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A logical calculus in nervous activity [McCulloch & Pitts 1943] (Re: Turing machines have neurons)

From Mild Shock <janburse@fastmail.fm>
Newsgroups sci.physics, sci.physics.relativity, comp.lang.prolog
Subject A logical calculus in nervous activity [McCulloch & Pitts 1943] (Re: Turing machines have neurons)
Date 2025-12-02 17:20 +0100
Message-ID <10gn3ko$114kh$4@solani.org> (permalink)
References (2 earlier) <10gjqeu$t54i$2@solani.org> <10gjsij$t6es$2@solani.org> <10gjsu5$t6s1$1@solani.org> <10gn3hj$114kh$2@solani.org> <10gn3j7$114kh$3@solani.org>

Cross-posted to 3 groups.

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Hi,

You might also try this here:

McCulloch, Warren S.; Pitts, Walter (1943-12-01).
"A logical calculus of the ideas immanent in
nervous activity". The Bulletin of Mathematical
Biophysics. 5 (4): 115–133.
https://www.cs.cmu.edu/~epxing/Class/10715/reading/McCulloch.and.Pitts.pdf

It has a simple neuron model, and shows
for example in Figure 1. How it can act
in a Boolean algebra way.

If you have Booean algebra, you can also
build finite state machine. You can encode
state as bit vectors.

Bye

Mild Shock schrieb:
> 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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Thread

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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