Reminds me of a story I read about how if you had a can of food and bacteria got into it, and every day the bacteria doubled in size, and somehow this bacteria had conversations with itself with all of the other bacterias in the can about how long the food would last.
How long would it be before everything ran out?
At some point, the smart bacteria would stand up and say, “Hey, my fellow Amoebas, we’ve used 1/4 of all of the food in the can! If we’re not careful and if we don’t manage our resources we will run out of food!”
And the politician bacteria would say, “Don’t worry, everyone, we have 3 times as much food as we’ve ever used in all the months of our existence still in the can!”
And the bacteria was fruitful, and multiplied.
And when they hit the halfway mark the next day, the smart bacteria would stand up and say, “Hey my fellow Amoebas, we’ve used half of all of the food in the can! If we’re not careful and if we don’t manage our resources we will run out of food!”
And the bacteria politicians would say, “Everyone! Don’t worry! We still have as much food left as we have used in our entire existence to this point!”
And the bacteria was fruitful, and multiplied.
And then another day passed, and all of the bacteria died.
Mathematically it’s obvious and straightforward but the point is that it’s not intuitive from a typical person’s subjective perspective. It’s easy to underestimate or dismiss the rate of change until a situation becomes unmanageable.
Reminds me of a story I read about how if you had a can of food and bacteria got into it, and every day the bacteria doubled in size, and somehow this bacteria had conversations with itself with all of the other bacterias in the can about how long the food would last.
How long would it be before everything ran out?
At some point, the smart bacteria would stand up and say, “Hey, my fellow Amoebas, we’ve used 1/4 of all of the food in the can! If we’re not careful and if we don’t manage our resources we will run out of food!”
And the politician bacteria would say, “Don’t worry, everyone, we have 3 times as much food as we’ve ever used in all the months of our existence still in the can!”
And the bacteria was fruitful, and multiplied.
And when they hit the halfway mark the next day, the smart bacteria would stand up and say, “Hey my fellow Amoebas, we’ve used half of all of the food in the can! If we’re not careful and if we don’t manage our resources we will run out of food!”
And the bacteria politicians would say, “Everyone! Don’t worry! We still have as much food left as we have used in our entire existence to this point!”
And the bacteria was fruitful, and multiplied.
And then another day passed, and all of the bacteria died.
There’s also a good example of exponential change described using a doubling drop of water in The Power of Compounding
Meh.
It’s doubling each step.
If course it’s at
1/(2^n)of the final volume atnsteps before the final step.Mathematically it’s obvious and straightforward but the point is that it’s not intuitive from a typical person’s subjective perspective. It’s easy to underestimate or dismiss the rate of change until a situation becomes unmanageable.