# Re: Hole in a box

Date: Wed Feb 20 2002 - 08:31:26 MST

On Wed, Feb 20, 2002 at 07:33:03AM -0500, Louis Newstrom wrote:
> ----- Original Message -----
> > You can only move slower than c. Storage and retrieval of data will
> > take exponentially increasing time as it gets longer.
> > ...
> > If you
> > settle for a 100 billion lightyear distance, then you can't use any
> > character higher than 92 (backslash in ascii) if you want to fit it in.
>
> First of all, that was only a simple example to show it could be done. The
> distance problem could be optimized a little.

Sure. But distance is still not a particularly efficient way of storing
information. An integer X holds log(X) bits of information, which means
that if the resolution of a system is r and maximum size is R, the most
information a distance can provide is log(R/r) = log(R)-log(r). If we
use the planck length 1.6e-35 m for r and the size of the visible
universe 1.4e26 m for R, we only get 202.5 bits for each atom pair.
Compare this to the rough megabyte of information that can be stored in
the volume/mass of a single hydrogen atom by the Bekenstein bound (a
more realistic estimate would of course be around one bit per hydrogen
atom, although Rydberg wavefunctions apparently hold some promise of
storing complex information).

Using more markers for distances won't help - each new marker can after
a while only be placed so as to provide three new distances to the
configuration of markers (four is an overdetermined problem), which
means that the total information of the system grows as
3M(log(R)-log(r))/m0 if the markers have mass m0 and the total mass is
M. Compare this to the Bekenstein bound 2.57e43 M R bits - even if you
find sufficiently low mass particles to make m0 very small, the growth
is still logarithmic in space.

> On the other hand, once people are uploaded, time is irrelevant. If the
> system takes a year per cycle, the uploads won't notice. They will always
> perceive "normal" speed.

If the cosmological constant is as large as is currently believed, time
is really running out. Cosmic expansion will, besides changing distances
in a fairly calculable manner, make horizons creep inwards. Eventually a
very large computing system will find its outer parts separated from the
inner ones.

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Anders Sandberg                                      Towards Ascension!