I want colors too

I Want to Feel Exponentially

Moore’s law is a well known prediction based on the observation made by Gordon Moore that the number of transistors able to be manufactured in a given area of silicon were doubling in density on an annual basis since the invention of the transistor. More recently, it was observed that the throughput in DNA sequencing machines has exceeded Moore’s law. These are examples of exponential growth.

I started by saying that Moore’s law was well known, but I lied. It is extremely hard for humans to know these phenomena deeply. Our brains are not well adapted to it. How often did our ancestors, even a hundred years ago observe an exponential event in nature and perceive it exponentially? The most likely candidates I can think of are bacterial growth (most dangerous when an injury is infected), spread of disease, and procreation by rabbits (I don’t think their population actually increases exponentially in nature but I haven’t seen the research on that). Bacterial growth was previously hard to observe because of the relatively small size of bacteria, and spread of disease was probably hard to observe for kind of the opposite reason.

It seems to me that most events we observe are either happening linearly or interpreted linearly in our brains. I can track an animal running at a constant speed easily, and everyone has experienced linear changes in velocity in a vehicle or due to earth’s gravity. When we experience sudden changes in velocity, which also indicates a change in acceleration, we feel shock and sometimes sickness. Phenomena which are exponential functions, like earthquakes, are measured by instrumentation on a logarithmic scale, yet I think I feel them on a linear scale.

When analyzing electronic circuits we humans find it easier to convert exponential models to linear piecewise ones <https://en.wikipedia.org/wiki/Diode_modelling>. When designing digital IC circuits, a digital IC engineer must be mindful of leakage current of the transistors, as the leakage current increases exponentially when decreasing the thickness of the oxide regions.

When I was pitching investors in Japan, it seems to me most of them failed to grasp the exponential improvements in DNA sequencing and the potential for rapid improvement in synthetic DNA manufacturing. Unfortunately you certainly cannot move or think linearly if you want to take advantage of an exponential change. Fortunately a piecewise reaction can work well, like standing up on a surfboard when a wave is coming. If you can’t estimate when the wave is coming you might miss it. And if you don’t stand up at all you ain’t gonna get on that wave.

There is no doubt that there are many people who understand the concept of exponential improvement, but understanding a math equation is not the same as imagining a future world with that equation in action. I wonder if there will be in the near future, or already are, humans that will perceive phenomena exponentially. It seems that we have no problem adapting to exponential changes, but do we really perceive anything exponentially? I’m not sure, but I’m leaning towards no.