HI Tricia and all,

your thoughtful questions are much appreciated

> Will you please try to clarify the differences in these definitions?
>
> 1) Is the Turing Machine simply a self-driven typewriter?

No.  The Turing machine is kind of like a typewriter that only
types one character -- X -- on a very (consider it infinite)
long tape.  But the point is that unlike a typewriter it not only
types on the tape but READS the tape.  I.e., at any given time,
its head is over one spot on the tape.  It reads what is there in
that spot on the tape (an X or not), and then based on what it
sees, it does two things:
        -- decides what to do (move the head right, move the
        head left, or print an X)
        -- decides what state to be in next
Its program tells it how to make these decisions
 

> 2) Is a Universal Computer one that's capable of completing every task
&
> that
> every
>     object could be simulated over time?

A Universal Computer is: A computer that, given enough time and
enough peripheral memory (e.g. tape, floppies, etc.), can
simulate ANY OTHER COMPUTER

The reason Turing created his toy "Turing machine" computer
(which was just a mathematical idea, never built in reality)
was so he could give an example of a very simple universal computer.
As primitive as Turing's X-reading and X-typing computer is, it
can simulate any other computer's behavior.
 

> 3) Does Godel's Incompleteness Theorum conclude that not everything
can
> be
>     proved true or false & that no system can know everything?

Yes.  It concludes that, for any mathematical system, there is
SOME statement that this mathematical system cannot prove true
or false -- that is, in other words, "undecidable" in regard to
the mathematical system.

What this means is that the whole body of mathematical truth
cannot be captured in ANY finite set of rules.
 

> 4) Isn't Godel saying the opposite of Turing, whose universal computer

> is
> supposed
>     to do it all?

Good point.  Indeed, Godel's concept of a "mathematical system"
is indeed equivalent to the concept of a "formal computer" that
Turing used.

But the two statements weren't really opposite.

The analogue of an undecidable proposition, in computer terms,
is a program that never stops running, never gives an answer.
Godel's theorem, applied to computers, says that for any
computer there are some questions that, if you write a computer
program to solve them, the program will never stop running
(i.e. never get to the answer).  This doesn't contradict the
notion that any universal computer can simulate any other
computer.  Running forever without stopping is one example of
behavior that a universal computer can simulate.
 
 

> 5) What is the distinction between Godel's Theorum & the Church-Turing

> Thesis?
 

The Church-Turing Thesis states that a computer can carry out
any procedure that can be precisely and finitely specified.
Alternately, it states that a computer can simulate any precisely
describable system.  (There are many other formulations too.)

Godel's theorem implies that for any PARTICULAR mathematical
system (or any particular computer), there are things it can't
do.  But this doesn't change the fact that any precisely
specifiable thing can be done by some computer.

Godel's theorem is a mathematical theorem which has been proved.
The Church-Turing thesis is a philosophical assertion which can
be believed or disbelieved but not proved.  It might be considered
a definition of "precisely describable", i.e. "Precisely describable
means describable as a computer program."

> Who determines how the internet is structured ( which parts connect to

> which others).

The answer is: Everyone and no one :)
There are government bodies that regulate it, but the actual growth
process is chaotic because new nodes are constantly added and the
addition process is under no one's global control.
Remember my long speech about the Internet as a growing, chaotic,
self-organizing system?  This is kinda the same thing.

> How does the Web relate to the Internet? ( I had always thought until
> reading the first chapters of Net.wars that the Web and the internet
> were
> synonomous.  Now I am only confused on that point.)

This terminology is worth reflecting on a bit...
The "Internet" is a well-defined entity, a network of computers
talking to each other by standard protocols (languages).
Actually the term "internet" arose when the TCP protocol was
introduced, allowing different kinds of networks to communicate
with each other -- thus "inter-net", i.e. "between different networks"

the "Web" is a slang term whose meaning is not clear.
The internet existed for a long time before hypertext and the
World Wide Web came about.
But now, some people use "Web" to be inclusive of pre-hypertext
internet stuff like e-mail, ftp, and telnet also.
 

ben