March 7, 2011 31 Comments
I’m kind of feeling my way, here, trying to work out how to explain a lifetime of treading my own path, and the comments to yesterday’s post have shown me just how far apart we all wander in our conceptual journey through life. It’s difficult even to come to shared definitions of terms, let alone shared concepts. But such metaphors as ‘paths’ and ‘journeys’ are actually quite apt, so I thought I’d talk a little about the most important travel metaphor by far that underlies the work I’m doing: the idea of a map.
This is trivial stuff. It’s obvious. BUT, the art of philosophy is to state the blindingly obvious (or at least, after someone has actually stated it, everyone thinks “well that’s just blindingly obvious; I could have thought of that”), so don’t just assume that because it’s obvious it’s not profound!
So, imagine a map – not a road atlas but a topographical map, with contours. A map is a model of the world. It isn’t a copy of the world, because the contours don’t actually go up and down and the map isn’t made from soil and rock. It’s a representation of the world, and it’s a representation with some crucial and useful correspondences to the world.
To highlight this, think of a metro map instead, for a moment. I think the London Underground map was the first to do this. A metro map is a model of the rail network, but unlike a topographic map it corresponds to that network only in one way – stations that are connected by lines on the map are connected by rails underground. In every other respect the map is a lie. I’m not the only person to have found this out the hard way, by wanting to go from station A to station B and spending an hour travelling the Tube and changing lines, only to discover when I got back to the surface that station B was right across the street from station A! A metro map is an abstract representation of connectivity and serves its purpose very well, but it wouldn’t be much use for navigating above ground.
A topographical map corresponds to space in a much more direct way. If you walk east from where you are, you’ll end up at a point on the map that is to the right of the point representing where you started. Both kinds of map are maps, obviously, but they differ in how the world is mapped onto them. Different kinds of mapping have different uses, but the important point here is that both retain some useful information about how the world works. A map is not just a description of a place, it’s also a description of the laws of geometry (or in the case of metro maps, topology). In the physical world we know that it’s not possible to move from A to B without passing through the points in-between, and this fact is represented in topographical maps, too. Similarly, if a map’s contours suddenly become very close together, we know that in the real world we’ll find a cliff at this point, because the contours are expressing a fact about gradients.
So a map is a model of how the world actually functions, albeit at such a basic level that it might not even occur to you that you once had to learn these truths for yourself, by observation and trial-and-error. It’s not just a static representation of the world as it is, it also encodes vital truths about how one can or can’t get from one place to another.
And of course someone has to make it. Actually moving around on the earth and making observations of what you can see allows you to build a map of your experiences. “I walked around this corner and I saw a hill over there, so I shall record it on my map.” A map is a memory.
Many of the earliest maps we know of have big gaps where knowledge didn’t exist, or vague statements like “here be dragons”. And many of them are badly distorted, partly because people weren’t able to do accurate surveys, and partly because the utility of n:1 mapping hadn’t completely crystallized in people’s minds yet (in much the same way that early medieval drawings tend to show important people as larger than unimportant ones). So maps can be incomplete, inaccurate and misguided, just like memories, but they still have utility and can be further honed over time.
Okay, so a map is a description of the nature of the world. Now imagine a point or a marker on this map, representing where you are currently standing. This point represents a fact about the current state of the world. The geography is relatively fixed, but the point can move across it. Without the map, the point means nothing; without the point, the map is irrelevant. The two are deeply interrelated.
A map enables a point to represent a state. But it also describes how that state may change over time. If the point is just west of a high cliff face, you know you can’t walk east in real life. If you’re currently at the bottom-left of the map you know you aren’t going to suddenly find yourself at the top-right without having passed through a connected series of points in-between. Maps describe possible state transitions, although I’m cagey about using that term, because these are not digital state transitions, so if you’re a computery person, don’t allow your mind to leap straight to abstractions like state tables and Hidden Markov Models!
And now, here’s the blindingly obvious but really, really important fact: If a point can represent the current state of the world, then another point can represent a future state of the world; perhaps a goal state – a destination. The map then contains the information we need in order to get us from where we are to where we want to go.
Alternatively, remembering that we were once at point A and then later found ourselves at point B, enables us to draw the intervening map. If we wander around at random we can draw the map from our experiences, until we no longer have to wander at random; we know how to get from where we are to where we want to go. The map has learned.
Not only do we know how to get from where we are to where we want to go, but we also know something about where we are likely to end up next – the map permits us to make predictions. Furthermore, we can contemplate a future point on the map and consider ways to get there, or look at the direction in which we are heading and decide whether we like the look of where we’re likely to end up. Or we can mark a hazard that we want to avoid – “Uh-oh, there be dragons!”. In each case, we are using points on the map to represent a) our current state, and b) states that could exist but aren’t currently true – in other words, imaginary states. These may be states to seek, to avoid or otherwise pay attention to, or they might just be speculative states, as in “thinking about where to go on vacation”, or “looking for interesting places”, or even simply “dropping a pin in the map, blindfold.” They can also represent temporarily useful past states, such as “where I left my car.” The map then tells us how the world works in relation to our current state, and therefore how this relates functionally to one of these imagined states.
By now I imagine you can see some important correspondences – some mappings – between my metaphor and the nature of intelligence. Before you start thinking “well that’s blindingly obvious, I want my money back”, there’s a lot more to my theories than this, and you shouldn’t take the metaphor too literally. To turn this idea into a functioning brain we have to think about multiple maps; patterns and surfaces rather than points; map-to-map transformations with direct biological significance; much more abstract coordinate spaces; functional and perceptual categorization; non-physical semantics for points, such as symbols; morphs and frame intersections; neural mechanisms by which routes can be found and maps can be assembled and optimized… Turning this metaphor into a real thinking being is harder than it looks – it certainly took me by surprise! But I just wanted to give you a basic analogy for what I’m building, so that you have something to place in your own imagination. By the way, I hesitate to mention this, but analogies are maps too!
I hope this helps. I’ll probably leave it to sink in for a while, at least as far as this blog is concerned, and start to fill in the details later, ready for my backers as promised. I really should be programming!