Re: Knowledge and Ignorance over Time

<markwh04_at_yahoo.com> wrote
> 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.
>
>

Biological systems (eg., humans) have a tendency to treat memory as somewhat malleable (I'm trying to be kind.) A much less scientific description I read some years ago asserted that memory can best be likened to a container of some shape and size.

You might be dealing with a shallow bowl which keeps much information (memory) near the surface, but does not support much volume. Or your memory might be shaped like a vase, with limited 'fast access', but much greater depth. Sadly, I seem to be approximating a thimble, in both shape and size ;-(

BFaux- Received on Mon Jan 16 2006 - 23:06:04 CET