[FOM] Re: Potgieter on hypercomputation

[Timothy Y. Chow]

Apostolos Syropoulos <apostolo at ocean1.ee.duth.gr> wrote:
> In addition, let me just note that recently two researchers in 
> astrophysics found evidence that space and time are not really discrete 
> but rather continuous [1]. If these results will be verified, then I 
> believe they will have a significant impact on our understanding of our 
> cosmos and consequently on our views of what can and cannot be computed.

The paper in question is http://arxiv.org/abs/astro-ph/0301184

In my opinion, saying that these results are "evidence that space and time 
are not really discrete but rather continuous" is highly misleading at 
best.  Lieu and Hillman discuss a method of experimentally probing the 
behavior of time at scales of 5.4e-44 seconds, the "Planck time."  Since
5.4e-44 is hardly infinitesimal, this says nothing about whether time is
continuous or whether it is discrete at much smaller scales (if indeed
"time" in the intuitive sense even means anything at much smaller scales).

I've argued before on FOM that most hypercomputation proposals rely on 
extrapolating theoretical predictions "all the way to infinity," and 
therefore cannot be verified experimentally in the same way that finite 
computations can, since finite human beings can only perform finite 
experiments.  I won't repeat all my arguments here, but will just point 
out that determining whether time is discrete or continuous would seem to 
require experimentally probing each and every time scale in an *infinite* 
decreasing sequence of time scales, and it is hard to see how finite human 
beings could do that.  The Lieu-Hillman paper is no surprise in this 
regard since it focuses on one specific time scale.

Tim