From: Anders Sandberg <asa@nada.kth.se>

Date: Wed Dec 10 1997 - 04:05:24 PST

Date: Wed Dec 10 1997 - 04:05:24 PST

"Perry E. Metzger" <perry@piermont.com> writes:

*> You are making an implicit assumption, which is that the number of
*

*> problems is countably infinite. It is not. Cantorian set theory shows
*

*> that many sets are NOT mappable into the integers.
*

Yes, but Turing machines can only deal with countably infinite

problems; if you allow devices which use true continuum calculations

you can deal with uncountable problems (and do things that are

Turing-uncomputable, I seem to recall?), but due to physics they are

not very likely. All problems we can generate are countable, since we

express them as symbol strings; if we start from a finite countable

set of problems we can only get a countable set of new problems.

*> However, it is trivial to state classes of problems that map into
*

*> the reals
*

But are they interesting? Most problems are just trivial

generalizations of other problems ("If x has property P, does

x+epsilon have property P?"). Can you suggest a class of problems that

map into the reals where every problem is of interest?

-- ----------------------------------------------------------------------- Anders Sandberg Towards Ascension! asa@nada.kth.se http://www.nada.kth.se/~asa/ GCS/M/S/O d++ -p+ c++++ !l u+ e++ m++ s+/+ n--- h+/* f+ g+ w++ t+ r+ !yReceived on Wed Dec 10 11:57:45 1997

*
This archive was generated by hypermail 2.1.8
: Tue Mar 07 2006 - 14:45:29 PST
*