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).