The busy beaver game consists in finding, for a given , the turing machine with states that writes the largest possible number of 1's on a tape initially filled with 0's. In other words, computing the busy beaver function for a given .
There are only finitely many Turing machines with states, so we are certain that there exists such a maximum. Computing the Busy beaver function for a given then comes down to solving the halting problem for every single machine with states.
Some variant definitions define it as the number of time steps taken by the machine instead. Wikipedia talks about their relationship, but no patience right now.
The Busy Beaver problem is cool because it puts the halting problem in a more precise numerical light, e.g.:
- the Busy beaver function is the most obvious uncomputable function one can come up with starting from the halting problem
- the Busy beaver scale allows us to gauge the difficulty of proving certain (yet unproven!) mathematical conjectures
A charismatic, perfect-English-accent (Received Pronunciation) physicist from University of Cambridge, specializing in quantum field theory.
He has done several "vulgarization" lectures, some of which could be better called undergrad appetizers rather, a notable example being Video "Quantum Fields: The Real Building Blocks of the Universe by David Tong (2017)" for the prestigious Royal Institution, but remains a hardcore researcher: scholar.google.com/citations?hl=en&user=felFiY4AAAAJ&view_op=list_works&sortby=pubdate. Lots of open access publications BTW, so kudos.
The amount of lecture notes on his website looks really impressive: www.damtp.cam.ac.uk/user/tong/teaching.html, he looks like a good educator.
David has also shown some interest in applications of high energy mathematical ideas to condensed matter, e.g. links between the renormalization group and phase transition phenomena. TODO there was a YouTube video about that, find it and link here.
Ciro Santilli wonders if his family is of East Asian, origin and if he can still speak any east asian languages. "Tong" is of course a transcription of several major Chinese surnames and from looks he could be mixed blood, but as mentioned at www.ancestry.co.uk/name-origin?surname=tong it can also be an English "metonymic occupational name for a maker or user of tongs". After staring at his picture for a while Ciro is going with the maker of tongs theory initially.
In the 2010's/2020's, many people got excited about getting children in to electronics with cheap devboards, notably with Raspberry Pi and Arduino.
While there is some potential in that, Ciro Santilli always felt that this is very difficult to do, while also keeping his sacred principle of backward design in mind.
The reason for this is that "everyone" already has much more powerful computers at hand: their laptops/desktops and even mobile phones as of the 2020s. Except perhaps if you are thing specifically about poor countries.
Therefore, the advantage using such devboards for doing something that could useful must come from either:
- their low cost. This would be an important consideration if you were to mass produce your product, but that is not going to be the case for learners, at least initially.
- their portability, and closely linked their ability to act as sensors
- their ability to act as actuators, which is often missing from regular computers
- them having hardware accelerators that are not normally present in regular computers, e.g. FPGAs or AI accelerators. And then the demo project must demonstrate that the project is able to do something significantly faster/cheaper on the devboard than on a desktop computer.
A computer is a highly layered system, and so you have to decide which layers you are the most interested in studying.
Although the layer are somewhat independent, they also sometimes interact, and when that happens it usually hurts your brain. E.g., if compilers were perfect, no one optimizing software would have to know anything about microarchitecture. But if you want to go hardcore enough, you might have to learn some lower layer.
It must also be said that like in any industry, certain layers are hidden in commercial secrecy mysteries making it harder to actually learn them. In computing, the lower level you go, the more closed source things tend to become.
But as you climb down into the abyss of low level hardcoreness, don't forget that making usefulness is more important than being hardcore: Figure 1. "xkcd 378: Real Programmers".
First, the most important thing you should know about this subject: cirosantilli.com/linux-kernel-module-cheat/should-you-waste-your-life-with-systems-programming
Here's a summary from low-level to high-level:
- semiconductor physical implementation this level is of course the most closed, but it is fun to try and peek into it from any openings given by commercials and academia:
- photolithography, and notably photomask design
- register transfer level
- interactive Verilator fun: Is it possible to do interactive user input and output simulation in VHDL or Verilog?
- more importantly, and much harder/maybe impossible with open source, would be to try and set up a open source standard cell library and supporting software to obtain power, performance and area estimates
- Are there good open source standard cell libraries to learn IC synthesis with EDA tools? on Quora
- the most open source ones are some initiatives targeting FPGAs, e.g. symbiflow.github.io/, www.clifford.at/icestorm/
- qflow is an initiative targeting actual integrated circuits
- microarchitecture: a good way to play with this is to try and run some minimal userland examples on gem5 userland simulation with logging, e.g. see on the Linux Kernel Module Cheat:This should be done at the same time as books/website/courses that explain the microarchitecture basics.
- instruction set architecture: a good approach to learn this is to manually write some userland assembly with assertions as done in the Linux Kernel Module Cheat e.g. at:
- github.com/cirosantilli/linux-kernel-module-cheat/blob/9b6552ab6c66cb14d531eff903c4e78f3561e9ca/userland/arch/x86_64/add.S
- cirosantilli.com/linux-kernel-module-cheat/x86-userland-assembly
- learn a bit about calling conventions, e.g. by calling C standard library functions from assembly:
- you can also try and understand what some simple C programs compile to. Things can get a bit hard though when
-O3is used. Some cute examples:
- executable file format, notably executable and Linkable Format. Particularly important is to understand the basics of:
- address relocation: How do linkers and address relocation work?
- position independent code: What is the -fPIE option for position-independent executables in GCC and ld?
- how to observe which symbols are present in object files, e.g.:
- how C++ uses name mangling What is the effect of extern "C" in C++?
- how C++ template instantiation can help reduce link time and size: Explicit template instantiation - when is it used?
- operating system. There are two ways to approach this:
- learn about the Linux kernel Linux kernel. A good starting point is to learn about its main interfaces. This is well shown at Linux Kernel Module Cheat:
- system calls
- write some system calls in
- pure assembly:
- C GCC inline assembly:
- write some system calls in
- learn about kernel modules and their interfaces. Notably, learn about to demystify special files such
/dev/randomand so on: - learn how to do a minimal Linux kernel disk image/boot to userland hello world: What is the smallest possible Linux implementation?
- learn how to GDB Step debug the Linux kernel itself. Once you know this, you will feel that "given enough patience, I could understand anything that I wanted about the kernel", and you can then proceed to not learn almost anything about it and carry on with your life
- system calls
- write your own (mini-) OS, or study a minimal educational OS, e.g. as in:
- learn about the Linux kernel Linux kernel. A good starting point is to learn about its main interfaces. This is well shown at Linux Kernel Module Cheat:
- programming language
The prototypical example is the Busy beaver function, which is the easiest example to reach from the halting problem.
Can the last disk access times be checked via forensic methods?
Pinned article: Introduction to the OurBigBook Project
Welcome to the OurBigBook Project! Our goal is to create the perfect publishing platform for STEM subjects, and get university-level students to write the best free STEM tutorials ever.
Everyone is welcome to create an account and play with the site: ourbigbook.com/go/register. We belive that students themselves can write amazing tutorials, but teachers are welcome too. You can write about anything you want, it doesn't have to be STEM or even educational. Silly test content is very welcome and you won't be penalized in any way. Just keep it legal!
Intro to OurBigBook
. Source. We have two killer features:
- topics: topics group articles by different users with the same title, e.g. here is the topic for the "Fundamental Theorem of Calculus" ourbigbook.com/go/topic/fundamental-theorem-of-calculusArticles of different users are sorted by upvote within each article page. This feature is a bit like:
- a Wikipedia where each user can have their own version of each article
- a Q&A website like Stack Overflow, where multiple people can give their views on a given topic, and the best ones are sorted by upvote. Except you don't need to wait for someone to ask first, and any topic goes, no matter how narrow or broad
This feature makes it possible for readers to find better explanations of any topic created by other writers. And it allows writers to create an explanation in a place that readers might actually find it.
Figure 1. Screenshot of the "Derivative" topic page. View it live at: ourbigbook.com/go/topic/derivativeVideo 2. OurBigBook Web topics demo. Source. - local editing: you can store all your personal knowledge base content locally in a plaintext markup format that can be edited locally and published either:This way you can be sure that even if OurBigBook.com were to go down one day (which we have no plans to do as it is quite cheap to host!), your content will still be perfectly readable as a static site.
- to OurBigBook.com to get awesome multi-user features like topics and likes
- as HTML files to a static website, which you can host yourself for free on many external providers like GitHub Pages, and remain in full control
Figure 3. Visual Studio Code extension installation.
Figure 4. Visual Studio Code extension tree navigation.
Figure 5. Web editor. You can also edit articles on the Web editor without installing anything locally.Video 3. Edit locally and publish demo. Source. This shows editing OurBigBook Markup and publishing it using the Visual Studio Code extension.Video 4. OurBigBook Visual Studio Code extension editing and navigation demo. Source. 
- Infinitely deep tables of contents:
All our software is open source and hosted at: github.com/ourbigbook/ourbigbook
Further documentation can be found at: docs.ourbigbook.com
Feel free to reach our to us for any help or suggestions: docs.ourbigbook.com/#contact