TITLE Turing machine engineering and Immortality AUTHOR Warren D. Smith ABSTRACT We address the either fundamentally important or silly question of whether the laws of physics permit a Turing machine (infinite computing device) to exist. ``Can life can exist forever?'' is a similar question. Although we do not settle the question, we propose a design which overcomes obstacles that at first would seem insuperable. It in fact is a Turing machine (and is an infinitely long-lived civilization) under certain restrictions. (Along the way we contribute several new cylindrically symmetric exact solutions of general relativity.) KEYWORDS Philosophy, general relativity, Turing machine, algorithmicity of physics. DATE 15 Nov 2003