On Thu, Sep 23, 2010 at 11:10 AM, jtd <[email protected]> wrote: > >> Mathematics is basically a form of formal reasoning. In fact all >> formal reasoning is mathematics. >> Computable mathematics forms a part of it. > > so is there some math which cannot be computed?
There is plenty of mathematics in which solutions cannot be attained through algorithms. The simplest example would be the process of finding limits of functions by the $\epsion-\delta$ definition. A soft solution to the problem of finding limits may be with a detailed set of rules over a primitive set of 'facts' or by a more detailed approximation theory. But the definition was not intended for computation in the first place. Goals in theoretical mathematics may be of the form 'Clarify the relation of A with respect to B'. A solution (theoretical) will typically aid investigators working from a practical point of view in solving or not solving classes of problems. There are many proposals (-isms) for the foundation of mathematics, and these would determine their own 'mathematics'. From the legal point of view, 'mathematics' would be all of the things covered by the AMS subject classification. >> Softwares are necessarily representation of reasoning >> processes/schemes. > > This is one very intuitive way to convey the relationship between math > and software. > >> These will always be copies of known things in >> AI, day to day life, human interaction etc in mathematical terms. > > But you can patent devices which do known things eg. device to make > sound. Thus if one were to create a device which mimics the larynx > and does not use a diaphragm, which includes some hardware and some > software, it would be patentable. Although individually none of the > hardware components are unique. This particular aspect is exploited > by separating the non unique hardware and claiming uniqueness for the > software to cause the hardware to do something unique. > Yes, the hardware is as open ended as paper and pencil. If the hardware does not behave as is expected then possibly it is doing something unique. Best A. Mani -- A. Mani ASL, CLC, AMS, CMS http://www.logicamani.co.cc _______________________________________________ network mailing list [email protected] http://lists.fosscom.in/listinfo.cgi/network-fosscom.in
