Accounts controlled by Ciro Santilli on Twitter:
- twitter.com/cirosantilli primary channel, contains only updates on Ciro's best technical content. Low volume.
- twitter.com/cirosantilli2 secondary channel, contains smaller technical updates that didn't make it to the primary channel, and some China fun. Higher volume.
This is what society gets for not using open knowledge: some of its best minds will be bound to waste endless hours reversing some useless technology.
With that said, even when you do have the source code, reading run logs and using debuggers are a sort of reverse engineering at heart.
One of the most jaw dropping reverse engineering projects Ciro has ever seen is the Super Mario 64 reverse engineering project.
Ciro Santilli often wonders to himself, how much of the natural sciences can one learn in a lifetime? Certainly, a very strong basis, with concrete experimental and physics, chemistry and biology should be attainable to all? How much Ciro manages to learning and teach in those areas is a kind of success metric of Ciro's life.
On one hand, yes, we need knowledge at all levels, and it is fine to start top-to-bottom with an overview.
The problem is, however, that there is a huge knowledge gap between the one liner "this is the truth" and the much more important "this is how we know it, these are the experiments" as mentioned at how to teach and learn physics.
Therefore, if you have that extremely rare knowledge, you should be writing that in addition to the dumbed down version with an open knowledge license. It takes time, but that's what really changes the world.
Ciro Santilli has always felt that there is a huge gap between "the very basic" and "the very advanced", as mentioned at: Section "The missing link between basic and advanced", which existing scientific vulgarization is not doing enough to address. In a sense, filling out this "middle path" is the main goal of OurBigBook.com.
Ciro really enjoyed the description of the "Arindam Kumar Chatterjee" YouTube channel:
Theoretical/mathematical physics at the graduate level and above. This is NOT a popular science channel. Here you find real theoretical physicists doing real theoretical physics. We think it is important for people to get a taste of the real deal, and for aspiring theoretical physicists to see what they are working towards, i.e., to provide the public with something beyond the ubiquitous Michio Kaku and Brian Cox.
One thing must be said however: there seems to be an actual bias against researchers tho try to create vulgarization material: How To Get Tenure at a Major Research University by Sean Carroll (2011), and that is terrible.
There is often more value in a tutorial by a beginner who is trying to fully learn and explain a subject, than by an expert who is trying to "dumb it down" too much.
If there is one thing that makes Ciro Santilli learn German, this is it (the Romance language are all the same, so reading them is basically covered for Ciro already).
Ciro Santilli intends to move his beauty list here little by little: github.com/cirosantilli/mathematics/blob/master/beauty.md
The most beautiful things in mathematics are results that are:
- simple to state but hard to prove:
- Fermat's Last Theorem
- number of unknown rationality, e.g. is rational?
- transcendental number conjectures, e.g. is transcendental?
- basically any conjecture involving prime numbers:
- many combinatorial game questions, e.g.:
- surprising results: we had intuitive reasons to believe something as possible or not, but a theorem shatters that conviction and brings us on our knees, sometimes via pathological counter-examples. General surprise themes include:Lists:
- classification of potentially infinite sets like: compact manifolds, etc.
- problems that are more complicated in low dimensions than high like:
- generalized Poincaré conjectures. It is also fun to see how in many cases complexity peaks out at 4 dimensions.
- classification of regular polytopes
- unpredictable magic constants:
- why is the lowest dimension for an exotic sphere 7?
- why is 4 the largest degree of an equation with explicit solution? Abel-Ruffini theorem
- undecidable problems, especially simple to state ones:
- mortal matrix problem
- sharp frontiers between solvable and unsolvable are also cool:
- attempts at determining specific values of the Busy beaver function for Turing machines with a given number of states and symbols
- related to Diophantine equations:
- applications: make life easier and/or modeling some phenomena well, e.g. in physics. See also: explain how to make money with the lesson
Good lists of such problems Lists of mathematical problems.
Whenever Ciro Santilli learns a bit of mathematics, he always wonders to himself:Unfortunately, due to how man books are written, it is not really possible to reach insight without first doing a bit of memorization. The better the book, the more insight is spread out, and less you have to learn before reaching each insight.
Am I achieving insight, or am I just memorizing definitions?
Here is a more understandable description of the semi-satire that follows: math.stackexchange.com/questions/53969/what-does-formal-mean/3297537#3297537
You start with a very small list of:
- certain arbitrarily chosen initial strings, which mathematicians call "axioms"
- rules of how to obtain new strings from old strings, called "rules of inference" Every transformation rule is very simple, and can be verified by a computer.
Using those rules, you choose a target string that you want to reach, and then try to reach it. Before the target string is reached, mathematicians call it a "conjecture".
Since every step of the proof is very simple and can be verified by a computer automatically, the entire proof can also be automatically verified by a computer very easily.
Finding proofs however is undoubtedly an uncomputable problem.
Most mathematicians can't code or deal with the real world in general however, so they haven't created the obviously necessary: website front-end for a mathematical formal proof system.
The fact that Mathematics happens to be the best way to describe physics and that humans can use physical intuition heuristics to reach the NP-hard proofs of mathematics is one of the great miracles of the universe.
Once we have mathematics formally modelled, one of the coolest results is Gödel's incompleteness theorems, which states that for any reasonable proof system, there are necessarily theorems that cannot be proven neither true nor false starting from any given set of axioms: those theorems are independent from those axioms. Therefore, there are three possible outcomes for any hypothesis: true, false or independent!
Some famous theorems have even been proven to be independent of some famous axioms. One of the most notable is that the Continuum Hypothesis is independent from Zermelo-Fraenkel set theory! Such independence proofs rely on modelling the proof system inside another proof system, and forcing is one of the main techniques used for this.
The landscape of modern Mathematics comic by Abstruse Goose
. Source. This comic shows that Mathematics is one of the most diversified areas of useless human knowledge.Not to be confused with algebra over a field, which is a particular algebraic structure studied within algebra.
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