On translation and quantum mechanics.

On translation and quantum mechanics.

We have many ways to express ideas.  In this essay, I’ll attempt to convey my thoughts with English words.  Although this is the only metaphoric language that I know well, humans employ several thousand others – among these there may be several that could convey my ideas more clearly.

The distinct features of a language can change the way ideas feel

Perry Link writes that,

In teaching Chinese-language courses to American students, which I have done about thirty times, perhaps the most anguishing question I get is “Professor Link, what is the Chinese word for ______?”  I am always tempted to say the question makes no sense.

Anyone who knows two languages well knows that it is rare for words to match up perfectly, and for languages as far apart as Chinese and English, in which even grammatical categories are conceived differently, strict equivalence is not possible.

Book is not shu, because shu, like all Chinese nouns, is conceived as an abstraction, more like “bookness,” and to say “a book” you have to say, “one volume of bookness.”  Moreover shu, but not book, can mean “writing,” “letter,” or “calligraphy.”  On the other hand, you can “book a room” in English; you can’t shu one in Chinese.

There is no perfect way to translate an idea from Chinese words into English words, nor the other way around.  In Nineteen Ways of Looking at Wang Wei, Eliot Weinberger reviews several English reconstructions of a short, seductively simple Chinese poem.  The English variants feel very different from one another – each accentuates certain virtues of the original; by necessity, each also neglects others.

Visual appearances can’t be perfectly described with any metaphoric language.  I could write about a photograph, and maybe my impression would be interesting – the boy’s arms are turned outward, such that his hands would convey a gesture of welcome if not for his grenade, grimace, and fingers curled into a claw – but you’d probably rather see the picture.

Here’s Diane Arbus’s “Child with a toy hand grenade in Central Park, N.Y.C.” 

This isn’t to say that an image can’t be translated.  The version posted above is a translation.  The original image, created by light striking a photosensitive film, has been translated into a matrix of numbers.  Your computer reads these numbers and translates them back into an image.  If you enlarge this translation, your eyes will detect its numerical pixelation.

For this image, a matrix of numbers is a more useful translation than a paragraph of my words would be. 

From a tutorial on computer vision prepared by Amy Jin & Vivian Chiang at Stanford.

Different forms of communication – words, pictures, numbers, gestures, sounds – are better suited to convey different ideas.  The easiest way to teach organic chemistry is through the use of pictures – simple diagrams often suffice.  But I sometimes worked with students who weren’t very visual learners, and then I’d have to think of words or mathematical descriptions that could represent the same ideas.

Science magazine sponsors an annual contest called “Dance Your Ph.D.,” and although it might sound silly – can someone understand your research after watching human bodies move? – the contest evokes an important idea about translation.  There are many ways to convey any idea.  Research journals now incorporate a combination of words, equations, images, and video. 

Plant-soil feedbacks after severe tornado damage: Dance Your PhD 2014 from atinytornado on Vimeo.

A kinetic, three-dimensional dance might be better than words to explain a particular research topic.  When I talked about my graduate research in membrane trafficking, I always gesticulated profusely.

My spouse coached our local high school’s Science Olympiad team, preparing students for the “Write It Do It” contest.  In this competition, teams of two students collaborate – one student looks at an object and describes it, the other student reads that description and attempts to recreate the original object.  Crucially, the rules prohibit students from incorporating diagrams into their instructions.  The mandate to use words – and only words – makes “Write It Do It” devilishly tricky.

I love words, but they’re not the tools best suited for all ideas. 

If you’re curious about quantum mechanics, Beyond Weird by Philip Ball is a nice book.  Ball describes a wide variety of scientific principles in a very precise way – Ball’s language is more nuanced and exact than most researchers’.  Feynman would talk about what photons want, and when I worked in a laboratory that studied the electronic structure of laser-aligned gas clouds, buckyballs, and DNA, we’d sometimes anthropomorphize the behavior of electrons to get our thoughts across.  Ball broaches no such sloppiness.

Unfortunately, Ball combines linguistic exactitude with a dismissal of other ways of conveying information.  Ball claims that any scientific idea that doesn’t translate well into English is an insufficient description of the world:

When physicists exhort us to not get hung up on all-too-human words, we have a right to resist.  Language is the only vehicle we have for constructing and conveying meaning: for talking about our universe.  Relationships between numbers are no substitute.  Science deserves more than that.

By way of example, Ball gives a translation of Hugh Everette’s “many worlds” theory, points out the flaws in his own translated version, and then argues that these flaws undermine the theory.

To be fair, I think the “many worlds” theory is no good.  This is the belief that each “observation” – which means any event that links the states of various components of a system such that each component will evolve with restrictions on its future behavior (e.g. if you shine a light on a small object, photons will either pass by or hit it, which restricts where the object may be later) – causes a bifurcation of our universe.  A world would exist where a photon gets absorbed by an atom; another world exists where the atom is localized slightly to the side and the photon speeds blithely by.

The benefit of the “many worlds” interpretation is that physics can be seen as deterministic, not random.  Events only seem random because the consciousness that our present mind evolves into can inhabit only one of the many future worlds.

The drawback of the “many worlds” interpretation is that it presupposes granularity in our universe – physical space would have to be pixelated like computer images. Otherwise every interaction between two air molecules would presage the creation of infinite worlds.

If our world was granular, every interaction between two air molecules would still summon an absurd quantity of independent worlds, but mere absurdity doesn’t invalidate a theory.  There’s no reason why our universe should be structured in a way that’s easy for human brains to comprehend.  Without granularity, though, the “many worlds” theory is impossible, and we have no reason to think that granularity is a reasonable assumption.

It’s more parsimonious to assume that sometimes random things happen.  To believe that our God, although He doesn’t exist, rolls marbles.

(This is a bad joke, wrought by my own persnickety exactitude with words.  Stephen Hawking said, “God does play dice with the universe.  All the evidence points to him being an inveterate gambler, who throws the dice on every possible equation.”  But dice are granular.  With a D20, you can’t roll pi.  So the only way for God to avoid inadvertently pixelating His creation is to use infinite-sided dice, i.e. marbles.)

Image of dice by Diacritica on Wikimedia images.

Some physicists have argued that, although our words clearly fail when we attempt to describe the innermost workings of the universe, numbers should suffice.  Neil deGrasse Tyson said, “Math is the language of the universe.  So the more equations you know, the more you can converse with the cosmos.

Indeed, equations often seem to provide accurate descriptions of the way the world works.  But something’s wrong with our numbers.  Even mathematics falls short when we try to converse with the cosmos.

Our numbers are granular.  The universe doesn’t seem to be.

Irrational numbers didn’t bother me much when I was first studying mathematics.  Irrational numbers are things like the square root of two, which can only be expressed in decimal notation by using an infinite patternless series of digits.  Our numbers can’t even express the square root of two!

Similarly, our numbers can’t quite express the electronic structure of oxygen.  We can solve “two body problems,” but we typically can’t give a solution for “three body problems” – we have to rely on approximations when we analyze any circumstance in which there are three or more objects, like several planets orbiting a star, or several electrons surrounding a nucleus.

Oxygen is.  These molecules exist.  They move through our world and interact with their surroundings.  They behave precisely.  But we can’t express their precise behavior with numbers.  The problem isn’t due to any technical shortcoming in our computers – it’s that, if our universe isn’t granular, each oxygen behaves with infinite precision, and our numbers can only be used to express a finite degree of detail.

Using numbers, we can provide a very good translation, but never an exact replica.  So what hope do our words have?

The idea that we should be able to express all the workings of our universe in English – or even with numbers – reminds me of that old quote: “If English was good enough for Jesus, it ought to be good enough for the children of Texas.”  We humans exist through an unlikely quirk, a strange series of events.  And that’s wonderful!  You can feel pleasure.  You can walk out into the sunshine.  Isn’t it marvelous?  Evolution could have produced self-replicating objects that were just as successful as us without those objects ever feeling anything.  Rapacious hunger beasts could have been sufficient.  (Indeed, that’s how many of us act at times.)

But you can feel joy, and love, and happiness.  Capitalize on that!

And, yes, it’s thrilling to delve into the secrets of our universe.  But there’s no a priori reason to expect that these secrets should be expressible in the languages we’ve invented.

On Ann Leckie’s ‘The Raven Tower.’

On Ann Leckie’s ‘The Raven Tower.’

At the beginning of Genesis, God said, Let there be light: and there was light.

“Creation” by Suus Wansink on Flickr.

In her magisterial new novel The Raven Tower, Ann Leckie continues with this simple premise: a god is an entity whose words are true.

A god might say, “The sky is green.”  Well, personally I remember it being blue, but I am not a god.  Within the world of The Raven Tower, after the god announces that the sky is green, the sky will become green.  If the god is sufficiently powerful, that is.  If the god is too weak, then the sky will stay blue, which means the statement is not true, which means that the thing who said “The sky is green” is not a god.  It was a god, sure, but now it’s dead.


And so the deities learn to be very cautious with their language, enumerating cases and provisions with the precision of a contemporary lawyer drafting contractual agreements (like the many “individual arbitration” agreements that you’ve no doubt assented to, which allow corporations to strip away your legal rights as a citizen of this country.  But, hey, I’m not trying to judge – I have signed those lousy documents, too.  It’s difficult to navigate the modern world without stumbling across them).

A careless sentence could doom a god.

But if a god were sufficiently powerful, it could say anything, trusting that its words would reshape the fabric of the universe.  And so the gods yearn to become stronger — for their own safety in addition to all the other reasons that people seek power.

In The Raven Tower, the only way for gods to gain strength is through human faith.  When a human prays or conducts a ritual sacrifice, a deity grows stronger.  But human attention is finite (which is true in our own world, too, as demonstrated so painfully by our attention-sapping telephones and our attention-monopolizing president).

Image from svgsilh.com.

And so, like pre-monopoly corporations vying for market share, the gods battle.  By conquering vast kingdoms, a dominant god could receive the prayers of more people, allowing it to grow even stronger … and so be able to speak more freely, inured from the risk that it will not have enough power to make its statements true.

If you haven’t yet read The Raven Tower, you should.  The theological underpinnings are brilliant, the characters compelling, and the plot so craftily constructed that both my spouse and I stayed awake much, much too late while reading it.


In The Raven Tower, only human faith feeds gods.  The rest of the natural world is both treated with reverence – after all, that bird, or rock, or snake might be a god – and yet also objectified.  There is little difference between a bird and a rock, either of which might provide a fitting receptacle for a god but neither of which can consciously pray to empower a god.

Image by Stephencdickson on Wikimedia Commons.

Although our own world hosts several species that communicate in ways that resemble human language, in The Raven Tower the boundary between human and non-human is absolute.  Within The Raven Tower, this distinction feels totally sensible – after all, that entire world was conjured through Ann Leckie’s assiduous use of human language.

But many people mistakenly believe that they are living in that fantasy world.

In the recent philosophical treatise Thinking and Being, for example, Irad Kimhi attempts to describe what is special about thought, particularly thoughts expressed in a metaphorical language like English, German, or Greek.  (Kimhi neglects mathematical languages, which is at times unfortunate.  I’ve written previously about how hard it is to translate certain concepts from mathematics into metaphorical languages like we speak with, and Kimhi fills many pages attempting to precisely articulate the concept of “compliments” from set theory, which you could probably understand within moments by glancing at a Wikipedia page.)

Kimhi does use English assiduously, but I’m dubious that a metaphorical language was the optimal tool for the task he set himself.  And his approach was further undermined by flawed assumptions.  Kimhi begins with a “Law of Contradiction,” in which he asserts, following Aristotle, that it is impossible for a thing simultaneously to be and not to be, and that no one can simultaneously believe a thing to be and not to be.

Maybe these assumptions seemed reasonable during the time of Aristotle, but we now know that they are false.

Many research findings in quantum mechanics have shown that it is possible for a thing simultaneously to be and not to be.  An electron can have both up spin and down spin at the same moment, even though these two spin states are mutually exclusive (the states are “absolute compliments” in the terminology of set theory).  This seemingly contradictory state of both being and not being is what allows quantum computing to solve certain types of problems much faster than standard computers.

And, as a rebuttal for the psychological formulation, we have the case of free will.  Our brains, which generate consciousness, are composed of ordinary matter.  Ordinary matter evolves through time according to a set of known, predictable rules.  If the matter composing your brain was non-destructively scanned at sufficient resolution, your future behavior could be predicted.  Accurate prediction would demonstrate that you do not have free will.

And yet it feels impossible not to believe in the existence of free will.  After all, we make decisions.  I perceive myself to be choosing the words that I type.

I sincerely, simultaneously believe that humans both do and do not have free will.  And I assume that most other scientists who have pondered this question hold the same pair of seemingly contradictory beliefs.

The “Law of Contradiction” is not a great assumption to begin with.  Kimhi also objectifies nearly all conscious life upon our planet:

The consciousness of one’s thinking must involve the identification of its syncategorematic difference, and hence is essentially tied up with the use of language.

A human thinker is also a determinable being.  This book presents us with the task of trying to understand our being, the being of human beings, as that of determinable thinkers.

The Raven Tower is a fantasy novel.  Within that world, it was reasonable that there would be a sharp border separating humans from all other animals.  There are also warring gods, magical spells, and sacred objects like a spear that never misses or an amulet that makes people invisible.

But Kimhi purports to be writing about our world.

In Mama’s Last Hug, biologist Frans de Waal discusses many more instances of human thinkers brazenly touting their uniqueness.  If I jabbed a sharp piece of metal through your cheek, it would hurt.  But many humans claimed that this wouldn’t hurt a fish. 

The fish will bleed.  And writhe.  Its body will produce stress hormones.  But humans claimed that the fish was not actually in pain.

They were wrong.

Image by Catherine Matassa.

de Waal writes that:

The consensus view is now that fish do feel pain.

Readers may well ask why it has taken so long to reach this conclusion, but a parallel case is even more baffling.  For the longest time, science felt the same about human babies.  Infants were considered sub-human organisms that produced “random sounds,” smiles simply as a result of “gas,” and couldn’t feel pain. 

Serious scientists conducted torturous experiments on human infants with needle pricks, hot and cold water, and head restraints, to make the point that they feel nothing.  The babies’ reactions were considered emotion-free reflexes.  As a result, doctors routinely hurt infants (such as during circumcision or invasive surgery) without the benefit of pain-killing anesthesia.  They only gave them curare, a muscle relaxant, which conveniently kept the infants from resisting what was being done to them. 

Only in the 1980s did medical procedures change, when it was revealed that babies have a full-blown pain response with grimacing and crying.  Today we read about these experiments with disbelief.  One wonders if their pain response couldn’t have been noticed earlier!

Scientific skepticism about pain applies not just to animals, therefore, but to any organism that fails to talk.  It is as if science pays attention to feelings only if they come with an explicit verbal statement, such as “I felt a sharp pain when you did that!”  The importance we attach to language is just ridiculous.  It has given us more than a century of agnosticism with regard to wordless pain and consciousness.

As a parent, I found it extremely difficult to read the lecture de Waal cites, David Chamberlain’s “Babies Don’t Feel Pain: A Century of Denial in Medicine.”

From this lecture, I also learned that I was probably circumcised without anesthesia as a newborn.  Luckily, I don’t remember this procedure, but some people do.  Chamberlain describes several such patients, and, with my own kids, I too have been surprised by how commonly they’ve remembered and asked about things that happened before they had learned to talk.

Vaccination is painful, too, but there’s a difference – vaccination has a clear medical benefit, both for the individual and a community.  Our children have been fully vaccinated for their ages.  They cried for a moment, but we comforted them right away.

But we didn’t subject them to any elective surgical procedures, anesthesia or no.

In our world, even creatures that don’t speak with metaphorical language have feelings.

But Leckie does include a bridge between the world of The Raven Tower and our own.  Although language does not re-shape reality, words can create empathy.  We validate other lives as meaningful when we listen to their stories. 

The narrator of The Raven Tower chooses to speak in the second person to a character in the book, a man who was born with a body that did not match his mind.  Although human thinkers have not always recognized this truth, he too has a story worth sharing.