The strange subway signs of Madrid (Notes on Navigation 2)

In a previous post, I talked about my Madrid trip and the experience of navigating with a guidebook as well as the relationship between carrying a guidebook and remembering a trip.

In this post, I want to talk about navigation signs, in particular how the subway signs I encountered in Madrid were so different from those in New York City*.

In New York, a subway sign will say something like this:





This means two things. To get to subway X, go left. To get to subway Y, keep walking straight.










Here's an example. The meaning, for anyone who's lived or traveled in NYC seems fairly obvious. (Image source.)







Now, this sign, usually means that subway X is to your left but to get to subway Z, walk down this staircase that that you see going down.









For example, check out the sign on the left. It points to a staircase going down.








This sign, however, means something totally different in Madrid, as I found to my astonishment. The subway X part is pretty clear: "go to your left for subway X". The part about subway Z is however interpreted as: "to get to subway Z, keep walking straight." When I saw this sign in Madrid, I paused and looked around me for a staircase going down and was surprised to see none. After about 5 seconds of looking around and realizing that no staircase could be found anywhere remotely close, I understood what the sign meant: "keep walking and you will get to subway Z".





For an example, see this figure (to your left, source here, the image has been doctored to change the name of the station). The sign is saying "keep walking along in this direction to get to Salida". There is no staircase involved (although that's hard to see in the picture).



I am going to discuss some implications and possible reasons for this difference in what the same sign means.

First, I think this is a great example of what is sometimes called the indeterminacy of writing as a representation**. We typically understand writing -- and what are these signs if not a form of writing? -- to represent certain stable features of the world and to describe them. A prototypical instruction set, for example, has a certain sequence of steps to assemble furniture or on how to accomplish a certain task using a computer program. Sometimes the aim is to make these instructions as "complete" and as "independent" as possible. We sometimes want these instructions to "stand on their own" and at still other times, this "standing on their own" is taken as the measure of the "goodness" of an instruction set.

The example of the street-signs of Madrid shows that instructions or signs or any kind of representation can't really "stand on their own". They need the world to give them meaning (or to "interpret" them) while they give meaning to the world at the same time. Stable features of the world don't really exist but emerge from the interaction of the sign with what it represents.

So instructions for assembling a piece of IKEA furniture make sense only when you look at the components of that piece and the instructions together. The instructions for how to use a computer program to do a certain task make sense only when you're "in" in the program. Subway signs -- the arrows -- don't have any meaning by themselves unless they're paired with the world they are supposed to represent. And as the example above shows, the "down arrow" can mean two different things New York and in Madrid.

Here's Agre on this:

The work of relating a text [in our case, the subway signs -- SAK] to a concrete setting -- looking around, poking into things, trying out alternative interpretations, watching someone else, getting help -- will generally be both "mental" and "physical", though it is best not to distinguish. Relating a text to a concrete setting takes work because the text might be relevant to the situation in a great variety of ways. The text has a great deal of "play", so that much of one's interpretive effort must wait until the time comes. This is the opposite of extracting a "meaning" from a text as soon as it arrives. The point is not that interpretation is wholly unconstrained by the text; rather, interpretation is constrained jointly by the text and by the circumstances in which it is interpreted.

Second, why does the "down arrow" come to mean two different things in New York and Madrid? Could this be a quirk of the Spanish language? E.g. perhaps in Spanish it may be more common to say "Stick to this path" rather than saying "Go straight ahead"? I am not sure and in any case, it doesn't seem like a good explanation anyhow (for which see below).




If you take a look at this page which has directions signs from many airports around the world (some are shown above). You can see that the Berlin and Istanbul airports have signs like those of Madrid i.e. the "down arrow" representing "go straight ahead" while Zurich, Singapore and Warsaw have signs like NYC i.e. the "up arrow" representing "go straight ahead". I don't think anymore that this has to do with "quirks of language". I do think this would be a fascinating research question: how did these simple arrow signs come to mean what they mean in different places?

Finally, here's a thought. If a gaping staircase does open up in a straight path in Madrid (as it does, say, on 42nd street in NYC when one walks between the 1 and the A trains), how would they represent it in a sign? I can't remember anything from my trip there so I would assume such things just don't occur all that much. But my hunch is that they would use a "down arrow", the same thing they use to show "walk straight ahead". This only proves further the indeterminacy of signs by themselves. A sign only means something when paired with what it shows. A "down arrow" above a staircase points to a staircase, the same "down arrow" when above a straight path tells me to "walk straight ahead."

Related posts: Notes on navigation.

* This post would have been so much better if I'd actually taken pictures of those strange signs. Alas, but no. Instead I'll be using diagrams and photos that I found on the web. Yay, Flickr and the Creative Commons License!

**For a good introduction to what this is, see Phil Agre's great paper: Writing and Representation.)

Economics and Sociology: What Scott Sumner's defense of EMH really proves

(Photo courtesy Flickr.)

Via John Quiggin, I came across (and really liked!) this piece by Scott Sumner defending Eugene Fama's Efficient Markets Hypothesis (EMH).

I interpret him as saying the following:

1. The claim that a "bubble" exists when asset prices violate economic "fundamentals" is full of s*^#. Because there's no (algorithmic, mathematical) way of knowing what the "fundamental" price of an asset is. Hence, there's no sure-shot (again, read algorithmic) way of predicting a bubble; people who make it sound really easy (take asset prices, compare them with the "fundamental" price, find the difference, and voila, you know if there's a bubble) don't know what they're saying.
2. Yes, people do predict bubbles and they have a 50/50 chance of being right. No one has been right 100% of the time, and certainly, no algorithm. It's only in retrospect, with 20/20 hindsight that one can know a bubble exists, because it's only in hindsight that one can know the factors that went into making a bubble.
3. The reason that people do keep predicting bubbles is because a "cognitive illusion" is at work here. Because they think they can predict bubbles but they really can't because they end up being wrong 50% of the time. If they build models that predict bubbles, the models will only work 50% of the time too.
   

I think this is all fairly persuasive but to me, it points to a very different conclusion, one that he almost certainly wouldn't agree with. Here it is.

Economists are famously open* about the fact that they consider their discipline to be superior to most other social sciences, like sociology and political science. More rigorous, more empirical, etc. etc. Of course, sociologists disagree.

What Sumner's piece reveals is that simply using a lot of mathematics in your models doesn't really guarantee that your discipline is any more rigorous than, say, sociology. (I don't mean that sociology is not rigorous, I am just saying economics isn't more rigorous than sociology, like, say, physics is. Or, in other words, the social sciences and the natural sciences are different sorts of beasts and economics is a social science, despite all its pretensions to be otherwise.) Sumner seems to be saying that is impossible to construct a general-purpose algorithm (or mathematical model, take your pick) that is able to predict a bubble correctly every single time. To perceive that a bubble exists (and more importantly, to do it before it bursts and takes us all down with it) requires careful interpretation, not a derivation.

It turns out people do predict bubbles, even if they are wrong 50% of the time. Sumner thinks this is because they have a "cognitive illusion". This is wrong-headed. I think what this says is that bubble-prediction seems to be some kind of lived-in, embodied, practical skill that people acquire by living in the world and being a part of it (so of course, they think they can predict bubbles). So I can feel that housing prices are too high, and will crash, and of course I can use mathematical models to justify it to others, but that feeling (or rather, intuition) is based on far more than what that any mathematical model (or algorithm) can capture. In other words, knowing that a bubble exists is a tacit skill, to use Michael Polanyi's phrase, and therefore is something that just can't be captured in a general-purpose model that works every single time. It needs to be done on a case-by-case basis.

So consider this scenario. Person A predicts that our current situation is a bubble and person B says it is not. Person A has a model and person B, perhaps, has one too. Then it is impossible to say who is right, A or B, and be right, every single time. And the decision can certainly not be made just by looking at each model. One needs to see the assumptions the model is based on, the factors a model may overlook, or something else altogether. In other words, it is not only impossible to construct a general-purpose algorithm to predict bubbles, it is also impossible to construct an algorithm that can tell us whether A or B is right. (This, of course, is Thomas Kuhn's point in Structure, only he talks about competing scientific paradigms.)

Sumner's post, it seems to me, leads inexorably to the conclusion that economists stop looking for "generalities, principles" of the economy as a whole (or at the very least, stop pretending that they possess some methodology that is superior to the other social sciences). That a "unified social science" is not really going to materialize and we (all of us social scientists) are all better off looking into issues (in this case, bubbles) on a case-by-case basis. Seems to me that this is something that sociologists and anthropologists have long acknowledged.

Would this be a completely wrong interpretation?

* Yes, even that anti-EMH Paul Krugman):

As for social sciences other than economics, I am interested in their subjects but cannot get excited about their methods -- the power of economic models to show how plausible assumptions yield surprising conclusions, to distill clear insights from seemingly murky issues, has no counterpart yet in political science or sociology. Someday there will exist a unified social science of the kind that Asimov imagined, but for the time being economics is as close to psychohistory as you can get.