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From: olcott <polcott333@gmail.com>
Newsgroups: comp.theory
Subject: Re: Flibble's Law
Date: Tue, 22 Apr 2025 17:46:27 -0500
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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.

> 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.

-- 
Copyright 2025 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer