Exponential Math or If We Don’t Stop Using Up All The Things, There Will Be Nothing Left.

Let’s do a quick thought experiment. Bacteria multiply by cell division or mitosis. Now let's say the bacteria have a doubling time of one minute, that they split by mitosis every minute. And let's give the bacteria some intelligence, allow that they are aware of their surroundings and can adapt. And let’s suppose that the at 11:oo pm there is one bacteria in a bottle and that by midnight the bottle is full.

This is an example of ordinary steady growth, with a doubling time of one minute, in a enviroment limited to one bottle.

At what time do you think the bottle will be half full?

To help you come up with the answer we have to learn a little bit about exponential math. It’s simple, really anyone can do this math.

If we have ordinary steady growth over time, we can easily measure the doubling time of the growth.

To calculate the doubling time, all you need is the percentage of growth. You divide 70 by the percentage to get the doubling time. In the case of our bacteria, with 100% growth, the doubling time is one minute.

let’s look at compound interest. Let’s say you have $100 in the bank and you are earning 5% interest a year. How long will it take to double your money? 70/5= 14. So it would take you fourteen years to double your money if you didn’t make another deposit and the interest rate didn’t change.

Or we could look at world population. Which is currently at 7.3 billion and has a growth rate of 1.1% per year. 70/1.1=63.6 years. That is how long it will take to double world population if the rate of growth does not change.

Now back to our bacterium!

At what time do you think the bottle will be half full?

11:59, one minute until midnight!

If you were one of the smart bacterium in the bottle at what time would not notice that you were running out of space?

At 11:55 the bottle is 1/32% full or 3.1 percent. Would you notice it then? I don’t think so.

At 11:56 the bottle is 1/16% or 6.3 percent full. Now? Nope.

At 11:57 the bottle is 1/8% or 12.5 percent full. There is still tons of room, nothing to worry about.

at 11:58 the bottle is 1/4% or 25 percent full. Things are getting crowded, sure, but we still have lots of free space for everyone.

Now lets say that some of the forward thinking bacterium decide that space might be getting tight and the launch a search for new bottles. Some brave bacterium search there known world and come back with 3new bottles at 2 minutes to midnight! They tripple there living space. Now they have lots of room for growth right?

So with 4 bottles total for growth, how long can the growth continue?

Until 12:02

This is all the math you need to understand why we can’t just keep increasing our rate of consumption of non-renewable resources like water, oil, land and minerals.

You might want to go back and look at population growth and it’s doubling time and give it some thought. I think we can handle one more doubling time. What do you think?

This concept and much of the words on this page were shamelessly stolen from one of my heroes. Dr Al Bartlett. Want to really understand exponential math, watch his video series.