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From: Richard Damon <richard@damon-family.org>
Newsgroups: comp.theory
Subject: Re: Flibble's Law
Date: Wed, 23 Apr 2025 18:38:09 -0400
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On 4/23/25 7:38 AM, Mr Flibble wrote:
> On Tue, 22 Apr 2025 22:24:44 -0400, Richard Damon wrote:
> 
>> On 4/22/25 6:46 PM, olcott wrote:
>>> On 4/22/2025 5:35 PM, Keith Thompson wrote:
>>>> Mr Flibble <flibble@red-dwarf.jmc.corp> writes:
>>>>> On Fri, 18 Apr 2025 17:13:23 -0400, Richard Damon wrote:
>>>>>> On 4/18/25 5:01 PM, Mr Flibble wrote:
>>>>>>> If Busy Beavers are allowed an INFINITE tape in the context of the
>>>>>>> Halting Problem then Simulating Halt Deciders are allowed INFINITE
>>>>>>> resources.
>>>>>>
>>>>>> Sure, they can use as much tape as they want, they just can't use
>>>>>> infinite time.
>>>>>
>>>>> If they REQUIRE infinite tape then by implication they REQUIRE
>>>>> infinite time.
>>>>
>>>> But they don't REQUIRE (does all-caps really help?) either infinite
>>>> tape or infinite time.  Unless I've misunderstood the concept, a Busy
>>>> Beaver by definition must terminate after a finite number of steps.
>>>>
>>>> We sometimes say "infinite tape" as a verbal shorthand for "as much
>>>> tape as is required".  Or we can say that infinite tape exists,
>>>> but we'll never use more than a finite amount of it.  The amount of
>>>> tape required is never actually infinite, but there is no specific
>>>> upper bound.
>>>>
>>>> (I sometimes wonder if we don't distinguish clearly enough between
>>>> "unbounded" and "infinite".)
>>>>
>>>>
>>> That is an important nuance that many people miss.
>>
>> Yes, there is a nuance, but there ARE some processes that aren't just
>> unbounded by go infinite. Unbounded can only reach countable infinity,
>> but not uncountable infinity. Thus a process that was performing the
>> super-task of writing out all the real numbers between 0 and 1 would use
>> TRULY infinite tape (needing at least Aleph-1 cells) and infinite time
>> to complete.
>>
>> In the same way, an unbounded process, could be thought of, as
>> "finishing" after a countable infinite number of steps, while another
>> process might just never stop as in a countable infinite number of steps
>> it never reaches its end (because it takes an uncountable infinite
>> number of steps).
>>
>>
>>>> There are actual (mathematically describable, not physically
>>>> implementable) Turing machines that consume infinite time and infinite
>>>> tape.  Busy Beavers do not.
>>>>
>>>>
>>> Busy Beaver seems to quickly consume much more memory than there are
>>> atoms in the universe.
>>>
>>>
>> Some do, but mostly it is the programs pretending to be Busy Beavers
>> that actually never halt, and thus are not actually Busy Beavers.
> 
> You have no clue about what you are talking about: it doesn't matter if
> the number of steps is uncountably infinite or countably infinite, it
> would still never complete and Flibble's Law still applies.
> 
> /Flibble


The halting depends on your theory of computation. In Hyper-Computation 
Theory, Super-Tasks can complete or not in unbounded time.

And Flibble's law only appplies to Flibble-Computation theory which 
hasn't been actually defined, so is worthless.