The tape size needed for a Turing machine is incalculable. Here's a reference to a proof: https://scottaaronson.blog/?p=2725 https://scottaaronson.blog/?p=2725

The tape size needed for a Turing machine is incalculable. Here's a reference to a proof: https://scottaaronson.blog/?p=2725 https://scottaaronson.blog/?p=2725. The machine with 7918-states, Z, stops (well, Z cannot be proven to run infinitly long) iff. ZFC is consistent. For this it needs a finite amount of space but we cannot calculate how much. If we could calculate an upper bound we've proven ZFC is consistent.