# Re: Are Philosophical Zombies possible?

`On Sun, Jul 14, 2024 at 9:00 PM Brent Meeker <meekerbr...@gmail.com> wrote:`
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* > What's your definition of a Turing machine?  *
>

*A Turing Machine is the simplest possible computer model that the logical
operation of any real computer can be reduced to if given enough internal
states, it has n States plus the HALT state.  A Turing Machine  consists of
two parts, a long tape with zeros and ones on it and a read/write head
which can only print a zero or a one on the tape, move one notch left or
right, and CHANGE INTO A DIFFERENT STATE. After the head has read a symbol
what it will do next depends on whether it has just seen a one or a
zero, and it depends ON WHAT STATE IT IS CURRENTLY IN. And in general, the
more states a Turing Machine can be in the richer and more complex its
behavior will be. *

*An easy way to understand Turing Machines is to separate the program and
the data. The data is on the tape and the program is on a series of cards.
You always start at card #1 and, depending on if you are reading a 1 or a 0
on the tape that card tells you to print a one or a zero, move left or
right, and it instructs you on which state to turn into next, that is to
say it tells you the number of the card (a.k.a. state) to read (a.k.a. be
in) next.  As I said, all Turing Machines have N states plus a HALT state.
The information on the cards could have originally come from the tape as in
a Universal Turing Machine, but for simplicity I will assume the cards have

*For a start let's look at a one state (card) Turing Machine, there are 8
different actions a card could tell you to perform if you first see a zero
on the tape :1) Write a 1 or a 0.2) Move left or right.3) Stay on card#1
(the only card) or halt.*

*So there are 2^3=2*2*2 =8 things you can do if you read a zero. But there
are also 8 things you can do if you first read a 1 on the tape, so there
are 8*8= 64 possible one card (aka one state) Turing Machines. 64 is a
small number so you can't do much with just a one state Turing Machine.*

*Now let’s look at a 2 card (state) Turing Machine, if you’re currently
reading 0 there are 12 things the first card could tell you to do; write a
zero or a one, shift left or right, go into state (card) 1 or card 2 or
halt, 2*2*3= 12.  And if you’re currently reading 1 there are also 12
things the first card could tell you to do: So there are 12*12=144
different things that first card could  tell you to do. However, each of
those 144 cards must be paired up with a second card, and there are also
144 things that the second card could tell you to do. So there are 144*144=
20,736 different 2 card (state) Turing Machines.*

*The general formula is, there are (2 N s +1)^(s N )Turing machines with N
states and with s symbols. A two symbol machine is the simplest and can do
everything a machine with more symbols can do, so if s=2 then the formula
for the number of 2 symbol N state (card) Turing Machines) is
[4(N+1)]^(2N). Thus the number of Turing Machines increases exponentially
with N, but the Busy Beaver number increases far far faster than
exponentially, faster than super-exponential, in fact the function is not
even computable despite the fact it's well defined and finite.*

>
> *I posted the definition from Wikipedia:*
>

*Thanks but I already figured out how to look things up in Wikipedia.*

John K Clark    See what's on my new list at  Extropolis