HP Blade Server by Brian Kirsch (2013)
Source. Featuring an HP DL380 blade server, presumably an older model of this series: buy.hpe.com/uk/en/servers/proliant-dl-servers/proliant-dl300-servers/proliant-dl380-server/hpe-proliant-dl380-gen10-server/p/1010026818.
In the video we can see that it contains RAM, disk storage, we are told about two CPUs, and networking interfaces, so it is a complete computer on its own. He also explains that unlike typical rack servers, each blade unit does not have its own coolers and power supply related hardware, which goes instead on the chassis.
Unfortunately, all software engineers already know the answer to the useful theorems though (except perhaps notably for cryptography), e.g. all programmers obviously know that iehter P != NP or that this is unprovable or some other "for all practical purposes practice P != NP", even though they don't have proof.
And 99% of their time, software engineers are not dealing with mathematically formulatable problems anyways, which is sad.
The only useful "computer science" subset every programmer ever needs to know is:
- for arrays: dynamic array vs linked list
- for associative array: binary search tree vs hash table. See also Heap vs Binary Search Tree (BST). No need to understand the algorithmic details of the hash function, the NSA has already done that for you.
- don't use Bubble sort for sorting
- you can't parse HTML with regular expressions: stackoverflow.com/questions/1732348/regex-match-open-tags-except-xhtml-self-contained-tags/1732454#1732454 because of formal language theory
Funnily, due to the formalization of mathematics, mathematics can be seen as a branch of computer science, just like computer science can be seen as a branch of Mathematics!
The model is extremely simple, but has been proven to be able to solve all the problems that any reasonable computer model can solve, thus its adoption as the "default model".
The smallest known Turing machine that cannot be proven to halt or not as of 2019 is 7,918-states: www.scottaaronson.com/blog/?p=2725. Shtetl-Optimized by Scott Aaronson is just the best website.
A bunch of non-reasonable-looking computers have also been proven to be Turing complete for fun, e.g. Magic: The Gathering.
This is the classic result of formal language theory, but there is too much slack between context free and context sensitive, which is PSPACE (larger than NP!).
By Noam Chomsky.
A good summary table that opens up each category much more can be seen e.g. at the bottom of en.wikipedia.org/wiki/Automata_theory under the summary thingy at the bottom entitled "Automata theory: formal languages and formal grammars".
There is a Turing machine that halts for every member of the language with the answer yes, but does not necessarily halt for non-members.
Set of all decision problems solvable by a Turing machine, i.e. that decide if a string belongs to a recursive language.
Or in other words: there is no Turing machine that always halts for every input with the yes/no output.
Every undecidable problem must obviously have an infinite number of "possibilities of stuff you can try": if there is only a finite number, then you can brute-force it.
Lists of undecidable problems.
Coolest ones besides the obvious boring halting problem:
One of the most simple to state undecidable problems.
A:
- decidable problem is to a decision problem
- like a computable problem is to a function problem
The prototypical example is the Busy beaver function, which is the easiest example to reach from the halting problem.
Difference between recursive language and recursively enumerable language by 
Ciro Santilli 37 Updated 2025-07-16
Ciro Santilli 37 Updated 2025-07-16 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