Some History of the Singularity

Many philosophers portray the cosmic process as an ascending curve of positivity. As time goes forward, the quantities of intelligence, power, or value are always increasing. These progressive philosophies have sometimes been religious and sometimes secular. Secular versions of progress have sometimes been political and sometimes technological. Technological versions have sometimes invoked broad technical progress and have sometimes focused on the recursive self-improvement of artificial intelligence.

The slowdown hypothesis (extended abstract)

Alessio Plebe and Pietro Perconti, University of Messina

The slowdown hypothesis 
 
The so-called singularity hypothesis embraces the most ambitious goal of Artificial Intelligence: the possibility of constructing human-like intelligent systems. The intriguing addition is that once this goal is achieved, it would not be too difficult to surpass human intelligence. A system more clever than humans should also be better at designing new systems as well, leading to a recursive loop towards ultraintelligent systems (Good, 1965), with an acceleration reminiscent of mathematical singularities (Vinge, 1993).

The singularity as a phase transition (extended abstract)

Béla Nagy, Santa Fe Institute
J.Doyne Farmer, Santa Fe Institute
John Paul Gonzales, Santa Fe Institute

The Finite Time Singularity Scenario

In his seminal article about “The Coming Technological Singularity” Vinge (1993) quotes how Ulam (1958) paraphrased John von Neumann as saying: “One conversation centered on the ever accelerating progress of technology and changes in the mode of human life, which gives the appearance of approaching some essential singularity in the history of the race beyond which human affairs, as we know them, could not continue.”

Of course, we can only guess exactly what kind of singularity the great Hungarian-born American mathematician had in mind, but one such guess is a finite time singularity, i.e. a mathematical singularity that can occur by trying to divide with zero. Graphically, this can be illustrated by a hyperbola approaching a vertical asymptote at the time of the singularity, such as 1/x approaching infinity as x goes to zero.

In this article, we are arguing that when we are talking about the potential outcomes of technological progress, such finite time singularity scenarios are possible, plausible, and should be taken seriously. This is counterintutive. Who in their right mind would seriously consider the possibility of such an explosive acceleration of technological progress that would actually reach infinity in finite time? Clearly, no sane person could or should be expected to entertain such a fantastic scenario. However, this entire analysis is exactly wrong.

There will be no singularity (extended abstract)

The following is an synopsis of an extended abstract provided by the author. 

Theodore Modis, Growth Dynamics

There Will Be No Singularity 

Many arguments can be made against the possibility of a Singularity around mid-21st century and I make them in my critique of Kurzweil's book (Modis 2006) and more extensively in a dedicated chapter in the upcoming Springer-commissioned volume. But let me present here the simplest and most fundamental one.

Every exponential curve that represents a real growth process constitutes part of some logistic curve (S-curve). The "knee" of an exponential curve defined as "the stage at which the pattern begins to appear explosive" is bound between an upper and a lower limit. The upper limit is around 13% penetration toward the S-curve’s ceiling because at that point the S-curve and the corresponding exponential differ by 15% which is difficult to overlook.