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 \displaystyle (t-t_s)^{-1} where there is a singularity at t=t_s.  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).


10 thoughts on “Is the singularity really singular?

  1. Meh!
    I do not believe in b) yet I believe in the feasibility of some kind of strong AI.
    Not the Kurzweil or Singularity way, intelligence cannot be measured on an unidimensional scale, these people are just techno-religious nutcases.


  2. I DO believe the current biology model is fully described by the current physics model, the problem is they are both MODELS according to our current paradigms, not likely the full reality.
    Which means yet unknown “covert channels” may interfere with our assumptions, nothing mysterious, just something like neutrinos hit DNA and they happen to carry (i.e. be correlated with) significant information.
    This just to make an example using known concepts.

    Most people do not understand that the irreducible difference between models and reality does not entails “spirits” or any “ineffable entities”, just the incompleteness of our investigations.

    I guess you know about the incompatibility of quantum mechanic and general relativity and the horrendous mess of high energy physics with its zoo of concepts and particles?
    I will certainly get better in the future but will there ever be a Theory of Everything?
    That is, will there ever be a COMPLETE FINITE DISCRETE model of the whole reality?
    There is no guarantee and I surmise this is not possible if the universe is actually infinite, because it may not only be infinite in the size of its various dimensions but also in the variety of any local quirks we won’t yet know about.
    We are finite beings and even if we “extend to the infinite” Singularity wise there will always be unexplored corners.

    The world is NOT digital!


  3. No, I think it is daft to try to “emulate” (not simulate) the brain.
    I believe that artificial intelligence and brain intelligence will overlap for a good part, each will strongly outperform the other on specific topics, yet the AI will be more “general” than the brain on some domains.
    The AI on “structured questions” is already outperforming the brain in machine learning.
    OTOH the brain performance on fuzzy questions requiring massive but “idiotic” parallelism will be very difficult to match.
    See also Monica Anderson video in the above link.


  4. OK, I understand. You believe AI is possible but brain emulation is not. That is a possibility that I did not include. It is another valid argument against biological complexity as a barrier to strong AI.


  5. I do want to add that the universe could be computable and yet still not ‘knowable’. In fact, I’m a strong proponent of us never obtaining a theory of everything. Hence, the dichotomy is not between finite or infinite but between countable or uncountable. However, even if it is countable, there is always a power set of its elements that is uncountable I blogged about this before at


  6. So beside some “minor” points we are close in agreement.
    To me:
    – Biological complexity is a barrier to brain emulation.
    – Brain emulation, were it possible, would not give use understanding of intelligence.
    – Anyway it would not be a good blueprint for intelligence.
    Some forms of strong AI are possible and better.
    – The universe could be actually not only infinite but uncountable.


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