No place like home

In 1990 the population of California was thirty million. Thirty years later it is forty million.

That’s a thirty-three percent increase. (30M + 10M = 40M and 10M/30M = 0.33 = 33%)

In 1990 the population of Yreka was seven thousand. Thirty years later it is seven thousand, six hundred.

That’s just under a nine percent increase. (7K + 0.6K = 7.6K and 0.6K/7K = 0.086 = 8.6%)

While the State has averaged a little over one-percent annual growth the City has managed just three-tenths of that. I think most would say the State has grown too much and the City has not grown enough. In the same time span Siskiyou County has grown by only 100 souls, from 43,500 in 1990 to 43,600 in 2020 (with a peak of 45,000 ten years ago). That’s only (100/43500) 0.2% growth! I think most would not call that growth but instead call it stagnation.

In capitalism you have to grow. Growing slowly is almost the same as not growing. There’s no such thing as a steady-state. The growth curve must trend upward—it cannot be flat. The entire edifice of the free market system is built on growth. Lack of growth means not simply diminished expectations for the citizen-consumer but collapse of their way of life.

Most folks think, with apparent logic and good intentions, that there is a growth-number sweet spot, a sort of Goldilocks “just-right” percentage that will allow a city, county, state, or country to grow and prosper without sacrificing the quality of life. There may be such a number. I don’t know, but I have my doubts.

Here’s where you need math. Don’t run away. This is easy, and I’ll put the nerd stuff in the “optional reading” section. It is called The Rule of 72. If you want to know how fast something will grow think of it in terms of doubling time. If you have a hundred bucks invested in something, how long will it take at that interest rate to get to two hundred bucks?

If you are making 1% interest, it will take 72 years because 72/1 = 72.

If you are making 2% interest, it will take 36 years because 72/2 = 36.

If you are making 3% interest, it will take 24 years because 72/3 = 24.

That’s the Rule of 72. Take 72 and divide by the interest rate. 72/4 = 18, so it will take 18 years for \$100 to become \$200 at 4% growth.

So if you live in a lovely town of 5,000 people and the city council wants to spur job creation and growth and they pick a target of 3% per year you can tell them that means the town will have 10,000 people in twenty-four years (72/3 =24). Ask them if this is their intention—to double the size of the town in one generation.

The Rule of 72 works for any kind of percent growth: people, bacteria, dollars, etc.

Yreka is a quiet place and lots of people have to leave because there just aren’t enough jobs. It is tough to make a living in a place where economic growth is slow-paced. In fast-growing places people often have to leave because housing and transportation costs outpace incomes. This is why we are always on the lookout for that sweet spot, where the growth is enough to sustain communities but not so much it prices people out. California is well-known for its high cost of living.

I don’t know the answer. Growth is one of those things we talk about every election cycle but we talk about it in vague terms. We equate growth with “good” but we don’t really know how much is good and how much is too much. We usually find out the hard way, after things have happened. We don’t really know how to plan for growth, or if we do, how to make it work. I think people in famous resort areas like Lake Tahoe would say they wished they’d planned for growth a little better. A weekend drive there can turn into car-maggedon in a hurry.

I do know that until we can quantify growth, and translate that into quality-of-life metrics that reflect the impact of growth on communities, we’ll just be trotting out the same B.S. and having the same arguments. I don’t think folks are willing to question the basic growth assumptions that underlie our capitalist society. I don’t think an austerity message will resonate with Americans. Capitalism is optimistic in its outlook. There’s always another market just around the corner, all it will take is a little innovation and elbow grease and we’ll all get rich. It’s hard to argue with that. Only later, when the ravenous maw of free enterprise has consumed your small town and left behind a strip mall, will you wish you’d done the math.

The Rule of 72 works because of the natural logarithm of 2, which is approximately 0.693 and is often rounded off to 0.7 for quick estimates. Dealing with percentages means we have to multiply by 100 so you get 70, and it is sometimes called the Rule of 70. The Rule of 72 works as a convenient approximation because 72 is divisible by 36, 24, 18, 12, 9, 8, 6, 4, 3, and 2 and is thus handier for mental math.

Why the natural logarithm of two (ln 2)? Since we are talking about doubling time, we need a solution to the exponential growth formula that is twice as big as what you start with.

Growth is calculated with the base e raised to the product of the rate and the time:

e^rt or ert (they mean the same thing, one is easier to type).

If you start with amount A you need to find the rt (rate x time) to get to 2A, or double the original amount.

2A = Aert

2 = ert

ln 2 = rt

r is expressed as a percent, thus r/100, so you get

100 ln 2 = t

t is time in years and ln 2 is about 0.7 so

70 = t