From: x@x.net   
      
   On 12/3/25 00:08, Mild Shock wrote:   
   > Hi,   
   >   
   > Actually the BB(5) does also construct machines,   
   > and does also look at the code of machines.   
   >   
   > It has an amazing history, since the candidate   
   > for the busiest beaver was already found in 1989:   
      
   So BB8 was a 'droid' in 'Star Wars' that moved   
   on a spherical motive platform rather than 'wheels'.   
   It was different from 'R2D2' which seemed to have   
   a more conventional movement.   
      
   A 'BB' is also a specific diameter measurement   
   of small spheres used for bird shot or in small   
   generally spring driven projectile machines.   
      
   What is a 'Busy Beaver' supposed to be and   
   why is '5' any different from '3', '1', '6'   
   or '8'?  What does 'BB5' mean to you?  If   
   you give some references I will try to   
   find out whether it has a personal meaning   
   to you or some sort of meaning in general.   
      
   > 47,176,870    4098    current BB(5), step champion   
   > https://turbotm.de/~heiner/BB/mabu90.html   
   >   
   > They use an amazing simple technique to speed up   
   > their search. Realizing macro turing machines, that   
   > encode what happens with k cells on a tape.   
   >   
   > Plus heuristics to "prove" that a TM does not halt,   
   > which seem to be sufficient for 5 state TMs. Plus   
   > heuristics to bring the number of considered 5 state   
   >   
   > TMs down, since without reduction they would be   
   > 26*10^12 many, but they needed only consider 5*10^7   
   > many. So that after about ten days using a   
   >   
   > 33 MHz Clipper CPU they got their result.   
   >   
   > Bye   
   >   
   > P.S.: My estimate, with todays laptop can do   
   > it in 2.5 hours, or maybe in 2.5 minutes if using   
   > an AI accelerator. Not 100% sure. Wasn't even   
   >   
   > thinking about such a modern replica of the   
   > problem. Coq used Rust. We could use even something   
   > else that would tap in AI accelerators, maybe   
   >   
   > even JavaScript and run it in a browser.   
   >   
   >> Hi,   
   >>   
   >> Well then get an education. Every Gödel   
   >> sentence G, has a size, doesn't it?   
   >> The formal analogue of the Liar Paradox,   
   >>   
   >> except it’s expressed arithmetically:   
   >>   
   >> G ≡ ∀y¬Proof(y,┌G┐).   
   >>   
   >> Gödel did explicitly construct a Gödel   
   >> sentence G in his 1931 paper. He did not   
   >> claim it was astronomically large,   
   >>   
   >> nor impossible to write. Now you can do   
   >> the encoded Liar also with Turing Machines TM:   
   >>   
   >> 1. Fix a formal proof system S (e.g. PA) and   
   >> an effective enumeration of all proofs.   
   >> 2. Build a TM M(x) that, given a code x, searches   
   >> for an S-proof of the formula with code a; if it finds   
   >> M(x) halts <=> exists y Proof(y,x) (i.e. Prov(x)).   
   >>   
   >> Etc.. etc..   
   >>   
   >> Bye   
   >>   
   >> dart200 schrieb:   
   >>> this shit makes me feel like i'm stuck in a mad house planet   
   >>>   
   >>> undecidability has nothing to do with computational complexity and   
   >>> the fact we think the limit to decidability is bounded by how well we   
   >>> can bit pack a self-referential turing machine into a proof is just   
   >>> literal nonsense   
   >   
   > Julio Di Egidio schrieb:   
   >> TL;DR: There is no such thing as an irrational reasoner,   
   >> i.e. not any more than there exists a married bachelor.   
   >>   
   >> [ Original subject: "daily puzzle: the rational reasoner".   
   >>    Salvaged from the Google Groups archive.]   
   >>   
   >> On November 19 2023, Rich D wrote:   
   >>  > On November 15 2023, Jeff Barnett wrote:   
   >>  > >> A rational person believes a finite number of propositions;   
   >>  > >> that is, he believes all of them they are true. (if he thought   
   >>  > >> any one was false, he'd disbelieve it)   
   >>  > >> A rational person also disbelieves in his own perfection.   
   >>  > >> He expects to be wrong occasionally.   
   >>  > >> This implies that one of the list of the propositions   
   >>  > >> referenced above, must be false. And he's aware of this   
   >>  > >> implication. Which means he believes he believes   
   >>  > >> something false.   
   >>  > >> Is this inconsistent? Is he rational? Explain.   
   >>   
   >> Yes, it/he is: to begin with because incorrect is not   
   >> the same as incongruous ("inconsistent", though that   
   >> is more of a mathematical term).  Moreover, we indeed   
   >> do hypothetical thinking, which means thinking with the   
   >> (meta-)knowledge that not (and not ever) all (domain)   
   >> knowledge is accurate and available.  And so much more,   
   >> we do...   
   >>   
   >>  > > Rational does not imply perfection in thought.   
   >>  >   
   >>  > I would not define rational as equivalent to perfection.   
   >>  > In order to discuss the concept, one must first define the concept.   
   >>  >   
   >>  > > You seem, above, to float a definition of a rational person then   
   >>  > > move on to ask a question given your definition.   
   >>  >   
   >>  > Define rational person: he attempts to avoid contradiction,   
   >>  > he doesn't knowingly accept any contradiction. He utilizes   
   >>  > the precepts of first order logic.   
   >>   
   >> No, he doesn't (or, shouldn't) use "FOL". To begin with,   
   >> do not conflate Logic proper (valid reasoning) with formal   
   >> and/or mathematical logic, not to even mention the unbounded   
   >> complexity of the real world.  At best Logic proper goes with   
   >> symbolic logic, whatever that even means...   
   >>   
   >>  > He attempts to recognize facts and reality,   
   >>  > assuming his perceptions of reality are accurate.   
   >>   
   >> Again, a rational thinker would never assume full   
   >> and fully accurate knowledge.   
   >>   
   >>  > He notices that no one is perfect. By induction, he presumes   
   >>  > himself to be imperfect; that is, he's occasionally wrong. Which   
   >>  > means one of his accepted propositions must be false.   
   >>   
   >> Yes, "(he very well knows that) he may be wrong", put simply.   
   >>   
   >>  > Therefore, he is aware that he believes a false proposition.   
   >>  > Hence is inconsistent. Knowingly.   
   >>  >   
   >>  > A modest man must therefore be inconsistent, unavoidably.   
   >>   
   >> It ain't about "modesty", it's a matter of "finiteness",   
   >> and, to reiterate, it ain't about consistency either, a   
   >> _rational_ (hu)man *is* "consistent", in so far as s/he is   
   >> being rational, for what rational even means.   
   >>   
   >>  > > If the definition was of a abstract system (e.g., something in   
   >> the class   
   >>  > > of Turing machines) you could ask if such a system could be   
   >> defined, not   
   >>  > > whether it is consistent.   
   >>  >   
   >>  > You could frame the original question in regard to an abstract   
   >>  > system, it wouldn't change anything pertinent.   
   >>  >   
   >>  > Here's a workaround: call on information theory. Assign b bits   
   >>  > of information to each correct proposition. Then recognize that   
   >>  > some of those are false, and strive to maximize the total   
   >>  > information. Don't sweat the small stuff, I always say -   
   >>   
      
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