4 ms·

Most people don't think of 2% annual growth as exponential.

alasdair_ 7y ago
“Most people” could not accurately define the word “exponential” even if they were offered an exponential amount of money every year to do so.
- croon 7y ago
  To be fair they'd be incentiviced not to... assuming they understand the exponential nature of the money, which I guess they don't. But as soon as they do learn they won't want to explain.
TeMPOraL 7y ago
Also, growth narrative is always about adding/subtracting percent points - which makes most people think this is a linear phenomenon, because they don't make the connection that the quantity discussed is a multiplier, and charts they see are on log scale.
- littlestymaar 7y ago
  As long as you stay with low percentages, the linear approximation works pretty well: two times 1% lead to a 2.01% increase. But it starts breaking down as soon as you reach 10%. Little trick to know (with some good approximation) the doubling time of some low-percentage growing system: count it linearly up to 10% and then multiply by 7 (which is roughly the doubling time for 10% growth). Example: 2% => 5*7=35 years to double.
  - TeMPOraL 7y ago
    Or, in this context, 20% daily growth of coronavirus cases -> 20% => 0.5*7 = 3.5 days to double.
  - bxparks 7y ago
    This is identical to the Rule of 72, https://en.m.wikipedia.org/wiki/Rule_of_72 https://en.m.wikipedia.org/wiki/Rule_of_72. Except that you are using 70. The amazing thing about the rule of 72 is that it works pretty well even for rates greater than 10%.
davidiach 7y ago
And even fewer realize that a 2.1% growth rate is itself exponentially faster than a 2% growth rate. If something grows by 2% per day, vs 2.1% per day, after a year the second one is >20x bigger.
- algorias 7y ago
  What you say is true in principle, but your numbers are wrong. I got a rather less dramatic 50% difference after a year: >>> 1.02**365 1377.4082919660768 >>> 1.021**365 1969.6808462403098 >>>
  - davidiach 7y ago
    Thanks for the correction, I didn't actually do the math for that, just remembered something I've read a while back, but the numbers where different 20% vs 21%. Apparently I don't understand exponential growth either cause I assumed a 5% difference scales linearly (as in the difference between 20% vs 21% growth rates for a given period should be the same as between 2% and 2.1%). Silly me.
    - hef19898 7y ago
      But a good exmple showing why numbers are so important. A 50% difference is an order of magnitude away from a factor 20. Thing is, once out there the wrong factor 20 is impossible to correct.

“Most people” could not accurately define the word “exponential” even if they were offered an exponential amount of money every year to do so.

croon 7y ago
To be fair they'd be incentiviced not to... assuming they understand the exponential nature of the money, which I guess they don't. But as soon as they do learn they won't want to explain.

TeMPOraL 7y ago

Also, growth narrative is always about adding/subtracting percent points - which makes most people think this is a linear phenomenon, because they don't make the connection that the quantity discussed is a multiplier, and charts they see are on log scale.

littlestymaar 7y ago
As long as you stay with low percentages, the linear approximation works pretty well: two times 1% lead to a 2.01% increase. But it starts breaking down as soon as you reach 10%. Little trick to know (with some good approximation) the doubling time of some low-percentage growing system: count it linearly up to 10% and then multiply by 7 (which is roughly the doubling time for 10% growth). Example: 2% => 5*7=35 years to double.
- TeMPOraL 7y ago
  Or, in this context, 20% daily growth of coronavirus cases -> 20% => 0.5*7 = 3.5 days to double.
- bxparks 7y ago
  This is identical to the Rule of 72, https://en.m.wikipedia.org/wiki/Rule_of_72 https://en.m.wikipedia.org/wiki/Rule_of_72. Except that you are using 70. The amazing thing about the rule of 72 is that it works pretty well even for rates greater than 10%.

davidiach 7y ago

And even fewer realize that a 2.1% growth rate is itself exponentially faster than a 2% growth rate. If something grows by 2% per day, vs 2.1% per day, after a year the second one is >20x bigger.

algorias 7y ago
What you say is true in principle, but your numbers are wrong. I got a rather less dramatic 50% difference after a year: >>> 1.02**365 1377.4082919660768 >>> 1.021**365 1969.6808462403098 >>>
- davidiach 7y ago
  Thanks for the correction, I didn't actually do the math for that, just remembered something I've read a while back, but the numbers where different 20% vs 21%. Apparently I don't understand exponential growth either cause I assumed a 5% difference scales linearly (as in the difference between 20% vs 21% growth rates for a given period should be the same as between 2% and 2.1%). Silly me.
  - hef19898 7y ago
    But a good exmple showing why numbers are so important. A 50% difference is an order of magnitude away from a factor 20. Thing is, once out there the wrong factor 20 is impossible to correct.