map, it's still hugely blurry and distorted next to the real terrain. But it's exactly because of this that digitalization can give everything a scale, and so this world of numbers becomes something you can quantify, measure, model, and compute.

The realm of numbers wasn't created in the information age. Its history reaches back to the very instant a human first used numbers to measure the scale of the world.

The real system, the actual system, is our present way of looking at things, which is reason itself. If you tear down a whole factory but the rationality that built it is still standing, then that rationality will simply build another factory. If a revolution destroys a government, but the systematic patterns of thought that produced that government are left intact, then those patterns will repeat themselves. There's so much talk about the system. And so little understanding.

Steel has no more shape than this old pile of dirt on the engine here. These bits of pebble. That's all steel is. Reason. The shape is all conceived in someone's head. That's important to see. The steel? Hell, even the steel is out of someone's head. There's no steel in nature. Anyone from the Bronze Age could have told you that. All nature has is a potential for steel. There's nothing else there. But what's "potential"? That's also in someone's head. Ghosts.

Pirsig, Zen and the Art of Motorcycle Maintenance

The realm of numbers is a lot like the Symbolic, but the realm of numbers allows no ambiguity. The realm of numbers is "formal."

"Formal" means a thing doesn't depend on its carrier. The nature of something is decided by a certain numerical relation, and everything is built into a harmonious order according to certain numerical proportions, while the material carrier underneath doesn't matter.

A video game draws mountains, rivers, and grass with computer graphics. What we see on the screen is a rendered two-dimensional image, while all the model entities (the matter) and the relations and interactions between them (the physics) are saved and recorded as data.

If the precision of the model entities is pushed to the extreme, they become no different from the matter of the real world. Push the precision of the relations and interactions between entities to the extreme, and the matter is given physical laws no different from the real world's. What a computer program really is, at bottom, is a stretch of data, a string of numbers. A computer program is "formal." Whether it runs on transistors or vacuum tubes, the abstract program is the same, and it runs either way.

Industry has the idea of the "digital twin." A digital twin reproduces every parameter of a real object inside a virtual space, so it can reflect the whole lifecycle of the corresponding physical equipment. A digital twin isn't only a model or a simulation. The digital twin is the real object itself. The matter and the carrier they rely on are different, but from the standpoint of form, there's no true or false between material elements and matrix data. The real object isn't truer than the digital twin, and the digital twin isn't any falser than the real object.

The world of the future is arriving far sooner than you imagine. The smartphone long ago stopped being just a "tool" for humans and is slowly becoming an "organ." In science fiction, the human brain can plug into external storage to boost memory.

In fact, that wish has already been partly granted. For people in the habit of jotting things down, the phone has become the brain's external hard drive. Instant messaging and social media have transgressed upon traditional relationships and ways of communicating. When you see someone on the street wearing Bluetooth earbuds and talking to a distant friend, you'll surely feel the tension of a future about to arrive.

In the post-pandemic era, the line between the virtual world and the real one has blurred. During lockdown, life in the online space was more real than life in reality.

In this sense, the cyborg (the fused system of human and electronic machine) is not what we are going to become. It is what we already are.

In mathematics, the natural sciences, the factory, and the program, Digital is natural, harmless, correct. The realm of numbers does not transgress upon the Symbolic here, because in these settings symbol and meaning are already formalized (an electron is an electron, with no room for being misread). The realm of numbers and the Symbolic are identical, so naturally there's no rupture.

The trouble with the "realm of numbers" is that in this tight, orderly picture there's no place for our joys and our pains, no place for our moral striving and our artistic ideals.

That last passage isn't mine. It's Chen Jiaying's criticism of the "scientific world," and the criticism applies just as well to the "realm of numbers." The "realm of numbers" is bigger than "the world science paints for us." The world of science is far from our daily life, but the realm of numbers is already part of it.

Digitalization cares about the general structures and laws across different things, about dividing nature into kinds and ordering them into hierarchies, about analysis.

When this way of thinking cuts into the complex psychological states and emotional experiences of human beings, into the imagining of a good society and a just politics, into literature, philosophy, and dreams, a second alienation and distortion of the person begins.

In 37: A Vast Resemblance Links All Things, Bao Ting brings up a phrase:

"Digital Singularity."

The "digital singularity" is the instant when everything in the world can be quantified and turned into numbers, the moment when information technology is everywhere and has fused with our lives.

By then, the territory of the "realm of numbers" will cover the whole human world, and there will be nothing that cannot be digitized.

The digital singularity is arriving sooner than you imagine.

Do you remember the last time you used cash in renminbi?

I can't remember anymore. The last time I dug a coin out of my little change pouch, it felt utterly strange to me. At some point cash in China became a nostalgic thing, a thing with a faint touch of the exotic.

Back when you could still travel abroad before the pandemic, I always liked to bring home some foreign currency I hadn't managed to spend, as a souvenir of the trip. Now the renminbi has become something like that for me. I think it's pretty, I like to carry a little of it, and yet I don't know how to use it, how to spend it.

You walk into a supermarket and everything is priced at something-point-99. If I paid in cash, how would the cashier even make change? I don't know, and just picturing it makes me want to laugh. Cash really does seem like a thing from the last era.

I once saw a joke on Douban. The poster went into a convenience store to buy an ice cream, happened to have cash on her, and figured she'd use the chance to spend it. She asked the owner, "Boss, do you take paper money here?" The owner froze. Only then did it hit her: "Oh, I mean cash. Do you take cash?"

Even the word "cash" has become this unfamiliar. Kids today, when they see a floppy disk (maybe you don't know what a floppy disk is either; here, it's this: 💾), ask out of curiosity, "Excuse me, is this a physical model of the 'save button'?"

Maybe kids someday, when they see cash, will ask too, "Is this thing 'physical money'?"

All of this happened in the span of just twenty years:

In 2004, Alipay broke off from Taobao and became a third-party payment platform.

In 2013, WeChat Pay burst onto the scene.

At first it was the e-commerce platforms that needed electronic payment. Then supermarkets and convenience stores took up mobile payment too. Now even the little street vendor grilling sausages has to stick a payment code on the grill, or a lot of customers won't know how to pay.

The "digital singularity" of payment has already happened.

Can the digital singularity in other fields be far behind?

By the logic of these things, when a public-account essay reaches this point, it's time to bring out something "deep and meaningful" for the reader.

It makes me think of the dessert plate at the end of a meal, where a waiter walks over and announces, "Here comes the meaning!" The diners chat and exchange pleasantries for a while, someone leaves the table to pay, and at last everyone walks out happy.

I'm sorry. In this essay, at the end of Getting to Know the World Again, I can't hand you that plate of "meaning."

Analog and Digital, the "realm of numbers" and the "realm of symbol and feeling," so many good and bad things are twisted together. In the text I did my best to sort it out for you, to lay it out piece by piece, but looking back at these two essays I still feel they came out messy and tangled. Cut it, and it won't part; sort it, and it tangles still.

So, what is there that we can do?

Or to put it another way: after thinking through all of this, how should we live with this world, and how should we live with ourselves?

This is an open question. I have no right to give you any settled answer.

But I can tell you about a new hobby I suddenly picked up lately: watching the clouds and the sky.

Usually a clear day is dull, even a little too saccharine. A blue sky, drifting white clouds, sunlight splashed everywhere. Quite lovely at first glance, ordinary once you've seen it often enough.

But even with an empty blue sky, I seem to have slowly learned to find pleasure in it. The sky doesn't have to be blue; it can be other colors too. And even when it is blue, every day can be a different blue, and the color shifts every hour.

The sky out the window looks one way from an empty conference room, and another way through a bright glass curtain wall.

Even dirty glass and fogged-up lenses lay a different filter over the sky.

You can watch the ground too. Shenzhen sits at a low latitude, and now and then around noon you can see the sunlight come straight down, the shadows of pedestrians and buildings falling small at their feet, and the world around you takes on a faint trace of unreality.

You can look at the buildings too. Now that I've left school, none of the buildings in view came from the hand of any great architect, of course. But the texture of light landing on a concrete wall or a glass window shifts as you walk and as time passes. The view changes step by step, and it's lovely, though a phone camera can't capture it at all.

Watching a movie in a theater is not the same as watching it on a laptop. Seeing an exhibition in person is not the same as seeing photos of the art. Chatting on WeChat is not the same as chatting in a café. Hearing a live concert is not the same as listening to lossless audio through earbuds.

Please take hold of life. Feel it. Don't let it slip away.

(The end.)

Image Photographed by the author in Shenzhen

References

  1. Incomputable 37: A Vast Resemblance Links All Things: https://www.xiaoyuzhoufm.com/episode/6063b931c62ceb1d7cf29f42 ↩

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