On Thu, 23 Jul 1998, Robin Hanson wrote:
> Michael Nielsen writes:
> >So my counterargument is that devices which exploit computational models
> >beyond the Turing model in terms of _efficiency_, such as quantum
> >computation is presumed to be, may be "incomprehensible" in the sense
> >that no classical computer, however large, constrained to run in our
> >Universe, could simulate the action of a modestly sized quantum
> >computer.
>
> This is a point worth making, but is that the relevant sense of
> "incomprehensible" w.r.t. the claim that there is a "singularity" beyond
> which we can see nothing?
I don't think it is. There's an important distinction to be made here: would a SI's behaviour be incomprehensible all of the time, some of the time, or never? My example was intended to illustrate that there may be at least some "thought processes" allowed by the laws of nature which we cannot possibly hope to follow in detail, even in principle.
This does not mean that those are necessarily the only, or even the most important thought processes to understand. I still hold, however, that this example invalidates Damien's "Very vague thesis".
> We have a growing body of understanding about
> quantum computers, which you are contributing greatly to, even without
> having any such computers in hand to play with. I'd guess that with more
> work by people like you, we'll be able to say a lot more about the
> capabilities of such machines, and to use that understanding to help
> envision a future when such machines are possible. Would you go so far
> as to say that we are now so incapable of understanding the concepts
> important to future intelligences that there's no use in trying to
> envision a future with them?
Certainly not. I'd say it's a very worthwhile task.
An already-existing example may be useful here, the quantum factoring algorithm due to Shor. Assuming large-scale quantum computers can be built, it ought to be possible to use that factoring algorithm to factor numbers which cannot be factored using our classical algorithms, even given a computer the size of the observed Universe.
It is believed that classical computational devices (including human brains) cannot efficiently follow, in detail, the operations used in the factoring algorithm. At a working level, it is "incomprehensible" to human beings. Yet a human being, using higher level tools, was still able to dream up that factoring algorithm, and prove that it works within the framework of quantum mechanics!
It seems to me that what is needed here is a robust abstract framework that can be used to understand the behaviour of a SI. Sure, we may not be able to follow the details of the SI's thought processes, but we can still make broadly applicable statements about the SI. Rather like the relationship of thermodynamics to mechanics for complicated systems -- we can't follow the detailed mechanics, but we still have some general principles to use.
Michael Nielsen
http://wwwcas.phys.unm.edu/~mnielsen/index.html