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From: Alex McDonald on 30 Jan 2006 16:06 Robert Redelmeier wrote: > Alex McDonald <alex_mcd(a)btopenworld.com> wrote in part: >> Can you name one theoretically insoluble problem that has >> an easy practical solution? > > Busy beaver, Travelling salesman and many scheduling problems > are intractible, but practically solved every day. The halting > problem also solves, albeit less often if you're running Microsoft > software :) > > -- Robert > I think you've cheated here! You said "theoretically insoluble". I wouldn't say busy beaver's been "practically solved" at all; it's not that kind of problem (and yes, it's theoretically insoluble). If you've got a definition of what constitutes a practical solution for busy beaver, I'd like to see it. As to travelling salesman problems, there's no efficient way of solving them for large n. You can get what appear to be good solutions for large n in reasonable times, but you don't know how far from optimal they are. Of course, the easiest solution is just to label the cities 1 through n and visit them in that order. Practical its not! "The halting problem also solves" I didn't understand... What does it solve? -- Regards Alex McDonald
From: Charles A. Crayne on 30 Jan 2006 16:28 On 30 Jan 2006 09:53:29 -0800 "Alex McDonald" <alex_mcd(a)btopenworld.com> wrote: :Can you name one theoretically insoluble problem that has an easy :practical solution? Design of a steam turbine. Physics has the concept of the behavior of an ideal gas, the key element of which is 'enthalpy', defined as u+pv. Unfortunately, most real world working fluids do not behave like an ideal gas, although many of them are close enough for an engineering approximation. Steam, however, is particularly intractable, and engineers do not even try to use mathematical calculations for it. Instead, they consult the standard 'Steam Tables' -- which were compiled from the results of much real world experience. -- Chuck
From: Charles A. Crayne on 30 Jan 2006 17:23 On 30 Jan 2006 08:59:41 -0800 "randyhyde(a)earthlink.net" <randyhyde(a)earthlink.net> wrote: :Chuck, how much time have you put into studying this problem? In the generic sense, I have been working with this problem for about forty years professionally, and for about 30 years with my own hobby systems. -- Chuck
From: Alex McDonald on 30 Jan 2006 17:45 Charles A. Crayne wrote: > On 30 Jan 2006 09:53:29 -0800 > "Alex McDonald" <alex_mcd(a)btopenworld.com> wrote: > > :Can you name one theoretically insoluble problem that has an easy > :practical solution? > > Design of a steam turbine. Physics has the concept of the behavior of an > ideal gas, the key element of which is 'enthalpy', defined as u+pv. > Unfortunately, most real world working fluids do not behave like an ideal > gas, although many of them are close enough for an engineering > approximation. > > Steam, however, is particularly intractable, and engineers do not even try > to use mathematical calculations for it. Instead, they consult the standard > 'Steam Tables' -- which were compiled from the results of much real world > experience. > > -- Chuck I'm grateful for the pertinent reminder that the steam age still has something to teach us here in ala. I believe you've hit the nail on the head and identified a winning strategy for Betov -- and you may have helped him to an easy practical solution for his cross-assembler and disassembler, where others have seen only theoretically insoluble problems. All he needs to do is put a bigger boiler in RosAsm and use a set of Steam Tables. -- Regards Alex McDonald
From: randyhyde@earthlink.net on 30 Jan 2006 18:31
Robert Redelmeier wrote: > Alex McDonald <alex_mcd(a)btopenworld.com> wrote in part: > > Can you name one theoretically insoluble problem that has > > an easy practical solution? > > Busy beaver, Travelling salesman and many scheduling problems > are intractible, but practically solved every day. The halting > problem also solves, albeit less often if you're running Microsoft > software :) No, the *problems* are not solved. Instead, people settle for a solution to a different problem. For example, a greedy algorithm implementation of the travelling salesman problem may produce an okay result, but it is *not* a solution to original problem. It may be "good enough" for government work, but it is not the solution to the original problem. |