Divide the mass by volume, and you have the formula for density. An increase or decrease in area is a change. Typically, density expresses the number of people compared to other regions, but density can measure everything within a field. Everything makes the “where” of density a valuable metric.

Yellowstone National is a commercial export. Central Park is also an export of New York City, attracting 35 million visitors. In 2016, the National Park Service celebrated its 100th year. The flagship of this service is Yellowstone National Park. In 2010, it saw 3.640 million people visit its 2.219 million acres 2010. The wilderness “preserved” is closing in on two persons per acre. Visitation is a key performance measure. It responds to Central Park’s design in New York City or Yellowstone’s natural beauty. Along the “edges” of Yellowstone and Central Park, we find a long list of economic uses. Open space is revenue if design well, or just untouched.

The thought of including a “park” such as Yellowstone in an open space ratio (people per sq. foot of park) serving residents of the surrounding urban area seems laughable now. How long will it be before Yellowstone starts to function like an immense Central Park? The policy implied is this: keep the pretty stuff and develop the rest. It isn’t good policy.

The designation of a national park boundary is an executive order power held by the United States president. The annexation of Yellowstone into the realm of wild open space increased preservation. Still, its two million acres pales compared to the urban area volume created by municipal annexations to reset bond ratings and recover infrastructure costs. After that, publicly owned zoning instruments with private development actors become marketable instruments. As an instrument, the state’s power to manage land is changed by its users. New rules put dimension ahead of form to keep the “metro-map” from becoming saturated with vaguely urbanized landscapes.1Core-based statistical areas hold at least 10,000 people. They now spread with little more purpose than a shelf product on a grocery store. Choices in how we live require much more attention.

Asymptotic Density

A Thought

Is urban density subject to spatial law? The ‘golden mean’ formula creates the graphic above. Developing urban space using the vast computational power of computers to shape buildings is well underway. Will an extensive and valuable urban landscape form in new ways? The prime number theorem offers some insight.

The percentage of prime numbers drops in the total field search area. Still, the total remains predictable regardless of the size defined. Like a city, the prime numbers are initially dense at the center of this field. You will find 25 primes in the first 100 numbers or 25%, and this share of the total continues to diminish by the area searched. At 100 million numbers, the percentage of primes becomes 5.76% and continues to approach but never reach zero.

The volume of space in urban use is similar to the density of prime numbers. The formula for determining the number of primes applies to all-natural functions, from galaxies to storms and flowers to human tissues. It is called the logarithmic spiral. It is also called the design for least resistance. The number of rotations of this system and the center’s distance leads to the highly accurate formula for prediction and value.

Like all machines, cities fail as objects and become a part of a new energy cycle or material process. Machine revitalization occurs given the processing power of the data packet that defines its function. Some seeds will begin their reproductive cycle with water and temperature even though a century may have passed. The essential trajectory of urban life has many of these qualities.

Hints, such as a machine-learning algorithm for organic computers made entirely from biological materials, may begin to hold this secret of this seed-like power. MIT’s DNA-based computation research envisions networks as living systems with data storage available at the atomic level. The practical use of the quantum realm of change in the use of discrete time-crystals is intensifying because there is no energy cost. Deep learning will store all the information produced by the material city and its people and make it public. It is a step resisted and welcomed given a position on the golden mean.

What data about a city could answer two questions drawn on one billionth of a square meter per second over its entire volume? Or the reverse, what questions would you have if you could do that? The information and pace of decision-making change the city from a coarse vehicle for survival into comfortable, self-renewing awareness and extraordinary connectedness.

Bucky Fuller was among the first to notice the vast acceleration of technology grasping at the human experience. In the first of his twelve summary lectures, “All I Know” (1975), he said the following:

“So I think we are apparently coming out of some common womb of designedly permitted ignorance, given faculties that we gradually discovered and learned to employ by trial and error, and we’re at the point we now have, which would also seem incredible to a generation before.”

Buckminster Fuller

During his lifetime (1895-1983), wireless radio communication would occur—the first fight by a human in a machine and the first use of a broadcast image. The list of “elements” would grow enormously. Fuller’s point was more about acceleration than achievements. Fuller recognized small group awareness as becoming global awareness. This experience would not transfer from one generation to the next; it would occur within generations and with specialized rapidity.

The discovery of the precise structures of DNA and its ability to bind with other molecules would have fit into his anticipation of a profound “pattern change” in the human experience. Patterns, the raw materials of science, create new ways to manage an ever-increasing rate of change. The urban world is an aggregate of non-simultaneous and only partially overlapping energy transformation events. Because of this, the city, like the universe, is eternally regenerative. Today we know life on this earth is not unique in the universe. It is chemically and mathematically inevitable. The world sends an epigenetic bill to urbanized humanity daily. It must pay. (Participate)

Post-Westphalian Politics of Density

Eric Snowden’s National Security Agency (NSA) data-rip highlighted the trading privacy crisis for added security as a performance measure. The debate facilitated breakthroughs in the public’s understanding of metadata. Understanding the importance of information about information is a very new subject, so putting a handle on it won’t be easy. I see it as a question of trust brought into a personal experience of all people.

Power companies in low-density areas tend to “blame trees” for service failures. An accurate event description shifts attention away from investments capable of anticipating the margin-biting prospect of inclement weather. Energy security should include compliance with urban policies that save energy. It comes down to trusting the data well enough to decide what is “affordable” or “safe” or “private” (insert any value) and what isn’t. That is the secret of metadata.1

You will find a massive application of remote sensing technologies with computational integration and networking capacity at the security regime center. Buckminster Fuller predicted this as a “comprehensive anticipatory design science.” On the other hand, the average person would like to keep it from being spooky, thus the term “big data.” The product offered by this data is something like getting “what you need when you want it before you have a want or need.” One flaw remains: trusting a source, from the correct number of seats on planes per port to energy savings per person to stopping wars and skirmishes per nation.

The drive for “a perfect union” is rooted in the Westphalian nation-state. It describes the origin of the 15th-century political organizations with sovereign economic power. The flaws of its application began to show following two world wars and the collapse of the Soviet Union and, by extension, in the colonial re-alignment death rattles of the Middle East, Eastern Europe, and various African states. Nevertheless, the goal of a never-ending improvement in governance practice will not be forgotten or discarded.

Urbanization will continue to cross and dissect old boundaries to form regions with different world views. The difficulty is the lack of a mechanism to make these views more than vague regional plans. It is not enough for micro-municipalities, city, county, and state governments to sustain public processes driven by constituent self-interests alone. A significant unifying force currently rests in many multi-state public benefit corporations. (Reference)

Urbanization brings forth new demands for sovereign political power across state boundaries. As mega-regions, they form to compete for examples of the post-Westphalian world. Still, they suggest the need for multi- or supra-national levels of political power. They range in structure from the European Parliament’s ambitious purpose to the thousands of public-benefit corporations attempting to manage the distribution of energy, water, and transit between regions.

These extra-political organizations build their power on vast data sets about everything from ships, containers, cars, and trucks to easy passes, tariffs, and every description. The dense urban environment produces data about people, housing, health, commodities, business, places, and thousands of other practices with growing daily resilience.

The data offered by these systems are redundant enough to describe alternatives to the way people want to live, sleep, work, and mature. Connecting these dots includes the presumption of socioeconomic improvements. The use of public funds for super connectivity ties to an index of our well-being.2 What agency, what set of rules will govern trust in this kind of city?

The dense urban infrastructure provides for the increased sensory capacity of technology. The savings are actual, but the technology does not create policies that level playing fields, correct past wrongs, or set policies that prevent human dignity damage. On the positive side, technology highlights the poor job done in defining fairness and hints at the means for compelling it. Just ask Eric Snowden.

The growing application of firewalls, “motes,” and wireless sensors monitor an exhaustive list of physical entities, from radiation by rad to vehicles by type, per threshold in real-time. Libelium is an IT company headquartered in Spain. It developed a series of case studies to apply open-source sensor platforms that enable M2M (machine-to-machine) networks to broadcast from local to global. They crushed the Westphalian model of how the world works in a silent keystroke. No one noticed. As the third millennium begins, the thing to look for is how dense urban growth locations around the earth supersede the state of sovereign national power.

Oregon and Maryland

Portland is an often-cited “green city” in the United States. Portland reduces energy use, has multimodal transit systems to its suburbs, and several successful rainwater harvesting systems in one of the country’s wettest areas. It has the “urban growth boundary,” an educated and diverse population. All of this is in response to a fast-growing low-density region. Being green is of little consequence to the solution density offers if kept super low or ultra-high in all the wrong places.

Portland’s “urban growth boundary” 229,000 acres began in 1979 and intended to accommodate 20 years of growth. Since then, it has produced two political camps. The first is “leave paradise alone for those who have it,” or more bluntly, the base says, “I’ve got mine, now get lost.” This group needs leaders to get them a better message, including one that would allow high densities in the right places.

They can prove low density creates negative tax efficiency, added water, air pollution costs, and increases energy consumption per capita. It does all that and more while advancing the fragmentation of the nation’s infrastructure with growing management and maintenance costs.

The leading watchdog group is Oregon’s Land Conservation and Development Commission. It is a policy-making panel appointed by the Governor and charged with overseeing the state Department of Land Conservation and Development. They see Portland as a creature of the State of Oregon, and its effort to contain the city is a way to promote the common good. The policy keeps sprawl problems from attacking pristine forests, farms, and Meadowlands. But, unfortunately, the “urban good” is in the negative.

Nevertheless, Portland’s 1.3 million people live on 238,000 acres. That averages less than six people per acre. For many, this is sprawl. The implication is the State of Oregon is attempting to contain Portland’s sub-urbanization potential.

In 1997, Portland’s Metro Council added 4,500 acres to its urban growth area (UGA).2  To an increase only 2 percent, but double the previous 30 years to yield an estimate of 30,000 new housing units. The additional site generates an average of seven units per acre. The addition marks the first significant opening of the boundary to supply the demand for more housing from all market sectors, from “affordable housing advocates” to the National Association of Home Builders. Unless there is an increase in per acre housing yield, the urban boundary might be Oregon’s Maginot Line.3

Portland vs. Vancouver

Cities that know the enormous demand for housing and economic development use regional plans to organize local government entities that appear small. The Portland and Vancouver corridor in the northwest (AKA Cascadia) have expressed the desire to produce something like a 10-fold increase in per acre housing yield, preferably with as little lateral expansion as possible.

Portland: Environmental Services

Detached, single-family homes of varying sizes dominate the typology. All of them represent enormous retrofit problems and slews of unregulated green gadgetry. For this reason, urban planners and architects are watching city and state attempts to manage sprawl. They have proof that sprawl produces an irrational loss of farmland and the tragic destruction of natural habitats.

A small part of this experience speaks to NYC’s housing history. It is about the struggle for reinvestment in an older urban area. From 19th-century housing reform movements to the crises in the 1970s and 80s when tens of thousands of homes became vacant or abandoned, the effort to establish confidence in reinvestment required a multi-dimensional strategy. Like Vancouver, NYC’s political ability to expand laterally has a state boundary limit, two rivers, and an ocean. As a result, NYC developed an income stream dedicated to investment in combining new and existing affordable housing in response.

Urban disinvestment has several causes, chief among them are 1) the rejection of reinvestment in first built environments, 2) an energy crisis coupled with 3) a recession, a burst of inflation, or both, and 4) social distress associated with 5) significant race/income disparities and concentrations of poverty.

Urban disinvestments stimulate ripples of threat events. The triggers may vary. A shrinking rust-belt city or the spread of new money conurbations are equally subject to the divestment process. All have a rise and fall history; the question is, as this uncontrollable pattern repeats, will it shroud the planet? Can better control of these cycles be acquired?

The dream of living in the woods by a lake with a couple of SUVs is what people want. Thus, development in an unplanned, free-market economy will provide everyone. Dense cores do not make the quiet suburban home perfect, but they contribute to a competitive increase in their value.

  1. Dense zero-waste urban clusters can serve 80% of a large region’s population with multiple transportation services.
  2. The creative economic recovery sources form in dense clusters composed of diverse housing, commerce activities, learning centers, and people.

The urban boundary could be the Maginot Line in Portland’s political sand or enforced in Vancouver. The experiment is on, and the studies are ongoing. 

In 2012, Mike Jordon, the Portland Metro Council’s Director, reported his concerns regarding mass transit development. The local government’s inability to establish a boundary requires an investment in light rail and how the change in route to a north/south right of way along Interstate 205 fails to serve urbanization. His position was,

“It’s in the wrong place to optimize public investment. It should run down 82nd Avenue. It would have spurred incredible redevelopment on 82nd Avenue. It would’ve raised a place in this region that is woefully in need of raising.”4

In June 2015, Mike Jordan became the Director of the Bureau of Environmental Services. He oversees wastewater and stormwater management services for 600,000+ commercial, industrial and residential customers. The lack of interest in refinancing and rebuilding an older town is a repeatable “decay” legacy. Keeping low-density urbanism weakens Portland’s urban boundary for the lack of density. It took NYC thirty years to recover from this “buy-low” lack of insight. Cascadia (Portland and Vancouver) does not have that kind of time.

Please look at Housing and Transportation Burden data by the Center for Neighborhood Technology (CNT) Link: Drill down to an urban core near you to see its benefits. The bottom line, households can trade auto-transportation costs into a housing subsidy by moving to places with multiple forms of transit. Portlands’ “Are you in or out” of the Growth Boundary website tool (here)

The CNT and others will eventually produce a policy for regionally planned transportation systems from a vast American infrastructure of smooth surfaces capable of supporting various transit services. New systems within a dense core provide light, flexible vehicles powered by the sun and the wind. Compact core-to-core centers support high-speed links. Practical, yet it is not without a sense of irony. The densities established thereby increase dependence on the automobile.

The State of Oregon empowered the Portland Metro Council to establish the Urban Growth Boundary (UGB) for the region in 1979. Unfortunately, the recession of the early 1980s slowed predicted growth rates. Still, as the economy recovered and the population grew, the Metro Council also recognized that it could not stop “sprawling development” within the UGB. So in 2009, the Portland Metropolitan Region turned a climate change corner.5 It determined development at low densities would exhaust the remaining land supply inside the UGB and force expansion onto 120,000 acres, much of which is productive farmland.  


Before developing Portland Metro as a government agency between state and local authorities, the Oregon Legislature enacted Senate Bill 100 in 1973. In 1979, Metro set goals for the state to follow a regional planning course that required every city and county to adopt a comprehensive plan that met nineteen planning goals.6

Millions of new hobbit-like homes are added every year because they are affordable. Unfortunately, for most households, they are in the wrong place. The detached house is super marketable. The cost per square foot, including a tasty bit of private open space, is highly flexible. The illusion of independence is tucked away in a forest likely to burn in the householders’ lifetime.

One super fact remains. The most affordable places are the suburban regions of Phoenix, Atlanta, and Las Vegas. They align with policies that encourage low-density development. For every dollar a household saves in low acquisition cost housing, they will spend close to that amount in added auto-transportation costs. Depending on the age of development, they will also face routine increases in property taxes. Oddly, hobbit-like homes are successful and lasting in dense cities but represent just 20 percent of the total and are not affordable. That leads to the success of NYS and NYC.

New York and New York City

There is a city of islands on the east coast of the United States. It combines a limited political and geographic boundary but continues to grow “in place.” It is an example of every mistake ever corrected. New York City has nicknames like the Big Apple or concrete jungle, and everyone knows it as “the city that never sleeps.” It is, without a doubt, a metropolis restored, and not once the restoration of the city is an annual activity.

“In the year 2028, when the populace is divided between workers and the rich, a man abandons his privileged life to join oppressed workers in a revolt.”

Metropolis (1927 2 hours 28min)

New Yorkers know that their city is not the world’s capital — that would be Gotham. It may be the world’s most helpful caldron for peering into excellent and lousy density. It has excellent examples of both.

The metro area population is approaching 20 million people, given a boundary of 6,720 square miles or about 2,800 people per square mile.7 New York City alone is 304.8 square miles of land, providing a place for the population of 8.2 million to live, a density of nearly 27,000 per square mile and consistently rising.

Good and bad density in New York City is not difficult to find. It is a matter of contrasts developed by design. The Bronx, Brooklyn, Manhattan, Queens, and Staten Island have every example imaginable. Additional detail can help, but the point is to understand the concept of the boundary. Excluding The Bronx, New York City is mainly an island, and much of it is just 10 meters above the average high tide.

The line around NYC that might save the region’s suburbs is a possible lesson from the northeast. The NYC population after the 2000 Census was just over 8.2 million and increased slightly in 2010. Based on a population of just over 19 million and a metropolitan area of 5,435.7/sq. mi. (2,098.7/km2), the overall density is around 3,000 people [≈ population of Falkland Islands, nation] per square mile. Walk briskly in a square for fifteen minutes on each side, and you would cover a square mile.

David Owen wrote about how density in Green Metropolis improves things. The sense of historical contradiction begins to rise because cities are the messy “downriver.” Nevertheless, places like New York City are per capita winners. When access to medical care is used, it wins and wins big when affordability is included. All transportation-related energy consumption is the lowest per capita. Density wins.

Owen postulates where all eight million New York City residents would live if it were at the same density as his community in a Connecticut suburb. It would require all New England (six states) plus Delaware and New Jersey.8

New York City’s per capita carbon footprint is smaller than other American places but significant compared to Toronto, Melbourne, Sydney, Hamburg, Frankfurt, Zurich, Paris, London, Amsterdam, Tokyo, Moscow, and the king of high density, low per capita energy, Hong Kong.

New York and cities with higher densities and low fuel use are “per capita” winners on all counts. It is still one hell of a congested mess from electricity use to high-priced gasoline when you add them all up. Nevertheless, congestion turns out to be a good thing as it forces the production of alternatives. Does this make the dense urban center better because there is less mess per person?9

Reducing catastrophic resolution probability requires accepting a few simple ideas. We know bicycles are viable when you have high urban density. Look at Amsterdam or any number of cities in Germany or China. The relatively unnatural urban landscape suggests possibilities for alternative vehicles. The need for advanced multi-mode travel may become urgent.


  1. According to Energy Information Association EIA data, national, annual electricity transmission and distribution losses average about 7% of the electricity that is transmitted in the United States.  State Profiles
  2. These figures come from a NYT article in 1997 found: here.  The council projects about 1.2 million people will move to the Portland metro area by 2060.  If  no reserves are added, the density of the region as a whole would be about 11 people per acre. If all of the requested reserves are added and urbanized, the density inside the urban growth boundary would drop to 9.1 persons per acre.  Source: Oregon Hillsboro Argus “Jobs, density, open space: Why reserves matter ”
  3. Also see: Beloved and Abandoned: A platting Named Portland For American planners, Portland, OR is held up as a shining example of urban planning, and credit is given to its compact grid. But is Portland’s grid worthy of adulation? Perhaps not,  Fanis Grammenos and Douglas Pollard of Urban Pattern Associates.  Full Story:  Douglas Pollard  Fanis Grammenos
  4. See Interview:
  5. Summary urban growth boundary debate in the archives of Oregon On Nov. 12, 2015 and for the first time in a decade, the Metro Council opted not to expand the Portland region’s urban growth boundary on Thursday, voting 7-0 to leave the boundary as-is.
  6. The following is a brief summary established in Senate Bill 100, 1973 Citizen Involvement, Land Use Planning, Agricultural LandsForest Lands, Natural Resources, Scenic and Historic Areas and Open Spaces, Air, Water and Land Resources Quality, Areas Subject to Natural Hazards, Recreational Needs, Economic Development, Housing, Public Facilities and Services, Transportation, Energy Conservation, Urbanization [Old 14] Willamette River Greenway, Estuarine Resources, Coastal Shorelands, Beaches and Dunes, Ocean Resources. A detailed review is here:
  7. “Annual Estimates of the Population of Metropolitan Statistical Areas: April 1, 2000 to July 1, 2007”. U.S. Census Bureau. Retrieved  2008-12-30 via Wikipedia
  8. See: Green Metropolis: Why Living Smaller, Living Closer, and Driving Less Are the Keys to Sustainability (David Owen, Riverhead Books)
  9. A brief look: The line remembered is “…congestion is like cholesterol – if you don’t have any, you die. And like cholesterol, there’s a good kind and a bad kind.”