5 ms·

> It’s hard for non-specialists to intuitively grasp the way an exponential rate increase can get out of control. The best way to explain the exponential growt

> It’s hard for non-specialists to intuitively grasp the way an exponential rate increase can get out of control. The best way to explain the exponential growth (and shock people) is ask them about https://en.wikipedia.org/wiki/Wheat_and_chessboard_problem https://en.wikipedia.org/wiki/Wheat_and_chessboard_problem

thedance 7y ago
Or you could present them with the classic cognitive reflection question: A lake has one lily pad. Every day the number of lily pads doubles. After fifty days the lake is completely covered by lily pads. How many days did it take to cover half the lake with lily pads?
- kspacewalk2 7y ago
  Is there some parable about getting too excited about exponential growth and taking the extrapolation game way too far?
  - fsckboy 7y ago
    Zeno concluded that all motion was an illusion, so that's taking things pretty far.
- __s 7y ago
  That's a big lake to have room for 1125899906842624 lily pads
  - kspacewalk2 7y ago
    Nonsense. Nothing in the real world can impede the progress of endlessly extrapolating exponential growth and impressing your friends with Really Big Numbers.
  - sk5t 7y ago
    Fortunately, it will only require space for 1125899906842623 pads.
adrianmonk 7y ago
I like the way a teacher explained it in grade school. She said to imagine we had a choice between two deals. One option is that someone would give us $100 each day for a month. The other is to receive 1 cent the first day, 2 cents the second day, 4 cents on the third day, doubling each day until a month has passed. Of course we all chose $100/day. Then she told us it was too bad we didn't take the other option, because we would have been multi-billionaires.
- tomp 7y ago
  Keep in mind that your teacher is wrong (or you remember incorrectly). Given that a month has at most 31 days, 0.01 * 2 ^ 30 = 10 737 418.24 (if you sum up all the payments, double that - $20m), so quite far away from "multi-billionaires". The general principle stands though.
  - adrianmonk 7y ago
    Oh right, of course I forgot to divide by 100. I should have also remembered what my other teacher said: always check your units.
- jbverschoor 7y ago
  21m. Not billion yet
- twistedpairs 7y ago
  Using max possible days in month gives ~21 million js: [...Array(31).keys()] .map(num => Math.pow(2,num)) .reduce((total,num) => total + num) / 100 $21,474,836.47 or since the sum is equal to the next sequential (2 to power of n+1) minus 1 cent => 2^31 - 1 = $21,474,836.47
- fsckboy 7y ago
  instead of pennies, she probably said $1 the first day, $2 the second, ... and then you would still have chosen the $100 a day, and not become billionaires.

thedance 7y ago

Or you could present them with the classic cognitive reflection question: A lake has one lily pad. Every day the number of lily pads doubles. After fifty days the lake is completely covered by lily pads. How many days did it take to cover half the lake with lily pads?

kspacewalk2 7y ago
Is there some parable about getting too excited about exponential growth and taking the extrapolation game way too far?
- fsckboy 7y ago
  Zeno concluded that all motion was an illusion, so that's taking things pretty far.
__s 7y ago
That's a big lake to have room for 1125899906842624 lily pads
- kspacewalk2 7y ago
  Nonsense. Nothing in the real world can impede the progress of endlessly extrapolating exponential growth and impressing your friends with Really Big Numbers.
- sk5t 7y ago
  Fortunately, it will only require space for 1125899906842623 pads.

adrianmonk 7y ago

I like the way a teacher explained it in grade school. She said to imagine we had a choice between two deals. One option is that someone would give us $100 each day for a month. The other is to receive 1 cent the first day, 2 cents the second day, 4 cents on the third day, doubling each day until a month has passed. Of course we all chose $100/day. Then she told us it was too bad we didn't take the other option, because we would have been multi-billionaires.

tomp 7y ago
Keep in mind that your teacher is wrong (or you remember incorrectly). Given that a month has at most 31 days, 0.01 * 2 ^ 30 = 10 737 418.24 (if you sum up all the payments, double that - $20m), so quite far away from "multi-billionaires". The general principle stands though.
- adrianmonk 7y ago
  Oh right, of course I forgot to divide by 100. I should have also remembered what my other teacher said: always check your units.
jbverschoor 7y ago
21m. Not billion yet
twistedpairs 7y ago
Using max possible days in month gives ~21 million js: [...Array(31).keys()] .map(num => Math.pow(2,num)) .reduce((total,num) => total + num) / 100 $21,474,836.47 or since the sum is equal to the next sequential (2 to power of n+1) minus 1 cent => 2^31 - 1 = $21,474,836.47
fsckboy 7y ago
instead of pennies, she probably said $1 the first day, $2 the second, ... and then you would still have chosen the $100 a day, and not become billionaires.