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MOOCs are a bad idea. We don't want to simply map the pre-computer classroom to the Internet. The Internet allows, and requires, fundamentally new ways to do things. More like Stack Overflow/Wikipedia. More like OurBigBook.com.
A website, usually hosted by an university, that takes what is done in class, and pastes it online. It is already much more rational and efficient, and opens up the way for potential sharing outside of the institution (or by default paywalling as the University of Oxford did.
The fundametnal problem with VLEs is that they tend to not have enough incentives for students to contribute at all to the content. This is basically the major motivation behind OurBigBook.com.
Someone who is not a pussy.
Someone once called Ciro Santilli that: archive.is/W1ocv. It's an overstatement, considering that Ciro's parents have some money. Not infinite. But still. Changes everything. A real Based God is someone like Charles Bukowski, who had to work decades at the post office.
Ciro feels that this resonates a lot with his OurBigBook.com.
Supercut:
The minute I dropped out I could stop taking the required classes that didn't interest me, and begin dropping in on the ones that looked far more interesting.And much of what I stumbled into by following my curiosity and intuition turned out to be priceless later on.Because I had dropped out and didn't have to take the normal classes, I decided to take a calligraphy class to learn how to do this.If I had never dropped in on that single course in college, the Mac would have never had multiple typefaces or proportionally spaced fonts.Of course it was impossible to connect the dots looking forward when I was in college. But it was very, very clear looking backward 10 years later.Again, you can't connect the dots looking forward; you can only connect them looking backward. So you have to trust that the dots will somehow connect in your future. You have to trust in something — your gut, destiny, life, karma, whatever. This approach has never let me down, and it has made all the difference in my life.
Then:
You've got to find what you love.Your work is going to fill a large part of your life, and the only way to be truly satisfied is to do what you believe is great work.And the only way to do great work is to love what you do. If you haven't found it yet, keep looking.So keep looking until you find it.Don't settle.
And:Mirror and morning are not required though, a computer screen will do just fine: www.reddit.com/r/depression/comments/6jtamj/im_at_work_just_staring_at_my_computer_screen/
When I was 17, I read a quote that went something like: "If you live each day as if it was your last, someday you'll most certainly be right."
And then he quotes form the Whole Earth Catalog, a paper Atlas from the '70s he admired:
Stay Hungry. Stay Foolish
There's not way to describe it as a classical function, making it the most important example of a distribution.
Applications:
- position operator in quantum mechanics. It's not a coincidence that the function is named after Paul Dirac.
The key and central motivation for studying Lie groups and their Lie algebras appears to be to characterize symmetry in Lagrangian mechanics through Noether's theorem, just start from there.
Notably local symmetries appear to map to forces, and local means "around the identity", notably: local symmetries of the Lagrangian imply conserved currents.
More precisely: local symmetries of the Lagrangian imply conserved currents.
TODO Ciro Santilli really wants to understand what all the fuss is about:
Oh, there is a low dimensional classification! Ciro is a sucker for classification theorems! en.wikipedia.org/wiki/Classification_of_low-dimensional_real_Lie_algebras
The fact that there are elements arbitrarily close to the identity, which is only possible due to the group being continuous, is the key factor that simplifies the treatment of Lie groups, and follows the philosophy of continuous problems are simpler than discrete ones.
Bibliography:
- youtu.be/kpeP3ioiHcw?t=2655 "Particle Physics Topic 6: Lie Groups and Lie Algebras" by Alex Flournoy (2016). Good SO(3) explicit exponential expansion example. Then next lecture shows why SU(2) is the representation of SO(3). Next ones appear to eventually get to the physical usefulness of the thing, but I lost patience. Not too far out though.
- www.youtube.com/playlist?list=PLRlVmXqzHjURZO0fviJuyikvKlGS6rXrb "Lie Groups and Lie Algebras" playlist by XylyXylyX (2018). Tutorial with infinitely many hours
- www.staff.science.uu.nl/~hooft101/lectures/lieg07.pdf
- www.physics.drexel.edu/~bob/LieGroups.html
What is Lie theory? by Mathemaniac 2023
. Source. The name is a bit obscure if you don't think in very generalized terms right out of the gate. It refers to a linear polynomial of multiple variables, which by definition must have the super simple form of:and then we just put the unknown and each derivative into that simple polynomial:except that now the are not just constants, but they can also depend on the argument (but not on or its derivatives).
Explicit solutions exist for the very specific cases of:
- constant coefficients, any degree. These were known for a long time, and are were studied when Ciro was at university in the University of São Paulo.
- degree 1 and any coefficient
Order of the highest derivative that appears.
This idea comes up particularly in the phase space coordinate of Hamiltonian mechanics.
This basically adds one more ingredient to partial differential equations: a function that we can select.
And then the question becomes: if this function has such and such limitation, can we make the solution of the differential equation have such and such property?
Control theory also takes into consideration possible discretization of the domain, which allows using numerical methods to solve partial differential equations, as well as digital, rather than analogue control 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 2. You can publish local OurBigBook lightweight markup files to either OurBigBook.com or as a static website.
Figure 3. Visual Studio Code extension installation.
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. 
- 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