I don&#x27;t know where this thinking gets us. My computer, once I disconnect it from the internet, is actually a finite state machine and not a Turing machine, which I think you acknowledge.  How does that help with anything?<p>If my program uses one kebibyte of memory -- no I&#x2F;O and harddrive, then it loops or halts within 2^(2^10) steps. For me to detect that, in general I need to store a history of length 2^(2^10), which is more than 10^300. That&#x27;s 10^301 bytes that I need to detect if a 1kb RAM program loops.