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ike comments on Does immortality imply eternal existence in linear time? - Less Wrong Discussion
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I've heard it argued that given the assumption of infinitely divisible time, one can theoretically achieve all the purported benefits of immortality in a finite amount of time, using a derivative of Zeno's paradox.
It would need an infinite amount of energy, though.
Does doing something in half the time take half the energy?
Depends on the something: flipping a bit faster and faster surely requires more and more energy (no system is a perfect solid, the speed the components need to develop doubles every time, etc.)
Probably you could get at least infinity energy density in the collapsing black hole,near its singularity
I think you may refer to Tippler Omega point. Also John Smart had similar ideas, as I remember, when he said that civilization would evolve to smaller and smaller entities, running on higher and higher speed. In result technological singularity will be also physical singularity.
Now we can't say if time is infinitely divisible. Plank time may be the limit.