From: Lee Corbin (lcorbin@rawbw.com)
Date: Wed Mar 12 2008 - 08:30:31 MDT
Jeff writes
> Lee 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.
*Unless* it turns out that computronium is even more capable of
performing calculations in a small space and at a greater rate than
we have imagined. It's also important to see---as I think you have
---that if I walk into a room with a GLUT-driven human shaped
robot, then because of the speed of light limitations, its physical
volume cannot be very big. No Jupiter Brain here. Yet it acts
perfectly as well under any test as would a real human being.
But the point is that on ****very**** theoretical grounds,
functionalism is be false. Who knows? Such computronium
might be possible.
So I agree perfectly with the remainder of your comments, and
could not have written them as well as you did. Thanks!
Lee
> 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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