But a Turing machine that is connected to the WWW is an oracle machine: MN> Yes, Turing describes NON-algorithmic machines (like the oracle machine—the o-machine as he called it)—but so far we are stuck in the algorithmic. The following article has a good readable historical development of the issues. (The word 'readable' means that if you had studied some of these topics many years ago and forgot almost everything, the article has enough clear discussion that you don't need to do any further studying elsewhere. If you remember a little more, you can flip through quite fast. That is not something you can say about most publications on these topics.) Turing Oracle Machines, Online Computing, and Three Displacements in Computability Theory Robert I. Soare, http://www.people.cs.uchicago.edu/~soare/History/turing.pdf Following is the final paragraph on p. 60: Conclusion 14.4. For pedagogical reasons with beginning students it is reasonable to first present Turing a-machines and ordinary computability. However, any introductory computability book should then present as soon as possible Turing oracle machines (o-machines) and relative computability. Parallels should be drawn with offline and online computing in the real world John ---------------------------------------- From: "Nadin, Mihai" <nadin(a)utdallas.edu> There is NO general intelligence—good for everything; rather concrete intelligence, as the context defines its characteristics. I hope that these notes explain my invitation to my respected colleagues to read Hilbert’s challenge and Turing’s paper. Yes, Turing describes NON-algorithmic machines (like the oracle machine—the o-machine as he called it)—but so far we are stuck in the algorithmic. Best wishes for a happy and healthy 2024 Mihai Nadin