On 15 February 2014 10:57, meekerdb <[email protected]> wrote: > On 2/14/2014 12:32 PM, LizR wrote: > > On 15 February 2014 09:12, meekerdb <[email protected]> wrote: > >> 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? >> > > I would guess because it isn't digital, but analogue? 'cause Turing > machines use discrete symbols, while slide rules use a continuous scale? > > > Yes, of course a real slide rule can't encode arbitrarily large integers > because it only has finitely many distinguisable locations for the the > cursor. But since a Turing machine is allowed an infinite tape, suppose my > slide rule (Sliding Machine?) is allowed to expand the number of distinct > positions arbitrarily? >
So you don't think the analogue/digital thing matters? I suppose a person using a slide rule could be trusted to correct for small errors....or could they? -- You received this message because you are subscribed to the Google Groups "Everything List" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. To post to this group, send email to [email protected]. Visit this group at http://groups.google.com/group/everything-list. For more options, visit https://groups.google.com/groups/opt_out.
