Density’s Constants

Density is a matter of taste and what might make compact living interesting. Density also has a fixed value and an unambiguous definition of space. Density’s constant is a mathematician’s view of it as a number. A good example is Archimedes’ constant π that gives you the area of a circle. Another view is Thomas Jefferson’s Rectangular Survey System – a mile square grid representing his vision for western expansion. Both are illustrated below. The circle defines limits, and the grid expresses infinity. Both gives density meaning, and as yet, an upper limit has not been determined, only architecturally imagined.

The Report

Nai010 publishes Grid Corrections (The Book)
By John Reid – Edited version of Image:Pi-unrolled.gif

These illustrations depict the idea of setting limits that define a place. A mathematical exploration by the city builders understands density in its place on the grid and finds locations for places to contain (a circle) in various combinations across the earth’s surface or imagined as billions of locations in the universe’s constant expansion. The following section explores this duality in a search for densities that fit the principles of control.

The capacity to pull knowledge from nature and raw material out of the earth’s crust to do things is most evident in the building of cities. We have learned we can literally throw things off the earth and into space. Arther C. Clark imagined an elevator for getting there that may prove to be an engineering possibility. The knowledge to identify and control the raw materials to accomplish this task reveals something astounding.

The practical Newtonian solutions will hold through most of the 21st century in accomplishing tasks such as city building or space elevators. Still, there is a problem ahead already reasonably well defined. Designers will continue to produce visions of urban shelters distinct from nature and retain the agreeable components of the wild. On the other hand, the city as an entity is a fail/success story of lessons learned, pre-history to the present, yet few of these lessons have held, which is the problem. We can’t seem to stop ourselves.

The Place Matters

Huge knowledge gains will reveal the terror inherent to a machine that will not turn off. Humanity may soon require an off-switch for the carbon dioxide machines. The range detailed by multiple energy-sensing systems hopes to complete the first census of all life forms on the earth. The data already reveals small changes have a cascading effect from a unique nurturing entity to multiple energy signatures to reveal enormous interdependence. Yet, we don’t see or notice it. Perhaps our lives are too short.

Human response to everything from war to environmental urbanism involves epigenetic factors that require control over carcinogens as the most obvious example. Most of the recognition is post-trauma, but hopefully, not forever. New management powers will form to respond to priorities such as global food and clean water with the capacity to serve about 10 billion people.    

Emerging from many of these signatures are massive diffusions of human-made stuff that threaten these dependencies and associations. Data on how the “urbanized world” and the natural earth have begun to share the same problems continue to grow. Solving them must be the urban part that takes a final leave-taking – an amicable divorce.

The separation of urban from the wild will retain comparisons valid to the evaluation of recovering natural environments. Still, it is incorrect to think urban landscapes are as crucial as equatorial places or the tundra near the poles’ latitudes north and south. If retained, they will thrive due to the added carbon dioxide and moisture in the earth’s atmosphere. If not, life will thrive in another way, unfearful of the deaths involved.

The impact of urban and natural systems over energy through renewable use has begun. Unlike the natural systems that waste nothing, the design for energy distribution built on the sun, winds, and waves is declared insufficient for urban living. A begging hand stretches out to technology for a fix, and it handed everyone a smartphone.

Millennium Ecosystem Assessment

The Millennium Ecosystem Assessment (M.A.) explores key differences between local and global, urban and natural. The MA takes the complex reports of leading international organizations such as the World Health Organization (WHO) and the International Programme on Chemical Safety (IPCS) with the intent of making their findings more broadly understood.

On the question of population and urban growth, the M.A. found

“…systems with the lowest net primary productivity and lowest GDP tended to have the highest population growth rate between 1990 and 2000.” 1

These areas are primarily the drylands (yellow on the map above). A part of this assessment was why urban areas with inland water and marine systems are not analyzed. The rationale given is the:

“…somewhat arbitrary nature of determining the net primary productivity of the system (urban) or population growth (freshwater and marine).”2

The link between population and GDP growth is in doubt. Refining the analysis proves the movement of settlements into dryland areas is a drain on the economy. Policies supporting alternative land uses, such as vast solar farms, are decisive steps toward successful density.

Housing is Local

From a local perspective, density in existing urban centers will produce various dense cores complemented with transit-rich conditions and multiple resources for movement.

Without a doubt, the dense urban environment yields a vast range of transportation choices and physical comforts in walkable settings. The city story of social and economic diversity with global implications continues. Bogotá’s Mayor, Enrique Peñalosa, enjoyed his visits to New York City. He also enjoyed making a point about our transit system in his talks on community development (TED) and transit with one requisite idea.

“A developed country is not where the poor have cars but where the rich use mass transit.”

Brooklyn experienced a period of decline in housing, population, and economic capacity for thirty years strictly due to racism, followed by the trend illustrated in the chart below. The Downtown Brooklyn Partnership. The graph (below) shows a rate of continuous development in Brooklyn’s relatively small downtown straight through the recession of 2008.

A 20-year Federal Reserve Board analysis published in 2005 shows that employment grows in direct proportion to increased housing supply for more than two decades in every metropolitan area. Conversely, thinly developed areas across a region will not see employment growth when more than 65% of the housing is in single-family buildings on small to medium-sized lots.3

Extreme distress associated with sporadic foreclosures, blight-related to high vacancy rates, overcrowding, and a decline in rental housing management and maintenance is a well-documented urban center experience. In 2008, a major economic recession illustrated how low-density areas are not equally subject to poor economic policies. Disinvestment has many faces, it is a degenerative and repetitive process, and low-density housing settlements are not immune. Nevertheless, the central cities have a rich and inspiring set of solutions, from community organizing to creative financing that less dense areas will need.

Low-density urban development slowed for the nation following the 2008 recession. The rash of foreclosures was merely the punctuation on the surface of the crisis. Alternatively, market-rate and affordable housing production continued to expand throughout New York City and other dense urban centers. While the amount of housing available to families earning 80% of the area median income falls short of the 20% of new units goal, the success of social and economic diversity remains equally important. Other factors include New York City’s growing migrant population increasing the total population to 8.36 million people in 2008, up from 8.31 in 2007 and 8.60 in 2020.4

The Rise of the Low Carbon Consumer City (Holian and Kahn 1/2013)5 analyzed several urban data sets. They document how “high quality of life consumer center cities are low-carbon cities.” In addition, the paper identifies causal channels for this association. An example of the data is in the table below.

Urbanized Plants

Joyce Kilmer’s poem, “I think I shall never see a poem as beautiful as a tree.” ends with a reminder that we cannot make these things. Yet, a century later, American Forests, a national advocacy group, began to advance tree and forest functions well beyond awe. Over the last twenty years, they have been busy planting over 40 million trees.

Replacing forests lost to fire, blight, disease, and other human/natural causes encourage closeness. Still, this effort’s main interest concerns the roots, and 46 million residences in 70,000 communities in the United States are at risk for wild/urban interface (WUI) fires.

Trees are active energy-saving devices for cities. They deliver pure water and simple beauty. Trees, especially the canopy along the streets and ample parks, can provide stormwater control and remove tons of pollution from the air and ground. Trees reduce building energy use and the sequestration and reduction of carbon emissions. Still, it appears there will never be enough data to validate Kilmer. The metrics vary by region, climate, and typology. The focus remains on billions of dollars embedded in the “structural value” of timber, tourism, and far less on the public health benefit.

The following is a summary of ten urban centers regarding the value of trees. Each city is a link to the extensive detail on the American Forest website in 2010. 

  1. Austin has 36.58 acres per 1,000 people using its 2000 total population of 790,390 – this is the nation’s most significant ratio. The percentage of land as the park is just under 18%. It has 14,925 trees, of which 6,465 are street trees with a balance of 8,460 in Austin’s 28,911 acres of parkland. 
  2. Milwaukee has 25.53 acres per 1,000 people, with a population of 594,833. The percentage of parkland is 9.8 %, given its 15,189 acres. Trees total 3,377,000 that can remove 496 tons of pollution annually.
  3. Charlotte has 25.36 acres per 1,000 people and a total population of 731,424. The percentage of parkland is 5.50%, with 18,551 acres with 85,551 park acres.
  4. Portland has 23.75 park acres per 1,000 people, given a population of 583,776.  It has 13,864 acres of parkland and 1.4 million trees. The percentage of land as the park is 16.13%.
  5. Minneapolis does 13.99 acres per 1,000 people, with a population of 382,578. The percentage of land as the park is 14.58%. It has 979,000 trees.
  6. Sacramento has 10.87 acres of park per 1,000 people, with a population of 466,488. The percentage of land as the park is 8.15% presenting 5,069 acres of parkland. The tree count is 115,000.
  7. Denver has 9.83 acres of park per 1,000 people serving a population of 600,158. The percentage of parkland is 6.01%, and the city has 5,902 acres of parkland. The mile-high city has 2.2 million trees.
  8. Seattle has 9.00 acres of park per 1,000 people.  Its population is 608,660. The percentage of parkland is 10.20% of 5,476 acres of parkland. It has a tree count is 4.35 million.
  9. New York City has 4.66 acres of park per 1,000, with a population of 8,175,133. The percentage of parkland is 19.51% comprising 38,060 acres. The number of trees is an impressive 5.2 million.
  10. Washington D.C. has 12.40 park acres per 1,000 serving a resident population of 601,723. The percentage of parkland is 18.99%, with 7,464 acres of parkland). It has a total number of 1,928,000 trees.

Density’s Variables

Density constants simplify housing. All the variables, on the other hand, require study. Lay aside all efforts criticizing the social and economic conditions of sprawl. It is useless to blame families looking for housing as a caveat-emptor fault in hindsight. Those who enjoy low-density urbanization still far outnumber those hurt by it.  They are not wrong, but many are looking thirty years out, and the variables get dangerous.

Todd Litman is the founder and executive director of the Victoria Transport Policy Institute. He is an observer of transportation plans throughout the world, and he confronts traffic congestion problems and reviews evaluation methods. He describes a sinkhole in the American landscape due to an over-reliance on cars and trucks. The following is an interpretation of transit in the Litman hierarchy.

Effects of Auto Reliance5

The Slippery Slope of Over-Reliance
  • Dispersed Development
  • Auto Dominated Land Use
  • Free Parking at High Cost
  • Degraded Abandoned Cities
  • Suburbanized Power
  • Discredited Transit
  • Auto-Oriented Mass Transit
  • Fragmented Open Space
  • Oil/Gas Addictions
  • Environmental Damage

Unintended consequences aside, a low-density, spreading city represents the planning of thousands of similar but unrelated small places. Moreover, after WWII, national, state, and local policies dispersed real estate development patterns, emphasizing housing stimulated by limited-access interstate highways. As a result, suburban zoning’s low densities and vast commercial surface parking supplies could become faultless by implementing two policy changes.

National “fix it first” rules for most national highways that connect suburban housing tracks encircling major cities. Public policy would not allow a new road built with public funds unless all the existing roads are certified as equal to a new route.

Over 65% of suburban housing is affordable and owned and controlled by owners with uncomplicated management and maintenance responsibilities. The opportunity to move from the urban core outward creates the framework for the second policy.

Design innovative movement systems from walking to high speed with combinations that reduce horizontal development by providing unlimited urban investment in density in carefully planned prominent places. What do they have to trade? An annual percentage of an enormous increase in property value is taken in advance.

The quiet home solitude of low-density hills with gas-fed transportation could stay that way, but they are threatened.  This threat will dissipate if the nation’s highway capacity (HCM) moves its massive auto dependency problem into integrated high-speed links between various dense centers. Planning practices that see “transportation as driving” and “traffic delay” as the problem put resources into roadway expansion over other transportation improvement options. This practice reduces value, as any Freakonomics student could illustrate all the way back to Olmstead’s Central Park.  Supply = affordable if controllable, but benefits in the short term complicate affordability with perverse incentives. In a visit to California, Olmstead recommended cabins could be allowed in the forest areas accessible by trails, but nothing larger as fire is inevitable.

New tools help transportation professionals define problems more accurately. Building more diversity into the system can transform this hammer-and-nail condition of smooth roads everywhere into more productive.6 Alternatives to silo agencies on the public dollar are unlikely to become the agents for dense development by producing new ways to think about mobility.

Think Variable

Imagine one highway connecting two significant cities leased to a nonprofit community development corporation. A group could own or control one-third to a half of the land surrounding its entrances and exits with the lease. Dense multi-use centers along this route could change all publicly held assets.

The variables associated with the auto/land alliance define attributes that differ widely. A dependent variable’s characteristics continuously change, but if the variable is independent, it influences change. The car is an independent variable affecting every aspect of the conurbation. The challenge is to replace movement as the independent variable with dense urban places with high-speed links.

In 2007, the U.S. Department of Transportation announced support for states to privatize roads and infrastructure. Little has happened due, in part, to the 2008 Recession. Secretary Mary Peters’ office forged legislation for states to authorize public-private partnerships for “building, owning, or operating highways, mass transit, railroads, airports, seaports, and transportation infrastructure.”

Can a lease mechanism remove obstacles to private investment in highways? Yes, if they can be made independent variables. The ideas about policy manipulation of the nation’s infrastructure and the vast capital it represents regularly come from the Reason Foundation. Its Annual Privatization Report: Surface Transportation is a good lead into the mobility quagmire. The 2011 report finds none of the top thirty public/private infrastructure firms are American. Readers will find analysis of changes in policy to 2020 can be accessed for (2016) & (2018). Privatization is conspicuous in the FY2018 Budget portending greater utilization of the private sector. The shift was not via policy. It was a coup.

The strategic opening is obvious. It can take high-speed multi-modal advantage of the vast interstate system within a new green deal framework in transportation systems. It really is that simple. However, no other county in the world has the power and capital to transform itself and pay for it with market changes and public start-up leadership.

Now ask how many of the top thirty of the world’s equity infrastructure firms are in North America? The answer is sixteen, of which three are in Canada. Now try to tell me federal, state, and local public policy cannot get a 180-degree turn of these companies.

Congestion is effective in the right place. Land uses that eliminate daily gas-fed trips will start with alternatives defined by planners who can alter car/land relationships. They present a long list of dependent variables associated with real estate investment practices over the last half-century. Research regarding the “commutes” that people are willing to take daily is extensive. A 2012 study in the Journal of the American Planning Association (JAPA) examined thirty metropolitan areas in the United States. It indicates that compact and centralized development is about ten times more influential than vehicle traffic speed on a metro area’s overall accessibility.7

Compact development improves transportation outcomes. Origin-destination combinations become unlimited. What commuters want from transit choices is predictability composed of three things 1) multiple forms of mobility, 2) social juxtapositions, and 3) network connectivity. 

Density Design

Practical Examples

The Twinbrook Metro-Performance (TMP) District, Urban Design Master Plan Guidelines produced by Street-Works LLC Development stimulates growth along mass-transit routes. It led to their role as entitlement strategists for Federal Realty. The aerial image (Google) illustrates a vast surface parking area, followed by the need to alter low-density zoning’s disincentive to use a train.

The Twinbrook Redline subway station is a half-hour from Union Station in Washington, D.C. The cars to trains drawback are the one-way transit of stations like Redline to Washington. Beyond walking, all other travel needs outside of the core competency for surface transportation resources.

The Rockville MD zoning map and legend govern everything from height to open space. It presents a negotiable range of square feet for categories and user groups. Some of the development envisioned by the zone produces dense mixed-use districts. These controls aid individual investors in many ways, but the main objective is the compatibility of uses based on performance. Over the last century, these newly designed zones occur when development needs a subsidy, incentives, or other encouragements.

In this case, the Redline “car-to-station” plan serves single-family detached country homes adjacent to large commercial/institutional centers and sophisticated multi-story housing with ample auto parking. The addition of a transit-oriented station-to-station density offer places that meet most needs by walking. Urban containment supports distinct sets of transit modes. Diversity is the most likely cause of superior solutions.

In this case, the population grew by 29.2 percent (2000-2010), slightly increasing the annexed area. Most of the population growth came from the developments on land added in the 1990s (King Farm and Fallsgrove). These were mixed-use developments with multifamily housing. Also, Congressional South and Town Square increased Rockville’s population and density since 2000.

Thousands of Rockville-like jurisdictions along transit corridors offer paces for dense mixed-use housing, commercial office, and retail developments in the northeast. Public benefit corporations designed “to prevent chaos” will do so with transportation services. But, without new forms of transportation authority tied and paired to high-density housing, commercial office, and retail development, cities fail.

Governing, the states and localities magazine ‘urban’ section has started to describe challenges to regional planners and policymakers in meeting new community development opportunities.  (See Rockville, MD) Based on the age-cohort analysis, housing demand through to 2050 will be from one-person households composed of two age groups. Both prefer dense urban areas. They are young professionals and those who are retired or about to do so.  They both like the lifestyle of walking to acquire convenience goods and services, ranging from food to continuing education classrooms.  Changing demographics such as a preference to walk vs. drive will re-shape quality living environments.

Density’s Big Problem

Lateral growth along the earth’s surface or unlimited vertical growth has a correct/incorrect dynamic. Phycologists explain how what is seen can be accurate or inaccurate at any time but always thought of as right. Without this, the ability to retain emotional stability would crumble. The willingness to absorb new experiences comes from the confusion about change. The challenge is knowing the difference between what people need and what people want. Density’s big problem is finding the balance between vertical and lateral.

Reflecting on events develops measures for the effects of progress. For the last three centuries, the government’s objective of governments, agencies, and business partners has been to get to a new place, even a new planet in the public’s imagination. The urgency for “newness” derives from wealth accumulation as an ancient need for security. Once acquired, wealth and power become wants and become very confused about requirements. If humans turn inward toward a more “mindful place,” urbanization policy will require set limits on development. It will succeed as a mindful place if it can end the social and economic stress it currently requires of vulnerable populations.

Following is a prompt to explore. Please return to refer photographers.


  1. GDP is the sum of gross value added by resident producers in the economy plus any product taxes and minus any subsidies not included in the value of the products. It is calculated without making deductions for the depreciation of fabricated assets or for depletion and degradation of natural resources.
  2. See:
  3. See:
  4. “The Rise of the Low Carbon Consumer City” NBER Working Paper No. w18735, San Jose State University – College of Social Sciences Email:, University of California, Los Angeles (UCLA) Email:
  5. Todd Litman, 2013 (c)Smart Congestion Relief – Comprehensive Analysis of Traffic Congestion Costs and Congestion Reduction Benefits“. Victoria Transport Policy Institute.
  6. The Psychology of Science, 1966, page 15 and his earlier book Abraham H. Maslow (1962), Toward a Psychology of Being: I suppose it is tempting, if the only tool you have is a hammer, to treat everything as if it were a nail. (cite)
  7. Jonathan Levine, Joe Grengs, Qingyun Shen, and Qing Shen (2012), “Does Accessibility Require Density or Speed?”  Journal of the American Planning Association, Vol. 78, No. 2, pp. 157-172,; at . Also see, Metropolitan Accessibility: Comparative Indicators for Policy Reform, at