Quantitative Literacy is Required

All resource usage and/or pollution will grow exponentially but with different couplings to the population growth this is what drives resource depeletion. For instance, the the previous "lecture" we learned that electricity generation scales as the population growth to the 3.5 power!

• At present we do a very bad job at "training" and educating people to look at the data. Data literacy, a key attribute for getting a job in the post 2010 world, is completly absent from the undergraduate curriculum. In addition, students think there is an "app" for that, so they seldom are motivated to develop good skills.

• We do an even worse job at presenting the raw data for objective analysis. Instead, we are a nation and community of SPIN doctors. This causes people to argue from a position of belief rather than a position of knowledge. This causes paralysis. This is why we can't do anything, anymore.

"Math, formulas and other things that don't apply to real life"

(--anonymous comment from student evaluation as the part they liked least about the course)

So we live in a society that is afraid of and doesn't understand numbers.

How fast will Resource X be depleted?

Well suppose we have the following situation:

• As of 2008, there are 100 units of Resource X still available to us
• In the year 2008, we will use 1 unit of Resource X.
• as measured over the last 6 years, our use of Resource X grows at the rate of 5% per year.

Dear Congressperson, when will resource X run out.

Congressperson says "oh don't worry, Resource X will be around for 100 years"

Really .... don't we use resources like rabbits?

Clearly, Exponential growth, in general, is not understood by the lay public. If exponential use of a resource is not accounted for in planning - disaster can happen.

The difference between linear growth and exponential growth is astonishing. Exponential growth means that some quantity grows by a fixed percentage rate from one year to the next.

In this animation, one can clearly see that no matter what the growth rate is, exponential growth stars out being in a period of slow growth and then quickly changes over to rapid growth with a characteristic doubling time.

A handy formula for calculating the doubling time for exponential growth is:

Doubling Time = 70/n years n = percentage growth rate; 5% n=5 70/5 = 14 years doubling time The math behind this

So

• for n = 1% the doubling time is 70/1 = 70 years.
• for n =2% the doubling time is 70/2 = 35 years
• for n =5% the doubling time is 70/5 = 14 years
• for n = 35% the doubling time is 70/35 = 2 years

Its important to recognize that even in the slow growth period, the use of the resource is exponential. If you fail to realize that, you will run out of the resource pretty fast. A good example of poor public understanding.

A survey of Boulder Colorado residents about the optimal size for growth returned a result that most residents thought that a growth in population at the rate of 10% per year was desirable.

Well 10% a year may not seem innocuous but let's see how these numbers would add up?

• Year 0 60,000
• Year 1 66,000
• year 2 72,600
• Year 3 79,860
• Year 4 87,846
• Year 5 96,630
• year 6 106,294
• Year 7 116,923

So by year 7 the population has almost doubled and by then 10,000 new residents per year are moving to Boulder (demanding more services against a tax-base that doesn't scale)!

If one had asked the question on the survey: Is it desireable for the population of Boulder to double in 7 years, there would have been an overwhelming NO. Clearly, the general population can not equate 10% growth rate with 7 year doubling time.

Calculating a growth rate from the data:

When considering growth over a period of years taking the natural logarithm of the ratio of the final value to the initial value and dividing by the time period in years gives the average annual growth rate.

Example:

Number of Building Permits in Pasco WA

Growth Rate:

• initial value (1992) = 400
• final value (2000) = 1600
• ratio of final/inital = 4
• natural log (ln) 4 = 1.39
• over 9 years, growth rate is then 1.39/9 = 15.4% per year
• doubling time is 70/15.4 = 4.5 years (and the sample has doubled twice from 400 to 1600 in 9 years self consistent