Notes for the Lifebox, the Seashell, and the Soul - Rudy Rucker

Notes for The Lifebox, the Seashell, and the Soul, by Rudy Rucker
(Turing A) The machine reads the symbol that is in the active cell. It combines the
read symbol with its current state to make a stimulus pair < internal state, read symbol >.
(Turing B) Given the stimulus pair < internal state, read symbol >, the machine looks
in its program code to locate a corresponding response triple < write symbol, move direction,
new state >.
(Turing C) On the basis of the response triple, the machine writes a symbol in the
active cell, moves the active cell location one step to the left or to the right, and enters a new
state. And then the machine returns to step (Turing A).
The software is the particular set of stimulus-response correspondences, while the
operating system is the endless cycling through Turing steps A, B, and C. Furthermore, a
Turing machine input is a string of symbols on the tape, and an output is any resulting pattern
of symbols that appears on the tape at a later times.
The rudimentary quality of Turing machines makes it possible both to reason about
their abstract capabilities, and to carry out exhaustive searches to find certain kinds of
interesting Turing machines. The drawback is that not many interesting computations would
be practically feasible for Turing machines, were we to actually build them. The Turing
machine hardware is too simple and the expressiveness of the Turing machine software
language is too limited. There’s a good reason why Dell and Intel don’t market Turing
machines. Instead they market real computers.
***
Older, clunkier version.
In his 1936 paper, “On Computable Numbers,” the British mathematician Alan
Turing carried out a penetrating analysis of what makes a possible computation in the style of
pencil-and-paper arithmetic. Recalling the old-style elementary school mathematics drill
paper ruled into squares, he suggested that we can think of arithmetic as a process of reading,
writing, and occasionally erasing and changing the symbols in an array of squares. Turing
refers to the squares as cells — not in the sense of living cells, but in the sense of spreadsheet
cells.
Next Turing suggested that we ought to be able to build a simple kind of machine to
carry out this kind of computation — these are what we now call Turing machines.
Turing made his machines as simple as possible. He supposed that one of his Turing
machines would have a read-write head which also remembers the machine’s current internal
state. He specified that each machine would have only some finite number N of states — the
higher the N you use, the “smarter” the machine.
As a further simplification, Turing proposed that his machines could get by with a
narrow tape of paper, a long row of cells. You could, for instance, have the tape act
something like two-dimensional paper by using extra symbols [ and ] to mark the starts and
ends of rows. Thus, at the beginning of computing the sum we mentioned above the tape
might look like the following.
[ 2 7 5 ] [ 4 8 4 ] [ ]
If we set the adding machine’s head down to the left of the first [, its course of action
might go like the following, with the machine using internal states to remember which task it
was doing and which digits it was moving around.
“Move right to the first ], go left one cell and read 5. Remember the 5 (by using an
internal state) and move right to the second ], go left one cell and read 4. Add the
remembered 5 to the 4 and get 9. Then move right to the second ], erase the ], write 9 in this
p. 52