During writing a paper for the 100 Year Starship Symposium, I wished to convince the starship designers that they should acknowledge the dynamics of high-technology economy, which may be crucial for interstellar missions. Thus motivated, I have made a new calculation regarding infinity point, also known as the singularity. According to this most recent revision of the theory of infinity point, it turns out that we should expect Infinity Point by 2035 in the worst case. Here is how and why.

Infinity Point was the original name for the hypothetical event when almost boundless amount of intelligence would be available in Solomonoff’s original research in 1985 (1), who is also the founder of mathematical Artificial Intelligence (AI) field. That particular paper gave a mathematical formulation of the social effects of human-level AI and predicted that, if human-level AI were available on a computing architecture to which Moore’s law was applicable, then given constant investment in AI every year, a hypothetically infinite amount of computing capacity and intelligence would be reached in a short period of time. His paper explained this event as a mathematical singularity, wherein the continuity of the computing efficiency function with respect to time was interrupted by an infinity. The term singularity was popularized later by science fiction authors and other researchers who favored the concept such as Ray Kurzweil. I encourage the readers to immerse themselves in the vision of the technological society in that paper, which predicts many other things such as application of psycho-history. In person, Solomonoff was every bit the pioneer of high technology and modernism his ideas revealed him to be. For he told me that he had proposed the idea of a machine that is more intelligent than man in 1940’s, much earlier than Dartmouth conference. If there were ever a true visionary and a man of devotion to future, he certainly fit the bill. Thus, he was not only the first man to formulate the general solution to AI, and to lay out the mathematical theory of infinity point, but also the first scientist to speak of the possibility with a straight face (however, similar ideas were conceived of in science fiction before).

The original theory arrives at the Infinity Point conclusion by making a few simple mathematical assumptions, and solving a system of equations. The assumptions may be stated in common language thus:

Computer Science (CS) community size ~ improvement in computing technology

CS community size ~ rate of log of computing efficiency

Fixed amount of money is invested in AI every year

These three assumptions are shown to produce a (theoretically) infinite improvement in a short time, as they depict a positive feedback loop that accelerates the already exponential curve of Moore’s law. Up to now, this is the same singularity that many H+ readers are all too well familiar with.

To remind Moore’s Law, well, it is: “number of transistors placed on a microprocessor at a fixed cost doubles every two years” as originally conceived. However, Moore’s law has tapered off; the number of transistors unfortunately doubles in three years nowadays. Yet, a seemingly more fundamental law has emerged which relates to energy efficiency of computing. That is known as Koomey’s Law (2), and some semiconductor companies like NVIDIA have even made future predictions based on this relation. Koomey instead observes that energy-efficiency of computing doubles every 18 month, by analyzing a trend (in log scale) that goes back to 1945.

Therefore, I updated the Infinity Point Hypothesis, using Koomey’s Law instead in two papers. In the first paper (3), I estimated human-level AI to be feasible by 2025, depending on Koomey’s Law. In the second, I combined this new projection with a worst case prediction of human brain computing speed. It is mostly straightforward to obtain this figure. The number of synapses in the adult neocortex is about $$1.64 \times 10^{14}$$ and the total number of synapses is less than $$5 \times 10^{14}$$. Since the maximum bandwidth of a single synapse is estimated to be about 1500 bits/sec (i.e., when information is being transmitted at maximum rate), the total communication bandwidth of the parallel computer is at most $$2.5 \times 10^{17}$$ bits/sec, which roughly corresponds to 3.8 petaflop/sec computing speed. There are some finer details I am leaving out for the moment, but that is a quite good estimate of what would happen if your entire neocortex were saturated with thought, which is usually not the case according to fMRI scans. I then calculate the energy efficiency of the brain computer and it turns out to be 192 teraflop/sec.W, which is of course much better than current processors. However, a small, energy efficient microchip of today can achieve 72 gigaflop/sec.W, which is not meager at all.

When I thus extrapolate using Koomey’s trend in log scale, I predict that in 17 years, in 2030, computers will attain human-level energy efficiency of computing, in the worst case.

I then assume that R=1 in Solomonoff’s theory, that is to say, we invest an amount of money into artificial intelligence that will match the collective intelligence of CS community every year. For the computer technology of 2030, this is a negligible cost, as each CS researcher already will have a sufficiently powerful computer, and merely continuously running it would enable him to offload his research to a computer at 20W; the operational cost to world economy would be completely negligible. At this low rate of investment, massive acceleration to Koomey’s law will be observed, and according to theory in about 5 years (4.62 to be exact), infinity point will be reached.

That is, we should expect the infinity point, when we will approach physical limits of computation to the extent it is technologically possible, by 2035 latest, all else being equal. Naturally, I imagine there to arise new physical bottlenecks, and I would be glad to see a good objection to this calculation. It is entirely possible that an inordinate amount of physical and financial resources would be necessary for realizing the experiments of and manufacturing the hypothetical super-fast future computers, for instance.

Nevertheless, we live in interesting times.

Onwards to the future!

References:

(1) Ray Solomonoff, 1985 The Time Scale of Artificial Intelligence:

Reflections on Social Efects, Human Systems Management, Vol. 5, pp.

149-153, 1985.

(2) Koomey, J.G., Berard, S., Sanchez, M., Wong, H.: Implications of

historical trends in the electrical efficiency of computing. IEEE

Annals of the History of Computing 33, 2011.

(3) Eray Özkural: Diverse Consequences of Algorithmic Probability,

Solomonoff 85th Memorial Conference, Nov. 2011, Melbourne, Australia.