Noisy-channel coding theorem by Ciro Santilli 35 Updated +Created
Setting: you are sending bits through a communication channel, each bit has a random probability of getting flipped, and so you use some error correction code to achieve some minimal error, at the expense of longer messages.
This theorem sets an upper bound on how efficient you can be in your encoding, for any encoding.
The next big question, which the theorem does not cover is how to construct codes that reach or approach the limit. Important such codes include:
But besides this, there is also the practical consideration of if you can encode/decode fast enough to keep up with the coded bandwidth given your hardware capabilities.
news.mit.edu/2010/gallager-codes-0121 explains how turbo codes were first reached without a very good mathematical proof behind them, but were still revolutionary in experimental performance, e.g. turbo codes were used in 3G/4G.
But this motivated researchers to find other such algorithms that they would be able to prove things about, and so they rediscovered the much earlier low-density parity-check code, which had been published in the 60's but was forgotten, partially because it was computationally expensive.
Great circle by Ciro Santilli 35 Updated +Created
List of Nobel Prizes by Ciro Santilli 35 Updated +Created
Horrors of open source by Ciro Santilli 35 Updated +Created
Not everything is perfect.
One big problem of many big open source projects is that they are contributed to by separate selfish organizations, that have private information. Then what happens is that:
  • people implement the same thing twice, or one change makes the other completely unmergeable
  • you get bugs but can't share your closed source test cases, and then you can't automate tests for them, or clearly demonstrate the problem
  • other contributors don't see your full semi secret important motivation, and may either nitpick too much or take too long to review your stuff
Another common difficulty is that open source maintainers may simply not care enough about their own project (maybe they did in the past but lost interest) to review external patches by people they don't know.
This is understandable: a new patch, is a new risk of things breaking.
Therefore, if you ever submit patches and they get ignore, don't be too sad. It just comes down to a question of maintenance cost, and means that you will waste some extra time on the next rebase. You just have to decide your goals and be cold about it:
  • are you doing the right thing and going for a specific goal backward design? Then just fork, run as fast as possible towards a minimum viable product, and if you start to feel that rebase is costing you a lot, or feel you could get some open source fame for cheap, open reviews and see what upstream says. If they ignore you, politely tell yourself in your mind silently "fuck them", and carry on with the MVP
  • otherwise, e.g. you just want to randomly help out, you have to ask them before doing anything big "how can I be of help". If I propose a patch for this issue, do you promise to review it?
Writing documentation in an open source project in which you don't have immediate push rights is another major pain due to code reviews. Code code reviews tend to be much less subjective, because if you do something wrong, stuff crashes, runs slower, or you need more lines of code to reach the same goal. There are tradeoffs, but in a limited number. Documentation code reviews on the other hand, are an open invitation to infinite bike-shedding, since you can't "run" documentation through a standardized brain model. Much better is for one good documenter person to just make one cohesive Stack Overflow post, and ping others with more knowledge to review details or add any missing pieces :-)
Pinned article: ourbigbook/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!
Video 1.
Intro to OurBigBook
. Source.
We have two killer features:
  1. 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-calculus
    Articles 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/derivative
    Video 2.
    OurBigBook Web topics demo
    . Source.
  2. 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:
    • 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
    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.
    Figure 5. . 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.
  3. https://raw.githubusercontent.com/ourbigbook/ourbigbook-media/master/feature/x/hilbert-space-arrow.png
  4. Infinitely deep tables of contents:
    Figure 6.
    Dynamic article tree with infinitely deep table of contents
    .
    Descendant pages can also show up as toplevel e.g.: ourbigbook.com/cirosantilli/chordate-subclade
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