A Physicist Solves the City | Hacker News Reader

A Physicist Solves the City

nytimes.com

189 pointsyarapavan55 comments

If you analyse reams of statistical data for patterns, it's really unsurprising that, after the fact, a few patterns (sewer system, traffic, crime rates and AIDS cases) cherry picked for the fact that they match well .. well, matches very well. In other words, it's not surprising that large data sets have patterns. What would be surprising would be if a very large number of variables were predictable, but that does not seem to be the case.

There's a section in The Black Swan devoted to the fallacy that we tend to project the fact that we understand the rather narrow field of physics very well - to the extend where we can predict things in that domain reliably - to an expectation that we can do the same for other fields, when in fact, it's physics that's the outlier in our ability to understand it so well.

In the end all his efforts seems to come down to the conclusion that cities exists because they provide economies of scale. I couldn't provide statistical proof for that fact to save my life, but still .. well, duh?

As West is a highly trained physicist, I'll believe he's a bit more statistically careful than that. In the most crude, there's a thing called the Bonferroni correction which helps to counteract cherry picking effects. Beyond that there are a great deal of other methods to account for overconfidence.

If we were not able to identify a small number of relevant patterns in a large sea of options, how would we learn anything?

If you've got a mountain of data and are willing to run a lot of models you can indeed identify ones with good tradeoff between prediction and generalization errors. It's very possible that some of your models are weaker than you expect due to cherry picking, but it's even more possible you've identified some useful trends.

As you said, he seems to be restating very common knowledge about economies of scale. Since he's not saying anything terribly surprising, I don't think there's much need to get up in arms about multiple comparisons.

Moreover he's looking for the on-average rates of growth of these economies of scale and identifying outliers which will likely be interesting. I think it's pretty exciting research.

I'm surprised he used a biological explanation, which I find to be faulty. I would have guessed that the growth and evolution of a city is more like that of a star. Every city lies somewhere along a "hertszprung-russell" diagram of urbanity.

He works with the Santa Fe Institute that specializes in studying complex adaptive systems. What all CAS have in common is the organic growth patterns that seem endemic to biological organisms. Also, if you consider the fundamental building block of the city to be its people rather than the physical infrastructure, then you are dealing with a biological system. This is no different than looking at an ant colony as a superorganism - yeah they have some dirt and tunnels and some rocks, but for the most part the important factor in the colony is the mass of individual ants.

Interesting point, which brings up a pseudo-philosophical question, should we consider humans living in large cities a kind of super-organism in a similar manner?

I couldn't provide statistical proof for that fact to save my life, but still .. well, duh?

There's an enormous difference between saying "I think X is true," and "I have significant evidence based on observation and theory to support the conclusion that X is true."

Also: http://lesswrong.com/lw/im/hindsight_devalues_science/

“There are always going to be people who say, ‘What about the crayfish?’ ” he says. “Well, what about it? Every fundamental law has exceptions. But you still need the law or else all you have is observations that don’t make sense. And that’s not science. That’s just taking notes.”

And a little take home message for start-ups (and companies in general):

    The graph reflects the bleak reality of corporate growth, in which efficiencies 
    of scale are almost always outweighed by the burdens of bureaucracy. “When a 
    company starts out, it’s all about the new idea,” West says. “And then, if the 
    company gets lucky, the idea takes off. Everybody is happy and rich. But then 
    management starts worrying about the bottom line, and so all these people are 
    hired to keep track of the paper clips. This is the beginning of the end.”

This is not a revolutionary idea. Economists have studied the productivity curves of businesses for decades. "Diminishing marginal returns" is part of most basic microeconomics courses. Here's the page where Mankiw describes it using the enthralling example of "Caroline's Cookie Factory":

http://books.google.com/books?id=oRgQ2goeFzwC&lpg=PP1...

Apparently, though, this "discovery" made a real impression on this NY Times writer. I don't like it when people take well-established ideas from another field, dress it up in new lingo and statistics ("corporate productivity, unlike urban productivity, was entirely sublinear") and try to market it as new research.

That was the impression I got from a lot the results claimed by this guy; I think he's wrong to pass off gross oversimplifications as scientific progress. I can see why he gets cited, and it's part of the mistake with correlating citations with influence: they were probably mostly negative mentions. To be honest this behavior is a little trollish. As we can see here, he gets his publicity for it.

Somebody said below "Title should be 'A Physicist Plays Economist'"--yes, indeed.

I like that he is using his physics background to find equations for cities, however, is it really a big surprise that if you know a cities area, country and population you can guess the average income to 85% accuracy? To me that seems rather obvious.

(population * (personal space)) / area = average income

solve for personal space:

((average income) * area) / population = personal space

..............

Using wikipedia we can find the population of San Francisco and the area. We can now solve for how much personal space people like in the USA.

((average income) * area) / population = personal space

I can only find per capita income for counties...

City and County of San Francisco:

average per capita income: $34,556

area: 600.7 km²

population: 776,773

($34,556 * 600.7) / 776,773 = 26.7

So USA's personal space is 26.7 $km² per person

...............

Lets try Los Angeles County:

average per capita income: $20,683

area: 10 517.9 km²

population: 9,802,800

remember our original equation:

(population * (personal space)) / area = average income

(9,802,800 * 26.7) / 10 517.9 = $24,884

$24,884 / $20,683 = 83%

Not the 85% goal we wanted but Im working with counties and not actual cities.

sources:

http://www.wordiq.com/definition/San_Francisco_County,_Calif...

http://www.wordiq.com/definition/California_locations_by_per...

http://www.wordiq.com/definition/Los_Angeles_County,_Califor...

"Every fundamental law has exceptions."

That's not my understanding of the word "law". Have I been mistaken all this time?

Even Newton's laws had exceptions, i.e. general relativity. No theory in physics is perfect, and neither are the theories in this article (they're just a lot less perfect). The usefulness of laws is in their simplicity and their predictive power.

If ever there was or will be a time when special relativity was or will be violated, I will be extraordinarily surprised. Newton's law wasn't fundamental, it was just a law, while special relativity may be the most fundamental law we have considering it manifests itself in everything. That's the difference between a mere law and a fundamental law.

Theories aren't laws. Laws are observations. Gravity is a theory: why do balls fall to the ground when you throw them? Gravitation is a law: balls fall to the ground when you throw them.

Relativity isn't an exception to Newton's law, it's just more accurate. An exception would be a ball not falling to ground after you threw it in the air.

There are precious few Laws like that. Gravity, Constant Proportions, Thermodynamics, etc. While they're taught as a separate, somehow more powerful thing than theory, really they cannot exist without a theoretical framework. Entropy and enthalpy don't exist outside of theory, gravity "always follows the inverse square law" under current beliefs about gravity and theoretical assumptions (when are there ever truly only two interacting bodies?)

I prefer to think of laws as statistical correlations that are so repeatable that their variance has gone to zero. These are words that only have meaning in context of a model though. They're embedded in theory, necessarily wrong theory.

Laws are just what scientists called what they thought were fundamental theories back in their more arrogant days; they've since matured and no longer promote any theory to law because they know they're probably wrong.

Newtons laws are theories just as Einsteins theories are just like Newtons laws. If Newton invented his laws today, we'd call them theories, not laws.

No theory is known to be perfect, but it can very well happen that we have perfect laws of physics in the future.

I prefer to look at general relativity not as exceptions to Newtons Laws but rather, Newton's Laws as a special limiting case of the more general theory of relativity.

So I posit a theory: For any given theory, there are areas outside its boundaries where it breaks down and can say nothing or only nonsense but that doesn't make it wrong (which need not be binary) - so long as it is contained in a more general and more accurate theory. We can then only measure its correctness based on how well it predicts within its domain and then how well it folds into the future more general theory.

Depends of what you mean by fundamental. Every law is an incomplete description of a part of the universe. One of first things you do when coming across such a law, is test it. This not only determines whether it is valid, but, perhaps more importantly, where and when it is valid.

Think for example of Newton's law of gravitation. It works remarkably well in all the cases available at the time, with, perhaps[1], one exception: the behavior of Mercury was a bit funky.

Wait a few hundred years, and here comes a young jewish scientist called Einstein with a strange new law of gravitation that not only agrees perfectly with Newton in most cases, it also takes care of all the nagging exceptions that are known. We're still looking for further [2] exceptions to Einsteins general theory of relativity, but I have no doubt that eventually some one else will come along with a new fangled theory that will take care of those as well.

This is how science works. Laws are idealized approximations to the real world with well defined (although sometimes unknown) boundaries of applicability. Whenever we find ourselves too constricted by them we eventually create a better description that, by adding some complexity, will remove or at least expand, some of the boundaries.

If this is true in something as fundamental as gravitation, it will be even more so in anything that deals with Human Behavior. People like to be different (or at least thing they are) but there are basic constants and mechanisms that are present in each of us.

[1] I'm not sure whether or not the problem with Mercury was already known by Newton's time.

[2] So far the only place where it doesn't seem to work well is when quantum effects are present as well.

1: It was, and they assumed it was due to the hypothetical planet Vulcan http://en.wikipedia.org/wiki/Vulcan_%28hypothetical_planet%2...

2: The Voyager anomaly, the rotation of galaxies, black holes.

The rotation of galaxies is assumed to be because of dark matter - but that's just giving a name to it - it doesn't actually answer anything.

It's not so much about the exceptions as it is about the domain the law applies in. Someone else mentioned Newtons law of gravity: In the very large domain of "stuff we can see and touch", Newtons law works perfectly. Even on the scale of planets, it's so close that it took centuries to detect that it was off. On the scale of atoms, it breaks down, so we can define the domain of Newtons law as the interval "bigger than molecules to the solar system" in which it can reliably be applied.

The bigger and better defined the domain is, the more useful the law. If the domain that you can reliably apply the law to is ill defined or has many unpredictable exceptions, it's probably not a very good law.

Unfortunately, yes, sorta.

What most science is about is building a mathematical model of the thing under description.

As software engineers, we know that models and other abstractions break down around the edges, especially when the abstractions leak.

No difference in scientific models. Just because he has a PhD in physics and a white coat doesn't mean that his models (in physics) aren't just as leaky as a software model. His are just better-defined.

It could be formulated as: "No fundamental law has an infinite application domain."

Every law is broken outside curtain boundaries.

If you are risk averse, then no.

Otherwise, it is a well known fact that disregarding [or exempting oneself from] the law can have more gains [sometimes even if you get caught]. You get a competitive advantage by exploiting the exceptions [if there aren't any, then you make yourself one].

I think http://lesswrong.com/lw/hr/universal_law/ can clear up some confusion. The key paragraph is this:

Sometimes - very rarely - we observe an apparent violation of our models of the fundamental laws. Though our scientific models may last for a generation or two, they are not stable over the course of centuries... but do not fancy that this makes the universe itself whimsical. That is mixing up the map with the territory. For when the dust subsides and the old theory is overthrown, it turns out that the universe always was acting according to the new generalization we have discovered, which once again is absolutely universal as far as humanity's knowledge extends. When it was discovered that Newtonian gravitation was a special case of General Relativity, it was seen that General Relativity had been governing the orbit of Mercury for decades before any human being knew about it; and it would later become apparent that General Relativity had been governing the collapse of stars for billions of years before humanity. It is only our model that was mistaken - the Law itself was always absolutely constant - or so our new model tells us.

I remember my physics teacher explained this one day. He said:

We start with a poor but general understanding, that things fall toward the ground. This is like a big square of stone, it's familiar but undefined and for most purposes it's useless.

We advance our understanding, chipping away at the stone to reveal a model that is more practical. To an understanding that is beyond simply observations. Objects fall at 9.81m/s/s. You'v now got an octagonal disc of stone, you could run a cart on it, but you probably wouldn't get far before you break your tail bone.

Then we go beyond just passively observing and begin testing. We find data, compile it and test it against models. This is like using a finishing chisel and sand paper. You get the Theory of Relativity, it's smooth, it's polished and it's a perfect wheel.

Now just wait for someone to invent a hover car and your wheel and the theory of relativity are old news.

Jonah Lerer, the author of the article is a brilliant guy, but a lot of his writing makes interesting claims that don't really hold up when you get into the details. In Geoffrey West he seems to have found his perfect subject: "While listening to West talk about cities, it’s easy to forget that his confident pronouncements are mere correlations, and that his statistics can only hint at possible explanations."

And as davidmathers pointed out: "Every fundamental law has exceptions."

Lehrer finds a really interesting angle to explain something, tries to apply that to a lot of things, and that's when it falls apart. See http://www.amazon.com/Proust-Was-Neuroscientist-Jonah-Lehrer...

About half-way down the page, the article said this:

Small communities might look green, but they consume a disproportionate amount of everything. As a result, West argues, creating a more sustainable society will require our big cities to get even bigger. We need more megalopolises.

That's what they call "burying the lead". Or "lede", depending on what country you're in. It should have been in the very first sentence of the article: holy crap, big cities are green. It's a counterintuitive assertion, and sure to draw in readers. Instead, the whole first paragraph is a bunch of human-interest waffle that has nothing to do with anything. I almost stopped reading right there.

I found the lead-in fascinating, the "search of fundamental laws". I have to admit that the first paragraph wasn't about that directly, but I also found it intriguing ("allergic to food", heh) - probably because I identify with the absent-minded professor portrayed (or would like to).

The "lead" of a story is partly a matter of perspective. Eg. did Einstein reveal a deeper view of reality, or facilitate nuclear weapons, or help end a war, or prove everyone wrong, or get away with crazy hair? The "lead" depends on the reader.

The idea that increasing density is good for the environment has been conventional wisdom among environmentalists and planners for decades. (Synonyms that are often used for popular appeal include 'transit-friendly,' 'smart growth,' and 'anti-sprawl.') If West has made progress in quantifying this effect, that's great, but the conclusion alone would be much too banal to be the lede of an article in 2010.

I think you underestimate how banal people in 2010 are willing to make a lede. As evidence for this, I offer the first paragraph of the article in question.

The other day I have been looking at some of the large cities and countries. I'm a medicine student and if you have had the change for a deep study of the human body, you'll notice that humans and cities are quite similar.

A Country is the human body. Cities are like organs. They have similarities, but each one has got a special function/strength (industrial, financial, agricultural). Houses and building are like cells. Roads are like vessels. People and different products are like proteins, electrolytes, and chemical components. People channel in roads, they go by foot but also by car (different chemical components has car-like proteins to drive them in blood).

Let's get into a cell. It has different components: Wall, Mitochondria, kernel, ribosome... A house has similar things. It has a wall like the cell has, with openings which aren't just holes (doors in the house and special kind of proteins in the cell).

I really can't describe that clearly, due to my poor English and also to the complexity of the idea. I hope you get the idea and you try to expand it.

Another interesting point is how they both started. The city (in the dark ages) was very simple, and now has progressed. The same way for the human which started from a cell that has multiplied and become a fully functioning animal.

Now cities don't start from 0, just like human. It doesn't need another billion year for a human to be created, but only 9 months, which is the same in the city.

I hope you get the idea, sorry for the bad release.

It is important avoid confusing metaphors for scientific theories.

Don't harsh on this. Analogical reasoning is where scientific theories come from. Well, perhaps from there and from elegant math.

I thought it was a very interesting metaphor, and you can start thinking of diseases of the national infrastructure, or the infrastructure of the body.

Science shouldn't stop at metaphor, sure. But it often starts there! Think about concepts from fluid dynamics that leaked into electromagnetism.

This struck me an interesting, and very pertinent.

Why are corporations so fleeting? ... Bettencourt and West discovered that corporate productivity, unlike urban productivity, was entirely sublinear. As the number of employees grows, the amount of profit per employee shrinks ...The graph reflects the bleak reality of corporate growth, in which efficiencies of scale are almost always outweighed by the burdens of bureaucracy. “When a company starts out, it’s all about the new idea,” West says. “And then, if the company gets lucky, the idea takes off. Everybody is happy and rich. But then management starts worrying about the bottom line, and so all these people are hired to keep track of the paper clips. This is the beginning of the end.

I assume this is why revenue per employee is an important measure of company productivity/health?

NASDAQ 100 Revenue per Employee

http://www.jbryanscott.com/2009/02/07/nasdaq-100-revenue-per...

Its important because the more employees a companies has, the more overhead it has, in the form of salaries, and in the services to support the employees, healthcare, etc. The company also loses its ability to iterate quickly, to rapidly respond to change etc. This would be fine, if revenue was to increase proportionally, but if this does not occur (as the article found) then companies are more susceptible to market changes, and its easier to lose more faster. Its the "beginning of the end" as the article put it.

This implied that the real purpose of cities, and the reason cities keep on growing, is their ability to create massive economies of scale, just as big animals do.

Perhaps a better analogy: large corporations exist because they can lower the cost of transactions to produce certain products. Cities exist because conditions and spatial concentration can also reduce the cost of transactions.

>According to the data, whenever a city doubles in size, every measure of economic activity, from construction spending to the amount of bank deposits, increases by approximately 15 percent per capita. It doesn't matter how big the city is; the law remains the same. "This remarkable equation is why people move to the big city," West says. "Because you can take the same person, and if you just move them to a city that’s twice as big, then all of a sudden they’ll do 15 percent more of everything that we can measure."

Am I missing something or is this reasoning fallacious? Correlation is not causation, and here it kind of looks like selection bias. I very much suspect that more productive people are more likely to move to bigger cities in the first place.

(That's all on the assumption that the first half of the paragraph is from data and the second half is a conclusion he's drawing from those data, which is how it reads to me.)

It would be interesting to know if those numbers apply in examples overseas, eg in Korea or Japan, where you have a single dominant mega-city in which basically 30% or 40% of the country live. Far too many for a strong selection bias to be at work.

Title should be "A Physicist Plays Economist"

In general, it was an interesting read even though there wasn't that much substance to it. This bit frustrated me:

“We broke away from the equations of biology, all of which are sublinear. Every other creature gets slower as it gets bigger. That’s why the elephant plods along. But in cities, the opposite happens. As cities get bigger, everything starts accelerating. There is no equivalent for this in nature.”

It's inaccurate to compare the growth of human society to the physical growth of creatures. Primates aren't the first species to benefit from society; What about ants, or bees, or even hyenas?

Regarding the contrast in durability between corporations and cities: I think this mostly a matter of definition. Nearly everything about a city - who lives there, what language is spoken, what industries it has - can change, and we'd call it the same city. Yet a company can be bought out, and keep most of the same staff, and we'd say the company "died."

That's because a company is defined by ephemeral things, such as what activities it engages in and what its name is. At base, it is a collection of people working on the same task. A company could dissolve, and all its people could keep working in the same building, doing different things, but again, the company would be dead.

On the other hand, the only thing that really ties a city's inhabitants together is that they happen to be in the same place. And unless the city is nuked, SOMEONE will probably always want to live there. So the city has a seemingly continuous life, even though nearly everything about it changes over time. What doesn't change is, say, the fact that it's located on a river. Which will always be a desirable feature.

There's more Geoffrey West here: http://www.radiolab.org/2010/oct/08/

This is a great article, but I prefer this solution:

http://www.viceland.com/blogs/uk-games/2010/05/10/the-totali...

Video: http://www.youtube.com/watch?v=NTJQTc-TqpU

I thought it was an interesting article, and the research sounds interesting and worthwhile, but I also couldn't help thinking of this:

http://xkcd.com/793/

Wouldn't the internet enable interaction without colocation?

It might (?) explain: "in the last decade, suburbs have produced six times as many jobs", as the home-office proliferates.

This is a talk West gave at Google Techtalk in 2007:

Scaling Laws In Biology And Other Complex Systems

http://video.google.com/videoplay?docid=7108406426776765294#

In addition to looking at corporations perhaps he can also study governments and give us some insight there, where it is really very badly needed.

Does anyone know what city that picture of that crazy spaghetti junction is from?

It doesn't really exist.

http://www.trendhunter.com/trends/hellish-road-junctions-roa...

It strikes me how unscientific this guy is. He gets the data, finds some correlations, implies casuations from them, and even "laws" that don't work 100% of the time.

I'm sorry, it was interesting, but kind of lame.

I agree with you. While other people above have bantered above about how absolute a "law" is supposed to be, in my opinion if you are going to call something a scientific "law" you had better be prepared to explain or at least enumerate all the exceptions. This guy just seems to get flustered and run off when people point out the exceptions to his oversimplified conclusions.

I found the adulatory tone of the article more than a little annoying, as well.

Reply on news.ycombinator.com