Moore's law refers to an observation made by Intel co-founder Gordon Moore in 1965. He noticed that the number of transistors per square inch on integrated circuits had doubled every year since their invention. The prediction repeated so well for so many years that we began calling it a law, an immutable set of observations. We have now reached a limit to compression and transistor is replaced with nanotubes or biomolecules if we are to compress more circuits in a small space. The death of Moore’s Law teaches us the wisdom of creating a new modeling base, which I am calling Discontinuous Exponential Evolution Model or DEEM.
Technology evolution has a way to be discontinuous as technology growth can affect its growth. The rate constant in an exponential equation, taken to be a constant in Moore’s law, itself is subject to change causing a discontinuous change, both as a spike or as a nadir. In the 1960s, as President Kennedy declared war on space to take us to the moon before the decade was over lead to billions of dollars invested in technology, the benefits of which are evident in just about every technology around us. The discovery of DNA fifty years ago altered the course of biotechnology. These were spike events, and the outcome growth of technology could not have been predicted based on the trend of growth in the past, a standard measure to develop models. Some name this change as double exponential growth, but that assumes that the variation in the rate constant is cumulative. The fact is that that rate constant can be additive or deductive creating a discontinuous evolution. The feedback circuit to the speed of change is not model-able because it cannot predict the course of technology growth in areas unpredicted. For example, new tools created by technology can create new technology that can produce better tools, significantly affecting the growth cycle.
The DEEM is better appreciated as we examine our evolution, coming out of East Africa about 100,000 years ago, as one of the many species of Homo genus. A sudden growth of our cerebral cortex allowed us to surpass other Homo species that had languished for over 2 million years. The superiority of this new Homo species, which we audaciously called sapiens, is is an example of spiking in the DEEM. While we can claim to know the arrival of spikes or nadirs, this claim negates that predictability model of certainty—we cannot.
Figure 1 shows a comparison of three situations. The bottom line is a normal exponential growth, in this case, 10% per year, the middle line is a double exponential model where the rate itself is changing by 10%, so it is 10.1%, and in the second year it will be 10.1%, and so on. The top curve is the DEEM curve where the rate is increasing by 10% per year (double exponential model) except for an additional bump every five years by an additional 10%. The DEEM model is a more realistic view of the change coming in technology. It explains that we may reach a stage where a continuous growth can skyrocket as we see these bumps.
If Moore’s Law is dead, we know that a spike is coming. However, we have learned is that we should not be too quick in declaring an observation a law, perhaps a hypothesis.
Figure 1. Multiples as a function of the time unit. Comparison of exponential, double exponential and double exponential plus periodic spikes.