Woah, I'd love to hear about confounding ITA if you're up for a chat, or a drink if you're in NY. My email is in my profile.
640 karma · joined August 20, 2009
Is this different from saying that second order logic contains unprovable true statements / that the incompleteness theorem applies?
Also thanks for the really well informed response!
Do you support an empiricist view of logic then (http://en.wikipedia.org/wiki/Is_logic_empirical%3F) ? That we justify logical rules because they so strongly correspond with our own experiences?
I'm really interested by questions like:
Why is second order logic irreducible to first order logic if I could use first order logic to reason about the behavior of a turing machine running a second order logic theorem prover with whatever inputs I like?
How do I get something that can do what I can do, which is to say take any formal system and prove theorems with it? How do you determine what formal systems are "valid" logics? (Leading to sensible conclusions rather than nonsense like A & ~A)
A good example of the sort of thing this lets you do is the fold fusion, which (under the conditions which you need to derive the equality) lets you collapse multiple calls to fold (reduce) in to a single call, with a combined function:
foldr f e (foldr g e' xs) = foldr h i xs
When the first foldr is something like tails, which produces a list of lists of length ~|xs| this can turn an N^2 operation into a linear one, mechanically!
Actually, you don't http://en.wikipedia.org/wiki/Panpsychism
Instead, he was honest about why a well funded competitor is a daunting prospect to someone who's prelaunch, and went on to say that that's not a reason to quit. On the whole, a pretty admirable post.
Read the damned post before you spew this self-righteous nonsense.
You can parallelize a cellular automaton trivially with any form of parallel computation, from multiple cores, to a GPU, to an FGPA. Hence my skepticism that their application is particularly revolutionary or brain-relevant, as the article seems to imply.
As for FPGAs you can get them fairly cheaply if you aren't looking for a top of the line beast. [1] Given that you can emulate anything up to and including a Pentium on a sufficiently powerful FPGA, I fail to see how you are "limited by the manufacturers design choices" or why you can't "apply a wide range of computational topologies" on one.
In any event, the breathless tone of the article about "brain-like" computing and this somehow being a parallelism silver bullet are unwarranted.