If Real computers have finite number of states, why Turing machines are needed?

[tgflynn]

This is a great question. What do we lose by thinking of real computers as Turing machines when they are in fact finite ? For one thing I believe the halting-problem doesn't exist in reality because it only holds for infinite systems (ie. Turing machines), not finite ones (ie. physical computers).

[dalke]

We lose very little. The Busy Beaver problem shows that even a small number of states can take time that's described with Knuth's up arrow notation.