Future Earth: A View from the Rainbow Bridge

Abstract

We reach out to future generations by mitigating climate risk to them, while they reach us by persuading us to have compassion for them. Both mitigation and persuasion are, therefore, critical to their well-being and our own well-being. They form a feedback loop. As I look closely at the feedback loop, I become concerned that we tend to emphasize mitigation at the expense of persuasion.

Appendix: The Compassion Loop in Math

In the text, I refer to “steady state” of the compassion loop. Here I derive it in the simplest mathematical model of the feedback loop. I also show that Fig. 2 is a property of the model.

The Compassion Loop, in Fig. 1, consists of two branches: the evolution of compassion and the evolution of climate risk. These branches are captured by two differential equations:

$$\frac{ dS}{dt} = pR - bS$$

(1)

$$\frac{ dR}{dt} = c - (dR + mS)$$

(2)

In the equations,

t :

time;

S :

compassion;

R :

climate risk;

p (>0):

strength of persuasion;

b (>0):

rate of fading of compassion;

c :

“business-as-usual” growth in climate risk;

d :

Earth’s ability to reduce climate risk by breaking down greenhouse gases;

m :

strength of mitigation.

We find the steady state by setting the left-hand sides of the equations to zero and then solving them for S and R:

$$S = \frac{c}{{\left( {\frac{bd}{p}} \right) + m}}$$

(3)

$$R = \frac{c}{{\left( {\frac{pm}{b}} \right) + d}}$$

(4)

From these expressions, we can tell by inspection how extra strengths in persuasion and mitigation affect the steady state:

• (i) A rise in the strength of persuasion (i.e., parameter p) shall raise compassion but lower climate risk, as shown Fig. 2.

• (ii) A rise in the rate of mitigation (i.e., parameter m) shall lower both compassion and climate risk, as shown in Fig. 2.