Moore's Law - Other Formulations and Similar Laws

Other Formulations and Similar Laws

Several measures of digital technology are improving at exponential rates related to Moore's law, including the size, cost, density and speed of components. Moore himself wrote only about the density of components (or transistors) at minimum cost.

Transistors per integrated circuit. The most popular formulation is of the doubling of the number of transistors on integrated circuits every two years. At the end of the 1970s, Moore's law became known as the limit for the number of transistors on the most complex chips. The graph at the top shows this trend holds true today.

Density at minimum cost per transistor. This is the formulation given in Moore's 1965 paper. It is not just about the density of transistors that can be achieved, but about the density of transistors at which the cost per transistor is the lowest. As more transistors are put on a chip, the cost to make each transistor decreases, but the chance that the chip will not work due to a defect increases. In 1965, Moore examined the density of transistors at which cost is minimized, and observed that, as transistors were made smaller through advances in photolithography, this number would increase at "a rate of roughly a factor of two per year". Current state-of-the-art photolithography tools use deep ultraviolet (DUV) light from excimer lasers with wavelengths of 248 and 193 nm — the dominant lithography technology today is thus also called "excimer laser lithography" — which has enabled minimum feature sizes in chip manufacturing to shrink from 0.5 micrometer in 1990 to 45 nanometers and below in 2010. This trend is expected to continue into this decade for even denser chips, with minimum features approaching 10 nanometers. Excimer laser lithography has thus played a critical role in the continued advance of Moore's Law for the last 20 years.

Hard disk storage cost per unit of information. A similar law (sometimes called Kryder's Law) has held for hard disk storage cost per unit of information. The rate of progression in disk storage over the past decades has actually sped up more than once, corresponding to the utilization of error correcting codes, the magnetoresistive effect and the giant magnetoresistive effect. The current rate of increase in hard drive capacity is roughly similar to the rate of increase in transistor count. Recent trends show that this rate has been maintained into 2007.

Network capacity. According to Gerry/Gerald Butters, the former head of Lucent's Optical Networking Group at Bell Labs, there is another version, called Butter's Law of Photonics, a formulation which deliberately parallels Moore's law. Butter's law says that the amount of data coming out of an optical fiber is doubling every nine months. Thus, the cost of transmitting a bit over an optical network decreases by half every nine months. The availability of wavelength-division multiplexing (sometimes called "WDM") increased the capacity that could be placed on a single fiber by as much as a factor of 100. Optical networking and dense wavelength-division multiplexing (DWDM) is rapidly bringing down the cost of networking, and further progress seems assured. As a result, the wholesale price of data traffic collapsed in the dot-com bubble. Nielsen's Law says that the bandwidth available to users increases by 50% annually.

Pixels per dollar. Similarly, Barry Hendy of Kodak Australia has plotted the "pixels per dollar" as a basic measure of value for a digital camera, demonstrating the historical linearity (on a log scale) of this market and the opportunity to predict the future trend of digital camera price, LCD and LED screens and resolution.

The Great Moore's Law Compensator (TGMLC), generally referred to as bloat, and also known as Wirth's law, is the principle that successive generations of computer software acquire enough bloat to offset the performance gains predicted by Moore's Law. In a 2008 article in InfoWorld, Randall C. Kennedy, formerly of Intel, introduces this term using successive versions of Microsoft Office between the year 2000 and 2007 as his premise. Despite the gains in computational performance during this time period according to Moore's law, Office 2007 performed the same task at half the speed on a prototypical year 2007 computer as compared to Office 2000 on a year 2000 computer.

Library expansion was calculated in 1945 by Fremont Rider to double in capacity every 16 years, if sufficient space were made available. He advocated replacing bulky, decaying printed works with miniaturized microform analog photographs, which could be duplicated on-demand for library patrons or other institutions. He did not foresee the digital technology that would follow decades later to replace analog microform with digital imaging, storage, and transmission mediums. Automated, potentially lossless digital technologies allowed vast increases in the rapidity of information growth in an era that is now sometimes called an "Information Age".