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From: Richard Damon <richard@damon-family.org>
Newsgroups: comp.theory
Subject: Re: Flibble's Law
Date: Fri, 18 Apr 2025 20:19:25 -0400
Organization: i2pn2 (i2pn.org)
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On 4/18/25 7:19 PM, 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 issue is he writes as if he is working in "the system", and there is 
a basic system that is generally assumed.

As I point out, f he want to create his own system, that is fine, but 
then you need to actually DEFINE it, and be clear that you are in your 
own specia 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.

Yes, but require that you be clear that you ARE working in an alternate 
system. (And some alternate systems, like the complex numbers, can 
become "standards", and you need to be clear which one you are working 
in, at least by your context.

> 
> 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.
>