Re: Knowledge and Ignorance over Time
Date: 16 Dec 2005 13:31:05 -0800
Message-ID: <1134768664.994303.94950_at_g43g2000cwa.googlegroups.com>
David Cressey wrote:
> My apparent knowledge grows like the radius of the sphere (like R).
> My apparent ignorance grows like the surface area of the sphere (like R
> squared).
> And the number of things I must keep in my head grows like the volume of the
> sphere (like R cubed).
The Bekenstein Bound, in fact, places a hard limit on the information capacity of any region of space, with the limit proportional to the area (not volume!) of the surface enclosing the region.
For spherical regions, the limit is reached when enough information is packed into the region that the resulting concentration of matter and energy leads to a black hole. The Bekenstein Bound is equal to the entropy of the black hole, with the conversion
1 bit = Boltzmann's constant * ln(2)
This makes 4 times a Planck unit of area equal to a bit, or 1/4 (I
don't recall off-hand, which).
So, under no circumstances can it possibly be true that the number of things you need to know grows like the volume of the sphere. It only grows like the area of the sphere. The sphere in question being any sphere you care to circumscribe the region of interest with (e.g. the Earth and its immediate space).
A consequence of this, also, is that the maximum amount of information a machine (or anything else) can store is proportional to the amount of material used to make the box enclosing it or less; rather that the amount of material inside. Received on Fri Dec 16 2005 - 22:31:05 CET