# Russell's Blog

## Travel notes (part 2)

Posted by Russell on December 30, 2008 at 7:48 p.m.
As I mentioned in the previous post, I saw an awful lot of houses. Some of them made me a little jealous, and others made my skin crawl. All of them got me thinking about the housing crisis.

While the housing bubble was in full swing, I had a very strong intuitive reaction to house prices; everywhere I looked, I saw prices that felt two to ten times too high. As it turns out, my intuition was right. Houses that were worth something were vastly overvalued, and there were an awful lot of houses that simply should not have been built at all. The latter was usually due to a combination of uninspired design, remote location, and natural hazards. Again, it turned out that I was right. (I don't claim exclusive clairvoyance here. Lots of people felt the same way.)

There are many things that helped create this situation. The answer the idiot-media has been pushing is that subprime loans flooded the market with money by giving loans to people who didn't qualify. The flood of cash drove up prices, which are now coming down. Leverage is definitely part of the problem, but the subprime aspect is overblown and widely misunderstood.

The fundamental problem is that there simply isn't enough affordable housing. People need homes, and there are good financial reasons why people want to own their homes. If home prices are out of reach, then of course people will abuse leverage whenever it is available. The market simply isn't supplying enough affordable housing.

Why not? The simple answer is the conflict of geography and geometry.

There are two categories of factors that contribute to the value of a home; the home itself, and the resources that can be tapped from the home. The resources available from the house provide options to the homeowner; more options mean better quality of life. More options also mean that a particular house could satisfy the needs of a greater number of potential owners, giving it more resale value. History has proved again and again that the second category is vastly more important than the first. Hence the expression, "location, location, location." This is why airless, vermin-infested closet space in Manhattan sells for millions of dollars while palatial estates in Riverside can be had for less than a tenth as much. It goes without saying that the owner of the airless Manhattan flat has access to more resources, and resources of higher quality, than the owner of the ranch in Riverside. That is the geographical aspect of the problem.

The geometry aspect comes into play when you consider how structures are distributed and how resources are made available in these structures. The Earth provides an approximately two-dimensional plane (actually, modern economic and military history can be viewed as a consequence of the increasing importance of the Earth's spherical geometry, but right now I'm thinking of more local effects -- read, for example, the chapter "Global Midway" in War and Remembrance to get a sense of what I mean). Resources available from a particular location scale like the square of the density of resources within the distance accessible from that point. As the density increases, people will start building upwards (sky scrapers) and downwards (excavation). This introduces a volumetric effect, causing the available options to scale like the cube of the local density of resources. As density continues to increase, it becomes financially viable to build mass transit, which extends the radius of practically available options. This introduces a quartic scaling. As the density increases further, it becomes necessary to seek synergies and greater efficiency to minimize use of space. This introduces a scaling at the fifth power of density.

So, as the density of a settlement increases, geometry militates the use of ever more potent means to reduce the footprint of an available resource, which in turn facilitates greater density. Each new means of increasing density adds an additional linear scaling, so that the ultimate scaling is approximately

${\cal O}(1+n+n^2+n^3+n^4+n^5+\ldots)={\cal O}(e^n)$

Of course, a polynomial of infinite order is the Taylor expansion of the exponential function. So, we can claim that the approximate value of a home scales exponentially with the density of resources in that area. The first three terms are required by simple geometry, and higher terms increasingly represent technological and social responses.

Really, this is the lower bound on the value; the value of a home also depends on how many other people might want it. If people select a home mostly for the choices it makes available to them, and each person has a different collection of choices they want, then there is some kind of combinatorial scaling as well (I'll leave this one as an exercise; you can get several different scalings depending on the assumptions you make).

Meanwhile, the value of the house itself scales linearly with the cost of the stuff you put into building it (labor and materials). However, nicer houses tend to be larger, and thus neighborhoods of big houses tend to be sparse. Thus, if the value of a home is the sum of the value of its location and its embodied value, embodied value will inevitably be overwhelmed by the locational value. This is a classical Malthusian conflict, but in this case the functions represent different things.

So, why the crisis? Well, we have artificially capped the growth of density. Zoning laws forbid the construction of new Manhattans, and require the gradual erosion of existing high-density neighborhoods as their buildings wear out and need to be renovated or replaced.

This is the story we tell each other about how this happened; the automobile gave people greater mobility, allowing them to live in the suburbs and countryside while they still work in the city. So, there was a great exodus from city centers to suburbia. This narrative has things exactly backwards. Density at the city periphery was legally capped and aggressively driven down, which forced people into the suburbs to seek affordable houses, making automobiles necessary to access resources that were previously available on foot. The first story is a marketing pitch, the second is recorded history.

In the early post-war period, opinion surveys consistently showed that the top transportation issue on the minds of Americans was the improvement of streetcar service, and the top housing issue was the rapid inflation of rent and other prices in city centers after the wartime price controls were lifted. People did not particularly want cars and suburban bungalows; they simply made a rational choice in the face of exploding rent and decaying public transportation. Even so, suburbia remained relatively unattractive for most people until Brown vs. Board of Education in 1954, and picked up steam in the early 1960s when racial tensions transformed the suburban exodus from an economic issue into a racial one. See, for example, the abandonment of Detroit, or white flight from Los Angeles to Orange County. That is the story of suburbia.

There is one more geometric factor to consider regarding the value of a house. The cheapest possible thing to add to a house is square footage. The "core" of the house -- the appliances, utilities, cabinetwork and main structural elements -- represent the bulk of the cost of home construction. Big houses are worth less, on a per-area basis, than small ones.

For the last 50 years, we've been building increasingly sparse neighborhoods of increasingly big houses. In real terms, the cost of ownership has gone up dramatically (heating, cooling, lighting, transportation, maintenance, taxes), while the real value of our houses and neighborhoods has decreased. Both of these scalings are exponential in nature; a modest increase in square footage translates into an exponential reduction in value per square foot.

In 1950, the average American home was 983 square feet. In 2004, it was 2349 square feet. In the neighborhoods most impacted by the building frenzy from 2004 to 2007, it almost doubled again, to around 4000 square feet for new construction. We're talking about a quadrupling of home sizes in 50 years!

Bigger homes require more land, and so density of resources available from these places must scale inversely with the square of home size -- and by the reverse of the argument above, decreasing density introduces higher order scalings whose sum produces an negative exponential effect. So, as homes increase in size, their value will exponentially approach the cost of the raw materials that went into them, until at some point the value falls beneath the associated costs, and owning one becomes a net liability.

The benefits and costs of owning a particular home are tied to labor market conditions, commodity prices, nearby development, and many other things. Thus, the narrower the margin between the benefits and the costs, the more likely the normal fluctuations of the economy will land you with a net liability. Adding leverage into the mix just makes the margins even narrower.

There is the nub of the issue. "Affordable" doesn't mean low price; it means getting a lot of value for a given cost (I am using the terms 'value' and 'cost' in a concrete sense, so you may substitute 'enjoyment' and 'effort' if you like). It means having a comfortable margin between the benefits of home ownership and its associated costs. It means a margin that is wide enough to absorb the risks we face in the event that they become realities. It means that you can still pay your bills if gas prices go up, or if you get a new job, or whatever. This lack of affordable housing doesn't just hurt poor people, it hurts all home buyers. We have a huge glut of houses that have virtually no value in them it all, except maybe as firewood, and almost no available houses with a decent number of readily available resources.

This isn't a situation we can bounce back from through financial mumbo-jumbo. The problem is intrinsic to our built infrastructure. The solution requires physical changes to our landscape. It will take a long time. Much hay has been made about the culpability of Wall Street in this crisis, usually portraying "Main Street" as the innocent victim. This is bullshit. Main Street is just as culpable, and maybe more so. Solving this crisis will require re-writing building codes and zoning laws, not just baking regulations. The crisis will ease up when we have enough compact, high-quality homes in good neighborhoods. By "enough," I mean we have to keep building them until the prices for these places puts them within reach of households at or below the median income.

It really doesn't help that our cultural prejudices insist on equating square footage with value; it is a false economy. Square footage is the high-fructose corn syrup of our financial system; cheap to produce, tragically unhealthy, and no matter how much you have, it never satisfies.

## Travel notes (part 1)

Posted by Russell on December 28, 2008 at 2:54 a.m.
After almost fifty-some hours riding the train, I have a few impressions worth sharing. I had a lot of time to think, and a lot of things to think about, so I'm going to break this up into a couple of posts.

I expected to get a great deal of work done in that time, and I accomplished absolutely none of it. Not a single jot. I basically spent the whole trip either looking out the window, or happily asleep. There is just too much to look at; breathtaking snow-capped mountains too numerous to name, scores of towns and a dozen cities, the vast arid emptiness of New Mexico, lonely volcanic prominences rising from Euclidean flatness, knots of green trees rioting in pocket valleys bracketed by sterile sun-blasted volcanic rocks, and the profane, hideous pointlessness of Texas cities.

The trip was a grand tour of the majestic beauty of our country, and an industrial colonoscopy showcasing a great deal of what is wrong and twisted about its economy.

I will spare you my gasping about mountains and trees. I lack the skill with words necessary to even crudely sketch such things. You simply have to see it. Instead, I'll tell you about the ugly and fascinating things I saw. They leave me truly awed.

The first thing that struck me was the vast and penetrating impact of exurban development.

It was heartbreaking to see just how much of the land is already destroyed. In California, luxury homes and golf courses fill every level patch of ground from the outskirts of incorporated Los Angeles to Palm Springs. Tuscon and Phoenix have similar, lower-budget penumbras of sprawling exurbs stretching two hundred miles in every direction. In the space between the outskirts of Palm Springs and the outskirts of Tuscon, people are busily making preparations to link these two cities with a continuous smear of houses. I was relieved to notice that many developments in the margins seem to be abandoned. One of them was nothing but rain-swelled chip-board and wind-tattered Tyvek nailed to dozens of identical frames. I regret that the photos didn't turn out.

That isn't to say that I don't have sympathy for the lives and fortunes that are suffering as a result of the economic pestilence that ruined these ventures, especially the craftsmen and laborers. But the fact is, nobody should be building out there. America's natural spaces should be treated like places of worship. Look at these houses huddling at the foot of this mountain:

These are money changers in the temple. I'm not against money changers in general, but they shouldn't ply their trade in my temple. Actually, this is quite a bit worse than the New Testament parable. The money changers could be thrown out and the sacred space restored. After the developers are thrown out, millions of their innocent dupes remain.

As beautiful as it is, this land is both exquisitely fragile and damn miserable to live on. Fragile because there is so little water, and miserable for its looming and contrarian propensity for devastating floods. Fragile because of the trophic poverty of the nutrient-starved ecosystem, and miserable for its tendency to erupt in sudden racing conflagration. Fragile because of the extreme sensitivity of the wildlife to disturbance -- a few scattered bottle caps have likely doomed the recovery of the California condor -- and miserable for the tendency of the wildlife to apply claws and fangs and venom to pets and loved ones. Fragile for the delicate balance of commodity prices and labor market conditions that make inhabitation possible, and miserable for the stress and strain of living on the knife's edge of financial viability, and doubly miserable when the distant rumbling of our global economic system brings your financial house crashing down on your head.

The only way most people can be comfortable in this kind of place is to obliterate it. Suck dry the aquifers, poison coyotes, shoot the mountain lions and the red-tail hawks, pave the chaparral, relocate factories and office buildings and depots from the distant city, blast and grade the mountainsides for drainage ditches and flood control swails, murder the night with the eyewatering glare of sodium vapor floodlamps. Then what have you got? Just another hot, boring place.

Yes, we can inhabit these places. Such is human ingenuity and power that given sufficient amounts of dynamite, concrete, oil and steel, we can probably live anywhere we can reach. We can blast and pave and bulldoze and burn any landscape to suit our purposes. The great challenge of the 19th and early 20th was to learn how to do these things on the scale required by the lethally difficult lands of the American West. A hundred years ago, life in the Mojave desert was so hardscrabble that few of even the most intrepid adventurers bothered to attempt it. Today, we build full-scale replicas of Scottish seascapes on which we play golf.

The great challenge of the centuries to come will be to abstain from exercising this power, and instead develop better enterprises in which to invest our blood and treasure.

## All aboard, and suchlike

Posted by Russell on December 21, 2008 at 12:24 p.m.
Since I've been telling anyone who'll listen for the last couple of years that we've got to use trains for travel more often, I decided that I should take my own advice. I'm going to visit my little sister in Oklahoma, so I'm taking Amtrak there from Los Angeles. I'm taking the Texas Eagle to Fort Worth, and then the Heartland Flyer to Norman, Oklahoma.

It's going to be a long trip (about two days). It could be a lot shorter, but we've been letting our passenger rail service rot for sixty years. I'll post pictures from the trip when I get to Norman, and sooner if I can snipe some WiFi along the way. Until I do, here is a picture of the Capital Corridor train rolling into Davis.

## Published!

Posted by Russell on December 10, 2008 at 4:01 p.m.
I just got the email from AIP a few hours ago; my first paper as first author is published!

It was a surprisingly long process. I think most of the delays were due to my own lack of experience. Hopefully, they are lessons learned, and my next trip through the publishing gauntlet will be easier, faster, and hopefully even more fun.

My uncle asked me if I would try to explain what I did in simple terms, so here it goes.

There is a thingy called a tokamak that is basically a very fancy Thermos. It keeps hot things hot. If you can make the stuff inside hot enough, it will work like a nuclear reactor. This is interesting because it is possible to build much better, much safer nuclear reactors this way. The trouble is, these Thermos things cost billions of dollars. The one they are building in France is going to cost something like nine billion bucks, and it will get barely hot enough enough to work as an experiment. Real ones would cost even more.

The good news is that the current designs for these fancy bottles only use a few percent of their heat-trapping capacity. That's what 'beta' means in the title; you can think of it as the heat-trapping efficiency of the machine. This is different from the energy efficiency, though. The heat trapping efficiency is more like how full you can fill the Thermos. Right now, we are building a nine billion dollar Thermos, and only filling it to 2% of its theoretical capacity. If we could use more of the heat-trapping capacity, then you could maybe reduce the cost by a factor of ten or a hundred (or increase the performance by that much).

So, this line of research is all about computer simulations of these doughnut-shaped nuclear Thermoses, and how they behave when they are nearly full.

In some other papers, I helped show that it is likely possible to build a nuclear Thermos that you can fill almost all the way up. In another paper, I also helped my friend Pierre show that it is possible to start with a nearly empty Thermos, and fill it to nearly full without anything bad happening (it all comes down to how you pour, to stretch the metaphor).

Typically, you have a theory that you trust, and you want to know if your computer simulation matches the theory. In this case, however, we built a computer simulation that contained very few assumptions. It solves Maxwell's equations (for magnetic fields and currents) and Newton's equations (for moving masses). This is nice, because those equations have been tested really, really well over the last 130 years. It also means that you can take the output of the computer program, and very easily check to see if it is correct.

As a result, we had the opposite problem one normally faces in science; a computer program that we trusted, and a theory that maybe we didn't. In this paper, I used the computer program to validate that the theory was correct. I did this in an unusual way. The theory is approximate, and so we expected it to go funny in some places. I treated the computer-generated output as the "exact" solution, and showed that when you subtract the theoretical result from the result we got from the computer, the difference is precisely the amount by which we expected the theoretical result to go funny. (In more rigorous language, I proved that the deviation from the numerical result has the same scaling as the error term in the expansion.)

## Arches

Posted by Russell on December 09, 2008 at 6:59 p.m.
It was a nice day today, so I decided to walk around for a few minutes and take some photos. It was a nice break from studying for finals. I thought this was an interesting juxtaposition.

The arch of an open boxcar I saw today...

...and the Arch of Constantine

What do you think?

## Tanta at Calculated Risk

Posted by Russell on December 02, 2008 at 12:29 p.m.
One of my favorite bloggers died on Sunday. I didn't know anything about her personal life until today. She was fighting ovarian cancer with a poor prognosis, and died at 47. Her obit is in the New York Times.

She was probably the clearest, most readable and best informed voice on the mortgage crisis, period. She was also pretty much the only person who had anything positive or funny to say about it. Or, at least she set mood for the general commentary at "dry wit," when it easily could have been "catatonic depression."

From her platform as a co-blogger on Calculated Risk, she wowed people from Nobel laureates to analysts at the Federal Reserve. Pretty much everything I know about the details of the mortgage crisis I either know because she explained it to me, or because she explained it to someone else I read (e.g., certain Nobel laureate economists).

She had hoped to return to mortgage banking after the crisis and after recovering from cancer, but she made such a mark with her writing over the last two years that most people doubt that would have been possible.

One thing that makes big media so stupid is that they always turn to the same stable of pundits for commentary on complex issues. Unfortunately, most of these guys are not very bright and not very informed. But there is a solution. For every issue, even issues as murky and choked with dull tedium as the mortgage banking industry, there are people like Tanta. She was an expert straight from the trenches, but with a view broader than anyone could see from the ivory towers of academia or the skyscraper corner offices of industry. She was exactly the sort of person that major media outlets should recruit for beat reporting. The murkier the issue, the brighter such people can shine.

Alas, this particular glimmer in the gloom has gone out.