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 irrational numbers.

Picture 3It was Pi Day over the weekend.  March fourteenth.  Which is something a lot of scientifically- and mathematically-inclined people already celebrate.  A friend of mine who’s currently a professor of economics stumbled across a sidewalk where local children had used chalk to write out many decimal points, then filmed himself walking along, recording his footsteps tromping along the digits.  His film was about two and a half minutes, which means he recorded about a thousand digits… a tiny bit of pi.

Which is cute.  A nice way to convey the un-ending, patternless strings that you get from irrational numbers (although any irrational number would do to show this; pi just happens to be the most famous, even though the coolest is Euler’s number e, in my opinion).  You could walk along a representation of pi for a long, long time and it would never look quite the same.

But I think there’s a slightly cutesier way to convey how strange irrational numbers are.  And this one works for you liberal arts majors out there, too!  Like, okay, let’s imagine two things to start: 1) You’re trying to write a short story, and, 2) You and some friends have decided to use a code to represent the alphabet, maybe something like 01 for a, 02 for b, 27 for A, 28 for B, and so on through all the uppercase and lowercase letters.  Might be worth throwing in some punctuation, too… you’ll have the numbers 73 through 99 waiting for you, so that’s a lot of special characters you could cram into your code.

Given those two assumptions, the neat thing about pi is, it already wrote your story.  Hamlet is in there, too.  Every work of literature you’ve ever loved, snuck into pi in code.  Because the series of digits goes on forever, and because the appearance of digits one to the next is (as far as anyone knows) patternless the entire way, all the literature that’s ever been made and all the literature that ever will be is already there, hiding deep in pi.