Power and Danger of Compounding (Exponential) Growth

Power and Danger of Compounding (Exponential) Growth

Exponential Population Growth

Video of the Program: http://www.tvo.org/cfmx/tvoorg/tvoutils/globalfiles/VideoPop.cfm?spot_id=5566&sitefolder=theagenda

I watched a program on TVO last night about overpopulation. I usually steer clear of this issue because I find it depressing. Just the same, it’s always in the back of my mind. With last night’s program, I posted a comment on their blog which I’ve included here:

A great program on an issue few are willing to discuss. However, it touched on, but didn’t flesh out the issue of exponential (or compounding) growth which lies at the core of the issue. A common math problem given to students in this regard is called the Lily Pad Problem.

Suppose a pond has one lily pad. The lily pad doubles each day. That is 1 lily pad turns into 2 lily pads each day. Given that at the end of one month (30 days) the pond is covered in lily pads: When is the pond 1/2 covered? When is the pond 1/4 covered?

Human psychology is not geared towards thinking in exponential terms. When you push a certain amount on the gas pedal, the car goes a certain speed. When you push a bit more, the car goes a bit more faster. The gas pedal is a linear system and it’s how humans think.

So let’s answer the lily pad problem and comment on the ‘poor record’ of the ‘population alarmists’ in one felled swoop. Suppose someone on day 27 shouted: “my heavens, the pond is almost full!” Casual observers may be perplexed because the pond would be 7/8ths or 88% empty. On the next day, day 28, the pond would be 3/4rs or 75% empty. Even the next day, day 29, the pond would be 1/2 or 50% empty. The alarmist would likely be dismissed out of hand. However only one short day later, day 30, the pond would be completely covered and the naysayers would be proved wrong, only too late.

“Compound interest is the most powerful force in the universe” wrote Albert Einstein. Powerful yes, but counter intuitive for humans and the guests on last night’s program. They pointed to the advents in technology and agriculture which have staved off any population crisis. Going back to our lily pond: doubling the size of our pond gives us how many more days before the pond is covered again? One. Quadrupling the size of the pond gives us how many extra days? Two. Not to mention, that the agricultural revolution the guests mentioned was largely brought about by petroleum based fertilizers. Petroleum in turn is undergoing and exponential growth in consumption and in price.

As a parting parable about the power of compounding: Suppose your child asks you, in lieu of a raise in his/her allowance, to give them a penny a day, doubling it every day. Sounds like a good deal, but with our new found understanding of exponential growth, we need to be cautious. After two weeks, we’d owe our child some $163 which is a hefty allowance but no big disaster financially. However, two short weeks later (30 days from the start) we’d owe them nearly $11 million dollars. Clever kid. Can the human race be this clever? Can we afford not to be?

Further reading:
http://www.ciesd.org/influence/LilyPad.shtml http://mathforum.org/dr.math/faq/faq.doubling.pennies.html
http://youtube.com/watch?v=F-QA2rkpBSY

3 thoughts on “Power and Danger of Compounding (Exponential) Growth

  1. My father started a website to discuss this very issue at 29thday.org, named after the lily pad story to relate in this post. His premise is that everything actually works that way. He calls it CIC (pronounced ‘kick’, which stands for creativity, information and communication). We just never noticed because we always lived at the left side of the curve, which looks linear.

    Advances in computing, network and information technologies in the last 20 years have moved us to the right side of the curve but we still think the world is linear.

    This has caused people to try to solve exponential problems with linear solutions and then wonder why their solution didn’t work.

    The focus of the site is to develop the general principles of CIC and present examples. His goal is to help people understand apply these things to everyday life.

  2. This world depends on oil to fuel its’ agricultural machines and technologies. When the price of oil rises so will the price of food, causing starvation in third world nations. When we run out of oil, the famine will be world-wide. In order to support our population even at current levels, we will need agricultural machines that run on electricity and farms that are wired to run them.
    No one is planning for this eventuality, thus when it happens (and it will) millions if not billions will starve before the problem is resolved.
    I hope I’m already dead before that happens.

  3. You should read Kurzweil. He is a futurist who observes that technology proceeds at an exponential rate. Hence, our technology will eclipse our impact on the environment.
    For example, what if in 20 years we have machines that can directly tap atmospheric CO2 and sequester it in some way?

    Now, it’s great that technology is ‘likely’ to solve our problems, but I say, for safety’s sake, we shouldn’t live beyond our means and live in concordance with our current technological capabilities.

Leave a Reply

Your email address will not be published. Required fields are marked *

This site uses Akismet to reduce spam. Learn how your comment data is processed.

Back To Top