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

Power-law scaling, a central concept in critical phenomena, is found to be useful in deep learning, where optimized test errors on handwritten digit examples converge as a power-law to zero with database size. For rapid decision making with one training epoch, each example is presented only once to the trained network, the power-law exponent increased with the number of hidden layers. For the largest dataset, the obtained test error was estimated to be in the proximity of sta...

Advances in robotics and additive manufacturing have become game-changing for the prospects of space industry. It has become feasible to bootstrap a self-sustaining, self-expanding industry at reasonably low cost. Simple modeling was developed to identify the main parameters of successful bootstrapping. This indicates that bootstrapping can be achieved with as little as 12 metric tons (MT) landed on the Moon during a period of about 20 years. The equipment will be teleoperate...

We find that improvements in speedrunning world records follow a power law pattern. Using this observation, we answer an outstanding question from previous work: How do we improve on the baseline of predicting no improvement when forecasting speedrunning world records out to some time horizon, such as one month? Using a random effects model, we improve on this baseline for relative mean square error made on predicting out-of-sample world record improvements as the comparison ...

For the last 60 years, advances in conventional computing platforms have been driven by the empirical notion known as Moores law. In its essence, Moores law is a ubiquitous description of the exponential increase in transistor density acting as a proxy for computing power as a function of time. While this trend started as an interesting observation, it has evolved into a self-fulfilling prophecy used to drive the entire semiconductor industry. Arguments for or against the end...

We suggest partial logarithmic binning as the method of choice for uncovering the nature of many distributions encountered in information science (IS). Logarithmic binning retrieves information and trends "not visible" in noisy power-law tails. We also argue that obtaining the exponent from logarithmically binned data using a simple least square method is in some cases warranted in addition to methods such as the maximum likelihood. We also show why often used cumulative dist...

The national space programs have an historic opportunity to help solve the global-scale economic and environmental problems of Earth while becoming more effective at science through the use of space resources. Space programs will be more cost-effective when they work to establish a supply chain in space, mining and manufacturing then replicating the assets of the supply chain so it grows to larger capacity. This has become achievable because of advances in robotics and artifi...

Exponential growth occurs when the growth rate of a given quantity is proportional to the quantity's current value. Surprisingly, when exponential growth data is plotted as a simple histogram disregarding the time dimension, a remarkable fit to the positively skewed k/x distribution is found, where the small is numerous and the big is rare. Such quantitative preference for the small has a corresponding digital preference known as Benford's Law which predicts that the first si...

The study of spacetime, and its role in understanding functional systems has received little attention in information science. Recent work, on the origin of universal scaling in cities and biological systems, provides an intriguing insight into the functional use of space, and its measurable effects. Cities are large information systems, with many similarities to other technological infrastructures, so the results shed new light indirectly on the scaling the expected behaviou...

When launching or landing a spacecraft on the regolith of a terrestrial surface, special attention needs to be paid to the rocket exhaust cratering effects. If the effects are not controlled, the rocket cratering could damage the spacecraft or other surrounding hardware. The cratering effects of a rocket landing a planet's surface are not understood well, especially for the lunar case with the plume expanding in vacuum. As a result, the blast effects cannot be estimated suffi...

An indispensable part of our lives, computing has also become essential to industries and governments. Steady improvements in computer hardware have been supported by periodic doubling of transistor densities in integrated circuits over the last fifty years. Such Moore scaling now requires increasingly heroic efforts, stimulating research in alternative hardware and stirring controversy. To help evaluate emerging technologies and enrich our understanding of integrated-circuit...