Computational complexity theory is a huge, sprawling field; naturally this essay will only touch
on small parts of it...One might think that, once we know something is computable, whether it takes 10 seconds or
20 seconds to compute is obviously the concern of engineers rather than philosophers. But that
conclusion would not be so obvious, if the question were one of 10 seconds versus 101010
seconds! And indeed, in complexity theory, the quantitative gaps we care about are usually so vast that one
has to consider them qualitative gaps as well. Think, for example, of the difference between reading
a 400-page book and reading every possible such book, or between writing down a thousand-digit
number and counting to that number. More precisely, complexity theory asks the question: how do the resources needed to solve
a problem scale with some measure n of the problem size...
Need it be primarily one or the other? But if I must pick one, I pick philosophy.
I’m afraid I don’t see how this article is analogous. The article points out that computational complexity puts a very real limit on what can be computed in practice. Thus, even if you’d proved that something is computable in principle, it may not be computable in our current Universe, with its limited lifespan. You can apply computational complexity to practical problems (f.ex., devising an optimal route for inspecting naval buoys) as well as to theoretical ones (f.ex., discarding the hypothesis that the human brain is a giant lookup table). But these are still engineering and scientific concerns, not philosophical ones.
Need it be primarily one or the other? But if I must pick one, I pick philosophy.
I still don’t understand why. If you want to know the probability of FAI being feasible at all, you’re asking a scientific question; in order to answer it, you’ll need to formulate a hypothesis or two, gather evidence, employ Bayesian reasoning to compute the probability of your hypothesis being true, etc. If, on the other hand, you are trying to actually build an FAI, then you are solving a specific engineering problem; of course, determining whether FAI is feasible or not would be a great first step.
So, I can see how you’d apply science or engineering to the problem, but I don’t see how you’d apply philosophy.
Sorry, I couldn’t parse your comment at all; I’m not sure what you mean by “content”. My hunch is that you meant the same thing as TimS, above; if so, my reply to him should be relevant. If not, my apologies, but could you please explain what you meant ?
An analogy:
http://eccc.hpi-web.de/report/2011/108/
Need it be primarily one or the other? But if I must pick one, I pick philosophy.
I’m afraid I don’t see how this article is analogous. The article points out that computational complexity puts a very real limit on what can be computed in practice. Thus, even if you’d proved that something is computable in principle, it may not be computable in our current Universe, with its limited lifespan. You can apply computational complexity to practical problems (f.ex., devising an optimal route for inspecting naval buoys) as well as to theoretical ones (f.ex., discarding the hypothesis that the human brain is a giant lookup table). But these are still engineering and scientific concerns, not philosophical ones.
I still don’t understand why. If you want to know the probability of FAI being feasible at all, you’re asking a scientific question; in order to answer it, you’ll need to formulate a hypothesis or two, gather evidence, employ Bayesian reasoning to compute the probability of your hypothesis being true, etc. If, on the other hand, you are trying to actually build an FAI, then you are solving a specific engineering problem; of course, determining whether FAI is feasible or not would be a great first step.
So, I can see how you’d apply science or engineering to the problem, but I don’t see how you’d apply philosophy.
To fill in the content the term “FAI” stands for, science isn’t enough. Engineering is by guess and check, I suppose, but not really.
Sorry, I couldn’t parse your comment at all; I’m not sure what you mean by “content”. My hunch is that you meant the same thing as TimS, above; if so, my reply to him should be relevant. If not, my apologies, but could you please explain what you meant ?
I meant what I think he did, so you got it.