On Sun, Sep 2, 2018 at 2:19 PM Bruno Marchal <[email protected]> wrote:
> A function is computable if we can explain to a dumb (but docile) human > being how to compute it, on any of its argument. > And some functions (the Sine function for example) can be proven to be computable and some functions (the Busy Beaver function for example) can be proven to be non-computable) but there is no general way to know if any given function is computable or not. > > *Each f_n is computable (by definition!) and so each f_n(n) can be > computed, and adding one is certainly computable, so, the only thing which > can be NOT computable is the bijection itself. This means that the f_i, > although enumerable, are not recursively enumerable.* > *If a universal language exist, then it cannot compute the enumeration of > all computable function from N to N.* > The Ackermann function is not primitive recursive and yet it is computable, like the Busy Beaver the numbers soon become huge (although finite) but unlike the Busy Beaver a Turing Machine can always calculate them. > > Then the Löbian machine are those universal machine which knows that > they are universal, and so get acquainted with the consequences (the > infinite, the non provable, the non observable, …). > Nobody on this planet uses the term "Löbian machine" except you. Turing explained exactly precisely how to build one of his machines but you have never given the slightest hint of how to build a "Löbian machine" or even clearly explained what it can compute that a Turing Machine can't. Can it tell if any given function is computable? Can it find the 8000th Busy Beaver number? Can it even find the 5th? *>Here there is a second miracle, which is that the propositional part of > the theology is decidable!* > Homemade gibberish. How would things be different if "the propositional part of the theology" were not decidable? John K Clark John K Clark -- You received this message because you are subscribed to the Google Groups "Everything List" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. To post to this group, send email to [email protected]. Visit this group at https://groups.google.com/group/everything-list. For more options, visit https://groups.google.com/d/optout.
