[HN Gopher] Scooping the Loop Snooper (2000)
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       Scooping the Loop Snooper (2000)
        
       Author : soferio
       Score  : 76 points
       Date   : 2024-04-23 22:42 UTC (1 days ago)
        
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       | skulk wrote:
       | Diagonalizations are some of the easiest to understand, yet most
       | profound proofs in math. Another example is the proof that any
       | continuum is larger in cardinality than the set of integers.
       | 
       | https://en.m.wikipedia.org/wiki/Diagonal_argument
        
       | g___ wrote:
       | Suppose O is the oracle for the halting problem.
       | 
       | We create a machine: given a program P, ask O whether P halts
       | given input P and negate the answer.
       | 
       | lP. ~O (P P)
       | 
       | Now we ask whether this machine will halt given its own source
       | code as input. In symbols:
       | 
       | (lP. ~O (P P)) (lP. ~O (P P))
       | 
       | which is the Y-combinator in lambda calculus.
        
         | thedudeabides5 wrote:
         | aren't oracles, just attempts to escape the halting problem?
         | 
         | assume you have an O which doesn't halt
         | 
         | now feed P which DOES halt into O
         | 
         | oh look it catches it!
         | 
         |  _misses the boat_
        
           | bongodongobob wrote:
           | No, in fact you can use oracles to prove the halting problem.
        
       | QuinnyPig wrote:
       | The halting problem--a tough endeavor
       | 
       | "Will the loop complete or run forever?"
       | 
       | Many fixes were attempted
       | 
       | (Lambda's 15 minute limit doesn't get exempted)
       | 
       | You'll quickly find there is no winning
       | 
       | As the LOADING ball keeps spinning
       | 
       | To date there remains a single hack:
       | 
       | Rip the cable out the back
       | 
       | You'll have an answer clarified:
       | 
       | "The loop is done; the power died."
        
         | QuinnyPig wrote:
         | ...this comment made a lot more sense when the title was "a
         | poem about the halting problem." Now I just look more deranged
         | than I usually do.
        
           | stainforth wrote:
           | Is your name an anagram for PunnyQuip
        
       | beders wrote:
       | Sweet poem. I remember being blown away when I studied computer
       | science. The whole idea that there are inherit limits to
       | computing on Turing machines seemed crazy.
       | 
       | Godel's incompleteness theorems has a similar proof that will
       | mess with your brain :)
        
       | srcreigh wrote:
       | Obligatory mention that although Halt doesn't exist for arbitrary
       | P, there are Halt_N for every natural N where Halt_N works on
       | empty-input TMs with at most N states.
       | 
       | Undecidability is more about compression than it is about whether
       | we can determine if TMs halt.
        
         | snarkconjecture wrote:
         | For sufficiently large N, it's impossible to prove Halt_N
         | correct.
         | 
         | (The N required depends on your axioms.)
        
       | VikingCoder wrote:
       | I've been working on a proof for a long time, but I'm just not
       | sure if I'll finish it...
        
       | dang wrote:
       | Related:
       | 
       |  _Scooping the Loop Snooper (2000)_ -
       | https://news.ycombinator.com/item?id=30783422 - March 2022 (31
       | comments)
       | 
       |  _Scooping the Loop Snooper: Proof That the Halting Problem Is
       | Undecidable (2000)_ -
       | https://news.ycombinator.com/item?id=20956756 - Sept 2019 (33
       | comments)
       | 
       |  _Scooping the Loop Snooper (2000)_ -
       | https://news.ycombinator.com/item?id=10077471 - Aug 2015 (2
       | comments)
        
       | flanfly wrote:
       | I quoted this, in full, in my MSc thesis. It's both a light
       | hearted introduction to the Halting Problem and something you
       | need to reference quite often when writing about static program
       | analysis. Good times.
        
       | fragmede wrote:
       | so, for classes of problem where it's been talked about enough in
       | the training data, gpt 4 manages to solve the halting problem.
        
       | vincent-manis wrote:
       | But he rhymed "data" (in British pronunciation, "dattah") with
       | "later"!
        
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