On 2/14/2014 8:14 AM, Bruno Marchal wrote:
With some definition of the abacus, it is Turing universal. With others it is
not.
The slide rules is not Turing universal. You can add and multiply approximation of
natural numbers only, or, if you want, you can analogically add and multiply the real
numbers, and that is not Turing universal. (That is not entirely obvious).
That's an interesting point to me (I own a collection of circular slide rules). Of course
you can add and subtract on a slide rule as well as multiply, divide, exponentiate, and
compute the value of other functions encoded on the rule (sin, tan), but the rule doesn't
do it by itself; you provide the sequence of operations consisting of reading a cursor and
moving the rule. So why would that not be Turing universal?
Brent
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