In his famous article, Computing Machinery and Intelligence, Allan Turing talks about discrete-state machines and the largeness of the number of states provided by that time state-of-the-art machine, Manchester Machine, which he states is about 2^165,000. Link to the articleWell, that was 1950's. I'm trying to compare it with modern day computers and get an average number of states for a usual commercial machine. How can I find it? Is it related to memory size (Turing calculates it by the number of stores, or sheets of paper available)? If so, would this make the number of states tend to infinity due to the current possibility of writing/erasing memory at will?
How to find the number of discrete states possible by current computers?
discrete mathematics
Acording to the suggestions that were given in the comments to the question, the number of distinct discrete states possible by a machine are related to the size the machine's of memory (or stores space, using Turing's nomenclature).Since a bit has two distinct discrete states, a byte then have $$ 2^{2^3}=2^8 $$ discrete states. Two bytes, $$2^{2*2^3}=2^{16}$$Hence, a commercial availabe 4GB DDR3 RAM machine would roughtly be $$ 2^{2^2*2^{30}*2^3} =2^{2^{35}}=2^{34,359,738,368} $$Further, today's (March 2017) world fastest computer, Sunway TaihuLight, with more than 1 PB memory, would have rougthlty $$ 2^{2^{50}*2^3}=2^{53}=2^{9,007,199,254,740,992}$$ distinct discrete states.Correct math if wrong, but the idea is this, taking in account only main memory (disregarding cpu registers, secondary memory and cache, as j_random_hacker stated that could be done).