XPost: comp.theory, comp.ai.philosophy, comp.software-eng   
   From: david.brown@hesbynett.no   
      
   On 17/07/2021 18:40, olcott wrote:   
   > On 7/17/2021 9:37 AM, David Brown wrote:   
   >> On 16/07/2021 21:56, Mr Flibble wrote:   
   >>> On Fri, 16 Jul 2021 19:46:28 -0000 (UTC)   
   >>> Alan Mackenzie  wrote:   
   >>>   
   >>>> Mr Flibble  wrote:   
   >>>>> On Fri, 16 Jul 2021 19:28:12 +0100   
   >>>>> Ben Bacarisse  wrote:   
   >>>>   
   >>>>>> Mr Flibble  writes:   
   >>>>   
   >>>>>>> A pathological program that executes a black box decider and   
   >>>>>>> returns the opposite result can be detected by the black box   
   >>>>>>> decider.   
   >>>>   
   >>>>>>> So there are THREE possible results the black box decider can   
   >>>>>>> return:   
   >>>>   
   >>>>>>> 1) Program halts   
   >>>>>>> 2) Program does not halt   
   >>>>>>> 3) Program is pathological and can be discarded as invalid.   
   >>>>   
   >>>>>>> Halting problem solved.   
   >>>>   
   >>>>>> This one came up every year when one teaches this material.  Every.   
   >>>>>> Single.  Year.  In the end, I decided to bring it up myself and set   
   >>>>>> explaining what's wrong the argument as an exercise.  I wonder if   
   >>>>>> any of the students here would like to have a go at that?   
   >>>>   
   >>>>>> (By student, I mean anyone reading this who has not read a   
   >>>>>> textbook on this topic.)   
   >>>>   
   >>>>> I simply don't believe you. You appear to be a pathological liar;   
   >>>>> feel free to provide evidence of what you are claiming.   
   >>>>   
   >>>> That's quite uncalled for.  Reading (or browsing) these interminable   
   >>>> threads over the last months, it's quite clear that Ben is an expert.   
   >>>> You, by contrast, are merely exercising your freedom of expression.   
   >>>>   
   >>>> That you, in all apparent seriousness, put forward your 1), 2), 3)   
   >>>> above indicates you are far from an expert.  These things aren't a   
   >>>> matter of opinion, they're a matter of settled fact.   
   >>>   
   >>> Expert? I have a CompSci BSc (Hons) degree, dear.   
   >>   
   >> So do lots of people - but some paid attention in class, and some have   
   >> enough mathematical understanding to know how proof by contradiction   
   >> works, and also to know that you cannot "solve" a problem by re-defining   
   >> it to suit yourself.   
   >>   
   >   
   > He is much smarter than most here to understand that:   
   > when an input is deliberately defined to do the opposite of whatever its   
   > corresponding halt decider decides this has pathological communication   
   > between the input and the halt decider.   
      
   Mr. Flibble might be smart - I wouldn't put it past him to be trolling   
   all along here.   
      
   >   
   > Every scientist knows that the independent variable and the dependent   
   > variable must be completely isolated so that the only effect on the   
   > dependent variable comes from the independent variable.   
   >   
   > By providing a pathological back channel where the dependent variable   
   > can effect the behavior of the independent variable the halt status   
   > analysis is tainted.   
      
   The halting problem concerns finding a program H that takes an   
   /arbitrary/ program P and an /arbitrary/ input X and determines whether   
   it will halt or not (giving a yes/no answer).   
      
   Now, I agree that the simplest and most common proof that there cannot   
   be such a program H is based on a "pathological" case from proof by   
   contradiction :   
      
   	G() =   
   		if H(G, G) then loop forever   
   		else 0   
      
   With that program, H(G, G) is guaranteed to give the wrong answer -   
   therefore no such H exists.   
      
   Since that this applies for /any/ conceivable H, there are no "dependent   
   variables".  This (when made rigorous) proves that the halting problem   
   is undecidable.   
      
      
   But suppose - just for fun - we imagined that you are right - what would   
   that give us?   
      
   It would mean you have a claim (without proof - but we are assuming you   
   are correct) that you can find an algorithm H that correctly tells if a   
   given computation will halt or not, but only works for some functions.   
   If you call H with input (P, X) which it likes, it will correctly give   
   out yes or no.  If it doesn't like (P, X) - the input is "pathological",   
   then it might say "yes", it might say "no", it might say "neither", it   
   might never stop with an answer.   
      
   Basically, it would be useless.   
      
   --- SoupGate-Win32 v1.05   
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