I have a question on a part from the wikipedia page on Savitch's theorem: https://en.wikipedia.org/wiki/Savitch%27s_theorem
The part in question is the following:
[...], if a nondeterministic Turing machine can solve a problem using f(n) space, an ordinary deterministic Turing machine can solve the same problem in the square of that space bound. Although it seems that nondeterminism may produce exponential gains in time, [...] shows that it has a markedly more limited effect on space requirements.
So, simply stated, it says deterministic Turing machines need more space AND more time to solve a problem (correct me if I'm wrong). If this is the case, then why bother turning any Turing machine deterministic? Thanks