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Wednesday, July 26, 2023

A Mathematical Form and Pattern Language for City Design

Letter to Dr. Mohammed ouda, Ph.D


 I have spent many years attempting to correlate two-dimensional urban patterns with their three-dimensional implications using mathematics. These patterns grow one cell at a time to produce the urban form we inhabit. Some results have been referred to as sprawl and others as excessive intensity. Neither has had an adequate leadership definition preventing us from repeating these results. (These cells are more commonly referred to as lots, parcels, projects, and so on.)

My effort has focused on the characteristics and growth options for an individual shelter cell since it combines with others to form a Shelter Division served by the Movement, Open Space, and Life Support Divisions of its Built Domain anatomy. The effort has involved a new building design classification format, new design specification templates related to each building design category (BDC), template algorithms that distill the values entered to produce the values needed by a BDC master equation, and gross building area options predicted by the equation based on the floor quantity alternatives entered in the template after all other relevant two-dimensional site plan design value percentages are entered.

The result is a prediction of gross building area alternatives related to the floor quantity options entered. When these gross building area options are divided by the buildable acres identified, the result is a series of shelter capacity alternatives that have physical intensity, intrusion, and dominance implications that be calculated.

The design specification values related to existing projects can also be measured for evaluation. The implication calculations will form a new language based on measurement and evaluation that we can call the science of city design. It is perfectly suited to landscape architecture, urban design, and city planning. It requires no architectural prerequisites to address the form and pattern of an urban anatomy that cannot continue to grow and indefinitely consume its source of life with sprawl and excessive intensity.

I have written four books and over 200 essays on this subject. The essay list can be found on my blog at www.wmhosack.blogspot.com. My last book is entitled, “The Equations of Urban Design” and is available from Amazon.com at a very nominal price. It contains my attempt to correlate two-dimensional patterns with their three-dimensional physical implications using a new scientific language based on the persuasive vocabulary of mathematics as its foundation. I have made the effort because I believe we need the language to speak in more credible and convincing terms based on measurement, evaluation, and accumulation of lasting knowledge to support ephemeral design talent.

Walter M. Hosack: July, 2023

Monday, July 3, 2023

Confronting Sprawl: with the language & mathematics required to build knowledge and leadership credibility

I don’t believe the use of land to shelter increasing population activity has been seriously considered a threat to our survival. If it has at some intellectual level, the concern has not been converted to a definition of sustainable geographic limits for cities that protect agriculture and the Natural Domain. We continue to rely on unlimited annexation to expand the land area needed to shelter the activities of increasing populations, and this continues to consume our source of life with sprawl.

The law of limits for all other species is a simple equation related to the land available. We are no different, but have considered land as property and a convertible commodity without limit. Part of this attitude, I believe, is due to our incredibly small individual presence on the planet; hubris that fails to recognize our parasitic behavior; and an inability to lead shelter capacity decisions with the abstract comprehension, measurement, prediction, and evaluation required. We represent microscopic activity expanding in a petri dish being observed by a universe that will not intervene to diagnose and treat behavior that exceeds the planet’s law of limits. We are expected to recognize the obligation.

There is no question in my mind that there is a power beyond our comprehension, but I don’t believe it exists to save us from ourselves. We have been given guidance, permitted choice, and are expected to make the right decisions.

In the case of shelter for the activities of growing populations, it is one of four divisions in the Urban and Rural Phyla of a Built Domain that is in competition with our source of life - the Natural Domain. The other three divisions serve the Shelter Division and provide the movement, open space, and life support infrastructure it needs to survive.

The path we follow in our cities will depend on our ability to build knowledge that can lead us away from unlimited sprawl. This direction will not be provided by divine guidance. We must acquire the knowledge needed to define direction and correlate the many professions that must contribute. Until then, we seem to have concluded that we can rely on citizen participation for decisions. I hope to show in this essay that this participation cannot command the detail required to plan the strategy needed for leadership. The goal is rather self-evident. We must learn to shelter the activities of growing populations within a geographically limited Built Doman designed to protect their quality and source of life – the Natural Domain.

I have mentioned this topic in many essays. At its heart has been a conviction that we do not have the city design language needed to step beyond conflict over opinion with the measurement, evaluation, and prediction needed to build knowledge, gain credibility, and introduce restraint within a political environment that does not recognize the issue as one of survival. The protection of health, safety, and welfare has helped us to survive. It has overlooked the implications of unlimited growth and consumption on a planet that is no longer a “land without end”.

Our course can be adjusted by classifying building design categories in a way that permits us to accurately measure and predict the shelter capacity of land and the intensity these options imply. This is relevant because the combination of gross building area and activity on a given land area produces shelter capacity, intensity, and economic productivity per buildable acre. It may take a minute to digest this, but may come into focus when I point out that gross building can be occupied by any activity. Compatibility of activity has been a city planning concern, but the quantity of activity and its revenue potential per square foot and per buildable acre has been a mystery that determines a city’s financial stability. In other words, a land use activity plan without a correlated gross building area and condition plan will struggle to define a stable financial strategy over time. It will be forced to fight endless tactical battles over project proposals with only a vague understanding of the role they will play in a comprehensive financial strategy. Calculated correlation of these relationships on every lot within a city’s land use plan will indicate its current economic stability, quality of life, and future course of action; since the average annual revenue received per buildable acre in a city should equal its average annual cost per acre to provide essential services. If the imbalance is great enough, the debate over the definition of “essential” begins as budget cuts become an issue. 

I should also mention that excessive gross building area on a given land area produces excessive intensity. Intensity seeking to magnify profit has been a term without a definition and source of frequent conflict. Floor quantity is only one of many design specification topics that combine to form intensity. Those who have read some of my previous essays have read about these topics and the correlation involved. I won’t repeat myself here for the sake of brevity. I’ll simply mention that intensity is a function of shelter capacity and can now be measured. The relationship of intensity to gross building area and activity determines the revenue potential of a given land area, and the physical dominance introduced within the urban pattern we inhabit.

The objective is to accurately predict gross building area and intensity options for a given land area based on the design specification decisions entered in a building category’s forecast model. This definition is not only useful for prediction. The specification topics can also be measured at existing locations to benchmark a host of related observations and evaluations from many professional perspectives. I think we may agree that measurement can lead to knowledge.

I would like to introduce the entire list of building design categories, activity groups, and master equations I have proposed. It is included on three pages as Table 1. I am not including the digital templates that permit a set of design specifications for a building design category to be evaluated with a few keystrokes. They are beyond the scope of this limited format. I hope you get acquainted, since the cellular structure of a city currently represents the anatomy of a parasite that does not understand the discipline required to survive.

The master equations referenced in Table 1 have been included to show they exist. I have not included explanations for the abbreviations shown and derivations involved. My primary objective has been to present the classification needed to proceed with the evaluation of design specification decisions and shelter capacity implications.

POSTSCRIPT

Economic development will continue to struggle until it can accurately correlate shelter capacity with activity, intensity, and revenue on every lot in a city. At this point it can begin to understand the current and future potential of the land involved. This is when strategic discussions can begin with the information needed. Until then, cities will continue their annual dance with deficits and city design opinion will continue seeking a stronger foundation.

Walter M. Hosack: July, 2023