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Groups > sci.physics > #894581 > unrolled thread
| Started by | Mild Shock <janburse@fastmail.fm> |
|---|---|
| First post | 2025-11-30 13:38 +0100 |
| Last post | 2025-12-04 12:59 +0800 |
| Articles | 20 on this page of 105 — 14 participants |
Back to article view | Back to sci.physics
Could AlphaEvolve find the sixth busy beaver ? Mild Shock <janburse@fastmail.fm> - 2025-11-30 13:38 +0100
An old Busy Beaver ASIC (Application-Specific Integrated Circuit) (Was: Could AlphaEvolve find the sixth busy beaver ?) Mild Shock <janburse@fastmail.fm> - 2025-11-30 13:54 +0100
An old Busy Beaver ASIC (Application-Specific Integrated Circuit) (Was: Could AlphaEvolve find the sixth busy beaver ?) Mild Shock <janburse@fastmail.fm> - 2025-11-30 13:55 +0100
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
Re: parallel random-access machine (parallel RAM or PRAM) Thomas Heger <ttt_heg@web.de> - 2025-12-04 07:50 +0100
Re: parallel random-access machine (parallel RAM or PRAM) Janis Papanagnou <janis_papanagnou+ng@hotmail.com> - 2025-12-04 09:57 +0100
Re: parallel random-access machine (parallel RAM or PRAM) Thomas 'PointedEars' Lahn <PointedEars@web.de> - 2025-12-06 17:02 +0100
Re: parallel random-access machine (parallel RAM or PRAM) Thomas Heger <ttt_heg@web.de> - 2025-12-07 10:22 +0100
Re: parallel random-access machine (parallel RAM or PRAM) Thomas 'PointedEars' Lahn <PointedEars@web.de> - 2025-12-07 10:39 +0100
Re: parallel random-access machine (parallel RAM or PRAM) Thomas 'PointedEars' Lahn <PointedEars@web.de> - 2025-12-07 10:46 +0100
Re: parallel random-access machine (parallel RAM or PRAM) Janis Papanagnou <janis_papanagnou+ng@hotmail.com> - 2025-12-07 11:42 +0100
Re: parallel random-access machine (parallel RAM or PRAM) Michael S <already5chosen@yahoo.com> - 2025-12-07 16:26 +0200
Re: parallel random-access machine (parallel RAM or PRAM) Janis Papanagnou <janis_papanagnou+ng@hotmail.com> - 2025-12-08 04:25 +0100
Re: parallel random-access machine (parallel RAM or PRAM) Thomas 'PointedEars' Lahn <PointedEars@web.de> - 2025-12-08 08:51 +0100
Re: parallel random-access machine (parallel RAM or PRAM) Michael S <already5chosen@yahoo.com> - 2025-12-08 13:58 +0200
Re: parallel random-access machine (parallel RAM or PRAM) Thomas Heger <ttt_heg@web.de> - 2025-12-09 09:15 +0100
Re: parallel random-access machine (parallel RAM or PRAM) Thomas Heger <ttt_heg@web.de> - 2025-12-08 08:21 +0100
Re: parallel random-access machine (parallel RAM or PRAM) Janis Papanagnou <janis_papanagnou+ng@hotmail.com> - 2025-12-08 09:06 +0100
Re: parallel random-access machine (parallel RAM or PRAM) Thomas Heger <ttt_heg@web.de> - 2025-12-09 09:19 +0100
Re: parallel random-access machine (parallel RAM or PRAM) The Starmaker <starmaker@ix.netcom.com> - 2025-12-09 11:43 -0800
Re: parallel random-access machine (parallel RAM or PRAM) Thomas Heger <ttt_heg@web.de> - 2025-12-10 08:19 +0100
Re: parallel random-access machine (parallel RAM or PRAM) Thomas 'PointedEars' Lahn <PointedEars@web.de> - 2025-12-10 09:56 +0100
Re: parallel random-access machine (parallel RAM or PRAM) The Starmaker <starmaker@ix.netcom.com> - 2025-12-10 10:01 -0800
Re: parallel random-access machine (parallel RAM or PRAM) Thomas Heger <ttt_heg@web.de> - 2025-12-11 09:02 +0100
Re: parallel random-access machine (parallel RAM or PRAM) The Starmaker <starmaker@ix.netcom.com> - 2025-12-11 08:48 -0800
Re: parallel random-access machine (parallel RAM or PRAM) Thomas 'PointedEars' Lahn <PointedEars@web.de> - 2025-12-12 01:58 +0100
Re: parallel random-access machine (parallel RAM or PRAM) The Starmaker <starmaker@ix.netcom.com> - 2025-12-11 20:45 -0800
Re: parallel random-access machine (parallel RAM or PRAM) The Starmaker <starmaker@ix.netcom.com> - 2025-12-11 23:07 -0800
Re: parallel random-access machine (parallel RAM or PRAM) The Starmaker <starmaker@ix.netcom.com> - 2025-12-12 00:49 -0800
Re: parallel random-access machine (parallel RAM or PRAM) "Paul.B.Andersen" <relativity@paulba.no> - 2025-12-14 14:27 +0100
Re: parallel random-access machine (parallel RAM or PRAM) The Starmaker <starmaker@ix.netcom.com> - 2025-12-14 10:25 -0800
Re: parallel random-access machine (parallel RAM or PRAM) "Paul.B.Andersen" <relativity@paulba.no> - 2025-12-14 21:22 +0100
Re: parallel random-access machine (parallel RAM or PRAM) The Starmaker <starmaker@ix.netcom.com> - 2025-12-14 12:52 -0800
I have a great idea The Starmaker <starmaker@ix.netcom.com> - 2025-12-14 13:11 -0800
Einstein refrigerator (was: parallel random-access machine (parallel RAM or PRAM) Thomas 'PointedEars' Lahn <PointedEars@web.de> - 2025-12-15 03:00 +0100
Re: Einstein refrigerator (was: parallel random-access machine (parallel RAM or PRAM) The Starmaker <starmaker@ix.netcom.com> - 2025-12-14 19:46 -0800
Re: parallel random-access machine (parallel RAM or PRAM) The Starmaker <starmaker@ix.netcom.com> - 2025-12-14 10:27 -0800
Re: parallel random-access machine (parallel RAM or PRAM) The Starmaker <starmaker@ix.netcom.com> - 2025-12-14 10:58 -0800
Re: parallel random-access machine (parallel RAM or PRAM) Thomas Heger <ttt_heg@web.de> - 2025-12-15 07:50 +0100
Re: parallel random-access machine (parallel RAM or PRAM) "Paul.B.Andersen" <relativity@paulba.no> - 2025-12-15 14:05 +0100
Re: parallel random-access machine (parallel RAM or PRAM) Thomas Heger <ttt_heg@web.de> - 2025-12-16 08:44 +0100
Re: parallel random-access machine (parallel RAM or PRAM) "Paul.B.Andersen" <relativity@paulba.no> - 2025-12-16 22:58 +0100
Re: parallel random-access machine (parallel RAM or PRAM) Thomas Heger <ttt_heg@web.de> - 2025-12-17 08:50 +0100
Re: parallel random-access machine (parallel RAM or PRAM) "Paul.B.Andersen" <relativity@paulba.no> - 2025-12-17 14:00 +0100
Re: parallel random-access machine (parallel RAM or PRAM) The Starmaker <starmaker@ix.netcom.com> - 2025-12-17 10:49 -0800
Re: parallel random-access machine (parallel RAM or PRAM) The Starmaker <starmaker@ix.netcom.com> - 2025-12-17 11:23 -0800
Re: parallel random-access machine (parallel RAM or PRAM) "Paul.B.Andersen" <relativity@paulba.no> - 2025-12-17 14:24 +0100
Re: parallel random-access machine (parallel RAM or PRAM) The Starmaker <starmaker@ix.netcom.com> - 2025-12-18 22:13 -0800
Re: parallel random-access machine (parallel RAM or PRAM) The Starmaker <starmaker@ix.netcom.com> - 2025-12-19 12:02 -0800
Re: parallel random-access machine (parallel RAM or PRAM) Thomas 'PointedEars' Lahn <PointedEars@web.de> - 2025-12-17 18:24 +0100
Re: parallel random-access machine (parallel RAM or PRAM) John Hasler <john@sugarbit.com> - 2025-12-17 11:58 -0600
Re: parallel random-access machine (parallel RAM or PRAM) Maciej Woźniak <mlwozniak@wp.pl> - 2025-12-12 07:19 +0100
Re: parallel random-access machine (parallel RAM or PRAM) "Paul B. Andersen" <relativity@paulba.no> - 2025-12-12 11:35 +0100
Re: parallel random-access machine (parallel RAM or PRAM) Lawrence D’Oliveiro <ldo@nz.invalid> - 2025-12-18 06:49 +0000
Re: parallel random-access machine (parallel RAM or PRAM) Thomas 'PointedEars' Lahn <PointedEars@web.de> - 2025-12-06 05:30 +0100
Re: Could AlphaEvolve find the sixth busy beaver ? Thomas 'PointedEars' Lahn <PointedEars@web.de> - 2025-11-30 14:06 +0100
You shouldn't use NPM hacked services (Was: Could AlphaEvolve find the sixth busy beaver ?) Mild Shock <janburse@fastmail.fm> - 2025-11-30 22:27 +0100
Its a subconscious hypothesis (Was: You shouldn't use NPM hacked services) Mild Shock <janburse@fastmail.fm> - 2025-11-30 22:33 +0100
What if of the cosmos does a BB dance? (Was: Its a subconscious hypothesis) Mild Shock <janburse@fastmail.fm> - 2025-11-30 22:43 +0100
Re: What if of the cosmos does a BB dance? (Was: Its a subconscious hypothesis) Thomas 'PointedEars' Lahn <PointedEars@web.de> - 2025-12-01 23:43 +0100
Re: What if of the cosmos does a BB dance? Thomas 'PointedEars' Lahn <PointedEars@web.de> - 2025-12-01 23:45 +0100
newsreader where you can see the message source (Was: What if of the cosmos does a BB dance?) Mild Shock <janburse@fastmail.fm> - 2025-12-02 00:00 +0100
Re: newsreader where you can see the message source (Was: What if of the cosmos does a BB dance?) Python <python@cccp.invalid> - 2025-12-02 03:10 +0000
Re: newsreader where you can see the message source (Was: What if of the cosmos does a BB dance?) Mild Shock <janburse@fastmail.fm> - 2025-12-02 11:51 +0100
Re: newsreader where you can see the message source (Was: What if of the cosmos does a BB dance?) Thomas 'PointedEars' Lahn <PointedEars@web.de> - 2025-12-02 20:36 +0100
Re: newsreader where you can see the message source (Was: What if of the cosmos does a BB dance?) Ross Finlayson <ross.a.finlayson@gmail.com> - 2025-12-01 21:42 -0800
Orbits of planets in the Sol System (was: newsreader where you can see the message source) Thomas 'PointedEars' Lahn <PointedEars@web.de> - 2025-12-04 03:29 +0100
Orbits of planets in the Sol System Thomas 'PointedEars' Lahn <PointedEars@web.de> - 2025-12-04 03:30 +0100
Re: newsreader where you can see the message source (Was: What if of the cosmos does a BB dance?) Thomas 'PointedEars' Lahn <PointedEars@web.de> - 2025-12-02 20:35 +0100
Spock thinks I am interested in his gibberish (Re: newsreader where you can see the message source) Mild Shock <janburse@fastmail.fm> - 2025-12-02 23:22 +0100
Is it like "Wirres Mückengelaber" ? (Was: Spock thinks I am interested in his gibberish) Mild Shock <janburse@fastmail.fm> - 2025-12-02 23:28 +0100
newsreader where you can see the message source (Re: What if of the cosmos does a BB dance?) Mild Shock <janburse@fastmail.fm> - 2025-12-02 00:11 +0100
Re: What if of the cosmos does a BB dance? Thomas Heger <ttt_heg@web.de> - 2025-12-03 07:22 +0100
Re: What if of the cosmos does a BB dance? The Starmaker <starmaker@ix.netcom.com> - 2025-12-03 08:27 -0800
Re: What if of the cosmos does a BB dance? Thomas Heger <ttt_heg@web.de> - 2025-12-04 07:57 +0100
Re: Its a subconscious hypothesis (Was: You shouldn't use NPM hacked services) Maciej Woźniak <mlwozniak@wp.pl> - 2025-11-30 23:14 +0100
Re: You shouldn't use NPM hacked services (Was: Could AlphaEvolve find the sixth busy beaver ?) Thomas 'PointedEars' Lahn <PointedEars@web.de> - 2025-12-01 23:23 +0100
Re: You shouldn't use NPM hacked services (Was: Could AlphaEvolve find the sixth busy beaver ?) Mild Shock <janburse@fastmail.fm> - 2025-12-02 00:05 +0100
Re: You shouldn't use NPM hacked services Thomas 'PointedEars' Lahn <PointedEars@web.de> - 2025-12-02 20:29 +0100
What Spock aka Thomas 'PointedEars' Lahn missed (Was: Different Hubble Theories: de Sitter Energy) Mild Shock <janburse@fastmail.fm> - 2025-12-03 01:09 +0100
The size of a Gödel sentence G (Re: Could AlphaEvolve find the sixth busy beaver ?) Mild Shock <janburse@fastmail.fm> - 2025-12-03 09:00 +0100
The size of a Gödel sentence G (Re: Could AlphaEvolve find the sixth busy beaver ?) Mild Shock <janburse@fastmail.fm> - 2025-12-03 09:00 +0100
Attacking the Busy Beaver 5 [1989] (Re: The size of a Gödel sentence G) Mild Shock <janburse@fastmail.fm> - 2025-12-03 09:10 +0100
Re: Could AlphaEvolve find the sixth busy beaver ? Sylvia Else <sylvia@email.invalid> - 2025-12-04 12:59 +0800
Page 1 of 6 [1] 2 3 4 5 6 Next page →
| From | Mild Shock <janburse@fastmail.fm> |
|---|---|
| Date | 2025-11-30 13:38 +0100 |
| Subject | Could AlphaEvolve find the sixth busy beaver ? |
| Message-ID | <10ghds1$tg19$2@solani.org> |
Hi, What we thought: Prediction 5 . It will never be proved that Σ(5) = 4,098 and S(5) = 47,176,870. -- Allen H. Brady, 1990 . How it started: To investigate AlphaEvolve’s breadth, we applied the system to over 50 open problems in mathematical analysis, geometry, combinatorics and number theory. The system’s flexibility enabled us to set up most experiments in a matter of hours. In roughly 75% of cases, it rediscovered state-of-the-art solutions, to the best of our knowledge. https://deepmind.google/blog/alphaevolve-a-gemini-powered-coding-agent-for-designing-advanced-algorithms/ How its going: We prove that S(5) = 47, 176, 870 using the Coq proof assistant. The Busy Beaver value S(n) is the maximum number of steps that an n-state 2-symbol Turing machine can perform from the all-zero tape before halting, and S was historically introduced by Tibor Radó in 1962 as one of the simplest examples of an uncomputable function. The proof enumerates 181,385,789 Turing machines with 5 states and, for each machine, decides whether it halts or not. Our result marks the first determination of a new Busy Beaver value in over 40 years and the first Busy Beaver value ever to be formally verified, attesting to the effectiveness of massively collaborative online research https://arxiv.org/pdf/2509.12337 They claim not having used much AI. But could for example AlphaEvolve do it somehow nevertheless, more or less autonomously, and find the sixth busy beaver? Bye
[toc] | [next] | [standalone]
| From | Mild Shock <janburse@fastmail.fm> |
|---|---|
| Date | 2025-11-30 13:54 +0100 |
| Subject | An old Busy Beaver ASIC (Application-Specific Integrated Circuit) (Was: Could AlphaEvolve find the sixth busy beaver ?) |
| Message-ID | <10gher3$tgp1$1@solani.org> |
| In reply to | #894581 |
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, that also use 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
[toc] | [prev] | [next] | [standalone]
| From | Mild Shock <janburse@fastmail.fm> |
|---|---|
| Date | 2025-11-30 13:55 +0100 |
| Subject | An old Busy Beaver ASIC (Application-Specific Integrated Circuit) (Was: Could AlphaEvolve find the sixth busy beaver ?) |
| Message-ID | <10gheso$tgp1$2@solani.org> |
| In reply to | #894581 |
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
[toc] | [prev] | [next] | [standalone]
| From | Mild Shock <janburse@fastmail.fm> |
|---|---|
| Date | 2025-12-01 11:25 +0100 |
| Subject | What is analog computing nowadays? (Re: An old Busy Beaver ASIC (Application-Specific Integrated Circuit) (Was: Could AlphaEvolve find the sixth busy beaver ?) |
| Message-ID | <10gjqeu$t54i$2@solani.org> |
| In reply to | #894583 |
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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| From | Mild Shock <janburse@fastmail.fm> |
|---|---|
| Date | 2025-12-01 12:01 +0100 |
| Subject | Wake-up call until everybody gets ear-bleeding (Re: What is analog computing nowadays?) |
| Message-ID | <10gjsij$t6es$2@solani.org> |
| In reply to | #894590 |
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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| From | Mild Shock <janburse@fastmail.fm> |
|---|---|
| Date | 2025-12-01 12:07 +0100 |
| Subject | BB(745) is independent of ZFC (Was: Wake-up call until everybody gets ear-bleeding) |
| Message-ID | <10gjsu5$t6s1$1@solani.org> |
| In reply to | #894591 |
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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| From | Mild Shock <janburse@fastmail.fm> |
|---|---|
| Date | 2025-12-02 17:18 +0100 |
| Subject | Write ZFC formulas on a tape (of a Turing machine) (Re: BB(745) is independent of ZFC ) |
| Message-ID | <10gn3hj$114kh$2@solani.org> |
| In reply to | #894592 |
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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| From | Mild Shock <janburse@fastmail.fm> |
|---|---|
| Date | 2025-12-02 17:19 +0100 |
| Subject | Turing machines have neurons (Re: Write ZFC formulas on a tape (of a Turing machine)) |
| Message-ID | <10gn3j7$114kh$3@solani.org> |
| In reply to | #894616 |
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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| From | Mild Shock <janburse@fastmail.fm> |
|---|---|
| Date | 2025-12-02 17:20 +0100 |
| Subject | A logical calculus in nervous activity [McCulloch & Pitts 1943] (Re: Turing machines have neurons) |
| Message-ID | <10gn3ko$114kh$4@solani.org> |
| In reply to | #894617 |
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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| From | Mild Shock <janburse@fastmail.fm> |
|---|---|
| Date | 2025-12-02 17:39 +0100 |
| Subject | Busy Beaver and Theory Consistency (Was: A logical calculus in nervous activity [McCulloch & Pitts 1943]) |
| Message-ID | <10gn4n8$115gk$1@solani.org> |
| In reply to | #894618 |
Hi, If you know BB(N), you have a halting decision procedure for N-turing machines. Since if BB(N) is maximum number S(N) of steps before halting, you can just run an arbitrary turing machine, and when its steps exceeds S(N), you know its not a halting turing machine. So knowing BB(N) makes the halting problem decidable. But the halting problem is not decidable. So there must be some M maybe where BB(M) has no S(N) , no maximum. Idea is to construct turing machines that relate to consistency problems, consistency problems can be even harder than halting problems, we might ask for the opposite, does a program never halt. Since never halt could be interpreted that no inconsistency is derived. Again knowing BB(N) would help, since dedidability via S(N) is established both ways, saying "Yes" to halt, and saying "No" to halt. So we can show a reducibility from consistency to busy beaver, I guess. Bye
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| From | Mild Shock <janburse@fastmail.fm> |
|---|---|
| Date | 2025-12-02 17:43 +0100 |
| Subject | Busy Beaver and Theory Consistency (Was: A logical calculus in nervous activity [McCulloch & Pitts 1943]) |
| Message-ID | <10gn505$115gk$5@solani.org> |
| In reply to | #894618 |
Hi, If you know BB(N), you have a halting decision procedure for N-turing machines. Since if BB(N) is maximum number S(N) of steps before halting, you can just run an arbitrary turing machine, and when its steps exceeds S(N), you know its not a halting turing machine. So knowing BB(N) makes the halting problem decidable. But the halting problem is not decidable. So there must be some M maybe where BB(M) has no S(N) , no maximum. Idea is to construct turing machines that relate to consistency problems, consistency problems can be even harder than halting problems, we might ask for the opposite, does a program never halt. Since never halt could be interpreted that no inconsistency is derived. Again knowing BB(N) would help, since dedidability via S(N) is established both ways, saying "Yes" to halt, and saying "No" to not halt. So we can show a reducibility from consistency to busy beaver, I guess. Bye
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| From | Mild Shock <janburse@fastmail.fm> |
|---|---|
| Date | 2025-12-02 23:18 +0100 |
| Subject | Re: Busy Beaver and Theory Consistency (Was: A logical calculus in nervous activity [McCulloch & Pitts 1943]) |
| Message-ID | <10gnojk$11ij8$2@solani.org> |
| In reply to | #894620 |
Hi, I don't have a problem with the notion of computability. What makes you think citing an interesting research paper, implies that I have a problem with computability? Could you explain yourself? Bye Richard Damon schrieb: > On 12/2/25 11:06 AM, Mild Shock wrote: >> Hi, >> >> Do not underestimate turing machines. I said neurons >> in the "head". But a turing machine has to parts a "head" >> and a moving "tape". It can then write ZFC formulas on > > I think your problem is you just don't understand what computing is, as used in Computation theory. Mild Shock schrieb: > Hi, > > If you know BB(N), you have a halting decision procedure > for N-turing machines. Since if BB(N) is maximum number > S(N) of steps before halting, > > you can just run an arbitrary turing machine, and when > its steps exceeds S(N), you know its not a halting > turing machine. > > So knowing BB(N) makes the halting problem decidable. > But the halting problem is not decidable. So there > must be some M maybe where BB(M) has no S(N) , no > > maximum. Idea is to construct turing machines that > relate to consistency problems, consistency problems > can be even harder than halting problems, we might > > ask for the opposite, does a program never halt. > Since never halt could be interpreted that no > inconsistency is derived. Again knowing BB(N) would > > help, since dedidability via S(N) is established both > ways, saying "Yes" to halt, and saying "No" to not halt. > So we can show a reducibility from consistency > > to busy beaver, I guess. > > Bye
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| From | Maciej Woźniak <mlwozniak@wp.pl> |
|---|---|
| Date | 2025-12-01 12:09 +0100 |
| Subject | Re: What is analog computing nowadays? (Re: An old Busy Beaver ASIC (Application-Specific Integrated Circuit) (Was: Could AlphaEvolve find the sixth busy beaver ?) |
| Message-ID | <187d12daedf1c2ff$5163849$2551467$c2365abb@news.newsdemon.com> |
| In reply to | #894590 |
On 12/1/2025 11:25 AM, Mild Shock wrote: > 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 No, they don't, they just add one (or some) more layer on top of it. On the other hand, neural networks were always outside. So were quantum computers. It was never the only one and never the most powerful one.
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| From | Mild Shock <janburse@fastmail.fm> |
|---|---|
| Date | 2025-12-01 12:15 +0100 |
| Subject | parallel random-access machine (parallel RAM or PRAM (Was: What is analog computing nowadays?) |
| Message-ID | <10gjtck$t77m$1@solani.org> |
| In reply to | #894593 |
Hi, You wrote: > No, they don't, they just add one (or some) > more layer on top of it. Techically they are not von Neuman architecture. Unified Memory with Multiple Tensor Cores is not von Neuman architecture. But the architecture is possibly toned down by Data Flow, so that in principle one can run the same thing on a von Neuman architecture. But in principle the architecture is rather: parallel random-access machine (parallel RAM or PRAM) is a shared-memory abstract machine. https://en.wikipedia.org/wiki/Parallel_RAM The above class of machines is not widely know. But PRAM has been also studied, already in the 80's. Bye Maciej Woźniak schrieb: > On 12/1/2025 11:25 AM, Mild Shock wrote: >> 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 > > No, they don't, they just add one (or some) > more layer on top of it. > > On the other hand, neural networks were > always outside. So were quantum computers. > It was never the only one and never the > most powerful one. > > > >
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| From | Maciej Woźniak <mlwozniak@wp.pl> |
|---|---|
| Date | 2025-12-01 13:23 +0100 |
| Subject | Re: parallel random-access machine (parallel RAM or PRAM (Was: What is analog computing nowadays?) |
| Message-ID | <187d16ebd71933aa$26917881$2534374$c2565adb@news.newsdemon.com> |
| In reply to | #894594 |
On 12/1/2025 12:15 PM, Mild Shock wrote: > Hi, > > You wrote: > > > No, they don't, they just add one (or some) > > more layer on top of it. > > Techically they are not von Neuman architecture. > Unified Memory with Multiple Tensor Cores is > not von Neuman architecture. We can use von Neumann architecture to emulate other architectures, but as long as it is performed by our computers it is technically von Neumann's.
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| From | Mild Shock <janburse@fastmail.fm> |
|---|---|
| Date | 2025-12-01 17:12 +0100 |
| Subject | Nope, you can't, because of the CRCW instuction (Was: parallel random-access machine) |
| Message-ID | <10gkept$vec1$1@solani.org> |
| In reply to | #894595 |
Hi, Simulation is not so easy. You would need an element of non-determinism, or if you want call it randomness. Because PRAM has this instructions, ERCW, CRCW, etc.. - Concurrent read concurrent write (CRCW)— multiple processors can read and write. A CRCW PRAM is sometimes called a concurrent random-access machine. https://en.wikipedia.org/wiki/Parallel_RAM Modelling via von Neuman what happens there can be quite challenging. At least it doesn't allow for a direct modelling. What a later processor sees, depends extremly on the timing and which processor "wins" the write. Also I don't know what it would buy you intellectually to simulate a PRAM on a random von Neuman machine. The random von Neuman machine could need more steps than the PRAM in summary, because it has to simulate a PRAM. But I guess its the intellectual questioning that needs also a revision when confronted with the new architecture of unified memory and tensor processing cores. Bye Maciej Woźniak schrieb: > On 12/1/2025 12:15 PM, Mild Shock wrote: >> Hi, >> >> You wrote: >> >> > No, they don't, they just add one (or some) >> > more layer on top of it. >> >> Techically they are not von Neuman architecture. >> Unified Memory with Multiple Tensor Cores is >> not von Neuman architecture. > > We can use von Neumann architecture > to emulate other architectures, but as long as it > is performed by our computers it is technically > von Neumann's. >
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| From | Mild Shock <janburse@fastmail.fm> |
|---|---|
| Date | 2025-12-01 17:31 +0100 |
| Subject | Algorithm introduced in Hogwild! SGD (Niu et al., 2011) (Was: Nope, you can't, because of the CRCW instuction) |
| Message-ID | <10gkftk$vf6k$1@solani.org> |
| In reply to | #894597 |
Hi, PRAM effects are a little bit contrived in AI accelerators, since they work with matrix tiles, that are locally cached to the tensor core. But CRCW is quite cool for machine learning. When the weights get updated. ChatGPT suggested me to read this paper: Hogwild!: A Lock-Free Approach to Parallelizing Stochastic Gradient Descent https://arxiv.org/pdf/1106.5730 Didn't read yet... You might also have read the recent report how Google trained Gemini. They had to deal with other issues as well, like failure of a whole tensore core. Bye Mild Shock schrieb: > Hi, > > Simulation is not so easy. You would need an > element of non-determinism, or if you want > call it randomness. Because PRAM has this > > instructions, ERCW, CRCW, etc.. > > - Concurrent read concurrent write (CRCW)— > multiple processors can read and write. A > CRCW PRAM is sometimes called a concurrent > random-access machine. > https://en.wikipedia.org/wiki/Parallel_RAM > > Modelling via von Neuman what happens there > can be quite challenging. At least it doesn't > allow for a direct modelling. > > What a later processor sees, depends extremly > on the timing and which processor "wins" the > write. > > Also I don't know what it would buy you > intellectually to simulate a PRAM on a random > von Neuman machine. The random von Neuman > > machine could need more steps than the PRAM > in summary, because it has to simulate a PRAM. > But I guess its the intellectual questioning > > that needs also a revision when confronted > with the new architecture of unified memory > and tensor processing cores. > > Bye > > Maciej Woźniak schrieb: >> On 12/1/2025 12:15 PM, Mild Shock wrote: >>> Hi, >>> >>> You wrote: >>> >>> > No, they don't, they just add one (or some) >>> > more layer on top of it. >>> >>> Techically they are not von Neuman architecture. >>> Unified Memory with Multiple Tensor Cores is >>> not von Neuman architecture. >> >> We can use von Neumann architecture >> to emulate other architectures, but as long as it >> is performed by our computers it is technically >> von Neumann's. >> >
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| From | Mild Shock <janburse@fastmail.fm> |
|---|---|
| Date | 2025-12-01 18:02 +0100 |
| Subject | PRAMs might be closer to physics: Boltzman machines, etc.. (Was: Algorithm introduced in Hogwild! SGD) |
| Message-ID | <10gkhnb$vggj$1@solani.org> |
| In reply to | #894598 |
Hi, The bottom line is often, PRAMs might be closer to physics. Especially for certain machine learning algorithms or questions from modelling perception or action. You might get better results if you model the problem in terms of Boltzman machines, or whatever from the arsenal of physics. Bye Mild Shock schrieb: > Hi, > > PRAM effects are a little bit contrived in AI > accelerators, since they work with matrix tiles, > that are locally cached to the tensor core. > > But CRCW is quite cool for machine learning. > When the weights get updated. ChatGPT suggested > me to read this paper: > > Hogwild!: A Lock-Free Approach to > Parallelizing Stochastic Gradient Descent > https://arxiv.org/pdf/1106.5730 > > Didn't read yet... > > You might also have read the recent report how > Google trained Gemini. They had to deal with other > issues as well, like failure of a whole > > tensore core. > > Bye > > Mild Shock schrieb: >> Hi, >> >> Simulation is not so easy. You would need an >> element of non-determinism, or if you want >> call it randomness. Because PRAM has this >> >> instructions, ERCW, CRCW, etc.. >> >> - Concurrent read concurrent write (CRCW)— >> multiple processors can read and write. A >> CRCW PRAM is sometimes called a concurrent >> random-access machine. >> https://en.wikipedia.org/wiki/Parallel_RAM >> >> Modelling via von Neuman what happens there >> can be quite challenging. At least it doesn't >> allow for a direct modelling. >> >> What a later processor sees, depends extremly >> on the timing and which processor "wins" the >> write. >> >> Also I don't know what it would buy you >> intellectually to simulate a PRAM on a random >> von Neuman machine. The random von Neuman >> >> machine could need more steps than the PRAM >> in summary, because it has to simulate a PRAM. >> But I guess its the intellectual questioning >> >> that needs also a revision when confronted >> with the new architecture of unified memory >> and tensor processing cores. >> >> Bye >> >> Maciej Woźniak schrieb: >>> On 12/1/2025 12:15 PM, Mild Shock wrote: >>>> Hi, >>>> >>>> You wrote: >>>> >>>> > No, they don't, they just add one (or some) >>>> > more layer on top of it. >>>> >>>> Techically they are not von Neuman architecture. >>>> Unified Memory with Multiple Tensor Cores is >>>> not von Neuman architecture. >>> >>> We can use von Neumann architecture >>> to emulate other architectures, but as long as it >>> is performed by our computers it is technically >>> von Neumann's. >>> >> >
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| From | Maciej Woźniak <mlwozniak@wp.pl> |
|---|---|
| Date | 2025-12-01 17:59 +0100 |
| Subject | Re: Nope, you can't, because of the CRCW instuction (Was: parallel random-access machine) |
| Message-ID | <187d25f3d3fb6ffa$8329102$2551467$c2365abb@news.newsdemon.com> |
| In reply to | #894597 |
On 12/1/2025 5:12 PM, Mild Shock wrote: > Hi, > > Simulation is not so easy. I've never said it is easy. Some randomness or pseudorandomness existed for a long time, it's not enough for me to speak about a different architecture.
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| From | Mild Shock <janburse@fastmail.fm> |
|---|---|
| Date | 2025-12-01 18:05 +0100 |
| Subject | PRAMs might be closer to physics: Boltzman machines, etc.. (Re: Nope, you can't, because of the CRCW instuction) |
| Message-ID | <10gkhs8$vggj$2@solani.org> |
| In reply to | #894600 |
Hi, The bottom line is often, PRAMs might be closer to physics. Especially for certain machine learning algorithms or questions from modelling perception or action. You might get better results if you model the problem in terms of Boltzman machines, or whatever from the arsenal of physics. Bye P.S.: Whats was a little popular for a certain moment of time, was also the idea of partical swarm optimization, for machine learning or for problem solving: Particle swarm optimization https://en.wikipedia.org/wiki/Particle_swarm_optimization Not sure how much of it got supperseeded by multi sample updates, or some such. Maciej Woźniak schrieb: > On 12/1/2025 5:12 PM, Mild Shock wrote: >> Hi, >> >> Simulation is not so easy. > > I've never said it is easy. Some randomness > or pseudorandomness existed for a long time, > it's not enough for me to speak about a > different architecture. >
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