From: Jeff L Jones (jeff@spoonless.net)
Date: Wed Mar 12 2008 - 01:20:13 MDT
On Tue, Mar 11, 2008 at 9:17 PM, Lee Corbin <lcorbin@rawbw.com> wrote:
> Perhaps in another post, I will have to say how the above can be
> extended in a TRULY HUGE GLUT to encompass an intelligent
> reply to every possible question that you may put to it. In effect,
> it merely "looks up" the answer. Unlike Searle's Chinese Room,
> however, it doesn't manipulate information or perform calculations.
> The lookup is merely indexical.
As you mention afterwards, this is a "super extreme thought
experiment" since it's not only practically impossible, but also
physically impossible even in principle. Let's say you want to ask it
any question that can be fit into a 100 byte string. (I could imagine
asking questions which take more than a line to type out, but let's
make the conservative assumption that every possible question fits
into a 1-line short string like this.) That means there are 2^800
different possible questions you could ask it (let's ignore the issue
of whether all of the possible strings you could make correspond to
meaningful questions... if only 1 in a million correspond to a
meaningful question, then add a few more bytes to the length of the
allowed string to get up to the full 2^800 possibilities).
Since there are 2^800 possible questions, it needs a lookup table that
is at least 2^800 bits long. This is assuming every question has a
yes/no answer. If they require freeform response, then you'd need an
even larger lookup table... something like 800^800 = 2^7715 bits if
the answers can be 100 bytes just like the questions. However, the
total number of quantum bits in the entire universe is only 10^120 =
2^400 (from the Bekenstein bound). This is the maximal amount of
information which can be stored in the entire universe. 2^7715 simply
won't fit! Even if you believe the universe extends forever past the
cosmological horizon, it still doesn't help because there is an event
horizon about 16 billion light years away beyond which nothing will
ever be able to affect us so it cannot be used for computing. So
we're stuck always with this 10^120 bit limitation... no global lookup
tables are allowed, even if you are only interested in yes/no
questions limitted to 100 bytes in length.
Jeff
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