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 Cosmos and working through the math.

CosmosK and I have been watching that new Cosmos television show.  The library had the whole set of DVDs, and she and I have both been tired enough that it’s felt nice to zonk out with some television in the evening while N is having her fifth dinner.

K really likes the show.  Things were perhaps stacked in her favor: she is a scientist, she likes Neil deGrasse Tyson, and she teaches Earth & Space Science, which covers a lot of the same topics as the Cosmos show (and is, incidentally, not the field of science either she or I was trained in – E&SS just happens to be what you need to teach if you want to work with people who get signed up for the most introductory level science class in this state.  Elsewhere I think the equivalent course is Integrated Chemistry & Physics or something?).

So, K likes Cosmos.

Whereas I have mostly failed to enjoy the show as much, even though it’s clear that a  lot of people worked very hard on it and it has some very redeeming qualities, too.

So, last night we watched the episode about Faraday’s experiments with electricity and magnetism.  And then this morning I went berserk and had to set N up for some self-directed play while I watched a video deriving the Maxwell equations.  Which is something I used to know, and probably still should, but almost a decade has passed since I last used them.  And when they were flashed up on the screen at the end of the Cosmos episode, I realized that I couldn’t think through the derivation.  That felt sad.  I’ve already been feeling sad about being very unpracticed with my math these days, to the point that shortly before N was born I picked up a book on differential equations and another covering specifically Fourier transforms.  I did not work through very much of either before she was born and have not picked them up since – as it happens, taking care of a baby can be a fair bit of work.

But my reason for feeling uncomfortable about Cosmos isn’t just that it reminds me of my own current ineptitude.

For me, the problem is that the show often seems to be contrasting stories from mythology, often Christian mythology, against stories as elucidated by science.  But all of it is presented without math, and much of it is presented without data of any kind, or even descriptions of the necessary experiments.  I have to admit, the particular episode that made me sad did a better job of that than most – many of Faraday’s experiments were described.  But, still, the Maxwell equations were tossed up at the end with no attempt at an explanation.

And I know that mathematical and scientific literacy is often described as, um, not good in this country.  And television is not a very good medium for conveying math.  I’ve watched some math videos online (Dr. Arthur Mattuck at MIT made some charming ones), and, yes, sometimes you might space out, or maybe want to pause them, or glance at the screen and read an equation wrong and feel confused.  But not everybody can pause broadcast television.  And a lot of mathematics presupposes familiarity with basic concepts that many people haven’t had a chance to feel comfortable with.

But the problem is, in my opinion, that science without math is very akin to mythology.

It becomes an expert telling you what you ought to think because he happens to be blessed with great truths, either because he can do the math or because he has studied his bible or communed with god or read the portents from an eagle overhead.  I am teaching you, and you should believe.  Whereas I think that science should be presented more humbly.

Yes, to my mind, having (once upon a time) worked through the math, science is more real than any religious claims.  But for someone who has not worked through the math, and currently can not work through it, I can see how scientific or religious claims would seem like equal mysteries.  You have to trust an expert.  Maybe you choose an expert in a white coat, maybe you chose one in a black cassock.

So I would much rather see science outreach like Cosmos attempt to guide people through the details – this is how the math works, and these are resources you could consult if this is hard, and these are experiments that you could do to reproduce these findings.  Which is hard, obviously.  I am (was?) pretty good at math, but I don’t have the training to follow serious astrophysics.  I did well with the physics of small things (quantum mechanics) during college and graduate school, but I’ve never studied the physics of big things.  I don’t really know gravity, for instance.  That’s something I’d like to take a few courses in, after I finish the novel I’m working on.  So, sure, there is a lot of complicated math involved.

But I’d like to think there are better ways to convey a respect for people’s lack of exposure to math than trying to convey science without it.  Obviously, it’s tricky.  I’m not trying to argue that the team that made Cosmos didn’t try very hard, or aren’t clever, or anything like that.  I’m just not super happy with the final product, even if I couldn’t necessarily do it better.  Like, okay, the introduction to Christian Rudder’s Dataclysm seem to do a good job of walking cheerily through some basic statistics.  And, sure, there are differences – statistics is an easier branch of mathematics for people to understand visually than some of the math you need for astrophysics, and, more importantly, Dataclysm is a book, which means there’s less worry that someone will get bored and change the channel during a brief math interlude – but I felt as though Rudder conveyed a more respectful attitude about wanting his audience to know where his claims were coming from.

And, right, it’s not as though this problem – trying to convey science sans numbers to non-scientists – is unique to Cosmos.  I feel a lot of similar frustration in reading editorials by scientists or medical doctors regarding the recent upsurge in Americans opting out of vaccines.  Which, again, I should make clear: I am a scientist.  I have been vaccinated against many diseases.  My daughter has received all her recommended vaccines on time.  But my impression is that scientists and medical doctors promoting vaccines do not always show sufficient sympathy.

Like, okay, there was a research paper claiming that vaccines cause autism, which I am not linking here.  There are research papers claiming that vaccines do not cause autism.  Sure, there are more of the latter, but for someone without enough scientific literacy to evaluate the data for themselves, you’re stuck picking someone to trust.  And, honestly, scientists and medical doctors have done some pretty terrible things, often in the guise of vaccines – you could have a pretty unpleasant weekend reading about some of these in Against Their Will: The Secret History of Medical Experimentation on Children in Cold War America.  So there are reasons why someone who was just picking whom to trust would not choose the doctors.

So, it’s not that I think the Earth is only 6000 years old.  Or that I think anyone should believe that.  I just think that, by trying to present science without math, the product is a competing narrative that still relies on faith.  As with vaccines, as with climate change.  And, who knows, maybe I am watching their show with the wrong attitude – maybe they were not hoping that people would watch and say, “oh, the Earth was actually formed 4.5 billion years ago,” maybe they were hoping that people would watch and think, “gee, that’s cool, I should learn how to figure this stuff out myself.”  But that’s not the impression that I got.