Exponential Growth

[jordansparks]

Exponential growth refers to a doubling over a period of time. For example, computer hardware power has been doubling every 3 years or so. Kurzweil claims that this exponential growth can be generalized to technology as a whole, and that this has been happening for thousands of years or longer. I agree with this. But it will not result in any sort of runaway AI scenario or sudden change in our society. There is definitely no "singularity" where the growth looks nearly vertical.

Exponential growth is mathematically equivalent to compound percentage growth, such as with money. An investment that is growing at 10% per year will double in about 7 years. When graphed out, exponential/compound growth looks something like a hockey stick, gradual at first, and then an upswing at the end. This is an optical illusion. When graphed logarithmically, it's just a straight line. It's infinite, and never has an upswing.

So why do we have two different words for exactly the same thing? It has mostly to do with whether the growth is short term or long term. Did the growth just start? Is it likely to stop soon due to limited resources? Are we emphasizing danger or excitement? Clearly, something like Covid growth should be called exponential rather than compound. By contrast, the growth of money has no beginning or end, so it should be called compound percentage growth. The only time you might talk about growth of money as exponential would be when you are trying to emphasize the power of investing early. The growth of technology is clearly long term and it's clearly more accurate to refer to it as compound percentage growth. It will just keep marching onward like it always has. It's boring and predictable with no beginning or end.

There is also the issue of the conclusions we can make about what that compound growth means. Can you claim that a certain level of progress will result in androids, VR, or curing of disease? No, of course not. We don't know how much power we will need to solve these very difficult problems.
Here's an example: Sequencing the human genome looked very difficult at first. Even after they had been sequencing it for years, it still looked like they would never finish. And then they were done. Exponential growth allowed them to accomplish far more in those last few years. But it also hasn't stopped. The exponential growth continues. In the news today is a $1000 sequencing device that plugs into a smartphone and gives results in less than a day. But what we need to be really clear about here is that this constant progress does not translate into actual utopian solutions. We sequenced the human genome a long time ago, but it didn't cure any diseases or lead to designer babies. It resulted in more questions than answers. All progress is going to be painfully slow, just like this example. The scientific consensus continues to be correct that progress will be slow -- in spite of "exponential" growth.

[jordansparks]

Ha ha. I just read an article in Politico where the author referred to the spread of the virus in California as logarithmic. That's not quite right. Logarithmic growth (aka logistic growth) usually refers to the inverse of exponential growth, when the curve starts out steep and then levels off. It's what happens when a curve turns sigmoidal (s-shaped) after exponential growth. I sympathize with the author who made the subtle error. These are not simple concepts.