“because they are incapable of conceiving that any event whatsoever in the outside universe could change the computational structure of their own operations.”
Self-modifying systems are Turing-equivalent to non-self-modifying systems. Suppose you have a self-modifying TM, which can have transition functions A1,A2,...An. Take the first Turing machine, and append an additional ceil(log(n)) bits to the state Q. Then construct a new transition function by summing together the Ai: take A1 and append (0000… 0) to the Q, take A2 and append (0000… 1) to the Q, and so on and so forth (append different things to the domain and codomain Q when that particular state leads to self-modification). This non-self-modifying machine should replicate the behavior of the self-modifying machine exactly, as every computation is equivalent to the self-modifying machine.
“because they are incapable of conceiving that any event whatsoever in the outside universe could change the computational structure of their own operations.”
Self-modifying systems are Turing-equivalent to non-self-modifying systems. Suppose you have a self-modifying TM, which can have transition functions A1,A2,...An. Take the first Turing machine, and append an additional ceil(log(n)) bits to the state Q. Then construct a new transition function by summing together the Ai: take A1 and append (0000… 0) to the Q, take A2 and append (0000… 1) to the Q, and so on and so forth (append different things to the domain and codomain Q when that particular state leads to self-modification). This non-self-modifying machine should replicate the behavior of the self-modifying machine exactly, as every computation is equivalent to the self-modifying machine.