From: Eliezer S. Yudkowsky (email@example.com)
Date: Sun Feb 15 2004 - 09:36:42 MST
>>Actually, it's not that all information inside a sphere is being mapped
>>onto the surface, but that the entanglement between the outside of the
>>sphere and the inside is bounded by the area of the surface. But it would
>>apply to any attempt at data storage.
> then it is self evident!
> I mean the maximum bandwidth that can be transferred from the inside of
> sphere A to the outside, is evidently limited by the surface area. Imagine
> having many little cables sticking out of the sphere, if the smallest cable
> has planck diameter, then these are your degrees of freedom.
> Even stuff that operates at a distance such as magnetic and gravitational
> fields can be thought of as reducible to a single point value at each
> position on the sphere since they add up along any one radius of the sphere.
> Am I missing the genius behind this discovery? :-)
Yes, completely. It's not a bound on bandwidth, it's a bound on
entanglement, which is, to a first approximation, a bound on the
information inside the sphere that can be stored, period, not a bound on
the information that can be transferred per unit time.
There ain't nothing self-evident about the holographic principle, nor is
it easy to explain, nor am I qualified to do so. I am just trying to
explain that for deep, nonobvious reasons there is probably an absolutely
fundamental bound on how much information you can store inside, say, the
radius of a hydrogen atom, which no amount of nonphysicist ingenuity can
bypass, just as no amount of nonphysicist ingenuity will get you a
perpetual motion machine or an FTL drive.
-- Eliezer S. Yudkowsky http://intelligence.org/ Research Fellow, Singularity Institute for Artificial Intelligence
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