Is the singularity really singular?

Time magazine has an article this month that summarizes the ideas of Ray Kurzweil and the Singularity, which he defines as the point in time  when machine intelligence surpasses that of humans.  I’ve posted on this topic  here and here.  What strikes me in this article and others  is the lack of precision in the arguments used for and against the occurrence of the Singularity.  Here are four examples:

1) Exponentials are not singular. Kurzweil and his colleagues argue that technology grows exponentially so by a generalized Moore’s law, computers and algorithms should improve enough  in forty years to achieve the Singularity.  The irony of this statement is that an exponential function is mathematically nonsingular.  In fact, it is the epitome of a well-defined (entire) function.    If they wanted a real singularity, they could have chosen a rational function like where there is a singularity at .  What they should say is that there will be a kink in the growth rate when machines exceed humans because we will then go into hyper-Moore’s law growth, which is the definition that Robin Hanson uses.  The singularity would then be in the derivative of the growth function.

2) Reaching the Singularity has nothing to do with exponential growth. If the Singularity is defined as the time when machines exceed humans then it doesn’t matter how fast we are growing.  Even if we grew linearly, there would be a time when machines would exceed humans although we may have to wait a long time.  The exponential growth is not important for the Singularity per se but only important for wnen it arrives.

3) Exponential growth does not necessarily  imply progress.  In the same week that the Singularity article appeared in Time magazine, influential economist and blogger Tyler Cowen penned an opinion piece in the  New York Times lamenting that innovation has done little in making our lives better recently.  He writes: “My grandmother, who was born in 1905, spoke often about the immense changes she had seen, including the widespread adoption of electricity, the automobile, flush toilets, antibiotics and convenient household appliances. Since my birth in 1962, it seems to me, there have not been comparable improvements.”  I also posted previously wondering why the growth rate of innovation seemed so slow (see here).

Independent of whether you believe progress is slowing or not,  increases in the speed and performance of computers do not necessarily imply that we will attain strong AI soon. Put it this way, developing strong AI is very hard (in the colloquial and the computational complexity sense).  Given that there is no known systematic approach to achieving it means that we could fail an exponentially large number of times before we reach it.  So even with exponential growth, this doesn’t imply that we’re close.  A breakthrough could come tomorrow or perhaps in a thousand years.  We just don’t know.

4) Biological complexity is not an argument against AI. The article says that biologist Dennis Bray argued against the possibility of strong artificial intelligence (AI) because cells are too complex.  The article quotes him saying “they are set apart by the huge number of different states they can adopt. Multiple biochemical processes create chemical modifications of protein molecules, further diversified by association with distinct structures at defined locations of a cell. The resulting combinatorial explosion of states endows living systems with an almost infinite capacity to store information regarding past and present conditions and a unique capacity to prepare for future events.”  The italics are mine.  The irony in this statement is that Bray, who is an eminent computational biologist, in conceding that biological information is not infinite sinks his argument since all finite objects can be simulated on a computer.

This is something that I see a lot of AI detractors get confused about.  The issue isn’t about whether biology or the brain  is too complex, it is only  about whether a) biology is fully described by physics and b) physics is computable (i.e. can be simulated on a computer).  If you believe in these two statements, then you believe the brain can be simulated by a computer and hence strong AI.  Conversely, if you don’t believe in strong AI then you don’t believe in either a) or b).