Tag Archives: parallax

reflection

We do so many things by reflex these days, and so seldom pause for reflection. We are too often too likely to view things through a single lens, and not to put them in perspective.

Let us reflect on reflection. The word reflection is formed by derivation (not inflection) from reflect, which comes from Latin re plus flectere ‘bend’: a reflection bends – or bounces – light back. A mirror is, semiotically, as Umberto Eco has explained, a prosthesis, not a sign in itself. Any object that reflects does not contain the image it reflects; what you see in it depends on your position. The reflection of a tower in a pool of water is just your line of sight reflecting to the tower in that position, and seeing the tower scattering light that was scattered onto it from countless molecules of atmosphere and surrounding matter, starting at some point with the sun: a myriad of reflections. That glowing glass building shining with the sun only shines it there for you because your line of sight bounces off it at that point towards the sun. The sun’s rays are bouncing equally off all parts of the building that face it; every square metre is glowing brightly for some eye in some location, but you only see the part that glows for your position. Reflection may lead to illumination, but what is illuminated depends entirely on your personal viewpoint.

Which is your personal perspective, of course. Perspective is simply a geometrical consequence of a single point (an eye or other lens) gathering reflected light from all around, and interpreting the diverging (or converging) lines of sight as parallel. It helps us gain a sense of the relative size of things, but what helps even more is binocular vision: add a second eye and the lines of sight converge slightly differently, and allow depth perception. When we talk about putting things in perspective, we really ought to talk about putting them in parallax.

Parallax is how a rangefinder camera – such as a Leica M-series camera, or the Ricoh that was my first camera – allows the user to focus: you line up two images at the point you want in focus, as your eyes do. On the other hand, an SLR allows through-the-lens focusing: the image bounces off a mirror onto a screen that is the same distance from the lens as the film or sensor, and you see on the screen what is in focus. This is why it’s an SLR: single-lens reflex. Reflex because the light reflects. Off the mirror.

That’s not a joke or a pun; that’s what the word reflex means: bounce-back. Some stimulus affects your nerves; you give a response automatically, like a mirror – or those Newton balls. Tack, tack; tack, tack; tack, tack…

I don’t use an SLR anymore (though I do have one). I don’t usually use a rangefinder camera, either (though I do have one). I use a camera (two of them, in fact) that shows on a screen on the back the image that is striking the sensor. This makes it smaller and lighter – quieter too (the mirror doesn’t have to flip up and down). It also means I don’t have to hold it up to my eye. Which is good because I wear glasses, but also good because when you hold a camera to your eye people react to it: they see your specular act with the prosthetic of the camera and they flinch, or turn away, or stare, or grin senselessly. The act of seeing is presented as not a passive reception but an active taking, and there is a reflex response to that.

When I hold a mirrorless camera at waist or chest level, especially a smallish one, it simply receives; few people take any notice of it. But it is still a prosthetic for my eyes, a single-lensed prosthetic giving me a different perspective from what my eyes see – different because lower, but also because it has a different angle of view, wider or narrower depending on the lens. I see things not just in perspective (as one always does) but from a different perspective. I see reflections – light bounced once or many times from its source or sources (and at night there are so many sources!), objects showing their positions because they reflect not smoothly but roughly, diffusing, scattering the light that comes to them, and shiny objects that do reflect smoothly, letting my position dictate what I see. You must know the position of what is being reflected before you can know with certainty the position of the reflector… unless there are points of opacity and diffusion on the reflector, which will allow your parallax to fix them.

When we pause for reflection, we do so to become more aware of our position and the positions of others. We do it to stop acting by reflex. Which means that, really, we pause for diffusion. And to put things in parallax, or at least to see them through another lens.

parallax

I mentioned two days ago that I recall first encountering sidereal in Isaac Asimov’s The Universe: From Flat Earth to Quasar. Another word I’m fairly sure I saw there first was parallax.

When you first see this word, you very likely assume that it has something to do with parallel. Indeed, the form accidentally gives a good clue: both words have the parallel lines ll in the middle (and, by the way, it’s just coincidence that I’m posting this on 2011.10.11), but whereas in parallel there’s a third l running in parallel with the other two, in parallax you end up with two lines x not in parallel but meeting at a certain point. So is parallax a laxity in parallelism?

The two words are not derived quite so simply. Lax is not an ancient Greek word (it comes from Latin laxus), unlike our two parallel words here. Both begin with para, meaning “beside, alongside, etc.”; both have second halves that come from allos “other”. But in parallel it’s allelos “one another”, while in parallax it’s allassein “change”. So one is “beside one another”, while the other is “alternation”.

What has this to do with stars? Well, stars aren’t all the same distance away. How do we know how far away a star is? By parallax. I’ll explain.

Let me give an example. Your eyes are two different viewpoints. Hold your finger halfway between them and the computer screen. Close one eye and look at your finger in front of the screen, or at the screen behind your finger. Now open that eye and close the other and look again. Or, more simply, just focus on the screen and notice how you see two fingers, or focus on the finger and notice how you see two screens. That’s parallax: the difference between the relative positions of two objects that are at different distances (finger, screen) when you see them from different viewpoints (left eye, right eye).

You can use basic geometry to work out the distance of the screen if you know the distance of your finger, or vice-versa, as long as you know the distance between your eyes. You just use the principle of similar triangles. In fact, that principle saved me a bit of money a few years ago. I had – still have – a 1950s-era folding medium-format camera (a Zeiss-Ikon Ikonta), which has no rangefinder and certainly no through-the-lens focusing – you turn the focus dial to the distance desired, but it’s up to you how you know what that distance is. I could have bought a rangefinder for it. Instead I measured the space between my pupils, measured the distance from my eyes to the thumb and forefinger of my outstretched arm, and made marks accordingly on the back of a business card.

(Here’s how that works. Picture a capital A, where the bases of the legs are my eyes, the legs are the lines of sight from them, the point is where the lines of sight meet on the object focused on, and the crossbar is the distance on the business card between where the lines of sight cross it – the parallax. The principle of similar triangles says that if the card, held in my outstretched hand, is halfway to the object – the height of the top part of the A is the same as of the bottom part – the distance on the card will be half the distance between my pupils; if the top part of the A is two-thirds of the total height of the A, the distance on the card will be two-thirds the distance between my pupils; and so on. So I have a bunch of pen marks on the card, and I simply note where the edge, as seen from one eye, overlaps the pencil marks, as seen from the other, when I’m focusing on the object I want to photograph.)

Parallax can be very useful in photography when you’re using a rangefinder camera such as a Leica – it imitates the parallax of the eyes, using a double finder and mirrors to produce the double image and so that the images line up when you’re focused on the right distance. Parallax for the win. But parallax can also be a nuisance if you’re using a viewfinder camera or a twin-lens reflex, if you happen to be focusing on something close enough that the parallax between what you see (through the viewfinder or upper lens) and what the film will see (through the object lens) is significant. (Yes, yes, I know, very few people use such cameras anymore. But there are indeed digital rangefinder cameras, such as the Leica M9, which I would own if I could afford it.)

And, to get to the original point, parallax can also be very useful in knowing the distance of object much farther away, such as stars. You can know the distance to a star by measuring its parallax against some other star the distance of which is known (and which can be assumed not to be moving enough to make a difference). The earth moves around the sun, and so the difference in viewing positions at different times of year produces the same kind of effect as the distance between your eyes, though you can’t see from more than one position at the same time – you have to keep track.

On a more human scale, parallax is also, of course, very useful in avoiding injury and death. Depth perception relies on parallax (and the brain’s interpretation of it). You do not want to be lax in a time of peril: if a tiger or snake – or a swinging ax – is moving towards you, or if you are moving towards a tree, you want to have a good sense of exactly how far you are from danger. You don’t want what you took to be a brobdingnagian peril far away to turn out to be a lilliputian peril much, much closer; at the very least, parallax can save you a pair o’ slacks (impending peril can be a powerful laxative).