Last night, trying to catch a cab in a Manhattan rain, it occured to me that it really shouldn’t be so surprising that so many of our systems fail exactly when we need them most. I was standing blocks from the nearest subway or bus and had no umbrella; I needed a cab to get home. But so did everyone else. Result: no cabs available for anyone. The real surprise is that we expect those systems to work at such times.
The number of available cabs is a (somewhat) efficiently determined quantity. At any moment, the supply of taxis matches the demand for private transportation. But when demand spikes, there is a scarcity of cabs. The trouble is that these demand spikes only occur infrequently – they are tail events. But more than that, they are wrong-way risk events. Not only is demand higher in terms of quantity demanded, but demand is also escalated in terms of how much people need cabs (think of this as the minimum price a person is willing to pay having gone up as well). Thus, the time I need a cab the most is the exact time it will be hardest to find.
It is in many ways a futile exercise to apply central measures to tail events. The real surprise is that we expect those systems to work.
Any system which is based on the center of the distribution will fail to give satisfactory results when tail outcomes appear, such as rainy nights or the United Nations convening. On the other hand, any system which is designed to operate smoothly 90% or 95% of the time must, by definition, be based on the center of the distribution. To deal properly with tail events, a system must either a) ignore the center or b) undergo a regime shift to deal with the tail (which is just a sneaky way of saying it should be two systems, one for the center and one for the tail). Taxis operate based on the center; therefore the system breaks down in the tail. However, tail events for cabs are generally forecastable – I would think that supply could adjust relatively easily and undergo the necessary regime change. If I drove a cab and I saw it was raining, you bet I’d be out looking for extra fares.
The BLS birth/death model which I discussed yesterday is another example. Designed to represent the manner in which businesses change over time, it must be built in accordance with normal (i.e. central) behavior. It therefore fails anytime the economy experiences sharp growth or contraction – tail events.
And how about value at risk? The analogy should be obvious by now. On the one hand, the distributional assumptions for VaR come from historically observed data. Thus, the system is based on the center. On the same hand, VaR doesn’t tell us anything about the tail event – it merely defines what constitutes such an outcome. By the time you experience the tail, you’re beyond VaR’s ability to help you. So VaR, for all its comfort and reassurance, is another system which fails to account for the periods it will be needed most. Better risk measures deal exclusively with the tail, which is to say the outcomes they are being used to evaluate.
Anyway, I got a cab after a few minutes. It was my yellow swan.
The Burj Dubai is by far the tallest building in the world, despite being unfinished. However, I find it difficult to grasp just how massive it is. A recent Gizmodo post came close to capturing its immense height (see the image below) but still, a true sense of scale is absent.
The trouble is that I have no concept of relative height when I’m looking at those images; yes, the tower looms over other buildings that I know deep down would be considered immense in their own right, but they might as well be townhouses. They provide no context because I have nothing tangible to compare them to. Meanwhile, silhouette comparisons such as this one convince me of the Burj Dubai’s height, but do little to impress any grand sense of scale:
What I need is a comparison that marries the abstraction of the silhouette with the concrete grounding of the actual photos. Once again quoting Tom Lehrer, I have a modest example here…
Turning to Google Earth, I mocked up the views from two popular Manhattan observation decks – the Empire State Building and the Rock (that’s Rockefeller Center for the non-30 Rock fans New Yorkers among you). Then, I raised the viewpoint to 2,690 feet – the height of the Burj Dubai’s hypothetical observation deck. The result is an impossible view of Manhattan which instantly captures the building’s enormous scale by putting its height in a familiar context. If you are unfamiliar with the New York cityscape, then these examples may be as abstract as the actual Dubai pictures are to me; however this is an experiment well worth repeating in your own urban backyard.
Note: Clicking the following images will launch an image gallery in a lightbox. The first image will show the view from an existing New York observation deck. Clicking the right side of that image will load the next image, which shows the same view from the top of the Burj Dubai. Click outside the lightbox to close it. Note that all the images below will load, so you can click through all five viewpoints without leaving the lightbox.
Note also: The effect is much more dramatic in Google Earth, which supplies smooth transitions between the viewpoints – like taking an elevator up the spire. But I’m having trouble embedding the 3D view here, so I hope these images suffice…
First up, the view from the ESB looking north toward Central Park. The real view is impressive but the Burj Dubai can practically see upstate:
Next, a similar view – the ESB looking northeast into midtown and across the East River. The Burj Dubai view makes the surrounding buildings look tiny:
Another view familiar to tourists – the ESB looking south toward the Financial District. From the Burj Dubai, you could see clear across New York Harbor and out into the Atlantic:
Turning now to the Rock, here’s a similar view to the south, including the Empire State Building and Chrysler Building. The Burj Dubai towers over these New York giants:
Finally, here’s another view north, this time from the Top of the Rock. The difference is unbelievable:
I hope that these visual comparisons give some greater meaning to how incredibly tall the Burj Dubai is by supplying a familiar context for its height. In a final push for perspective, we are all familiar with this iconic view of downtown Manhattan:
Typically, a helicopter would be used to capture an image from such height. But in this case – you guessed it – all you’d have to do is take the elevator. Yurtle the Turtle had nothing on this!
A very nice graphic is making the rounds (though I believe it originated in a 2007 issue of Time Magazine) which shows Manhattan’s population density by day and by night. The difference is striking:
Happily, the density bars mimic the placement of Manhattan’s skyscrapers – this follows because obviously the tallest buildings support the highest population density. What’s striking, however, is the breakdown – commercial buildings are indicated in the “day” graph and residential buildings in the “night” graph.
This means the building categories can be identified merely by time rather than any other dimension. Ordinarily, asking someone to pick out whether a building was primarily commercial or residential would probably involve a study of tenants or usage. Here we see that merely counting the daily/nightly inhabitants suffices: a clever use of data to avoid an otherwise grueling task.
Aside, the density heights have clearly been scaled for dramatic purposes. This means the two panes are not intuitively comparable; for example the daytime population seems much higher than the nighttime. While there’s certainly more people working in the city than living in it, the exponential scaling makes it difficult to see just big a difference there is.
(via Kenny Herman)
