Feedback Loops

POLS 3220: How to Predict the Future

Recap

  • Last time, we discussed how to think about long-term trends in terms of stocks and flows.

  • Today, a brief introduction to feedback loops.

    • A positive feedback loop occurs when larger stocks \(\rightarrow\) faster inflows

    • A negative feedback loop occurs when larger stocks \(\rightarrow\) slower inflows

Positive Feedback Loop

Positive Feedback Loop

Positive Feedback Loop

Positive Feedback Loop

Exponential Growth

  • Pure positive feedback generates exponential growth.

  • Looks like a “hockey stick”.

Exponential Growth

Plotted on a logarithmic scale, exponential growth appears linear.

Exponential Growth

Other Examples

Other Examples

Rule of 72

  • One way to get an intuition for the speed of exponential growth is to think in terms of doubling time (i.e. how long it takes for the stock to double in size).

  • The Rule of 72 is a useful shorthand for estimating doubling time.

\[ \text{Doubling Time} = \frac{72}{\text{Growth Rate (%)}} \]

  • So a country whose economy is growing at 3% per year will:
    • roughly double in 36 years
    • grow 4x in 72 years
    • grow 8x in 108 years

Two Common Mistakes

  • Two very common prediction errors in the presence of positive feedback loops:

    • Mistake 1: ignoring it; underestimating how quickly exponential growth can accelerate

    • Mistake 2: naive extrapolation; assuming positive feedback can continue indefinitely

Mistake 1: Ignoring It

Mistake 1: Ignoring It

Mistake 1: Ignoring It

Mistake 1: Ignoring It

Mistake 1: Ignoring It

Mistake 1: Ignoring It

Mistake 1: Ignoring It

  • Disease epidemics are a classic example of positive feedback.

  • Your probability of catching a virus increases with the total number of cases.

  • But this exponential growth is deeply counter-intuitive. It accelerates much more rapidly than we expect.

Mistake 2: Naive Extrapolation

Other times forecasters make the exact opposite mistake, overstating the impact of exponential growth.

Mistake 2: Naive Extrapolation

Negative Feedback

  • Pure positive feedback does not exist in nature.

  • There is almost always some negative feedback loop that eventually places a limit on growth.

    • For bunnies, it’s grass.

      • More bunnies \(\rightarrow\) less grass \(\rightarrow\) fewer births

    • For disease epidemics, it’s the stock of susceptible people.

      • More cases \(\rightarrow\) fewer susceptible people \(\rightarrow\) fewer new cases

  • Combining positive and negative feedback yields an S-curve.

    • Exponential growth at first

    • Gradually flattens out as negative feedback overtakes positive feedback.

S-Curves

S-Curves

  • If this doubling rate continues, then five years from now we will be living in a wildly different world.

  • Key question: what negative feedback loop might kick in here? What are the fundamental limits on growth of AI capabilities?

Next Time

  • A deeper dive into what happens when a system has both positive and negative feedback loops.

  • Can generate counter-intuitive behaviors, including tipping points, chaos, and path dependence.

  • These phenomena make long-term predictions significantly more difficult than short-term predictions!