Moore's law, Wright's law and the Countdown to Exponential Space

Emergent technologies such as solar power, electric vehicles, and artificial intelligence (AI) often exhibit exponential or power function price declines and various ``S-curves'' of adoption. We show that under CES and VES utility, such price and adoption curves are functionally linked. When price declines follow Moore's, Wright's and AI scaling "Laws,'' the S-curve of adoption is Logistic or Log-Logistic whose slope depends on the interaction between an experience parameter ...

It has long been known that scientific output proceeds on an exponential increase, or more properly, a logistic growth curve. The interplay between effort and discovery is clear, and the nature of the functional form has been thought to be due to many changes in the scientific process over time. Here I show a quantitative method for examining the ease of scientific progress, another necessary component in understanding scientific discovery. Using examples from three different...

This paper introduces a method for linking technological improvement rates (i.e. Moore's Law) and technology adoption curves (i.e. S-Curves). There has been considerable research surrounding Moore's Law and the generalized versions applied to the time dependence of performance for other technologies. The prior work has culminated with methodology for quantitative estimation of technological improvement rates for nearly any technology. This paper examines the implications of s...

We show that, in the context of Moore's Law, overall productivity can be increased for large enough computations by `slacking' or waiting for some period of time before purchasing a computer and beginning the calculation.

When the probability of measuring a particular value of some quantity varies inversely as a power of that value, the quantity is said to follow a power law, also known variously as Zipf's law or the Pareto distribution. Power laws appear widely in physics, biology, earth and planetary sciences, economics and finance, computer science, demography and the social sciences. For instance, the distributions of the sizes of cities, earthquakes, solar flares, moon craters, wars and p...

As it is pretty sure that Moore's law will end some day, questioning about the post-Moore era is more than interesting. Similarly, looking for new computing paradigms that could provide solutions is important. Revisiting the history of digital electronics since the 60's provide significant insights on the conditions for the success of a new emerging technology to replace the currently dominant one. Specifically, the past shows when constraints and {\guillemotleft} walls {\gui...

Experience curves are widely used to predict the cost benefits of increasing the deployment of a technology. But how good are such forecasts? Can one predict their accuracy a priori? In this paper we answer these questions by developing a method to make distributional forecasts for experience curves. We test our method using a dataset with proxies for cost and experience for 51 products and technologies and show that it works reasonably well. The framework that we develop hel...

Power-law distributions occur in many situations of scientific interest and have significant consequences for our understanding of natural and man-made phenomena. Unfortunately, the detection and characterization of power laws is complicated by the large fluctuations that occur in the tail of the distribution -- the part of the distribution representing large but rare events -- and by the difficulty of identifying the range over which power-law behavior holds. Commonly used m...

A foundational model has been developed based on trends built from empirical data of space exploration and computing power through the first six plus decades of the Space Age which projects earliest possible launch dates for human-crewed missions from cis-lunar space to selected Solar System and interstellar destinations. The model uses computational power, expressed as transistors per microprocessor, as a key broadly limiting factor for deep space missions' reach and complex...

Recent years have witnessed an exponential growth of the commercial space industry, including rocket launch, satellite network deployment, private space travel, and even extraterrestrial colonization. Several trends are predicted in this unprecedented transition to an era of space-enabled broadband access.