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

Notes for The Lifebox, the Seashell, and the Soul, by Rudy Rucker
orderly, “well-formed” patterns can actually serve as inputs. The reckoner can easily
recognize these acceptable inputs, which are what we call arithmetic problems.
• Corresponding to each arithmetic problem is a standard procedure for the reckoner to
follow, and the reckoner knows by heart which procedures apply to which kinds of
problems.
• In applying an arithmetic procedure to an input, the reckoner begins a process which
produces a series of successive patterns. This process is called a calculation. The
reckoner can easily determine when the calculation is over, and the pattern on the
paper at this time is the target output, that is, the answer to the arithmetic problem.
To complete these basic observations, here’s a list of various kinds of elementary
steps that are hooked together to make up the standard arithmetic procedures used to generate
the reckoner’s calculations.
• Reading symbols and noticing blank cells.
• Shifting attention from cell to cell.
• Remembering intermediate results.
• Using memorized look-up tables for single digit sums like 5 + 4 = 9.
• Writing symbols.
• Recognizing when the procedure is over.
Two Premature Turing Machine Explanations in Chap One
I’m having trouble not putting this in. But I really don’t need to, and it’s hard, and
there’s no reason to mention it. Maybe later in Chapter 3, I can talk about it.
***
Newer, simpler version.
Starting with simple thoughts about arithmetic, Alan Turing formulated a definition
of computation in the 1930s — well before any real electronic computers had been built.
Turing’s approach was to describe an idealized kind of computer called a Turing machine. A
Turing machine is similar to a human reckoner, but without all the squishy stuff on the
inside. A Turing machine has only some finite number of internal states. These are
analogous to a reckoner’s mental states, such as remembering to carry a one.
As a further simplification, a Turing machine uses a linear tape of cells instead of a
two-dimensional grid of paper. A Turing machine focuses on one cell at a time on its tape.
During each update, it reads the symbol in the cell, possibly changes the symbol in the cell,
shifts its attention one cell to the left or one cell to the right, and enters a new internal state.
Having completed one update step, it begins the next: reading the new cell, changing it,
moving its head, and altering its internal state once again.
What determines the Turing machine’s behavior? Look at it this way: each stimulus
pair of leads to a unique response triple of . We can think of the software for a Turing machine as being a
lookup table that supplies a response triple for each possible stimulus pair.
The operating system for a Turing machine is the background machinery that causes
it to behave in this way. To be more precise, we can say that a Turing machine’s operating
system forces it to cycle through the following three steps:
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