There are other possibilities to obtain hypercomputers or Infinite Time Turing Machines:

For instance, from general relativity: put a computer in orbit around a black hole,
start an infinite computation on it, arrange that the results are sent to you by radio,
and jump into the black hole:
when you reach the horizon, you get the result of the infinite computation
(and witness the end of the rest of the universe).

For a survey:

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