Future of Computation is Infinite

Roland Piquepaille's Technology Trends has a new post called Future of Computation Is Finite which discusses the conclusions made by a couple of scientists. I disagree with their conclusions. I think the more likely scenario is there are ultimately no limits to computation at all. But first, here is an excerpt:

According to PhysicsWeb, two cosmologists from Case Western Reserve University have shown that the acceleration of the expansion of our universe leads to physical limits on the total amount of information that can be stored and processed in the future. They also determined a time limit for Moore's law which will still be valid for the next 600 years. Finally, they calculated that the total number of computer bits that could be processed in the future will not exceed the 10¹²⁰ range. In a previous story, "Universe is a computer," another physicist estimated that the number of calculations the Universe would have performed since the Big Bang -- if it was a computer -- and also came with a 10¹²⁰ number. I'm not sure if both studies are speaking about the same exact things. But if they are, does this mean that we are exactly at the midlife point of our Universe?

The acceleration of the expansion of the universe places limits on future developments in technology according to two US cosmologists. Lawrence Krauss and Glenn Starkman of Case Western Reserve University have shown that the acceleration could put a fundamental limit on the total amout of information that can be stored and processed in the future. They also calculate that Moore's Law will remain valid for no more than 600 years -- although workers in the semiconductor industry are more pessimistic and think that the famous law will break down in the next decade or two.

They also found other physical limitations.

The duo calculated that the total number of computer bits that could be processed in the future would be less than 1.35120. This means that the effective information available to any observer within the event horizon of an expanding universe will be significantly less than the total so-called Hawking-Beckenstein entropy -- the entropy that is associated with a black hole -- in the universe. Many cosmologists predict that an accelerating universe will ultimately contain nothing but black holes, which will then eventually disappear themselves.

Right or wrong, the physicists seem to enjoy their work.

"It is remarkable that results from cosmology can provide such definite limits on the nature of technology," Krauss told PhysicsWeb. "In addition, it is also remarkable that simple laws of physics put such robust constraints on life, and technology, even when we don't know what that technology will be like."

For more information, the research paper has been published by ArXiv in its astrophysics section under the name "Universal Limits on Computation" on April 26, 2004. Here are the links to the abstract and to the full text (PDF format, 3 pages, 89 KB).

I disagree with these conclusions, and think they are made in part because of a confusion of semantics. For example, as our knoweldge of cosmology increases, we have had to continually revise what we mean when we say universe. The original definition of this word implied everything that is. Now it's quite common for cosmologists to refer to our universe as one among an infinite number of possibilities. Tegmark in last years SciAm introduced to the general public his "ensemble theory" which postulates an infinite number of other universe, not just an infinite number similar to ours but an infinite number of dissimilar universes. Since we are dealing with infinite sets of infinity, we are actually discussing a transinfinite set of universes of every "mathematical" possibility.

So when these scientist above discuss Universal computation, they aren't discussing something truly universal in light of the latest cosmological models. A more accurate way of articulating it might be to say somthing like, "These are the limits of computation as far as we know in our local finite bounded universe."

As I have postulated many times before, all of these predictions about the limits of computation are being devised by 3lb mind-brains on a small rock around an ordinary star. Given sufficient time and intelligence, all such perceived limits will evaporate in the presence of greater intelligence.

For more information on that idea, please read:
Sans-Celing Hypothesis
Apothesosis
Reality 3.0: Hypermediation & Paradise Engineering

Posted by paul at May 10, 2004 12:33 PM | TrackBack