Albert Einstein famously said, "Compound interest is the eighth wonder of the world. He who understands it earns it...he who doesn't ...pays it."
This
is an adaptation of an example of compounding numbers adapted from Dr.
Albert Bartlett by the always very alarmed Chris Martinson.
Dr. Bartlett said, “The greatest shortcoming of the human race is the inability to understand the exponential function.”
Dr. Bartlett said, “The greatest shortcoming of the human race is the inability to understand the exponential function.”
"Suppose I had a magic eye dropper and I placed a single drop of water
in the middle of your left hand. The magic part is that this drop of
water is going to double in size every minute.
At first nothing seems to be happening, but by the end of a minute, that tiny drop is now the size of two tiny drops.
After another minute, you now have a little pool of water that is slightly smaller in diameter than a dime sitting in your hand.
After six minutes, you have a blob of water that would fill a thimble.
Now suppose we take our magic eye dropper to Fenway Park, and, right at 12:00 p.m. in the afternoon, we place a magic drop way down there on the pitcher’s mound.
To make this really interesting, suppose that the park is watertight and that you are handcuffed to one of the very highest bleacher seats.
My question to you is, “How long do you have to escape from the handcuffs?” When would it be completely filled? In days? Weeks? Months? Years? How long would that take?
I’ll give you a few seconds to think about it.
The answer is, you have until 12:49 on that same day to figure out how you are going to get out of those handcuffs. In less than 50 minutes, our modest little drop of water has managed to completely fill Fenway Park.
Now let me ask you this – at what time of the day would Fenway Park still be 93% empty space, and how many of you would realize the severity of your predicament?
Any guesses? The answer is 12:45. If you were squirming in your bleacher seat waiting for help to arrive, by the time the field is covered with less than 5 feet of water, you would now have less than 4 minutes left to get free.
And that, right there, illustrates one of the key features of compound growth…the one thing I want you take away from all this. With exponential functions, the action really only heats up in the last few moments.
We sat in our seats for 45 minutes and nothing much seemed to be happening, and then in four minutes – bang! – the whole place was full."
At first nothing seems to be happening, but by the end of a minute, that tiny drop is now the size of two tiny drops.
After another minute, you now have a little pool of water that is slightly smaller in diameter than a dime sitting in your hand.
After six minutes, you have a blob of water that would fill a thimble.
Now suppose we take our magic eye dropper to Fenway Park, and, right at 12:00 p.m. in the afternoon, we place a magic drop way down there on the pitcher’s mound.
To make this really interesting, suppose that the park is watertight and that you are handcuffed to one of the very highest bleacher seats.
My question to you is, “How long do you have to escape from the handcuffs?” When would it be completely filled? In days? Weeks? Months? Years? How long would that take?
I’ll give you a few seconds to think about it.
The answer is, you have until 12:49 on that same day to figure out how you are going to get out of those handcuffs. In less than 50 minutes, our modest little drop of water has managed to completely fill Fenway Park.
Now let me ask you this – at what time of the day would Fenway Park still be 93% empty space, and how many of you would realize the severity of your predicament?
Any guesses? The answer is 12:45. If you were squirming in your bleacher seat waiting for help to arrive, by the time the field is covered with less than 5 feet of water, you would now have less than 4 minutes left to get free.
And that, right there, illustrates one of the key features of compound growth…the one thing I want you take away from all this. With exponential functions, the action really only heats up in the last few moments.
We sat in our seats for 45 minutes and nothing much seemed to be happening, and then in four minutes – bang! – the whole place was full."
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