No Apparent Limits: Addressing Common Arguments Against Continuous Computational Acceleration

No Miniaturization Limit: Moore's Law and The Developmental Spiral

First, let's consider the miniaturization limit argument against continual acceleration. Many of the stunning advances we have seen in computer technologies in the last century have been aided by continuous miniaturization of computational architecture. This miniaturization has been particularly dramatic in the computer manufacturing paradigm known as metal oxide semiconductor (particuarly, silicon oxide) integrated circuit ("IC") design, a paradigm that has been operating since the early 1960's, and one that is still dominant today. In 1964, in a now-famous feat of prognostication, Gordon Moore, co-founder of Intel, coined "Moore's law," a prediction that growth in IC transistor density would continue on a very reliable doubling period of every 18-24 months, allowing a rough halving in the price performance of computational systems over the same time period. Moore's law has applied faithfully ever since, and recent data suggest that the price performance of computation actually grows slightly faster than Moore's curve, though this data is controversial. But periodically, distinguished scientists and engineers propose that we are running into fundamental limits to miniaturization, and encountering these limits may take us to a new and perhaps slower mode of computational development. For example, Andy Grove, another co-founder of Intel, has recently proposed that gate current leakages in IC's may cause us to fall off Moore's curve circa 2010, and others have said we will run into quantum tunneling problems (electrons randomly jumping to neighboring circuits) around the same time, as IC circuit sizes are now only a few molecules thick.

It is true that Moore's law has essentially been a committee expectation, a recurring project manager's deadline, since its inception. But what's truly interesting is the way that the physics of the microcosm has allowed this manufacturer's expectation to hold up over almost fifty years of engineering history. In spite of, and perhaps as a direct result of, our engineers' incessant concerns and expectations that physical and resource limits might dash Moore's law at any time, this doubling function has been permitted, by the confluence of human desire and the special structure of the physical universe, to continue through a long and relentless series of advances in solid state physics and materials science.

In the latest concern, today's chip designers worry about gate current leakage in silicon oxide semiconductors as a threat to continuing longstanding miniaturization trends. But we have recently discovered that hafnium oxide, a more exotic metal oxide, has a thousand times less leakage than silicon oxide. Such are the surprising and ever more computationally-permissive physical properties of the microcosm. Modern chip designers are also concerned about quantum tunneling. But have you heard of quantum dots, electron corrals, optical waveguides, quantum computers, or quantum cascade lasers? Such already functional and semi-functional systems show us the amazing ability of the microcosm to route around miniaturization problems. The physics of small devices, apparently due to preexisting, intrinsic universal structure, has continued to reveal surprising paths toward ever faster, more efficient, and more powerful computational architectures.

Perhaps even more importantly, when we finally do hit an intrinsic limit to circuit miniaturization as we move inexorably closer to computing at the quantum level, several insightful observers have noted that we'll finally be able to switch our miniaturization goals at that time to process and architecture miniaturization, trends which may be a far more important measure for understanding the coming singularity. Once it is no longer cost effective to shrink logic gates and circuit designs circa 2015, the fabrication industry can move en masse to shrinking higher-level computational systems, and thence to more biologically-inspired forms of computing. Such systems will involve closely connected, massively parallel, but widely differentiated circuits, similar to the construction of the human brain, circuits that can internalize high-level computational algorithms and engage in increasingly sophisticated physical processes.

Massively parallel, biologically-inspired computing systems are not yet economically feasible to develop in our present environment of accelerating circuit miniaturization, and cannot be for at least a few decades hence, as long as miniaturization and automation at the circuit level continues to yield such easy and powerful performance gains. Few have today realized the importance of that developmental reality in limiting the forms of artificial intelligence that Earth's sociotechnological infrastructure can presently afford to produce. MEMS (micro-electro-mechanical systems), SOC's (systems on a chip, such as the coming cellphone-on-a-chip), molecular, optical, magnetic, and even quantum computing are all dramatic examples of tomorrow's broader and more complex types of miniaturization, as we begin to move beyond the "die size" (circuit miniaturization) paradigm in early but unmistakable ways, even today.

Considering this panoply of related miniaturization trends allow us to understand that a generalized Moore's law appears to be in operation. In other words, given past history, it presently seems most reasonable to assume that technological systems will continue to increase their computational capacities at Moore's amazing rate, or faster, as far ahead as we can see into our extraordinary future.

Just how long have miniaturization trends held, when they are generally defined to include the emergence of different physical computational systems? Moore's curve of exponential growth has been continuing since the mid 1960's, when conventionally defined circuit miniaturization on metal oxide semiconductors. But subsequent to his observations, futurists and systems theorists beginning in the 1970's noted that this exponentiation has held since at least the invention of the transistor, in 1948.

Perhaps the first popular global analysis of accelerating trends in computer technology, their expnential growth through a variety of computing substrates (manual, mechanical, electromechanical, vacuum tube, transistor, integrated circuit, and microprocessor) and their broad implications for the future of humanity, was made by Hans Moravec in Mind Children, 1988. This slim, revolutionary work introduced many computer scientists, technologists, and lay readers to the idea that biological intelligence may be a transitory phase in a universal program of exponential growth in computational capacity.

More recently, Ray Kurzweil (Age of Spiritual Machines, 1999) valuably updated Moravec's work by documenting a double exponential growth in computational capacity since at least 1890, through five separate computer engineering substrates (mechanical, electromechanical, vacuum tube, transistor, and integrated circuit). Kurzweil's data demonstrate that the complexity doubling times themselves are gently shrinking with each doubling (e.g., the acceleration is a gently "double exponential", "hyperexponential" or perhaps even "asymptotic" process), a feature that had been suspected for decades by several observers of the Moore's law phenomenon.

For Moravec and Kurzweil, one key metric of acceleration is the price performance of computation (computing power purchasable every year, in constant dollars). Yet while this is a valuable and accessible measure, one that shows the uniqueness of computing systems, perhaps an even more fundamental metric is the physical resource efficiency of computation. What is most curious about the developmental history of computation is that each new system discovers how to use much less matter, energy, space, and time to compute any equivalent information. This creates accelerating emergences of increasingly local (e.g., more miniaturized, at both the systems level and the logic gate level) and more resource efficient computational systems over universal time.

This idea of universal acceleration was first popularized by Carl Sagan (in Dragons of Eden, 1977) with his powerful metaphor, the Cosmic Calendar (a.k.a., the "accelerating cosmic timeline"), which highlights the ever-faster emergence of important physical-computational events throughout the last six billion years of universal history. More recently, Eric Chaisson (Cosmic Evolution, 2001) has cleverly given this cosmologic acceleration a clear thermodynamic basis, in terms of the quantity Phi, the free energy rate density of emergent complex systems.

The pioneering work of Moravec, Sagan, Kurzweil, Chaisson, and other systems theorists strongly implies that there is something about the construction of the universe itself, something about the nature and universal function of local computation that permits, and may even statistically mandate, continously accelerating computational development in our local environment. This fascinating process of accelerating emergence of increasingly localized and miniaturized systems, a phenomenon that has been called the developmental spiral, has been noted by an increasing number of careful thinkers since Darwin's age. An overview of the long history of discussion of accelerating change can be found in our Brief History of Intellectual Discussion of the Singularity, recommended for those seeking a broader context for these fascinating ideas.

While the developmental spiral metaphor is commonly known to systems theorists, it is also somewhat psychologically disturbing to our slow-switching biological brains and still poorly understood, so the spiral remains, like a naked emperor, a phenomenon seen by many but discussed by few. This website, and with your help, our growing ASF community will seek to rectify that oversight in coming years.

The acceleration is the most common feature noted when the developmental spiral is discussed. The trends toward miniaturization and localization are much less commonly noted, but are also fundamentally important, from my perspective.

Today, fat-fingered early 21st century human beings are running programs on a single atom of calcium. We have managed to create functional seven qubit quantum computers, and to instantaneously teleport a beam of light. These advances are breathtaking, and entirely unprecedented. The extreme permissiveness of the universe to accelerating computational miniaturization as far down as we can probe may not be accidental, but central to its special, self-organized structure. Ongoing miniaturization may be a necessary element of the larger purpose, or teleology, of computational intelligence in the universe. Popularizing and interpreting trends and implications of accelerating miniaturization is one of my own contributions to the ongoing dialog.