Monday, October 26, 2009

Calculating Growth, Doubling Times, and etc.

Calculating Growth: What does Baker City's "Slow Growth Option" really mean?

An article in the Herald (Baker City officials look at slow-growth option; stated that:

"Over the past three months, 14 focus groups comprising 133 community volunteers spent hundreds of hours studying and debating the pros and cons of three planning options for Baker City’s future, including a no-growth do nothing strategy, a slow-growth strategy designed to see Baker City expand over 25 years to a population somewhere between 15,000 to 30,000, and a fast-growth model that helped the Bend-Redmond area soar from a population of around 30,000 to more than 80,000 during the last 25 years."

In a letter to the editor, Councilor Milo Pope, a primary Brocato devotee, stated "Well, “growth” is a bad word and we’re not going to permit Baker City to look like Bend. Their fears are unfounded." (

All this struck me as interesting because if we were to grow to the upper limit 30,000 scenario envisioned in the "slow-growth strategy," we would actually be growing at a rate that exceeded the "fast-growth model" in the Bend-Redmond area over the last 25 years. This is not too difficult to calculate from the figures provided above. If Baker City were to grow from the current approximate of 10,000 people to the 30,000 endpoint, we would triple our population in the 25 year period (30,000/10,000 = 3 times our current population). Contrast this with the expansion of population in the Bend-Redmond area over a 25 year period that was characterized as "fast-growth." They went from 30,000 to 80,000 which is 2.7 times what their population was at the beginning of the 25 year period (80,000/30,000 = 2.7 times). Therefore, if we grow at the upper limit of what was envisioned in the Planning Department's (Don Chance, et. al.) "slow-growth" scenario, we would be growing faster than the Bend-Redmond area's "fast-growth" scenario over the 25 years cited. Will the Baker City Herald or Don Chance please explain what's up with this? People asked for slow-growth, not fast-growth. What actually constitutes slow-growth?" Surely it is not something in the range of 3.5 to 3.6% per year.

As the article below explains, there is a simple way to calculate the doubling time in population: "Because we are discussing a “doubling” time, i.e. the time for a quantity in question to double (or halve), the exponential function has a user-friendly aspect that is very helpful. It turns out that any finite rate of change expressed as a percent (e.g. 5% per year) can be converted, to a good approximation, to a doubling time simply by dividing it into 70. For example, if the rate is 2%, you might expect to have twice the number, i.e. 100% more stuff, in 100/2=50 years, but because of the compounding effect the correct answer is 70/2 = 35 years. The proof of this statement makes a good exercise for a math class at the appropriate grade level. Rates of loss (for instance, depletion of resources) have a halving time that is calculated the same way. For anything diminishing at 2% per year there will only be half as much in 35 years."

So, a growth rate of 3.5% per year means that Baker City would double in population in 20 years (and be 40,000 in 40 years). (Do the Math: 70/3.5 = 20 yrs. and etc.) While Baker County is not growing rapidly, what growth there has been is certainly noticeable, and is having an effect on the quality of life most of us moved here for. Areas approved for development and the 80 or so Measure 39 claims moving through the approval process, coupled with national population growth and other trends, will ensure that County growth continues. Some of the traffic issues we already face in Baker City are coming from visits by the growing number of County residents rather than from City residents. One must envision a rural farm/ranch landscape covered with houses, reminiscent of what happened to the Land of Milk & Honey, Southern California, over the period from 1950 to the 1990's, to understand the possibilities, although many insist it can't happen here. I will make an attempt on some future date to show photos for those of you that may be too young or untraveled to know what I am talking about. All I can say at this point is that I lived through the destruction of Southern California by population growth and human greed. That could be your future if you do not control growth to a sustainable level here. Sustainability should be equated with population stabilization, in Baker County and Baker City. Baker City residents have had something approximating stabilization for years, and the surroundings you enjoy are the result.

You can buy in to the growth scenario, the boom thing, with a relatively short period of economic/monetary/spending nervana (especially for developers, realtors and construction folks), and ultimately kill it all--or you can stay in a population stabilization course, and enjoy what you have for generations to come.

Another thing to consider is the built in upper limit of property taxes in the state if Oregon. Under the current limit of 3%, the County tax collector can double your property tax burden in 23 years if they increase the tax by the allowable amount. My property taxes went up by a little over 2.9% this year.

I have provided below two essays: One on Doubling Time and its calculation, the other on Sustainability. Its not rocket science. It sometimes seems futile to provide such information, but I also realize that there are many inquiring and sometimes brilliant minds, no matter how impoverished, out there, who will take such information and use it to the benefit of their neighbors and humankind. For those of you of the latter description, please run with it and save your world and yourselves. Envision a world with a sustainable human population, getting by on the available resources, at a rate that ensures their availability for generations in the many centuries to come.

Doubling time:  
it works for ANY rate of change
A. R. Palmer, Institute of Cambrian Studies, Boulder, CO

To read all of the articles from the Boulder Area Sustainability Initiative Network about sustainability and stewardship of the global commons, see:

A parable: “When was the pond half full?”

I lived by a large pond with a thriving community of fish, so fishing was good.  One day not too long ago some algae began to grow in the pond.  Their population was doubling every minute.  Yesterday morning I went fishing and everything was fine.  Yesterday noon when I looked out at the pond, it was suddenly filled with green algal scum and the fish were dying from lack of oxygen.  Why didn’t I see the disaster coming and do something?  When was the pond half full [11:59]?  One-quarter full [11:58]?  One eighth full [11:57]?  Suppose, instead of my pond, we were considering an island, or a continent, or Spaceship Earth?

At the heart of the concept of doubling (or halving) is the exponential function familiar to many from mathematics, science and engineering.  Geologists are perhaps most familiar with this in its backward-running version, i.e. the description of the rates of decay of radioactive isotopes.  Most of us, however, learned about exponential growth as compound interest in the context of a personal savings account.  If we put our money in a bank and let the interest accumulate, our annual income grows as the capital increases. Even though the interest rate remains constant - our capital grows at an exponential rate.  Recognition of doubling (or halving) time for ANY rate of change was not always emphasized.

Because we are discussing a “doubling” time, i.e. the time for a quantity in question to double (or halve), the exponential function has a user-friendly aspect that is very helpful.  It turns out that any finite rate of change expressed as a percent (e.g. 5% per year) can be converted, to a good approximation, to a doubling time simply by dividing it into 70.  For example, if the rate is 2%, you might expect to have twice the number, i.e. 100% more stuff, in 100/2=50 years, but because of the compounding effect the correct answer is 70/2 = 35 years.  The proof of this statement makes a good exercise for a math class at the appropriate grade level.  Rates of loss (for instance, depletion of resources) have a halving time that is calculated the same way.  For anything diminishing at 2% per year there will only be half as much in 35 years.
This simple way to calculate doubling time (or halving time) should be an essential part of everyone’s education.  When the mayor is proud because the city has a healthy growth rate of 3% per year, that means the city will double in about 23 years if that rate continues, and double again in another 23 years, and double yet again in another 23 years, thus octupling from its original size in 69 years.  One might ask if a city with 8 times the present population is viable.  Garbage also has a rate of growth, as does traffic, pollution, schools and housing.
A city is not a closed container, thus its limits to growth will be determined by cultural factors, but Earth IS a closed container for all practical purposes (more on this in Part IV ).  Growth in a closed container will ultimately fill it up.  Thus, we should look carefully at anything in our culture with a growth rate, calculate its doubling (quadrupling and octupling) time and make a judgment about whether we think this is healthy for our future.  We should do similar calculations and make similar judgments about those aspects of our culture where, as a result of our consumption habits, a resource is diminishing at a measurable rate.  Thus, calculations of doubling (or halving) time are critical components of the issue of sustainability – by which we mean the indefinite continuation of the entire human enterprise within some steady-state limits imposed by space and resource availability (see Part X in this series).
Global population growth rates may be diminishing, but they are still positive.  Thus population is still growing and it has a doubling time.  Currently the rate is about 1% per year (thus doubling in 70 years).  Consumption of resources (Part IV) increases with population size, even if individual rates of consumption do not increase.
If we could slow the present population growth rate to 0.1% per year, it would still be double its present size of about six billion in 700 years, quadruple in 1,400 years, and octuple in 2,100 years – equivalent only to the time represented by the Christian era.  Forty-eight billion people may make things a bit crowded.  Such a population, with its attendant FOOTPRINTS (the areas of productive land necessary to support each one of us, see the upcoming June essay), may not be sustainable.  It is not even clear that we can handle one more doubling with a reasonable quality of life for all.
Such doubling-time scenarios should make us wonder if there is such a thing as the politically popular “smart growth” – perhaps it’s a euphemism for “predictable and voluntary disaster”.  Every time you see a headline or magazine article mentioning rates of change (either increase or decrease), do the quick mental math to calculate the doubling (or halving) time.  It is a very revealing exercise.

E-an Zen, University of Maryland, College Park, MD
Whenever we ponder the future of the human enterprise, questions about material resources come up.  Will they run out?  Will they replenish themselves?  Will the demand for them diminish, or will alternatives be found?  Without a good estimate of those resources, we will never be able to predict or improve human welfare.  "Malthusians" have a doomsday outlook; "Cornucopians", a more optimistic view (McCabe, 1998).  Yet whichever school of thought seems more persuasive, the fact remains that we live in a materially closed system.  The Earth's resources are finite, so we must choose how best to use them.
A society needs reliable information on the resources available to it and on the consequences of their use.  How it will act on that information will depend on its value system.  For example, a society may place a high priority on fair distribution of wealth.  We in the developed nations have an opportunity to demonstrate a commitment to use resources in a sustainable way.  Do we want to act responsibly toward future generations of our species and toward other life forms as well? 

Material resources are whatever the society at a given moment either uses or recognizes as potentially usable.  Because that list changes with society's needs and technology, what is useless one day may become vital the next.  As recently as a century ago, aluminum, petroleum, and uranium were not significant resources. 
Geologists tend to think of "resources" as the stuff we take from the ground: metal ores, coal, petroleum, groundwater, limestone, phosphate, quartz sand and rock.  The earth's resources, however, also include living things that are subject to human exploitation. 
Trying to inventory resources for the future, thus, is like aiming at a moving target.  Yet some statements will remain valid for three reasons: (1) except for energy input from the sun, which supports and maintains our “ecosystem services”, the earth is a closed system having a fixed quantity of materials.  (2) Both the extraction and processing of materials and preservation of the environment require energy, itself a resource.  (3) Using a material generally changes its state of aggregation, and its adaptability for future use.  Thus, the processing of materials, including recycling or re-aggregating waste material into usable form, causes a thermodynamically inexorable loss of useful energy and/or material.  With regard to Earth’s material resources, there is no free lunch! 
To these factors must be added both an increasing global population (projected to reach about 9 billion people by 2050), and a higher per capita consumption rate reflecting  "improved" standards of living.  Obviously, resource considerations are crucial for the success of the human enterprise.

Traditionally, resources are grouped as "nonrenewable" and "renewable".  Nonrenewable resources (examples: ores, petroleum, coal) replenish at geological rates that are much too slow to benefit human society.  Once consumed, such finite resources are effectively removed from our inventory.  New discoveries or more efficient extraction methods merely postpone their inevitable exhaustion. 
"Renewable" resources (examples: timber, fishstock, groundwater) have rates of natural replenishment commensurate with the time- scales of human society (see DEMONSTRATION 1 below).  However, to consume such resources faster than they can replenish themselves is like withdrawing funds from a bank account faster than we make deposits; sooner or later that account will run out.  We have often been guilty of just such overwithdrawal.  Examples include overfishing, poor husbandry of arable and pasturable land, overpumping of aquifers, destruction of entire ecosystems such as Russia's Aral Sea.  Such "local" losses can have large systemic effects (see DEMONSTRATION 2 below).
More effective use of substitutes, recycling, and conservation can slow down depletion of a renewable resource (i.e., the amount of consumption that exceeds its renewal by all processes, natural or engineered), but they cannot halt the process.  To make a "renewable" resource truly renewable, the rate of consumption must not exceed the gross rate of renewal.  Reaching a "sustainable world" will demand many changes to our priorities regarding resource utilization.

Some vital resources, such as the "environment", are not material objects.  A healthy environment is a composite of many other items (e.g., water chemistry and temperature, nutrients and other chemicals in the soil, good habitats for wildlife).  A natural place of beauty and wonder is an intangible but valuable resource.  A less obvious intangible resource is the future generation's options, i.e., their capability to make real choices.  Options are not fixed commodities, but surely they will be important for future societies.  Like the options available to us today, many future options require the availability of material and energy.  Even if an earth material is not dispersed through use, their very processing automatically reduces future options of their use.

The results of human exploitation of resources cannot be predicted by looking at one commodity or one social force at a time.  Calculation of the effects of use and depletion of materials on the public commons (see Part I) must also include human values and cultural habits.  Justus von Liebig, a 19th century agricultural chemist, recognized the complexities that arise in a situation where humans and natural forces work interactively.  Historian Elliott West put von Liebig's view this way: "an organism's limits are set, not by the maximum profusion of necessary things, but by those things' minimum availability.. Look .. for how much is available when vital supplies are the tightest, lowest, stingiest". 
What is true for an organism is true for ecosystems.  Can we identify the "vital supplies", their mutual relations and their future trends?  Can we recognize the factors of "minimum availability" while there is yet time?  Or will they surprise us and perhaps blindside us?  Surely we need to be thinking about these issues.
To maintain a society's standard of living requires consumption of resources at some level.  In Part XX of this series, we will explore this subject within the "sustainability" context.
The author thanks Christine Turner of the US Geological Survey, Denver, for her contribution to the ideas and her critique of the text.
(1) Ask your students to list the resources that they encounter in one day of their activities, using the following categories:
A. "Nonrenewable" resources are those that may be replenished only at
     rates much exceeding the human time scale: for example, fossil fuel
     (what should be included here?), metals (where do they come from?).
B. "Renewable" resources are those that may be replenished on a human
     time scale, but only if the rate of withdrawal or destruction does not
     exceed the rate of replenishment: for example, timber, fishstock, soil,
     groundwater, environmental quality, mixed forests, ozone layer.
(2) Pick any material object: the gasoline you pump, a metal paper clip, the bricks of the building, the gravel in a driveway, a toothpaste tube, or a molded plastic chair.  For that object, ask the students to identify the resources embodied in it: where did the material come from, and in what original form?  Ask them to discuss what processes were needed to produce the object (e.g., mining, harvesting, refining, waste disposal, ecosystem disturbance, transportation, energy use).  What renewable or nonrenewable resources were used in the processing?  Are there substitutes that would require less energy and material?  How essential is this particular product to the students' comfort or well-being?  Could they make do with less?  What would be the tradeoff in making a more frugal choice?  Who might benefit from that choice, and in what way?
In a recent book, "Waiting for Aphrodite", Sue Hubbell, author-naturalist-apiarist, described recent stresses to communities of the green sea urchin, Strongylocentrotus droebachiensis, which lives off the rocky coast of Maine.  The population density of this sea urchin seems to go through cycles; in the 1980's they thrived.  Sea urchin eggs were a delicacy for the affluent Japanese.  When their local stock was becoming depleted at about this time, the Japanese merchants turned to Maine for a substitute.  Meanwhile, needing an alternative source of income because the coastal cod and haddock fishery had collapsed through overfishing, the fishermen of Maine started to dive for the green sea urchins.  Soon, however, the catch began to fall alarmingly.  Green sea urchin eggs are fertilized by sperm which last only a few minutes in seawater, so large congregations of urchins are essential for the species to survive.  Large congregations attract fishermen as well, but, luckily for the urchins, the Japanese yen weakened, the demand for pricey urchin eggs fell, and a Russian source became available.  Sea urchin "farming" is now being explored as a steady source of supply, so the natural communities of Maine sea urchins might yet recover. 
How might the disappearance of green sea urchins affect the ecology of the coastal waters?  We do not know.  Some years ago scientists thought that the long-spined black sea urchin, Diadema antillarum, of the Caribbean region was a useless species.  Then it was discovered that coral and sponge larvae can attach themselves to reefs only on surfaces kept clean by the sea urchins, which graze on the algae.  So the "useless" sea urchins turn out to be essential to the coral reef ecosystem, after all.
This particular story may be minor in the scale of things, but it provides a good example of the intricacies of an ecosystem.  If we act without adequate knowledge, we can easily throw an ecosystem out of balance, possibly irreversibly.
Hubbell, Sue, 1999, Waiting for Aphrodite: journey into the time before bones. 
Boston, Houghton and Mifflin.  242 p.
McCabe, P.J., 1998, Energy resources - cornucopia or empty barrel?  American
Association of Petroleum Geologists Bulletin, v. 82, p. 2110-2134.
von Liebig, Justus, 1847, Chemistry in its applications to agriculture and physiology:
London, Taylor and Walton.  418 p.
West, Elliott, 1998, The contested plains: Indians, goldseekers, and the rush to Colorado. 
University Press of Kansas.  422 p.

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