His argument is deeper than that; he's basically saying that there's no such thing as a universal machine if the function being simulated meets any of the 5 criteria he lists, since the function can't be simulated (that is, you can't compute it with any less steps than running the whole thing through, and it could require up to infinite variables). I don't know if this makes it non-crackpot-ish, though; I don't have the background in formal theory tell; but it doesn't seem something like a "it'll take arbitrarily long" argument.
It doesn't seem terribly crackpotish to me. He's absolutely correct in pointing out that it's very sloppy to define "computability" as "What the Universal Turing Machine Can Do." It's also not unreasonable at all to talk about variables that change with time, and he's absolutely correct that this is a gap in complexity theory. One which should excite new grad students, because eventually it will net someone a lot of academic fame and one hell of a PhD thesis.
Personally, I'm very interested in this and I'm going to keep an eye on it.
It is quite unreasonable to talk about variables that change with time in the context of a Turing machine. If a "Universal Computer" is one that deals with variables which change during the computation due to interaction, then it is not what Turing was talking about. And if he wasn't talking about it, he can't be wrong about it.
It's naming, plus some more: Turing never named his idealized entity a "Turing machine" - that was done by others. He claimed universality for the algorithmic "Universal Computing Machine" he defined, and proved it - for algorithms. Now Akl comes along and says the "Turing machine" is not universal, but he uses interaction, not algorithm, to base his definition of computation on. So it seems to me that he's not only renaming "the Universal Computing Machine" to "the Universal Computer" by ways of "the Turing Machine", but that he is also moving the goalposts in this process.
