The comedian Eddie Izzard has a bit in which he says the only French he knows is “the monkey is on the branch”, “the mouse is beneath the table”, and “the cat is on the chair”, so every time he goes to France he has to carry a monkey, a cat, a mouse, and a chair with him just so people won’t think he’s crazy.
This is a joke, so I feel compelled to ruin it. The reason why this is funny is because carrying a monkey, a cat, a mouse, and a chair every time you make a cross-Chunnel jaunt is absurd. You have to feed the monkey, the mouse will probably escape, and to carry the chair you have to take your arm out of commission by sticking it through the slats. These objects are heavy. It’s much easier to learn the damn French words, because those are light. This is obvious, sure, but what do “heavy” and “light” mean exactly? Something to do with monkey chow, a mouse cage, and slats, I guess. I have a general sense of it, but outside of a specific context I have a hard time characterizing the difference. Some things are hard and some things are easier. Physical objects fall into the first category, and language falls into the second category. At a first cut, let’s just leave it at that.
In semiotics, following the pioneering work of Ferdinand de Saussure, one makes a distinction between a signifier and a signified. Roughly speaking the signifier is a linguistic object and the signified is the real world entity to which the linguistic object refers. These two things are considered two parts of a whole called a sign. Conventionally one draws a sign as a circle, with a picture of the signified in the upper half and the signifier in the lower half.
This can seem simple to the point of vacuousness, but it actually makes some substantive claims: there are two kinds of things (not five, not three), there is a mapping between specific instances of these two kinds, and understanding language means understanding that mapping. You can spend a lifetime going back and forth over these claims–affirming, denying, and recombining them. To that end, the picture above is helpful because it lends itself to creative defacement. Perhaps you draw little thought bubbles around one or both of the halves’ contents, indicating that what we take to be reality is actually just the creation of our own minds. Or you slyly observe that the upper semi-circle contains not the actual shirtless Ryan Gosling but rather a picture of him, which is itself another signifier. And so forth. It’s up to you to decide which of these avenues are fruitful, but the notion that language operates on pairs of different kinds of things is a good starting point, because this is probably the simplest way to represent a notion of aboutness.
Heterogeneous pairs have been on my mind lately for quite different reasons: because they come up in computer programming. In particular the notion that keeps arising again and again in the programming realm is that of a pair as an index. Database rows have primary keys, files have filenames, locations in memory have pointers. In software, the notion of an index and an indexed thing forming a unified whole tends not to be foremost on programmers’ minds (largely because it is such a useful concept that programming languages strive to make it transparent), but hardware constraints make the notion of relative size a matter of daily concern. Say you are writing a program that processes images. A typical image file might have a size on the order of a thousand kilobytes. A byte is 8 bits, so let’s say a picture is worth 8,000,000 bits of information–that is: 8,000,000 answers to individual yes/no questions along the lines of “Does this tiny blob of color go here?” As a practical matter, when you write the program you won’t make multiple copies of each eight million bit array that corresponds to a particularly compelling picture of Kim Kardashian, Ryan Gosling, or what have you. Instead you will store the picture at some particular location in your computer’s memory, and then as needed you will reference the picture–with its full sexy payload–by means of an integer index into that memory. This integer is called a pointer. At this particular moment in the history of computer hardware, the pointer’s value will lie in the range [0, 264), but the specific values don’t matter so much. If you want to make reference to a Ryan Gosling picture stored in memory, it is not necessary to describe the particulars of his well-developed pectorals, meltingly boyish smile and so forth. It is sufficient to say, “picture number 542”.
In the computer realm, size is easy to quantify. We can count the number of bits in a pointer (64) versus the number of bits in the thing to which to pointer refers (8,000,000 or so). Imagine a sack of flour that weights sixty-four pounds versus one that weighs eight million pounds. Which one is light and which one is heavy? The analogy to physical weight proceeds readily, without any distracting sidetrips about how one goes about feeding a monkey.
So both semiotics and programming employ the concept of a heterogeneous pair. The former articulates a notion of aboutness to which we’d like to add a notion of quantity. The latter takes aboutness for granted, but can measure quantities of information very precisely. Maybe–pace warnings about facile analogies–the one could be used to illuminate the other. We could decide what goes above and below the Saussurean line by finding ways to count the number of bits in each.