“One of the things that I have discovered in my talking with politicians and policymakers is that most people don’t understand what an exponential is.”

—Geoffrey West

One small piece of the book is about exponential growth. I really liked his thought experiment on exponentials and I have applied his insight to game design and development.

Sure “politicians and policy makers” do not understand what an exponential is. But probably worse, mathematicians end up linearizing most problems because first order is the only one that doesn’t make calculations too complex for the human mind. And this leads to mistakes.

OTOH, I discoverd recently that assuming exponential when it’s clearly non-linear is also a mistake. Case in point, I wanted to explain why Ethernet displaced all other networking technologies. The argument was that going from 1Mbps to 10Mbps to 100Mbps to 1Gbps to 10Gbps to 100Gbps was each time _only_ around doubling/tripling the price, for a tenfold capacity. Other technologies like ATM were following powers of 2, and doubling/tripling the price between generations only brought a gain of 4 (STM-1 STM-4 STM-16). And I thought directly ln(10)=2.3, I got it ! It’s exponential.

Guess what, it’s not! Because if ln(10) and ln(100) gave promising results, ln(1000) _adds_ 2.3 making 6.9 while I expected it would be multiplied to give something around 10. Actually the ln(100) is also smaller than ln(10)², but it was less obvious to catch.

So I ended up with some square root/third root approximation that can be used. Any comment on this ? Another way of using exponentials that would fit my case ?

Hi Hans,

Sure “politicians and policy makers” do not understand what an exponential is. But probably worse, mathematicians end up linearizing most problems because first order is the only one that doesn’t make calculations too complex for the human mind. And this leads to mistakes.

OTOH, I discoverd recently that assuming exponential when it’s clearly non-linear is also a mistake. Case in point, I wanted to explain why Ethernet displaced all other networking technologies. The argument was that going from 1Mbps to 10Mbps to 100Mbps to 1Gbps to 10Gbps to 100Gbps was each time _only_ around doubling/tripling the price, for a tenfold capacity. Other technologies like ATM were following powers of 2, and doubling/tripling the price between generations only brought a gain of 4 (STM-1 STM-4 STM-16). And I thought directly ln(10)=2.3, I got it ! It’s exponential.

Guess what, it’s not! Because if ln(10) and ln(100) gave promising results, ln(1000) _adds_ 2.3 making 6.9 while I expected it would be multiplied to give something around 10. Actually the ln(100) is also smaller than ln(10)², but it was less obvious to catch.

So I ended up with some square root/third root approximation that can be used. Any comment on this ? Another way of using exponentials that would fit my case ?