The only way of discovering the limits of the possible is to venture a little way past them into the impossible (Arthur C. Clarke's 2nd law)

Tuesday, 29 March 2011

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.
The lower limit is around 10% and can be established by Infant mortality and common sense. Any natural-growth process that has achieved less than 10% of its final growth potential cannot have a very serious impact on society. In fact 10% growth is usually taken as the limit for infant mortality. A tree seedling of height less than 10% of the tree's final size is vulnerable to rabbits and other herbivores or simply to be stepped on by a bigger animal. (Of course, from the point of view of a cell embedded in one of the seedling's roots, the size of a few centimeters may seem unimaginably large, but this is really an inappropriate if not a distorted point of view - which may be the case with the point of view of the Singularitarians anyway).

In summary then, any trend that may appear exponential and approaching a "knee" today has a remaining growth potential of a factor between 7 and 10 on the size already achieved, and I cannot think of any growth process today that warrants particular concern in view of such remaining growth potential.

I am aware that this reasoning may sound simplistic, particularly in view of the fact that S-curves cascade and a new one may pick up where the old one leaves off, a phenomenon that I have studied and understand fairly well (see for example Modis 1994). But cascading S-curves involve slow-growth periods in between. During these lulls "things" regroup and reorganize themselves most often - and best - in the absence of conscious human intervention.

In any case, we will not see runaway exponential trends up to the mid-21st century.


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