“2035. Probably earlier.”

There’s fast, and then there’s … something more

Eliezer Yudkowski now categorizes his article ‘Staring into Singularity‘ as ‘obsolete’. Yet it remains among the most brilliant philosophical essays ever written. Rarely, if ever, has so much of value been said about the absolutely unthinkable (or, more specifically, the absolutely unthinkable for us).

For instance, Yudkowsky scarcely pauses at the phenomenon of exponential growth, despite the fact that this already overtaxes all comfortable intuition and ensures revolutionary changes of such magnitude that speculation falters. He is adamant that exponentiation (even Kurzweil‘s ‘double exponentiation’) only reaches the starting point of computational acceleration, and that propulsion into Singularity is not exponential, but hyperbolic.

Each time the speed of thought doubles, time-schedules halve. When technology, including the design of intelligences, succumbs to such dynamics, it becomes recursive. The rate of self-improvement collapses with smoothly increasing rapidity towards instantaneity: a true, mathematically exact, or punctual Singularity. What lies beyond is not merely difficult to imagine, it is absolutely inconceivable. Attempting to picture or describe it is a ridiculous futility. Science fiction dies.

“A group of human-equivalent computers spends 2 years to double computer speeds. Then they spend another 2 subjective years, or 1 year in human terms, to double it again. Then they spend another 2 subjective years, or six months, to double it again. After four years total, the computing power goes to infinity.

“That is the ‘Transcended’ version of the doubling sequence. Let’s call the ‘Transcend’ of a sequence {a0, a1, a2…} the function where the interval between an and an+1 is inversely proportional to an. So a Transcended doubling function starts with 1, in which case it takes 1 time-unit to go to 2. Then it takes 1/2 time-units to go to 4. Then it takes 1/4 time-units to go to 8. This function, if it were continuous, would be the hyperbolic function y = 2/(2 – x). When x = 2, then (2 – x) = 0 and y = infinity. The behavior at that point is known mathematically as a singularity.”

There could scarcely be a more precise, plausible, or consequential formula: Doubling periods halve. On the slide into Singularity — I.J.Good’s ‘intelligence explosion‘ — exponentiation is compounded by a hyperbolic trend. The arithmetic of such a process is quite simple, but its historical implications are strictly incomprehensible.

“I am a Singularitarian because I have some small appreciation of how utterly, finally, absolutely impossible it is to think like someone even a little tiny bit smarter than you are. I know that we are all missing the obvious, every day. There are no hard problems, only problems that are hard to a certain level of intelligence. Move the smallest bit upwards, and some problems will suddenly move from ‘impossible’ to ‘obvious’. Move a substantial degree upwards, and all of them will become obvious. Move a huge distance upwards… “

Since the argument takes human thought to its shattering point, it is natural for some to be repulsed by it. Yet its basics are almost impregnable to logical objection. Intelligence is a function of the brain. The brain has been ‘designed’ by natural processes (posing no discernible special difficulties). Thus, intelligence is obviously an ultimately tractable engineering problem. Nature has already ‘engineered it’ whilst employing design methods of such stupefying inefficiency that only brute, obstinate force, combined of course with complete ruthlessness, have moved things forwards. Yet the tripling of cortical mass within the lineage of the higher primates has only taken a few million years, and — for most of this period — a modest experimental population (in the low millions or less).

The contemporary technological problem, in contrast to the preliminary biological one, is vastly easier. It draws upon a wider range of materials and techniques, an installed intelligence and knowledge base, superior information media, more highly-dynamized feedback systems, and a self-amplifying resource network. Unsurprisingly it is advancing at incomparably greater speed.

“If we had a time machine, 100K of information from the future could specify a protein that built a device that would give us nanotechnology overnight. 100K could contain the code for a seed AI. Ever since the late 90’s, the Singularity has been only a problem of software. And software is information, the magic stuff that changes at arbitrarily high speeds. As far as technology is concerned, the Singularity could happen tomorrow. One breakthrough – just one major insight – in the science of protein engineering or atomic manipulation or Artificial Intelligence, one really good day at Webmind or Zyvex, and the door to Singularity sweeps open.”

[Tomb]

Moore and More

Doubling down on Moore’s Law is the futurist main current

Cycles cannot be dismissed from futuristic speculation (they always come back), but they no longer define it. Since the beginning of the electronic era, their contribution to the shape of the future has been progressively marginalized.

The model of linear and irreversible historical time, originally inherited from Occidental religious traditions, was spliced together with ideas of continuous growth and improvement during the industrial revolution. During the second half of the 20th century, the dynamics of electronics manufacture consolidated a further – and fundamental – upgrade, based upon the expectation of continuously accelerating change.

The elementary arithmetic of counting along the natural number line provides an intuitively comfortable model for the progression of time, due to its conformity with clocks, calendars, and the simple idea of succession. Yet the dominant historical forces of the modern world promote a significantly different model of change, one that tends to shift addition upwards, into an exponent. Demographics, capital accumulation, and technological performance indices do not increase through unitary steps, but through rates of return, doublings, and take-offs. Time explodes, exponentially.

The iconic expression of this neo-modern time, counting succession in binary logarithms, is Moore’s Law, which determines a two-year doubling period for the density of transistors on microchips (“cramming more components onto integrated circuits”). In a short essay published in Pajamas Media, celebrating the prolongation of Moore’s Law as Intel pushes chip architecture into the third-dimension, Michael S. Malone writes:

“Today, almost a half-century after it was first elucidated by legendary Fairchild and Intel co-founder Dr. Gordon Moore in an article for a trade magazine, it is increasingly apparent that Moore’s Law is the defining measure of the modern world. All other predictive tool for understanding life in the developed world since WWII — demographics, productivity tables, literacy rates, econometrics, the cycles of history, Marxist analysis, and on and on — have failed to predict the trajectory of society over the decades … except Moore’s Law.”

Whilst crystallizing – in silico — the inherent acceleration of neo-modern, linear time, Moore’s Law is intrinsically nonlinear, for at least two reasons. Firstly, and most straightforwardly, it expresses the positive feedback dynamics of technological industrialism, in which rapidly-advancing electronic machines continuously revolutionize their own manufacturing infrastructure. Better chips make better robots make better chips, in a spiraling acceleration. Secondly, Moore’s Law is at once an observation, and a program. As Wikipedia notes:

“[Moore’s original] paper noted that the number of components in integrated circuits had doubled every year from the invention of the integrated circuit in 1958 until 1965 and predicted that the trend would continue ‘for at least ten years’. His prediction has proved to be uncannily accurate, in part because the law is now used in the semiconductor industry to guide long-term planning and to set targets for research and development. … Although Moore’s law was initially made in the form of an observation and forecast, the more widely it became accepted, the more it served as a goal for an entire industry. This drove both marketing and engineering departments of semiconductor manufacturers to focus enormous energy aiming for the specified increase in processing power that it was presumed one or more of their competitors would soon actually attain. In this regard, it can be viewed as a self-fulfilling prophecy.”

Malone comments:

“… semiconductor companies around the world, big and small, and not least because of their respect for Gordon Moore, set out to uphold the Law — and they have done so ever since, despite seemingly impossible technical and scientific obstacles. Gordon Moore not only discovered Moore’s Law, he made it real. As his successor at Intel, Paul Otellini, once told me, ‘I’m not going to be the guy whose legacy is that Moore’s Law died on his watch.'”

If Technological Singularity is the ‘rapture of the nerds’, Gordon Moore is their Moses. Electro-industrial capitalism is told to go forth and multiply, and to do so with a quite precisely time-specified binary exponent. In its adherence to the Law, the integrated circuit industry is uniquely chosen (and a light unto the peoples). As Malone concludes:

“Today, every segment of society either embraces Moore’s Law or is racing to get there. That’s because they know that if only they can get aboard that rocket — that is, if they can add a digital component to their business — they too can accelerate away from the competition. That’s why none of the inventions we Baby Boomers as kids expected to enjoy as adults — atomic cars! personal helicopters! ray guns! — have come true; and also why we have even more powerful tools and toys —instead. Whatever can be made digital, if not in the whole, but in part — marketing, communications, entertainment, genetic engineering, robotics, warfare, manufacturing, service, finance, sports — it will, because going digital means jumping onto Moore’s Law. Miss that train and, as a business, an institution, or a cultural phenomenon, you die.”

[Tomb]