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Turing machines have neurons (Re: Write ZFC formulas on a tape (of a Turing machine))

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Hi,

The head of a turing machine is usually a finite
state machine. That digests the tape reading, and
creates a new top writing or head movement.

A finite state machines complexity can be measured
in the number of states. Transitions between states
are labeled with tape reading and tap wrinting/

head movement. So the state is not what is writte
on the tape. Its an internal state. Its relatively
easy to turn a finite state machine, into an

artificial neural network. Already ChatGPT does that,
when reads tokens and writes tokens, just like
a turning machine.

"A Turing machine is a mathematical model of
computation describing an abstract machine that
manipulates symbols on a strip of tape according
to a table of rules"
https://en.wikipedia.org/wiki/Turing_machine

Its really funnny how people really need some
ear bleeding to understand the two sides,
symbolism and connectionsim.

Have Fun!

Bye

Mild Shock schrieb:
> Hi,
> 
> Do not underestimate turing machines. I said neurons
> in the "head". But a turing machine has two parts a "head"
> and a moving "tape". It can then write ZFC formulas on
> 
> a "tape". But I haven't studied the proposals yet,
> 
> but its from here:
> 
> The Undecidability of BB(748)
> Understanding Gödel’s Incompleteness Theorems
> Johannes Riebel - March 2023
> https://www.ingo-blechschmidt.eu/assets/bachelor-thesis-undecidability-bb748.pdf 
> 
> 
> The problem was proposed already here:
> 
> The Busy Beaver Frontier
> Scott Aaronson
> https://www.scottaaronson.com/papers/bb.pdf
> 
> Bye
> 
> Richard Damon schrieb:
>  > On 12/1/25 6:08 AM, Mild Shock wrote:
>  >> Hi,
>  >>
>  >> Quizz: How much neurons are necessary in the
>  >> head of turning machine, to simulate ZFC?
>  >
>  > Which is just a category error, as ZFC is a set of definitions, and 
> thus not something that can be "simulated"
>  >
>  > Also, "Turning Machines" (if you mean Turing Machines) don't have 
> "neurons".
>  >
>  >>
>  >> You have possibly to look up some modelling
>  >> of the logic of ZFC by Bernays. Don't know the
>  >>
>  >> details but maybe check out:
>  >>
>  >> The Undecidability of BB(748)
>  >> Understanding Godels Incompleteness Theorems
>  >> Johannes Riebel - March 2023
>  >> 
> https://www.ingo-blechschmidt.eu/assets/bachelor-thesis-undecidability- 
> bb748.pdf
>  >>
>  >> Bye
>  >
>  > But that "Modeling" isn't the sort of thing you "simulate".
>  >
>  > One problem is we haven't found a way to actually "reason" with 
> "neurons".
> 
> 
> Mild Shock schrieb:
>> Hi,
>>
>> Quizz: How much neurons are necessary in the
>> head of turning machine, to simulate ZFC?
>>
>> You have possibly to look up some modelling
>> of the logic of ZFC by Bernays. Don't know the
>>
>> details but maybe check out:
>>
>> The Undecidability of BB(748)
>> Understanding Godels Incompleteness Theorems
>> Johannes Riebel - March 2023
>> https://www.ingo-blechschmidt.eu/assets/bachelor-thesis-undecidability-bb748.pdf 
>>
>>
>> Bye
>>
>> Mild Shock schrieb:
>>> Hi,
>>>
>>> I am doing the wake-up call until everybody
>>> gets ear-bleeding. It just too cringe to
>>> see the symbolics computing morons struggle
>>>
>>> with connectionism. But given that humans
>>> have a brain with neurons, it should be obvious
>>> that symbolism and connectionism are just two
>>>
>>> sides of the same coin.
>>>
>>> Good Luck!
>>>
>>> Bye
>>>
>>> Mild Shock schrieb:
>>>> Hi,
>>>>
>>>> 1) Classical computing = Boolean logic + von Neumann architecture
>>>>
>>>> For decades, all mainstream computation was built on:
>>>> Boolean algebra
>>>> Logic gates
>>>> Scalar operations executed sequentially
>>>> Memory and compute as separate blocks
>>>> Even floating-point arithmetic was implemented on top of Boolean logic.
>>>>
>>>> This shaped how programmers think — algorithms expressed
>>>> as symbolic operations, control flow, and discrete steps.
>>>>
>>>> 2) AI accelerators break from that model
>>>>
>>>> Modern accelerators — GPUs, TPUs, NPUs, and custom matrix
>>>> engines — use a different computational substrate:
>>>>
>>>> Instead of Boolean logic:
>>>> → Bulk linear algebra over vectors/tensors
>>>>
>>>> Instead of instruction-by-instruction control:
>>>> → Dataflow graphs
>>>>
>>>> Instead of sequential compute on registers:
>>>> → Massively parallel fused-multiply-add units
>>>>
>>>> Instead of manually orchestrated loops:
>>>> → High-level declarative specs (XLA, MLIR, TVM)
>>>>
>>>> Have Fun!
>>>>
>>>> Bye
>>>>
>>>> Mild Shock schrieb:
>>>>> Hi,
>>>>>
>>>>> Wonder why the Coq proof even should be
>>>>> different from anything that AI could produce.
>>>>> Its not a typical Euclid proof in a few steps,
>>>>>
>>>>> it rather uses also enumeration, just like the
>>>>> Fly Speck proof, for the Keppler Conjecture. So
>>>>> lets see what happens next, could AlphaEvolve
>>>>>
>>>>> find the sixth busy beaver?
>>>>>
>>>>> Bye
>>>>>
>>>>> P.S.: Here picture of an old Busy Beaver ASIC
>>>>> (Application-Specific Integrated Circuit)
>>>>>
>>>>> Application    Fun
>>>>> Technology    1500
>>>>> Manufacturer    VLSI Tech
>>>>> Type    Semester Thesis
>>>>> Package    DIP64
>>>>> Dimensions    3200μm x 3200μm
>>>>> Gates    2 kGE
>>>>> Voltage    5 V
>>>>> Clock    20 MHz
>>>>>
>>>>> The Busy Beaver Coprocessor has been designed to solve the Busy 
>>>>> Beaver Function for 5 states. This function (also known as the 
>>>>> Rado's Sigma Function) is an uncomputable problem from information 
>>>>> theory. The input argument is a natural number 'n' that represents 
>>>>> the complexity of an algorithm described as a Turing Machine.
>>>>> http://asic.ethz.ch/cg/1990/Busy_Beaver.html
>>>>>
>>>>> Mild Shock schrieb:
>>>>>> Hi,
>>>>>>
>>>>>> What we thought:
>>>>>>
>>>>>> Prediction 5 . It will never be proved that
>>>>>> Σ(5) = 4,098 and S(5) = 47,176,870.
>>>>>> -- Allen H. Brady, 1990  .
>>>>>>
>>>>>> How it started:
>>>>>>
>>>>>> To investigate AlphaEvolve’s breadth, we applied
>>>>>> the system to over 50 open problems in mathematical
>>>>>> analysis, geometry, combinatorics and number theory.
>>>>>> The system’s flexibility enabled us to set up most
>>>>>> experiments in a matter of hours. In roughly 75% of
>>>>>> cases, it rediscovered state-of-the-art solutions, to
>>>>>> the best of our knowledge.
>>>>>> https://deepmind.google/blog/alphaevolve-a-gemini-powered-coding-agent-for-designing-advanced-algorithms/ 
>>>>>>
>>>>>>
>>>>>> How its going:
>>>>>>
>>>>>> We prove that S(5) = 47, 176, 870 using the Coq proof
>>>>>> assistant. The Busy Beaver value S(n) is the maximum
>>>>>> number of steps that an n-state 2-symbol Turing machine
>>>>>> can perform from the all-zero tape before halting, and
>>>>>> S was historically introduced by Tibor Radó in 1962 as
>>>>>> one of the simplest examples of an uncomputable function.
>>>>>> The proof enumerates 181,385,789 Turing machines with 5
>>>>>> states and, for each machine, decides whether it halts or
>>>>>> not. Our result marks the first determination of a new
>>>>>> Busy Beaver value in over 40 years and the first Busy
>>>>>> Beaver value ever to be formally verified, attesting to the
>>>>>> effectiveness of massively collaborative online research
>>>>>> https://arxiv.org/pdf/2509.12337
>>>>>>
>>>>>> They claim not having used much AI. But could for
>>>>>> example AlphaEvolve do it somehow nevertheless, more or
>>>>>> less autonomously, and find the sixth busy beaver?
>>>>>>
>>>>>> Bye
>>>>>
>>>>
>>>
>>
> 

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What is analog computing nowadays? (Re: An old Busy Beaver ASIC (Application-Specific Integrated Circuit) (Was: Could AlphaEvolve find the sixth busy beaver ?) Mild Shock <janburse@fastmail.fm> - 2025-12-01 11:25 +0100
  Wake-up call until everybody gets ear-bleeding (Re: What is analog computing nowadays?) Mild Shock <janburse@fastmail.fm> - 2025-12-01 12:01 +0100
    BB(745) is independent of ZFC (Was: Wake-up call until everybody gets ear-bleeding) Mild Shock <janburse@fastmail.fm> - 2025-12-01 12:07 +0100
      Write ZFC formulas on a tape (of a Turing machine) (Re: BB(745) is independent of ZFC ) Mild Shock <janburse@fastmail.fm> - 2025-12-02 17:18 +0100
        Turing machines have neurons (Re: Write ZFC formulas on a tape (of a Turing machine)) Mild Shock <janburse@fastmail.fm> - 2025-12-02 17:19 +0100
          A logical calculus in nervous activity [McCulloch & Pitts 1943] (Re: Turing machines have neurons) Mild Shock <janburse@fastmail.fm> - 2025-12-02 17:20 +0100
            Busy Beaver and Theory Consistency (Was: A logical calculus in nervous activity [McCulloch & Pitts 1943]) Mild Shock <janburse@fastmail.fm> - 2025-12-02 17:39 +0100
            Busy Beaver and Theory Consistency (Was: A logical calculus in nervous activity [McCulloch & Pitts 1943]) Mild Shock <janburse@fastmail.fm> - 2025-12-02 17:43 +0100
              Re: Busy Beaver and Theory Consistency (Was: A logical calculus in nervous activity [McCulloch & Pitts 1943]) Mild Shock <janburse@fastmail.fm> - 2025-12-02 23:18 +0100
  Re: What is analog computing nowadays? (Re: An old Busy Beaver ASIC (Application-Specific Integrated Circuit) (Was: Could AlphaEvolve find the sixth busy beaver ?) Maciej Woźniak <mlwozniak@wp.pl> - 2025-12-01 12:09 +0100
    parallel random-access machine (parallel RAM or PRAM (Was: What is analog computing nowadays?) Mild Shock <janburse@fastmail.fm> - 2025-12-01 12:15 +0100
      Re: parallel random-access machine (parallel RAM or PRAM (Was: What is analog computing nowadays?) Maciej Woźniak <mlwozniak@wp.pl> - 2025-12-01 13:23 +0100
        Nope, you can't, because of the CRCW instuction (Was: parallel random-access machine) Mild Shock <janburse@fastmail.fm> - 2025-12-01 17:12 +0100
          Algorithm introduced in Hogwild! SGD (Niu et al., 2011) (Was: Nope, you can't, because of the CRCW instuction) Mild Shock <janburse@fastmail.fm> - 2025-12-01 17:31 +0100
            PRAMs might be closer to physics: Boltzman machines, etc.. (Was: Algorithm introduced in Hogwild! SGD) Mild Shock <janburse@fastmail.fm> - 2025-12-01 18:02 +0100
          Re: Nope, you can't, because of the CRCW instuction (Was: parallel random-access machine) Maciej Woźniak <mlwozniak@wp.pl> - 2025-12-01 17:59 +0100
            PRAMs might be closer to physics: Boltzman machines, etc.. (Re: Nope, you can't, because of the CRCW instuction) Mild Shock <janburse@fastmail.fm> - 2025-12-01 18:05 +0100
            PRAMs might be closer to physics: Boltzman machines, etc.. (Re: Nope, you can't, because of the CRCW instuction) Mild Shock <janburse@fastmail.fm> - 2025-12-01 18:08 +0100
              Physics more difficult than Rasperry LED cube? (Was: PRAMs might be closer to physics: Boltzman machines, etc..) Mild Shock <janburse@fastmail.fm> - 2025-12-01 18:25 +0100
        Re: parallel random-access machine (parallel RAM or PRAM (Was: What is analog computing nowadays?) Thomas Heger <ttt_heg@web.de> - 2025-12-03 07:17 +0100
          Re: parallel random-access machine (parallel RAM or PRAM (Was: What is  analog computing nowadays?) Python <python@cccp.invalid> - 2025-12-03 06:46 +0000
          Re: parallel random-access machine (parallel RAM or PRAM) Thomas 'PointedEars' Lahn <PointedEars@web.de> - 2025-12-03 08:02 +0100
      Linux kernel's RCU-protected hash tables (Re: Algorithm introduced in Hogwild! SGD (Niu et al., 2011)) Mild Shock <janburse@fastmail.fm> - 2025-12-01 22:26 +0100
        String interning is HashSet and not HashMap (Was: Linux kernel's RCU-protected hash tables) Mild Shock <janburse@fastmail.fm> - 2025-12-01 22:40 +0100
      POINT OF VIEW OF AN ALGORITHM (Re: Algorithm introduced in Hogwild! SGD (Niu et al., 2011)) (Re: parallel random-access machine) Mild Shock <janburse@fastmail.fm> - 2025-12-01 23:12 +0100
        Introduction to AMBA® 4 ACE™ (2011) (Was: POINT OF VIEW OF AN ALGORITHM) Mild Shock <janburse@fastmail.fm> - 2025-12-01 23:37 +0100
          Sputnik Schock: Academia is Disposable [I. J. Good Ultraintelligence] (Was: Introduction to AMBA® 4 ACE™ (2011)) Mild Shock <janburse@fastmail.fm> - 2025-12-01 23:53 +0100

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