Jan 062008

Main Points:

  • Factoring in growth is very important. You might not be able to do something now, but perhaps you will be able to someday in the future. You might change, the situation might change, but a lot can happen in time.
  • The way to think about growth to understand both linear growth and exponential growth. Linear growth is when things change fairly equally, while exponential growth is when things change rapidly and change faster and faster. A very important model.

For many people, change is not really something they think about much. For other people who have embraced change, however, there is one critical thought pattern they want to adopt, which is to factor in time and change into their decisions and evaluations.

For example, I am talking to someone about the general guideline of saving 10% of your paycheque automatically. Someone who has a fixed mindset might say, “Oh, I can’t save 10% of my money. That’s too much.” and leave it at that. However, someone with a growth-oriented mindset would factor in time and change might say, “I might be able to do that someday, but I can’t really do that today. Its too much money for me right now, but maybe I can start by saving 1% a month and work my way upto 10%.”

It requires faith, imagination and self-trust to say that you might be able to change in such a way that another situation would be possible. If you look at Steve Pavlina‘s story, you’ll find this level of trust in himself when he tells the story of his life in “The Meaning of Life“.

It was the idea that no matter how bad things are right now, I still have the capacity to grow through them and to emerge in a better position in the future. That idea was all I had, but it was enough to allow me to cope.

Another example of this sort of fixed mindset is when I was talking to a group of people about how things are getting better, every day, even in relation to global warming. And one person chimed in and said something to the effect of, “But people are going to malls and driving so many SUVs.” And I told him that he was not factoring in change, that, while things were as they were today, the public consciousness about this issue is rising and has been for the last fifty years, and each year we get better at dealing with climate change. The real question is, will we be able to cross the line of impending doom in time to be able to prevent it? You see, instead of seeing it as just a point, I wanted to see it as a point with a direction. Things are as they are, but they’re getting better.

This brings me to another concept. The current situation is a point, and a previous situation is also a point. If you were to graph it and draw a line between the two points, you might find that that that things have gotten better from point 1 to point 2, and that projecting into the future suggests that they will keep getting better:
Factoring Growth 1

That is with linear, predictable growth. You can find out the improvement by finding the slope of the line (don’t be scared, its pretty easy). In this case, let’s imagine that the growth is at the rate of one unit of improvement over one unit of time. So, after a day, I’ve can crank out 10 more widgets the day before that. Now imagine for a moment if the growth was exponential, that is, the rate of growth was also increasing, not just staying constant. So, today I might improve to 10 widgets, but tomorrow I might improve to making 25 widgets. That would look something like this:

Factoring Growth 2

So, essentially, in the first case, my growth rate is fixed, that is, I improve by a certain amount over each unit of time. In the second case, I improve more and more over each unit of time, basically that my growth rate is not fixed but it is itself improving, usally up to a certain point of diminishing returns, but that’s a discussion for another day.

I believe this is the most accurate way of thinking about growth. We grow exponentially.

One last thing to notice on these graphs is that if you compare them side by side:

Factoring Growth 3

You’ll notice that there is a period during which the linear growth is going faster than the exponential growth, until a crossover point. That is, exponential growth actually lags behind linear growth, but in the long run its a better idea.  People forget that it takes time to get good at something and that in time, things can change. The first few times you do something, you’ll prolly suck at it, and you might consider the space where exponential growth is lagging behind linear growth to be that time.

Another way to think about this might be the relationship between speed and acceleration. The first graph might be a graph showing the speed of a car (speed, or velocity, is the change in position over time, sorta like our improvement over time), while acceleration is the change in speed (so the change in the change in the position over time,  over time, or just the change of speed). Acceleration is what the second graph would look like.

I really do believe this is an important model to understand to comprehend the world around us, and how to move in it better.

Note: I know this is a tough topic to understand for some people. I’d suggest reading this entry once (and perhaps looking up exponential growth somewhere else) and then putting it aside for a bit and reading it again. You might like to leave me a comment, too. 🙂

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