Re: Flibble's Law

On 19/04/2025 00:19, Keith Thompson wrote:

Richard Damon <richard@damon-family.org> writes:

On 4/18/25 5:16 PM, Mr Flibble wrote:

[...]

I'm not claiming we can build a decider with infinite resources.
I'm saying that if the problem permits infinite machines, then
infinite analyzers are fair game in theory.

>
No, you don't get to say that.

 Well, actually ...
 Sure, Mr. Flibble gets to say anything he likes.  Anyone can
define a mathematical system with any consistent rules they like,
and derive results that apply within that system.
 

The Flibble Reciprocity Principle:
In theoretical computation, every permitted infinity in problem
formulation implies a permitted infinity in problem analysis.
It's about playing the game by the rules of the game.

>
No, it is making up your own rules and admittion that you think
cheating is ok.
>
The "Rules" exist, and are defined, and they say that decider do NOT
get infinite time.

 The "Rules" are fundamentally arbitrary (but ideally chosen for
their relevance to the real world).  Defining a new set of rules
is how we got useful and/or interesting things like non-Euclidean
geometry and complex numbers.
 The flaw in Flibble's reasoning is that he claims that some kind of
"fair game" principle implies that he can make certain specific
rule changes.  I suggest that he doesn't need that excuse.
 The rules under which most of us operate, and in which the Halting
Problem proof was constructed, are designed to correspond to
real-world computational models (with some simplifications like
not limiting storage size).
 Mr. Flibble, I think, is inventing new rules because he doesn't like
the results from the existing rules.  I think he dislikes the fact
that the Halting Problem is not solvable, and is trying to define a
new system in which it's solvable in some sense.  And sure, he can
(try to) do that if he likes.  But it's worth spending time on that
*only* if the results of the new rules are interesting and/or useful.
It's also a good thing if the new rules are clearly defined, for
example rigorously defining what a "pathological input" is.
 It would also be nice if Mr. Flibble acknowledged that the proof of
the unsolvability of the Halting Problem is valid within the usual
set of rules (and that he understands those rules), rather than
implying that the proof is invalid because the rules are "unfair"
or something.
 

I'm not convinced Mr.Flibble has had a proper shot at understanding the halting problem as it is properly stated (in mathematics / computer science).  Also I think he is far more sensible than PO, when it comes to understanding what's being said in an argument, although also it has to be said that's a very low bar...
I suspect Mr.Flibble's only visibility of HP has come via a combination of C.Strachey's "An impossible program" article, and PO threads on these newsgroups!  He might be forgiven for getting the wrong impression over issues of self reference etc., and he freely admitted on his first PO-thread posting that he was quite new to HP.  Unlike PO, I'm pretty sure he has actually changed his opinion about something(?) once he understood the background better.  PO has no prospect of ever undertanding the background of anything technical like HP.
So a great thing for Mr.Fibble to do would be to forget everything in Strachey's correspondence and everything that PO has said on these newsgroups about "pathelogical self reference" etc., and go back to reading e.g. Linz's HP proof to understand what HP says and the proof in particular.  PO has extracted the half a dozen or so pages from the Linz proof into a PDF which he has published somewhere, probably on ResearchGate.  [I'm sure I could find this if PO doesn't chip in with details]
If Mr.Flibble went back to a proper HP problem statement he might hopefully realise that the "pathelogical" self-reference is not of a type that is of any concern, due to the order things are done in the proper HP proof.  It is no different from the kind of self reference we see e.g. in a backup utility backing up its own source code, or even backing up its own executable file.  I doubt Mr.Flibble would be worried by this if he understood the situation!  In particular there is no "category error" anywhere in the proper statement and proof of HP, due to the careful order things are defined.
Then again, maybe he would understand it all as little as PO understands it!  But I would give him at least a chance at properly understanding rather than basing his views on PO threads + Strachey correspondence. :)
----------------
Regarding this thread and "Flibble's law" - you are right that there is no "fair game" law.  People just make up a variety of rules and analyse/discuss the consequences. That applies to HP as much as anything else.
[Also I don't know what Mr.Flibble means by "allowing infinite resources" to analyse halting.  He might just mean "TMs have an infinite tape, so TM analysers should be allowed a similar infinite tape".  That is indeed what is allowed, as analysers are taken to be TMs.  Or he might mean analysers should be allowed infinite time - but what would that actually mean??  Anyway, but the point of my post is that I'm not sure Mr.Flibble has given himself a fair shot at understanding HP, not to comment on this thread particularly.]
Regards,
Mike.