The Leporine Trap

7 min read Original article ↗

This writing begins with a copy of Aesop’s famous fable “The Hare and the Tortoise,” after which it presents the idea of limiting exponential economic growth.

The Hare and the Tortoise

A Hare was making fun of the Tortoise one day for being so slow.

“Do you ever get anywhere?” he asked with a mocking laugh.

“Yes,” replied he Tortoise, “and I get there sooner than you think. I’ll run you a race and prove it.”

The Hare was much amused at the idea of running a race with the Tortoise, but for the fun of the thing he agreed. So the Fox, who had consented to act as judge, marked the distance and started the runners off.

The Hare was soon far out of sight, and to make the Tortoise feel very deeply how ridiculous it was for him to try a race with a Hare, he lay down beside the course to take a nap until the Tortoise should catch up.

The Tortoise meanwhile kept going slowly but steadily, and, after a time, passed the place where the Hare was sleeping. But the Hare slept on very peacefully; and when at last he did wake up, the Tortoise was near the goal. The Hare now ran his swiftest, but he could not overtake the Tortoise in time.

The race is not always to the swift.

I ask of you, the reader, to read two more fables. One is that of “The Goose and the Golden Egg”, which says “Those who have plenty want more and so lose all they have.” The other is “The Fighting Bulls and the Frogs,” which teaches that “When the great fall out, the weak must suffer for it.”

Now, what is the Leporine Trap and why am I talking about these fables?

What is the Leporine Trap?

Leporine is an adjective that means: relating to or resembling a hare. Testudinal is an adjective that means: relating to or resembling a tortoise or a tortoise shell.

The Leporine Trap is the idea that exponential production growth causes catastrophic environmental degradation, whereas linear production growth avoids it. (This idea is a conjecture.) The word catastrophic is a warning that the environment would not be able to recover.

Environmental degradation as in:

  • depletion of resources, such as quality of air, water, and soil;
  • destruction of ecosystems;
  • habitat destruction;
  • extinction of wildlife;
  • or pollution.

Economic growth is the Golden Egg. The Goose is mother nature. Powerful businesses are the Fighting bulls. Laborers are the Frogs.

From the fable to the trap

Suppose the Hare Group and Tortoise Corporation each discover material Z, useful across many industries. Clearly, production of material Z would lead to economic growth, as it is of superior quality to any alternatives. So, Hare Group starts a production process, as does Tortoise corporation.

Time passes and demand skyrockets. But linear-growth production cannot meet demand. Hare Group Invests all hands to find increase production. Tortoise does not. With time, Hare succeed, but at a hidden cost. Unlike the safe dosage of the linear process, the dosage of chemicals used by Hare now harm the environment.

For Tortoise, linear growth rate production is the only acceptable choice. For Hare, it is a business expense, that is, if they are even caught causing the damage.

With time, Tortoise close their doors, outcompeted by Hare. With enough time, Hare close their doors, as the environmental damage dooms all.

What about a circular economy?

When I say linear production growth, I am not talking about a linear economy or a circular economy. In a linear economy, new products are made without reuse. In a circular economy, new products are made with reuse.

Linear production growth is linear in both a linear economy and in a circular economy. Exponential production growth is exponential in both a linear economy and in a circular economy.

Consider the following table. Suppose at year zero, both Hare and Tortoise make 2 units of material Z. While Hare doubles production each year, Tortoise increases production at a constant rate of 2 units. At 0.1 circular, Tortoise reuses 10 percent units of material Z from the previous year. At 0.9 circular, Hare reuses 90 percent units of material Z from the previous year. Compare the results. For the circular columns, the number to the left of the + sign is the number of new units, while the number to the right is the number of reused units.

TortoiseHare0.1 circular Tortoise0.9 circular Tortoise0.9 circular Hare
222 + 02 + 02 + 0
443.8 + 0.22.2 + 1.82.2 + 1.8
685.6 + 0.42.4 + 3.64.4 + 3.6
8167.4 + 0.62.6 + 5.48.8 + 7.2
10329.2 + 0.82.8 + 7.217.6 + 14.4
126411.0 + 1.03.0 + 9.035.2 + 28.8
1412812.8 + 1.23.2 + 10.870.4 + 57.6
1625614.6 + 1.43.4 + 12.6140.8 + 115.2
1851216.4 + 1.63.6 + 14.4281.6 + 230.4
20102418.2 + 1.83.8 + 16.2563.2 + 460.8

Clearly, for Hare, production growth is exponential both in a linear economy and in a 0.9 circular economy. What is more, at 0.9 circular economy, the left number (new units) is always greater then the right number (reused units). Now consider Tortoise. At 0.1 circular economy, the number of new units is greater than the number of reused units. At 0.9 circular economy, the number of new units (except for years zero and one) is smaller than the number of reused units. See, for Tortoise, the circular economy may grow, such that, more units are reused rather than created new. But that is not the case for Hare with a doubling growth rate.

But what happens for a different growth rate? Let us look at some examples of Hare with 1.25, 1.5, and 1.75 growth rates. Keep the circular reuse fraction at 0.9.

1.25 Hare1.5 Hare1.75 Hare0.9 Circular 1.25 Hare0.9 Circular 1.5 Hare0.9 Circular 1.75 Hare
2.002.002.002.00 + 0.002.00 + 0.002.00 + 0.00
2.503.003.500.70 + 1.801.20 + 1.801.70 + 1.80
3.134.506.130.88 + 2.251.80 + 2.702.98 + 3.15
3.916.7510.721.09 + 2.812.70 + 4.055.21 + 5.51
4.8810.1318.761.37 + 3.524.05 + 6.089.11 + 9.65
6.1015.1932.831.71 + 4.396.08 + 9.1115.94 + 16.88
7.6322.7857.452.14 + 5.499.11 + 13.6727.90 + 29.54
9.5434.17100.532.67 + 6.8713.67 + 20.5048.83 + 51.70
11.9251.26175.933.34 + 8.5820.50 + 30.7585.45 + 90.48
14.9076.89307.874.17 + 10.7330.75 + 46.13149.54 + 157.33

For growth rate 1.25, the number of reused units exceeds that of new units. The same happens for 1.5. But look at 1.75, the reuse nearly equals new units. Now, when exactly does reuse equals new units?

Definitions
p -> previous number of units
g -> growth rate
r -> reuse fraction
n -> new units
x -> multiplication operator

What we know
n = p x g - p x r

What we want to know
n = p x r

Solution
p x g - p x r = p x r
p x g = 2 p x r
g = 2 r

Reuse equals new units when the growth rate is twice the reuse fraction.

Limiting growth

It seems reasonable to limit exponential growth. Perhaps the number of new units should at most equal the number of reused ones. Then the growth rate is at most twice the reuse fraction.

So, which growth rates are then acceptable? It turns out, when the growth rate is between 1 and 2, the reuse fraction must be between 0.5 and 1.0 to meet the criteria. Any business with a reuse fraction below 0.5, should keep production growth linear.

      linear    |   exponential
    production  |   production
      growth    |     growth
----------------------------------
 0.0           0.5            1.0
          reuse fraction

Some questions to think about. How to measure reuse? How to stay competitive? How to design better limits to growth? How to prove the conjecture?

References