Specific values of the Busy beaver function by
Ciro Santilli 37 Updated 2025-07-11 +Created 1970-01-01
The following things come to mind when you look into research in this area, especially the search for BB(5) which was hard but doable:
- it is largely recreational mathematics, i.e. done by non-professionals, a bit like the aperiodic tiling. Humbly, they tend to call their results lemmas
- complex structure emerges from simple rules, leading to a complex classification with a few edge cases, much like the classification of finite simple groups
Bibliography:
Automated theorem proving by halting problem reduction by
Ciro Santilli 37 Updated 2025-07-11 +Created 1970-01-01
If you can reduce a mathematical problem to the Halting problem of a specific turing machine, as in the case of a few machines of the Busy beaver scale, then using Turing machine deciders could serve as a method of automated theorem proving.
That feels like it could be an elegant proof method, as you reduce your problem to one of the most well studied representations that exists: a Turing machine.
However it also appears that certain problems cannot be reduced to a halting problem... OMG life sucks (or is awesome?): Section "Turing machine that halts if and only if Collatz conjecture is false".
ECDH has smaller keys. youtu.be/gAtBM06xwaw?t=634 mentions some interesting downsides:
Conjecture reduction to a halting problem by
Ciro Santilli 37 Updated 2025-07-11 +Created 1970-01-01
bbchallenge.org/story#what-is-known-about-bb lists some (all?) cool examples,
- BB(15): Erdős' conjecture on powers of 2, which has some relation to Collatz conjecture
- BB(27): Goldbach's conjecture
- BB(744): Riemann hypothesis
- BB(748): independent from the Zermelo-Fraenkel axioms
- BB(7910): independent from the ZFC
wiki.bbchallenge.org/wiki/Cryptids contains a larger list. In June 2024 it was discovered that BB(6) is hard.
How many logical qubits are needed to run Shor's algorithm? by
Ciro Santilli 37 Updated 2025-07-11 +Created 1970-01-01
Turing machine acceleration refers to using high level understanding of specific properties of specific Turing machines to be able to simulate them much fatser than naively running the simulation as usual.
Acceleration allows one to use simulation to find infinite loops that might be very long, and would not be otherwise spotted without acceleration.
This is for example the case of www.sligocki.com/2023/03/13/skelet-1-infinite.html proof of Skelet machine #1.
This is a neologism by Ciro Santilli, it refers to the fact that Zatoichi was not fully blind, but extremely hard of sight, which makes him:and metaphorically refers to similar situations where a person or group of people are in the middle of two groups and not part of either of them.
- too capable for the blind people, who did not trust him
- too incapable for non-blind people, who despised him
A related thing that comes to mind is Aum Shinrikyo's Prophet Shoko Asahara, who was semi blind, and would bully the fully blind people of his school for blind people.
epigenetics mechanism.
This shows how to produce a minimized fully embedded CSS file with webpack from a sass:That example produces a
cd webpack/sass
npm install
npm run build
xdg-open index.html
dist/main.css
file which is a compresesd combination of:- webpack/sass/main.scss
- normalize.css, added to the project as a regular
node_modules
package
The example under verilog/interactive showcases how to create a simple interactive visual Verilog example using Verilator and SDL.
You could e.g. expand such an example to create a simple (or complex) video game for example if you were insane enough. But please don't waste your time doing that, Ciro Santilli begs you.
The example is also described at: stackoverflow.com/questions/38108243/is-it-possible-to-do-interactive-user-input-and-output-simulation-in-vhdl-or-ver/38174654#38174654
Usage: install dependencies:then run as either:Tested on Verilator 4.038, Ubuntu 22.04.
sudo apt install libsdl2-dev verilator
make run RUN=and2
make run RUN=move
File overview:
Silicon Photonics: The Next Silicon Revolution? by Asianometry (2022)
Source. - youtu.be/29aTqLvRia8?t=714 GlobalFoundries seems to be one of the leaders at the time. E.g. quantum computing company PsiQuantum uses them. Part of this was from acquiring IBM's microelectronics division in 2014.
Running Neural Networks on Meshes of Light by Asianometry (2022)
Source. - youtu.be/t0yj4hBDUsc?t=440 block diagram
- youtu.be/t0yj4hBDUsc?t=456 Lightmatter lightmatter.co/ seems to be using an in-silicon Mach-Zehnder interferometer to do analog matrix multiplication with light. It is an actual analog computer element!
Silicon Photonics for Extreme Computing by Keren Bergman (2017)
Source. Here is a vendor showcasing their device. They claim in that video that a single photon is produced and detected:
Concrete device described at: Video "How to use an SiPM - Experiment Video by SensLTech (2018)".
- youtu.be/9aOLwjUZLm0?t=1216 superconducting qubits are bad because it is harder to ensure that they are all the same
- youtu.be/9aOLwjUZLm0?t=1270 our wires are provided by lasers. Gives example of ytterbium, which has nice frequencies for practical laser choice. Ytterbium ends in 6s2 5d1, so they must remove the 5d1 electron? But then you are left with 2 electrons in 6s2, can you just change their spins at will without problem?
- youtu.be/9aOLwjUZLm0?t=1391 a single atom actually reflects 1% of the input laser, not bad!
- youtu.be/9aOLwjUZLm0?t=1475 a transition that they want to drive in Ytterbium has 355 nm, which is easy to generate TODO why.
- youtu.be/9aOLwjUZLm0?t=1520 mentions that 351 would be much harder, e.g. as used in inertially confied fusion, takes up a room
- youtu.be/9aOLwjUZLm0?t=1539 what they use: a pulsed laser. It is made primarily for photolithography, Coherent, Inc. makes 200 of them a year, so it is reliable stuff and easy to operate. At www.coherent.com/lasers/nanosecond/avia-nx we can see some of their 355 offers. archive.ph/wip/JKuHI shows a used system going for 4500 USD.
- youtu.be/9aOLwjUZLm0?t=1584 Cirac and Zoller proposed the idea of using entangled ions soon after they heard about Shor's algorithm in 1995
- youtu.be/9aOLwjUZLm0?t=1641 you use optical tweezers to move the pairs of ions you want to entangle. This means shining a laser on two ions at the same time. Their movement depends on their spin, which is already in a superposition. If both move up, their distance stats the same, so the Coulomb interaction is unchanged. But if they are different, then one goes up and the other down, distance increases due to the diagonal, and energy is lower.
- youtu.be/9aOLwjUZLm0?t=1939 S. Debnah 2016 Nature experiment with a pentagon. Well, it is not a pentagon, they are just in a linear chain, the pentagon is just to convey the full connectivity. Maybe also Satanism. Anyways. This point also mentions usage of an acousto-optic modulator to select which atoms we want to act on. On the other side, a simpler wide laser is used that hits all atoms (optical tweezers are literally like tweezers in the sense that you use two lasers). Later on mentions that the modulator is from Harris, later merged with L3, so: www.l3harris.com/all-capabilities/acousto-optic-solutions
- youtu.be/9aOLwjUZLm0?t=2119 Bernstein-Vazirani algorithm. This to illustrate better connectivity of their ion approach compared to an IBM quantum computer, which is a superconducting quantum computer
- youtu.be/9aOLwjUZLm0?t=2354 hidden shift algorithm
- youtu.be/9aOLwjUZLm0?t=2740 Zhang et al. Nature 2017 paper about a 53 ion system that calculates something that cannot be classically calculated. Not fully controllable though, so more of a continuous-variable quantum information operation.
- youtu.be/9aOLwjUZLm0?t=2923 usage of cooling to 4 K to get lower pressures on top of vacuum. Before this point all experiments were room temperature. Shows image of refrigerator labelled Janis cooler, presumably something like: qd-uki.co.uk/cryogenics/janis-recirculating-gas-coolers/
- youtu.be/9aOLwjUZLm0?t=2962 qubit vs gates plot by H. Neven
- youtu.be/9aOLwjUZLm0?t=3108 modular trapped ion quantum computer ideas. Mentions experiment with 2 separate systems with optical link. Miniaturization and their black box. Mentions again that their chip is from Sandia. Amazing how you pronounce that.
There are unlisted articles, also show them or only show them.