Mowing The Lawn Is Not Exponential

Last weekend it occurred to me that one of the reasons I like mowing the lawn is that it is linearly measurable. Linear is our natural thought form. It is also the reason so many financial plans fail. Another reason I like it is that it is not intellectually demanding so unusual trains of thought can occur.

Last weekend the thought process is this. Suppose I mowed the lawn under compound interest like rules. Suppose each minute I add speed. That means I cover more ground in minute two than I did in minute one. If I assume that I would take the same forty minutes to finish, then how “done” would I be at some intermediate times?

In a linear world I would be half done in half the time. Not the same in an exponential world. It depends on the growth rate. It is possible to get the drift of this while mowing the lawn but it works better with a spread sheet. Here’s what I found.

If the amount of lawn cut is analogous to capital owned and my speed of travel is analogous to yield, then I can find the percentage of the goal accomplished at any point in time.

I like 7.2% because it divides into .72 so nicely, and that matters with mental arithmetic, so I started there. At half the time, 20 minutes, I would be only about 25% done. Even at three quarter time I am not yet half done.

If I am a linear thinker and I saw so little progress for the time effort, do you think I would be pretty frustrated at 30 minutes? Probably. If the goal of finishing in 40 minutes was crucial, I would likely be more than frustrated? Frightened even. Half to do. Three quarters of the time to do the first half. Yikes.

Do you think your emotional involvement with your investment portfolio will be different than this? Not likely.

Once I got a spread sheet running, I found that at 10%, I would be less than 15% finished at half time and barely 38% done at three quarter time. It is easy to see how people become overly concerned. At 10%, year 33 of the 40 will show only half of the target.

If you want peace, you need to understand the system you are using. It is not linear so it is not intuitive. You are forced to find some tools. If you do not work it out rationally and believe the answer, your linear intuition will lead you astray. That can be devastating. You could easily stop doing something that is working. If you get too far astray, you will lose time and in exponential growth, time matters more than your capital. Avoid things that risk losing time.

Sometimes an external check is comforting. How have others fared? If you are out of debt and have saved a little by 45, you are likely pretty much bullet-proof to retire at 65. Ask your adviser how others like you are doing. Not a perfect answer but worth the asking.

The moral of the story is two-fold.

  1. Change usually has a cost, sometimes a big cost. Be sure the need is not merely intuitive.
  2. The last double is worth as much as all of the doubles before it. You could work it out. Be a little patient.

Don Shaughnessy is a retired partner in an international accounting firm and is presently with The Protectors Group, a large personal insurance, employee benefits and investment agency in Peterborough Ontario. | Twitter @DonShaughnessy | Follow by email at moneyFYI

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