In game theory, a **solved game** is a game for which an optimal strategy is known for all players involved. This means that the outcome of the game can be perfectly predicted, given the strategies employed by the players. Solved games typically have a defined structure, including a finite number of positions or states, which allows for thorough analysis.
It is so close that we can notice its proper motion, and its distance to us will vary significantly across a few tens of thousands of years!
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.
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