Bruno Marchal wrote:
On 29 Apr 2015, at 02:12, Bruce Kellett wrote:
Bruno Marchal wrote:
Any two numbers might have an indefinitely large number of programs
mapping from one to the other, but all such programs reduce to
simple additions of two numbers.
Addition, + multiplication.
multiplication = addition.
That is wrong.
It depends on how you define a 'step' in the algorithm. It depends on
the substitution level. If a step is taken as each arithmetical
operation, then addition is all you need. Multiplication is then just
repeated addition, and exponentiation is just repeated multiplication,
hence even more repeated additions. Sure, you need some control logic to
tell you how many repeats of each step you need at any stage. But that
is little more than the logic required to step through the basic program.
At a lower substitution level, the steps become smaller, and you then
have to specify accessing memory to get the numbers to add, incrementing
program counters, decrementing loop registers, comparing registers to
zero or anything else required. But then the steps become many, and one
is in danger of losing the forest among the trees.
I agree that all these things are necessary for programming and running
a real program on a real computer, but if one's purpose is merely to
give a schematic outline of the essential computational steps, then we
do not need a description at the CPU register level. There are no 'real'
computers in Platonia.
So what substitution level is required for consciousness/physics to
emerge? What does happen at each step?
Bruce
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